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Understanding anti-angiogenic signaling and treatment for cancer through mechanistic modeling
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Understanding anti-angiogenic signaling and treatment for cancer through mechanistic modeling
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Content
Understanding Anti-Angiogenic Signaling and Treatment for Cancer through Mechanistic Modeling
by
Qianhui (Jess) Wu
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
BIOMEDICAL ENGINEERING
August 2020
Copyright 2020 Qianhui (Jess) Wu
ii
Dedication
This dissertation is dedicated to everyone who have supported me along the way.
iii
Acknowledgements
First, I would like to express my sincere gratitude to my dissertation committee members, Professors
Stacey D. Finley, David Z. D’Argenio, Scott E. Fraser, Pin Wang, and Megan L. McCain, for their dedication
in supporting my research and growth as a scientist, their genuine curiosity about my research, and their
kindness to me that I can never take for granted.
I need to especially thank my advisor, Associate Professor Stacey D. Finley. Our relationship began
with me as one of the very first mentees that she took on when her career as a USC faculty just started. These
past five years has been a journey for both of us, one that I could have never asked more or better of. With the
struggles that I have had throughout my life, there were many things that I unconsciously looked for that were
beyond the responsibilities of an academic mentor. Stacey has fulfilled all of them without a moment of doubt,
with an exceeding amount of TLC. Truly, I appreciate every single hour that she puts in to work with me, to
look through my code, to read what I wrote, to care about my wellbeing, to plan and strategize for our projects,
to teach, and to communicate and encourage me to grow in my own way. Her grit, her realness, her composure,
are among the many things that inspire me. I would have neither become the person that I am now or done
the work here, without her being there for me to learn from and to rely on. I am glad to have mentally started
preparing for my departure from the lab early on, because I have been afraid of leaving this place that I finally
felt belong to. And I am glad that we both have reviewed our mentor-mentee relationship recently through an
unique opportunity – I am not one with eloquence, but there are so many things that I should acknowledge
Stacey for; and there are also so many things that I’d like to apologize for, but do not fit in this section. I hope
she knows.
Next, I would like to thank Professor Michael R. King, my research advisor during my Master of
Engineering program at Cornell. Prof. King accepted me into his lab with openness, knowing that I was only
able to work on his projects for about nine months during the short program. I found a passion in oncology
research, not only through the groundbreaking work being carried out in his lab that gave me a taste of
fulfillment, but also from the precious opportunity to be involved in research discussions. I remember the first
time I eagerly answered Prof. King’s question during a group discussion. That very moment, I felt a surge of
iv
confidence from within, and felt like I received recognition from others, something that I have always missed.
So I went on to look for more. Little does he know about this; Prof King is my enabler to pursue science.
I would like to thank two of our lab alumni, Dr. Mahua Roy and Dr. Jennifer A. Rohrs, both fierce,
brilliant, resilient scientists who I am so proud to be friends with and following the paths of. Mahua has always
been there for me as a close friend, sharing thoughts and feelings with me, and has always pushed me back up
when I was down, in the most understanding and loving way, without any judgement, without ever staying
distant. And Jen, who I see as a successful elder sister, always helped me so patiently with my experiments and
research, backed me up in my presentations, pointed out things to look out for in my projects, and now
supporting me in my career development. Thank you both for making me feel less lost, and standing in the
direction where I look up to.
Next, I would like to thank my lab members, Min Song, Ding Li, Sahak Makaryan, Colin G. Cess, and
Patrick Gelbach, and our most recent member Dr. Junmin Wang. Through our day to day interactions, they
continue to humble me, and teach me to never be complacent. They brighten up my days in the lab. Thank you
all for being so patient and understanding of me. I’d like to thank Mischalgrace Diasanta, Cynthia Castaneda,
Karen Johnson, Carla Stanard, Michelle Medina, William Yang, Angela Walker, and Kathlynn Alba, for their
effort in supporting the programs and always putting a smile on my face whenever I made a visit to their offices.
More often than not, it was these people who make me feel more like a part of a bigger family.
I’d also like to thank my friends who I met while at USC (in order of time when I met them): Joycelyn
Yip, Yuta Ando, Dr. Davi Lyra Leite, Gunce Cinay, Dr. Nathan Cho, Jonathan Wang, Dr. William Dempsy,
Niraj Holla, Umang Gupta, Dr. Michael Jorgenson, and everyone else that I missed while making this list, for
accepting me as I am and carrying me through my ups and downs in graduate school. Very special thanks to
6am Gainz, a small group of friends who lifted at the Lyon center at 6am almost every day: Dr. Cosimo
Arnesano, Dr. Kristopher Coombs, Dr. Alon Chapovetsky, Arash John Ramani, Dr. Nathan Ho, Peter Ta,
Evan Le, Jack Lee, Sarah Etter, and whoever I might have missed again. I am proud to identify with this group
of people who demonstrate not only the academic excellence, but also a dedication to routine strength training.
Thank you for keeping me in check, motivating me to stay disciplined, and occasionally enjoying with me
v
delicious food outside of our very stringent lifestyle. And thank you to my friends outside of school, Yiga Xu,
Yijin Wang, Crystal Chen, Mackenzie Higgins, Susan Zheng, Sweta Roy, Dr. Si Stacie Chen, Stefanie Cheng,
for always being in my corner, for being true and real with me, and for all of our long conversations, brief visits
to each other, and our precious memories as we grew up and take on this world together.
I’d also like to thank Jayson Ho, my boyfriend, for being my anchor for these past few years. He
provides me with a sense of home and certainty, which has been very precious in my somewhat turbulent world.
He held my hands through all my lows with love and the utmost patience. He supported me and gave me
answers in moments when I felt absolutely lost. Thank you. I think I would have been crazy(-ier) without you.
In the end, I want to say thank you to my parents, Zhiqiang Wu and Hang Zheng. We are an average,
middle-class family; I didn’t go to a privileged international high school and rather, I had been mostly living
with either of my parents and then a boarding school, for most of my childhood and teenage years, because
they had to work far away from home. Yet, my parents did their best to raise me; I would have not been able
to pursue any degrees outside of my home country without their support. My father, a former sailor, then
teacher in shipping and cargo stowage, and then business manager in the shipping industry, grew up in poverty
as his generation did, but made his own way out of his hometown to around the world. He taught me to be
tough, to be persistent in finding answers, to have an interest in science and engineering. My mother, a dedicated
professor in educational psychology all her career, is selfless in caring for our family. Despite her tremendous
amount of work, she cooked daily, gave me access to numerous books, and took care of everything in my early
life for me. Without a word, my mom taught me to be humble, considerate, and to care greatly for others. And
only as I grew older, I began to recognize the influence of their characters on mine. Both of my parents are
relatively more reserved, and we may have had more arguments than I would like to remember, but I know
that they have done more than anyone would to make sure that my future is bright, even though it meant
changing their own life trajectories. In the past ten years, we have been physically distant despite the at most
once a year visits by me back home, but I know that I can be where I want to be now, because of the sacrifices
that they made.
vi
Table of Contents
Dedication…………………...…………………………………………….……………….………………ii
Acknowledgements…………………...…………………………………………….……..………………iii
List of Tables.……………………...…………………..…………………………….…………….……….viii
List of Figures………………………………………..………………………..………………...…...………ix
Abstract………………………………………..……………………………..………………….....….…..xi
Chapter 1: Introduction………………..............……..……………………………………..……….…...……1
1.1 Tumor angiogenesis……………………………….…...……………………...……………1
1.2 The angiogenic signaling network……………………………….…...……………………...1
1.3 Anti-angiogenic therapy……………………………….…...……………………………….5
1.4 Computational modeling and systems biology approaches………………………..…….…..8
1.5 Dissertation Outline……………………………….…...………………………………...…8
Chapter 2. TSP1-mediated eNOS signaling via receptor CD47…………….………………….……………11
2.1. Abstract…………………………………………………………………………………...11
2.2. Introduction………………………………………………………………………………11
2.3. Methods…………………………………………………………………………………..16
2.4. Results……………………………………………………………………………………27
2.5. Discussion………………………………………………………………………………...40
2.6. Conclusion………………………………………………………………………………..47
Chapter 3: TSP1-mediated endothelial cell apoptotic signaling via receptor CD36………….….….………...49
3.1. Abstract…………………………………………………………………………………...49
3.2. Introduction………………………………………………………………………………52
3.3. Methods…………………………………………………………………………………..53
3.4. Results…………………………………………………………………………….………64
3.5. Discussion………………………………………………………………………………...81
3.6. Conclusion………………………………………………………………………………...85
Chapter 4: Integration of TSP1-mediated intracellular signaling network………………………………........87
4.1. Introduction………………………………………………………………………………87
4.2. Methods…………………………………………………………………………………..88
4.3. Preliminary results………………...………………………………………………………93
4.4. Discussion……………………………………………………………………………….98
4.5. Conclusion………………………………………………………………………………103
Chapter 5: Model of human breast cancer tumor-bearing mice receiving anti-VEGF treatment…………...104
5.1. Abstract………………………………………………………………………………….104
5.2. Introduction……………………………………………………………………………..105
5.3. Methods…………………………………………………………………………………107
5.4. Results…………………………………………………………………………………...116
5.5. Discussion……………………………………………………………………………….130
5.6. Conclusion………………………………………………………………………………133
Chapter 6: Tumor growth kinetics as biomarkers to predict anti-VEGF treatment outcome………………134
6.1. Abstract………………………………………………………………………………….134
vii
6.2. Introduction……………………………………………………………………………..134
6.3. Methods…………………………………………………………………………………137
6.4. Results…………………………………………………………………………………...145
6.5. Discussion……………………………………………………………………………….159
6.6. Conclusion………………………………………………………………………………162
Chapter 7: Conclusions. …………………………………………………………………………………..163
7.1. Overview………………………………………………………………………………...163
7.2. Summary…………….…………………………………………………………………...162
7.3. Future directions…………….………………………………………………………...…165
7.4. Concluding thoughts…….……………………………………………………………….166
References…………………………..……………………….…………………….…………………....…167
Appendices………..………………………………………………………………………………………191
viii
List of Tables
Table 2-1. List of eNOS model parameters………………………………………………………………….21
Table 2-2. List of Perturbations….…………………………………………………………………………..35
Table 3-1. CD36 model initial concentrations.………………………………………………………………54
Table 3-2. CD36 model estimated parameter values…………………………………………………………65
Table 3-3. Comparison of XIAP and PARP levels between non-apoptotic and apoptotic populations………..78
Table 3-4. Results from ROC analysis………………………………………………………………………80
Table 4-1. Quantification of average receptor numbers on HMVECs………………… …………………….87
Table 4-2. Estimated parameters for integrated model using CD36 pathway datasets. …………………….91
Table 5-1. Equations describing change in relative volume of the interstitial space…………………………110
Table 5-2. Experimental treatment from published papers……………………………………………….114
Table 6-1: Treatment protocols in tumor growth model simulations. ………………………………………140
Table 6-2. Estimated parameter values from fitting tumor growth model to Mollard dataset…...……………143
Table 6-3. Parameter bounds and values used in mice population simulations…………………………..…..144
Table 6-4. Summary of median survival of population separated by median ratio thresh………………………...150
Table 6-5. Statistics comparing the Kaplan-Meier survival curves of population separated by median ratio thresh
hazard ratio (95%CI) and log rank test p-values…..……………………………………………151
Table 6-6. Summary of median survival of population separated by median k 1,thresh…………………………..152
Table 6-7. Statistics comparing the Kaplan-Meier survival curves of population separated by median k 1,thresh:
hazard ratio (95%CI) and log rank test p-values. …………………………………………………153
ix
List of Figures
Figure 1-1. Major interactions involved in TSP1-mediated intracellular anti-angiogenic signaling……….…..…3
Figure 2-1. Model schematic of eNOS signaling network……………………………………………………13
Figure 2-2. eNOS signaling model training and validation.…………………………………………………..20
Figure 2-3. Distribution of estimated parameters in the eNOS model.…………………………………….21
Figure 2-4. Hill functions of TSP1 concentrations…………………………………………………………27
Figure 2-5. Sensitivity analysis to inform eNOS model fitting. ……………………………………………….28
Figure 2-6. Signaling dynamics predicted by the eNOS model for various levels of VEGF stimulation………30
Figure 2-7. Sensitivity analyses to inform perturbation simulations...…………………...……………………33
Figure 2-8. Perturbations to the eNOS pathway under basal condition.……………………………………...35
Figure 2-9. Effective perturbations in high VEGF condition.……………………………………….……….39
Figure 2-10. Model predicted dynamics with combined perturbations compared to a single perturbation…….45
Figure 3-1. Model schematic of TSP1-mediated apoptosis signaling via receptor CD36.……………………53
Figure 3-2. Comparison of minimal model of FasL signaling to experimental data.…………………………56
Figure 3-3. Global sensitivity analysis of parameters in the CD36 model.……………………………………57
Figure 3-4. Receptor number distributions of CD36 and Fas.……………………………………………….61
Figure 3-5. CD36 Model training and validation.……………………………………………………………65
Figure 3-6. Dose-dependent response of apoptosis signaling with varied initial concentrations………………69
Figure 3-7. Distribution of cPARP concentration in population-level model.………...………………………71
Figure 3-8. Population-level response to TSP1 stimulation.………………………………………………….73
Figure 3-9. Population-level response to 0.1 nM TSP1 stimulation.……..……………………………………74
Figure 3-10. Predicted population-based response to TSP1 stimulation.………………..……………………75
Figure 3-11. Relationship between initial conditions and predicted apoptotic response.……...………………78
Figure 3-12. ROC curves for classifying the apoptotic response.………………………………….………….80
Figure 4-1. Integrated model training and validation using apoptosis pathway datasets.……………………...89
Figure 4-2. Integrated model dynamics compared to datasets of the eNOS signaling pathway.……………….92
Figure 4-3. Model simulated effects of TSP1’s inhibitory effects on eNOS signaling dynamics...……………...94
Figure 4-4. Integrated model simulated apoptotic response to TSP1 stimulation as flow-cytometry like data…96
Figure 4-5. Population apoptotic response with varied receptor levels in response to treatments.………………97
Figure 5-1. Tumor growth model schematic……….………………………………………………………109
Figure 5-2. Sensitivity indices of tumor growth parameters.………………………………………………...119
Figure 5-3. Model fit and validation using full tumor growth time course for fitting.……………………….120
Figure 5-4. Estimated model parameters obtained from fitting.…………………………………………….121
Figure 5-5. Model validation after fitting initial tumor growth data.………………………………………123
Figure 5-6. Predicted response to anti-VEGF treatment.………………………………………………….125
Figure 5-7. Statistical analysis of the optimized parameter sets.……………………………………………126
Figure 5-8. Results from multivariate analysis.……………………………………………………………...127
Figure 5-9. Effect of VEGF receptor expression on tumor cells.…………………………………………...129
Figure 6-1. Schematic and overview of computational model of tumor-bearing mice.…………………….139
Figure 6-2. Comparison of normalized experimental data. …………………………………………………142
Figure 6-3. Model-simulated tumor growth data of in silico mouse populations. …………………………..…146
Figure 6-4. Scatter plot of RTV at the end of simulations versus tumor growth kinetic parameters.…………147
Figure 6-5. Range of kinetic parameter and threshold values.………………………………………………149
Figure 6-6. Kaplan-Meier curves for the six simulated groups of tumor-bearing mice using ratio threshold….150
Figure 6-7. Kaplan-Meier curves for the six simulated groups of tumor-bearing mice using k 1 threshold……152
Figure 6-8. Model-simulated tumor growth data with alternative treatment protocols..……………………154
x
Figure 6-9. Validation of ratio thresh and k 1,thresh values with an independent set of data..………………………156
Figure 6-10. Time course of relative tumor volume (RTV)………………………………………………….157
Figure 6-11. Tumor volume data plotted on the log-scale for all in silico mice and populations separated by
ratio thresh value of 13.8693……………………………………………………………………157
Figure 6-12. Dynamics of tumor volume. …………………………………………………………………158
Figure 6-13. Mean tumor growth. ………………………………………………………………………….159
xi
Abstract
Tumor angiogenesis is a critical step in tumor progression. By instructing vascular cells to form new
blood vessels from pre-existing ones, tumor cells continue to obtain nutrients and oxygen for growth. The
newly formed vessels also enable subsequent metastasis. Vascular endothelial growth factor (VEGF) is a crucial
angiogenesis promoter. VEGF binds with its major receptor VEGFR2 on endothelial cells (ECs) and promotes
signal transduction that induces long-term responses including cellular proliferation, survival, migration, and
vascular permeability, as well as an acute response including nitric oxide (NO) release. This pro-angiogenic
signal is balanced by angiogenesis inhibitors, such as thrombospondin-1 (TSP1), an endogenous matricellular
glycoprotein. TSP1 can directly bind to and sequester VEGF. At picomolar concentrations, this multi-domain
molecule also binds to its receptors CD47 and CD36 to redundantly inhibit VEGFR2-mediated endothelial
nitric oxide (eNOS) activity and other downstream pro-angiogenic signaling. Furthermore, TSP1 can induce
endothelial cell apoptosis via receptor CD36 at nanomolar concentrations. Meanwhile, existing anti-VEGF
agents often elicit systemic hypertension as an adverse side effect. In addition, responses to anti-VEGF agents
may be limited by parallel activation of the downstream pathways by additional angiogenic factors (such as
fibroblast growth factor) independent of the VEGF receptor. Therefore, inhibitors similar to TSP1 that act on
essential downstream pathways may be more effective than the existing VEGF/VEGFR antagonists for
controlling tumor angiogenesis.
To design treatments that achieve optimal anti-angiogenic outcome, we need to quantitatively
understand the dynamics of such a complex network that regulates angiogenesis itself. In this work, I present
a series of quantitative mechanistic models that examine the effects of a potent endogenous angiogenic inhibitor
TSP1. The models predict TSP1-mediated inhibition of the eNOS signaling pathway and activation of apoptotic
signaling in endothelial cells. Additionally, I present a model of tumor-bearing mice receiving anti-angiogenic
treatment, and demonstrate the utility of tumor growth kinetics in stratification of the animal survival outcome.
Ultimately, such model frameworks can be used to inform development of effective anti-angiogenic strategies
for cancer therapy.
1
Chapter 1
Introduction
1.1. Tumor angiogenesis
Tumor angiogenesis is a critical and distinct step in tumor progression. By instructing endothelial cells
(ECs) to promote new blood vessel formation from pre-existing vessels, cancer cells continue to obtain
nutrients and oxygen from the blood supply for growth[1], [2]. These newly formed vessels also provide the
necessary anchorage to facilitate subsequent tumor metastasis[3]–[5]. In healthy tissue, angiogenesis is
constantly regulated by a balance between its promoters and inhibitors. In solid tumor, the balance is often
disrupted, because tumor cells can secrete excessive angiogenic promotors. In some cases, the expression of
the inhibitors can also be downregulated. This imbalance turns on the “angiogenic switch” – the induction of
tumor vasculature[1], [2], [6], [7].
1.2. The angiogenic signaling network
1.2.1. VEGF signaling
In the development of tumor vasculature, VEGF is a crucial angiogenic promoter[8]–[14]. Several
biological factors in the tumor environment, including hypoxia, genetic mutations, metabolic and mechanical
stresses, often result in an increase of secretion level of VEGF and other angiogenic promoters[1], [15]–[18].
Inhibiting VEGF function reduces angiogenesis and the tumor size[19]. Therefore, it is important to understand
and control the VEGF signaling process in the tumor microenvironment.
VEGF acts upon ECs via its receptors including VEGF receptors -1 and -2 (VEGFR1,2) and
neuropilin-1 (NRP1). VEGFR2 is considered to be the main VEGF receptor on ECs, and is essential for EC
biology during development and in the adult, in physiology and pathology. VEGF-mediated signal transduction
through VEGFR2 activates PLCg/ERK, PI3K/Akt, and Src signaling pathways[20]–[22], which induce
biological responses including EC proliferation, survival, migration, and enhance vascular permeability[8], [10],
[13], [22]–[25].
2
VEGF-VEGFR2 signal transduction triggers endothelial nitric oxide synthase (eNOS) activation,
which contributes to both (A) long-term pro-angiogenic properties of VEGF in ECs[25] and (B) acute
vasodilation in the neighboring vascular smooth muscle cells (VSMCs). VEGF stimulation increases
intracellular calcium concentration, which promotes calmodulin binding to eNOS. Furthermore, the VEGF-
activated c-Src and Akt positively regulate eNOS activity[26]–[28]. Activated eNOS synthesizes nitric oxide
(NO) and citrulline (Cit) from L-arginine (Arg)[25], [29], [30]. NO activates soluble guanylyl cyclase (sGC) and
promotes cyclic GMP (cGMP) production from GTP. This pathway leads to downstream signaling that
promotes proliferation [31] (illustrated in Figure 1-1). Therefore, eNOS signaling mediates VEGF-induced
human EC proliferation and organization, contributing to the long-term pro-angiogenic properties of
VEGF[25]. The endothelium-derived NO production is also a fundamental mechanism of regulation of
vascular tone and tissue perfusion[32], a relatively acute effect compared to angiogenesis. NO generated from
ECs rapidly diffuses into the neighboring VSMCs where it activates sGC/cGMP pathway. cGMP activates
protein kinase G (PKG), which triggers a reduction of intracellular calcium level, and activates myosin light
chain (MLC) phosphatase, thereby inhibiting MLC phosphorylation and contraction[33]. Mice lacking eNOS
or PKG demonstrate moderate hypertension, indicative of increased vascular tone[34], [35].
3
Figure 1-1. Major interactions involved in VEGF- and TSP1-mediated intracellular signaling.
1.2.2. TSP1 signaling
The matricellular glycoprotein TSP1 is a potent endogenous angiogenic inhibitor In several cancer
types, expression of TSP1 is inversely correlated with malignant progression[36]. Tumors overexpressing TSP1
show decreased growth, metastases, and angiogenesis[37]. However, in the tumor microenvironment, hypoxia
often reduces the levels of the endogenous angiogenic inhibitor TSP1[38].
On the other hand, TSP1 inhibits NO signaling in both ECs and VSMCs by inhibiting activation of
sGC[39], [40]. In VSMCs and in vivo, TSP1 limits vasodilation by NO[41]. This inhibition can result in undesired
effects in managing vascular tone and tissue perfusion. I will discuss this aspect in section 1.3. Below, I briefly
summarize TSP1’s inhibitory effects on VEGF signaling observed in experimental studies.
TSP1 regulates the bioavailability and activity of VEGF via several mechanisms[39], [40], [42]–[51].
First, TSP1 can directly bind and sequester VEGF in the extracellular space[52]. The TSP1-VEGF complex
can be internalized via binding to the TSP1 receptor LDL-related receptor protein 1 (LRP1)[44].
Cit
VEGFR2
VEGF
CD47
TSP1
TSP1
CD36
myristate
Fyn
Fyn
pro3 casp3
apoptosis
cFLIP
1
Src Src
p
Arg
NO
eNOS CaM
p
sGC_b
sGC_5c
growth
p
Akt
Akt
p
unclear mechanism
GTP
cGMP
4
Second, TSP1 acts through its own receptors to antagonize VEGFR2 signaling intracellularly. The
CD47 receptor is an integral membrane protein expressed on a variety of cell types. It is expressed at lower
levels by most healthy cells[51], and over-expressed in ovarian cancer[53]. TSP1’s C-terminal signature domain
engages with CD47[45]. At physiological (picomolar) concentrations, TSP1 binds to its receptor CD47 on ECs
and potently inhibits VEGFR2 phosphorylation, NO production, sGC-dependent cGMP production, and
PKG (cGK-I) activation[40], [46], [49], [54] (illustrated in red in Figure 1-1). The TSP1/CD47 axis is a highly
redundant regulator of the NO/cGMP cascade, controlling both upstream activation of NO biosynthesis and
downstream effector functions in vascular cells[51].
CD36 is another TSP1 receptor, expressed on microvascular cells but not on ECs from larger
vessels[55]. At nanomolar concentrations, TSP1 induces EC apoptosis via receptor CD36[48], [56] (illustrated
on the left hand side in Figure 1-1). TSP1-CD36 association recruits Fyn, and activates the caspase cascade,
leading to phosphorylation of p38 MAPK. The signal upregulates production of Fas Ligand (FasL), which in
turn causes EC apoptosis through exogenous or endogenous binding with Fas receptor[57]. In the presence of
VEGF, TSP1-CD36 binding also reduces VEGFR2 phosphorylation and therefore modulates EC migration
and EC spheroid sprouting in in vitro angiogenesis assays, but this effect also requires CD36 association with
integrin b1[55].
In addition, CD36 acts as a fatty acid translocase (FAT) and takes up free fatty acids (FFAs) such as
myristate, which can promote eNOS activation[58]. CD36-dependent myristate uptake activates Src family
kinases, but the relative importance of myristate uptake in controlling eNOS activation through CD36 has not
been established. TSP1-CD36 binding limits myristate uptake in cultured vascular cells, specifically human
umbilical vein endothelial cells (HUVECs) and human aorta vascular smooth muscle cells (HAVSMCs)[47].
This inhibits membrane translocation and activation of Src family kinases, subsequently inhibiting eNOS
activation[47].
5
1.3. Anti-angiogenic therapy
1.3.1. Anti-angiogenic treatment in cancer
Since the concept of the angiogenic switch was first proposed in 1971 by Folkman, the fact that tumors
are dependent on blood supply has inspired many researchers to search for and develop anti-angiogenic agents
to stall tumor progression. The normal vasculature is highly quiescent, whereas the tumor vasculature is typically
comprised of highly proliferative ECs, making selective targeting of tumor-associated endothelium possible[59].
Besides completely inhibiting angiogenesis in the early stage, another potential target of anti-angiogenic
treatment is the improvement of delivery of co-administered chemotherapeutic drugs by pruning the abnormal,
chaotic tumor vasculature and decreasing the elevated interstitial pressure in tumors[60].
1.3.2. Limited treatment efficacy
Currently, most the US Food and Drug Administration (FDA)-approved angiogenesis inhibitors act as
VEGF-VEGFR2 antagonists, by sequestering free VEGF or antagonizing VEGFR2 phosphorylation.
However, many of these drugs have only achieved limited success. Bevacizumab, a humanized monoclonal
antibody, was the first VEGF inhibitor approved as a cancer treatment[61]. It has been approved as a
monotherapy or in combination with chemotherapy for many cancers, including renal cell carcinoma, metastatic
colorectal cancer, non-small cell lung cancer and metastatic cervical cancer[62]. In 2008, bevacizumab gained
accelerated approval for treatment of metastatic breast cancer. However, it failed to improve overall survival
and elicited significant side effects, and consequently its approval was revoked for use in first-line metastatic
breast cancer in late 2011[63]. Several Phase II and III clinical stage studies have also revealed contradicting
results regarding the benefit of add-on bevacizumab in the neoadjuvant treatment setting for breast cancer
patients[64]–[69]. Sunitinib, a tyrosine kinase inhibitor that targets VEGF receptors and other growth factor
receptors, has also shown limited success[19]. Together, these studies demonstrate that anti-angiogenic therapy
may not be effective across a wide range of patients.
Tumor heterogeneity contributes largely to the differences in response to anti-angiogenic therapy, as
revealed by both animal and preliminary human clinical trials[1]. Treatment response may depend on the types
6
or amount of angiogenic molecules expressed, or on other intrinsic tumor cell characteristics, such as oncogene
expression or hypoxia resistance[60], [70]–[72]. Therapeutic responses to VEGF inhibitors may be limited by
parallel activation of the downstream pathways by additional pro-angiogenic factors produced by tumors that
can activate NO/cGMP signaling independent of VEGF-VEGFR2[46]. These factors include adrenomedullin,
angiopoietin-1, angiopoietin-related growth factor, sphingosine-1-phosphate, lysophosphatidic acid, estrogens,
insulin, and fibroblast growth factor 2. Therefore, inhibitors such as TSP1 and its mimetics that act on essential
downstream pathways may be more effective than the existing VEGF-VEGFR2 antagonists for controlling
tumor angiogenesis.
1.3.3. Adverse side effect: hypertension
Besides inhibition of VEGF-induced pro-angiogenic signaling in ECs, VEGF-VEGFR2 antagonists
also lower the level of NO available for its paracrine regulation of VSMCs and platelets. Experimental studies
have established that NO plays a significant role in regulating regional blood flow by modulating VSM tone.
Reduced NO production can result in decreased local blood flow. Administration of VEGF-VEGFR2
antagonists therefore can induce systemic hypertension. In fact, hypertensive and pro-thrombotic activities are
frequent side effects of therapeutic angiogenesis inhibitors. Systemic hypertension could further limit treatment
efficacy as it affects drug delivery[73]. Similarly, TSP1’s antagonism of NO production results in acute inhibition
of tissue perfusion and acceleration of platelet hemostasis[74]. Therefore, to minimize the adverse effects of
anti-angiogenic treatment while achieving optimal anti-angiogenic outcome, we need to selectively target
components of the signaling network that mediate long term regulation of angiogenesis (vascular cell outgrowth
and vessel formation) but not acute cardiovascular responses.
It has also been proposed that hypertension induced by angiogenesis inhibitors indirectly increases
tumor perfusion, a paradoxical outcome named “vascular steal phenomenon”[74]. Tumor vasculature is
aberrant, chaotic and leaky, exhibiting abnormal blood flow, increased permeability and delayed maturation.
Therefore, tumor vasculature is less responsive to vasoactive agents than healthy tissue. This means that a
vasodilator used to counteract hypertension can indirectly decrease blood flow through the tumor, while a
7
vasoconstrictor (and often the angiogenesis inhibitor) can increase blood flow through the tumor but decrease
systematic blood flow in healthy tissue. This leads to challenges in drug delivery to the targeted tumor location.
On the other hand, overexpression of TSP1 by tumor cells has been shown to moderately decrease such indirect
tumor blood flow responses to NO (a vasodilator) and epinephrine (a vasoconstrictor)[73], demonstrating
TSP1’s promising role in regulating vascular responses in the context of anti-angiogenic therapy.
1.3.4. Unclear relative importance of TSP1 receptors
Two receptors (CD36 and CD47) mediate TSP1 inhibition of VEGF-induced, NO-driven
angiogenesis. Initial studies focused on CD36 for inhibiting angiogenesis and showed that engaging CD36 is
sufficient (but not necessary) to inhibit NO/cGMP signaling[43], [75]. Recombinant type 1 repeats of TSP1
and synthetic peptides derived, and some CD36 antibodies, mimic TSP1 to inhibit angiogenesis. The TSP1
mimetic drug ABT-510 binds to CD36 and inhibits angiogenesis via both translocase-dependent and caspase-
dependent mechanisms[76], [77]. ABT-510 reached Phase II clinical trials, but failed to show clear evidence of
efficacy and is no longer tested as a single-agent drug in clinical development[78], [79]. The combination of
bevacizumab and ABT-510 has been tested in clinical trials to treat advanced solid tumors; however, the
patients’ responses are highly variable and show disappointing outcomes[80].
Meanwhile, experimental evidence shows that native TSP1 acts through the more potent inhibitory
pathway mediated by the necessary receptor CD47[39]. However, the relative importance of the two receptors
CD36 and CD47, at various TSP1 levels has not been quantitatively investigated, and the activity of TSP1 via
CD47 largely remains unexploited in development of effective anti-angiogenic therapy.
Both CD36- and CD47-specific agonist agents have been developed[81], although they have not
demonstrated definitive clinical efficacy. Once a more clear, quantitative understanding of the response of the
anti-angiogenic signaling network is achieved, small molecules could potentially be developed and applied to
inhibit tumor angiogenesis based on a patient’s TSP1 receptor profile. Together, there is a need to better
understand the anti-angiogenic signaling network and its response to pro- and anti-angiogenic treatments, in
order to facilitate the development of effective treatment strategies.
8
1.4. Computational modeling and systems biology approaches
As described above, it is known that TSP1 acts through multiple mechanisms in ECs to inhibit
angiogenesis. To fully understand and exploit its inhibitory functions efficiently, it is important to consider both
its extracellular interactions and intracellular mechanisms. Detailing the signaling mechanisms and quantifying
the dynamics of intracellular species also allows us to understand the individual and total effect of TSP1’s
multiple functions on different time-scales, including both acute and long-term effects. Furthermore, because
TSP1’s signaling has regulatory effects on cellular behavior in multiple vascular cell types, quantitatively studying
the dynamics of TSP1’s signaling network in both ECs and VSMCs will aid in understanding of the relative
importance of each signaling component, and ultimately provide insight into strategies for a better control of
this multi-cell type network.
Computational systems biology approach allows for understanding of such complex biological
processes that involve multiple spatial- and time-scales. It aims to predict the behavior of a system by combining
quantitative experimental techniques and computational models. Taking advantage of mathematical modeling,
predictions of optimal treatment strategies as well as identification of biomarkers for patient screening can be
made efficiently.
To our knowledge, the majority of the computational modeling work has been focused on the pro-
angiogenic effects, while there is a lack of quantitative understanding of the mechanisms through which the
natural anti-angiogenic factors take effect. Particularly, TSP1 is thought to play an important role in regulating
angiogenesis, and yet the inhibitory functions of this potent endogenous molecule have not been quantitatively
and systematically studied. Therefore, it is important to incorporate the accumulated knowledge and
systematically study TSP1’s inhibitory functions in tumor angiogenesis.
1.5. Dissertation Outline
In this work, I present a series of quantitative mechanistic models that can predict the effects of TSP1-
mediated anti-angiogenic signaling at multiple-scales, and demonstrate the application of these models as a
framework for anti-angiogenic treatment optimization.
9
In Chapter 2, I develop a mechanistic model for the eNOS signaling pathway in endothelial cells,
mediated by the angiogenic factors VEGF and TSP1. TSP1 has been shown to redundantly suppress several
activated species in this pathway via its receptor CD47, however the exact mechanisms remain unknown. I first
construct and train the eNOS signaling model using in vitro datasets with VEGF-stimulation to constrain the
model. Then, I use the trained model to simulate a series of perturbations by directly altering the kinetic rate
parameters or initial conditions of species concentration. This set of simulations reveal possible combinations
of TSP1’s intracellular mechanisms. Furthermore, we simulate specific perturbations that take effect only in the
high VEGF condition. This set of results generates insight into potential ways to selectively target endothelial
cells experiencing high VEGF levels present in the tumor without harming cells in the normal tissue, opening
up avenues to avoid hypertensive side effects seen in current anti-angiogenic treatments.
In Chapter 3, I establish a mechanistic model for the TSP1-mediated apoptosis signaling pathway in
endothelial cells. In this model, TSP1-CD36 binding triggers activation of the caspase cascade and p38MAPK
activity and upregulates FasL. FasL triggers apoptotic respond by binding to the death receptor, Fas. First, I
train and validate the model using in vitro datasets for TSP1-induced species activation in this pathway. Then I
use the global sensitivity analysis to identify the influential components of the model. To investigate the
influence of heterogeneity on the cell’s response to TSP1 stimulation, I simulated a population of cells by
generating a large set of unique protein expression profiles. As a result of the variability in the intracellular initial
concentrations, the simulated population of cells exhibit different apoptotic responses to the same TSP1
stimulation. Then, I used the receiver operating characteristics (ROC) analysis to study whether certain initial
concentrations can be used as predictors for whether a cell would respond to TSP1 stimulation or not. I also
simulated several different perturbations to the system to predict effective strategies to enhance the apoptotic
signaling response.
In Chapter 4, I briefly describe the process to integrate the above two mechanistic models of TSP1
signaling. Having constructed the two pathway models individually with a great extent of mechanistic detail, I
take advantage of these two models to understand the influence of receptor heterogeneity, and the relative
importance of the two pathways. I first make necessary adjustments to combine the two models in a consistent
10
manner. Then, I use the integrated model to simulate the population response to TSP1 and VEGF stimulations.
Lastly, I discuss future steps to be taken in order to generate useful predictions of effects using TSP1 or its
mimetics based on the cell expression profile and the VEGF level in the tumor microenvironment. Ultimately,
the integrated model can serve as a framework to predict patient-specific anti-angiogenic treatment strategy.
In Chapter 5, I introduce a whole-body mouse model for breast cancer xenograft-bearing mice
receiving anti-VEGF (bevacizumab) treatment. In this study, we expanded on a previously established
compartment model to calculate the dynamic tumor volume as a function of the angiogenic signal, which is a
quantity that is affected by the drug and changes time. We train the model by fitting the tumor growth kinetic
parameters to in vivo tumor growth volume data without any treatment, and validate new model predictions of
tumor growth with treatment using the corresponding treatment data from the same studies. We then
investigate the utility of specific tumor growth kinetics to predict the endpoint relative tumor volume, an
indicator of treatment efficacy.
In Chapter 6, I continue the investigation of the utility of tumor growth kinetics as potential biomarkers
to predict anti-VEGF treatment efficacy. I use the estimated parameter sets from Chapter 5 to generate cohorts
of virtual mice, where each mouse exhibits a unique tumor growth profile. I simulate the Kaplan Meier survival
estimates for the control and treated mouse cohorts and investigated whether a specific value of any growth
kinetic parameter can be used to stratify the population survival estimates. Values of two kinetic parameters
that can serve this purpose are found in this set of analyses. I then validate these values using a new set of
tumor growth data from a separate study. This work demonstrates an approach to use mechanistic modeling
to identify kinetic parameters as potential biomarkers to predict the response to treatment.
Altogether, my work focuses on using mechanistic modeling to predict the effects of anti-angiogenic
signaling and treatment. These models can be expanded and adapted to simulate the effects of other pro- and
anti-angiogenic agents.
11
Chapter 2
TSP1-mediated eNOS signaling via receptor CD47
Portions of this chapter are adapted from:
Qianhui Wu and Stacey D. Finley. Journal of Clinical Medicine (2020)
2.1. Abstract
The endothelial nitric oxide synthase (eNOS) signaling pathway in endothelial cells has multiple
physiological significances. It produces nitric oxide (NO), an important vasodilator, and enables a long-term
proliferative response, contributing to angiogenesis. This signaling pathway is mediated by vascular endothelial
growth factor (VEGF), a pro-angiogenic species that is often targeted to inhibit tumor angiogenesis. However,
inhibiting VEGF-mediated eNOS signaling can lead to complications such as hypertension. Therefore, it is
important to understand the dynamics of eNOS signaling in the context of angiogenesis inhibitors.
Thrombospondin-1 (TSP1) is an important angiogenic inhibitor that, through interaction with its receptor
CD47, has been shown to redundantly inhibit eNOS signaling. However, the exact mechanisms of TSP1’s
inhibitory effects on this pathway remain unclear. To address this knowledge gap, we established a molecular-
detailed mechanistic model to describe VEGF-mediated eNOS signaling, and we use the model to identify the
potential intracellular targets of TSP1. In addition, we apply the predictive model to investigate the effects of
several approaches to selectively target eNOS signaling in cells experiencing high VEGF levels present in the
tumor microenvironment. This work generates insights for pharmacologic targets and therapeutic strategies to
inhibit tumor angiogenesis signaling, while avoiding potential side effects in normal vasoregulation.
2.2. Introduction
2.2.1. Overview of tumor angiogenesis and its importance in tumor progression.
Angiogenesis, the formation of new blood capillaries from pre-existing vessels, plays a critical role
in tumor progression[4]. For a solid tumor to expand beyond millimeters in size, it must promote new blood
vessel formation to achieve sustained blood supply[1], [4]. The process of angiogenesis is driven by a number
12
of pro-angiogenic factors, which promote several endothelial cell (EC) functions that contribute to new blood
vessel formation. The resulting new vessels carry oxygen and nutrients to the tumor, allowing the tumor to
enlarge, and also providing a path for the cancer cells to metastasize[4]. In fact, a meta-analysis revealed that
high intratumoral microvessel density (MVD) is a significant predictor of poor survival for breast cancer
patients[82].
2.2.2. VEGF-eNOS signaling and its importance.
One of the most well studied pro-angiogenic factors is vascular endothelial growth factor (VEGF),
which is often upregulated in the tumor microenvironment[15], [16], [18], [83]. VEGF-mediated signal
transduction through its principal receptor VEGFR2 (herein abbreviated as R2) induces biological responses
required for angiogenesis, including EC proliferation, survival, migration, and enhanced vascular
permeability[12], [21], [23]. VEGF signaling through R2 promotes the endothelial nitric oxide synthase
(eNOS) activity through multiple mechanisms[8], [11], [27], [84] (Figure 2-1). eNOS produces nitric oxide
(NO), an important vasodilator that rapidly diffuses throughout the endothelium. NO activates the enzyme
soluble guanylate cyclase (sGC) to produce cyclic guanosine monophosphate (cGMP)[84], [85]. This particular
part of the eNOS signaling pathway contributes to both an acute vasodilating effect in the neighboring vascular
smooth muscle cells (VSMCs)[8], [23], [86] and the long-term angiogenic functions of ECs such as
proliferation[8], [11], [87]. Given the biological significance of VEGF-mediated eNOS signaling, it is important
to understand the dynamics of this multi-faceted pathway and how it responds to angiogenic factors.
13
Figure 2-1. Model schematic of the eNOS signaling network. (a) Receptor module. The signaling pathway begins
with VEGF binding to receptor R2. Ligated R2 undergoes autophosphorylation and triggers the phosphorylation of Src
and PLCg. (b) Calcium module. Active PLCg converts PIP 2 to IP 3 through hydrolysis. IP 3 binds to its receptor on the ER
membrane and induces Ca
2+
release into the cytosol. The ER store Ca
2+
depletion triggers further Ca
2+
entry through the
CRAC channel which is quickly balanced by several homeostatic mechanisms. (c) eNOS module. Ca
2+
binds to and
activates CaM, which in turn activates eNOS. eNOS converts its substrate arginine to citrulline, producing NO. (d)
Src/Akt/Hsp90 module. Active Src activates Akt and the chaperon protein Hsp90. Hsp90 facilitates Akt association with
eNOS, which results in eNOS phosphorylation. The binding of eNOS with Hsp90 and phosphorylation of eNOS both
enhance eNOS activity. (e) sGC module. NO triggers cGMP synthesis from GTP. cGMP is degraded by PDE. TSP1
sequesters VEGF in the extracellular space and binds to its own receptor CD47 on the EC membrane, disrupting the
coupling of CD47 and R2. Furthermore, TSP1 has been shown to reduce VEGF-induced activation of R2, Akt, and
eNOS, agonist-stimulated Ca
2+
increase, basal eNOS activity, and basal or VEGF/agonist-induced cGMP production.
The signaling species observed to be affected by TSP1 are highlighted in blue. Shading indicates the relative location of
reactions in the network. Light red: Src/Akt/Hsp90; light purple: Ca
2+
system; light blue: eNOS activity; light green: sGC
activity.
Because tumor progression strongly depends on angiogenesis, in the past decades, researchers have
developed anti-angiogenic therapies to inhibit tumor angiogenesis[19], [61], [88]. Many of these angiogenic
inhibitors target VEGF and its receptor R2; however, they have only achieved limited success across a wide
range of patients[19], [61], [63]–[69], [89]. Therapeutic responses to VEGF inhibitors may be limited by parallel
14
activation of the downstream pathways by additional pro-angiogenic factors. In addition, inhibiting R2 signaling
can reduce the level of endothelium NO available for the paracrine regulation of VSMCs and platelets[74]. In
fact, hypertensive and pro-thrombotic activities are frequent side effects of therapeutic angiogenic inhibitors.
Furthermore, because the aberrant and leaky tumor vasculature is less responsive to vasoactive agents than
healthy tissue[60], [83], a vasodilator used to counteract hypertension can indirectly decrease blood flow
through the tumor. This can further cause challenges in drug delivery to the targeted tumor location.
2.2.3. TSP1 and its inhibitory functions
Physiologically, angiogenesis is controlled by a balance between the angiogenic promotors and
inhibitors[1]. The expression levels of both pro- and anti-angiogenic factors are often dysregulated in the tumor
microenvironment in favor of angiogenesis. For example, the matricellular glycoprotein thrombospondin-1
(TSP1) is a potent endogenous angiogenic inhibitor, and its expression is inversely correlated with the malignant
progression of several types of cancer[90]–[92]. TSP1 regulates the bioavailability and activity
of VEGF via several mechanisms. TSP1 can directly bind and sequester VEGF in the extracellular space[44],
[52]. TSP1 also antagonizes R2 signaling through its own receptors, CD36 and CD47. At physiological
(picomolar) concentrations, TSP1 binds to receptor CD47 on ECs and redundantly inhibits eNOS
signaling[39], [54]. At the nanomolar concentration, TSP1 blocks myristate uptake and induce EC apoptosis via
receptor CD36[43], [56], [76], [93].
Because of TSP1’s potency and redundancy in inhibiting angiogenic signaling, the use of TSP1 and its
mimetics in cancer therapy may be more advantageous than anti-VEGF treatments. Several CD47 antibodies
are currently being investigated in preclinical studies or Phase I & II clinical trials[94], [95]; however, rather than
the anti-angiogenic effect, these mimetics are sought after to overcome immune evasion of the tumor cells
expressing CD47[96], [97]. Meanwhile, the exact intracellular mechanisms of TSP1’s angiogenesis-inhibiting
functions remain unknown, and the relative importance of its multiple signaling pathways mediated by receptors
CD36 and CD47 are not quantitatively understood.
15
2.2..4. Need of computational modeling and systems biology approaches
With the incomplete understanding of TSP1’s role in angiogenic regulation intracellularly, it is important
to incorporate the accumulated knowledge and systematically study its inhibitory effects on angiogenic
signaling. A computational systems biology approach allows for understanding such complex biological
processes. Furthermore, by taking advantage of mathematical modeling, it is possible to predict optimal
treatment strategies and identify biomarkers for patient screening. Thus, modeling is a powerful tool to
efficiently generate testable hypotheses, which can reduce the cost of extensive “wet lab” and preclinical studies.
The vast majority of such modeling efforts have focused on the pro-angiogenic signaling networks. For
example, we and others have developed models in the context of angiogenesis on various scales: intracellular
signaling[98]–[106], cell and tissue level[70], [107]–[110], and whole-body compartment models[111]–[116].
Previously, we have established a model of TSP1’s apoptotic signaling through receptor CD36, predicting
several treatments strategies that may enhance the angiogenic inhibition in tumor[99]. However, this work
provided quantitative insight into only one pathway by which TSP1 exerts its anti-angiogenic effect. Meanwhile,
TSP1’s effect through its receptor CD47, remains understudied. Recently, Bazzazi et al. developed a mechanistic
model to demonstrate how TSP1 may a inhibit VEGF/R2 signaling via receptor CD47[102]; however, their
study focused on TSP1’s mechanisms at the receptor level, while the downstream, intracellular inhibitory
mechanisms of TSP1 were not evaluated.
In the present study, we focus on uncovering the intracellular mechanisms of TSP1 through receptor
CD47. We construct a molecularly detailed, quantitative mechanistic model of VEGF- and TSP1- mediated
eNOS signaling in ECs. We use the model to systematically explore the intracellular mechanisms of TSP1-
CD47 signaling. Specifically, we focus on the effects of varying influential parameter values in the model
without changing the model structure to hypothesize the mechanisms through which TSP1 inhibits the agonist-
induced Ca
2+
influx-plateau phase and the NO and cGMP generation in both basal and VEGF-stimulated
conditions. Then, we use the model to identify effective strategies that selectively target ECs that experience
higher VEGF level associated with the tumor microenvironment. Our results highlight several perturbations
that achieve the experimentally observed TSP1-mediated inhibitory effects on the signaling outputs of interest.
16
In addition, we show that certain perturbations can achieve selective inhibition of the pro-angiogenic signaling
when VEGF level is high (similar to the concentrations present in tumor tissue), but not at normal VEGF
levels. Thus, the model provides detailed insight regarding strategies to inhibit tumor angiogenesis, while
avoiding potential side effects in normal vasoregulation.
2.3. Methods
2.3.1. Mathematical model
We constructed a rule-based model to describe the intracellular eNOS signaling in ECs mediated by VEGF
and TSP1. The reaction rules are defined using the BioNetGen software. As depicted in Figure 1, the pro-
angiogenic signaling pathway begins with VEGF binding to its main receptor, R2, on the endothelial cell
membrane (Figure 1a). Ligated R2 undergoes autophosphorylation and triggers the phosphorylation of Src
and PLCg. Active PLCg converts PIP2 to IP3 through hydrolysis. IP3 binds to its receptor on the ER
membrane and induces Ca
2+
release into the cytosol. The ER store Ca
2+
depletion triggers further Ca
2+
entry
through the CRAC channel. This rapid increase in cytosolic Ca
2+
is quickly balanced by several homeostatic
mechanisms, including the resequestration of Ca
2+
into the ER via the sarco/endoplasmic reticulum Ca
2+
-
ATPase (SERCA), and the extrusion of Ca
2+
from the cell via the plasma membrane Ca
2+
-ATPase (PMCA).
The ER Ca
2+
may also passively leak to the cytosol (Figure 2-1b). Ca
2+
binds to and activates calmodulin
(CaM), which in turn activates the endothelial nitric oxide synthase (eNOS). eNOS converts its substrate
Arginine to Citrulline, producing Nitric Oxide (NO) (Figure 2-1c). Src activates Akt and the chaperon protein
Hsp90. Hsp90 facilitates Akt association with eNOS, which results in eNOS phosphorylation. The binding of
eNOS with Hsp90 and phosphorylation of eNOS both enhance eNOS activity. (Figure 2-1d) NO rapidly
diffuses throughout the endothelium and binds to the enzyme soluble guanosine cyclase (sGC). Active sGC
synthesizes cyclic guanosine monophosphate (cGMP) from guanosine triphosphate (GTP). cGMP binds to
and activates phosphodiesterase (PDE), which degrades cGMP to GMP (Figure 2-1e). This eNOS signaling
pathway is essential to VEGF-mediated EC proliferation. For TSP1’s known functions, we include that TSP1
binds to VEGF in the extracellular space and its own receptor CD47 on the EC membrane, disrupting the
17
coupling of CD47 and R2. For detail on the experimental evidence that supports the formulated biochemical
reactions in this model, see Supplemental Text in Appendix A. Excitingly, our model is an advance compared
to previous modeling works[102], [104], as it includes the set of interactions between Hsp90, CaM, Akt, and
eNOS, as well as signaling species downstream of eNOS. We apply this detailed model to understand the anti-
angiogenic effects of TSP1 and other targeted perturbations in conditions recapitulating the tumor
microenvironment.
2.3.2. Model implementation
We formulated the biochemical reaction network using a rule-based approach with
the BioNetGen software[117]. The reactions are assumed to follow well-established mass-action or Michaelis-
Menten kinetics. Based on the specified rules, BioNetGen produces a set of ordinary differential
equations (ODEs) that describe the rate of change in each species’ concentration over time. We describe this
process in more detail in Appendix A: Supplemental Text. Using the MATLAB (The MathWorks, Inc.) ODE
solver suitable for stiff problems, ode15s, we compute time courses of species concentrations. The
concentrations of the signaling species are computed for the same times used in the experimental time-course
data available. The model is comprised of 127 kinetic rate parameters, three geometric parameters, 160 total
species, with 18 non-zero initial conditions.
2.3.3. Publication selection and data extraction
We searched for publications on Pubmed and Google Scholar, and found papers through references and
citations. For full model fitting, the criteria for data inclusion are: 1) in vitro studies performed using the HUVEC
cell line, 2) cells were only stimulated by VEGF or TSP1, and 3) datasets showed time-course measurements
for species’ concentrations. We also include two datasets showing R2 dynamics upon stimulation with VEGF
and treatment with cycloheximide to estimate receptor internalization rates.
We extracted experimental data from figures found in various published studies[24], [40], [118]–[121] using
an online data extraction software, WebPlotDigitizer[122]. If the datasets were not already quantified, we used
18
Western blot images shown in the published paper. The images were extracted using Image J software based
on the density of the protein bands and were normalized to their respective controls[123]. For datasets with
arbitrary units, we normalized the data points to the maximum within each dataset.
2.3.4. Sensitivity Analysis
We performed the extended Fourier Amplitude Sensitivity Test (eFAST) to guide parameter selection for
both model training and perturbation simulations. This is a variance-based approach that identifies the model
parameters that significantly influence the model outputs[124], [125], the predicted species’ levels. In this
method, the parameter space is sampled within a specific range around the baseline parameter value, over a
specified distribution. We allowed the parameters to vary two orders of magnitude to investigate the influence
of each parameter over a wide range of values. The eFAST method computes a total sensitivity index (S ti),
which quantifies the variance of the model output with respect to the variances of each input and covariances
between combinations of inputs. The S ti is a measure of the global sensitivity, accounting for the correlations
among multiple inputs. The individual sensitivity indices are normalized by the sum total in order to be
compared. Furthermore, the resulting sensitivity indices for all parameters are compared to that of the random
“dummy” variable, and only indices significantly different from the dummy variable index (p<0.05) are
reported. The eFAST method has been used in our laboratory in our previous work[70], [98], [99], [107], [126].
The parameters with S ti values larger than a cutoff value of 0.2 were determined as influential.
2.3.5. Identifiability Analysis
Prior to parameter estimation, we performed a structural parameter identifiability analysis[127], [128]. This
analysis determines whether the calibration problem is well posed and identifies which parameters can be
uniquely specified from the available data. In this method, pair-wise correlation coefficients between model
parameters are calculated. Parameters that were locally identifiable had correlations with all other parameters
between −0.9 and 0.9. Parameters that were not locally identifiable, termed a priori unidentifiable, had
correlations of > 0.9 or < −0.9 with at least one other parameter. When two parameters are highly correlated,
19
unidentifiable, and their values are unknown, it is necessary to specify the value of one of the parameters
(described in model parameterization, described below) and estimate the value of the other parameter rather
than estimate both redundant parameters.
2.3.6. Model Parameterization
Initial parameter settings. We pursued model development in a modular fashion. We developed several
sub-modules that can be constrained independently, as illustrated in Figure 1. As a starting point, we first set
the unknown parameter values based on information from various sources, including experimental studies[121],
[129]–[131] and previously established computational models[70], [98], [102], [107], [132]–[138]. For CD47
receptor concentration, we obtained the geometric mean of the number of CD47 receptors on cultured human
microvascular endothelial cells (HMVECs) experimentally quantified using flow cytometry. Since there is no
quantitative data available regarding the receptor number for HUVECs, we made the assumption that CD47
expressed on HUVECs is at the same level as on HMVECs.
Model fitting. After model construction, we performed sensitivity analysis and identifiability analysis to
identify the influential and identifiable parameters to be estimated. We fixed the unknown, unidentifiable
parameters based on literature[139], [140]. In the full model training, a total of 23 uncorrelated, influential
parameters were estimated. We provide the details of the parameter estimation performed during model
development in Supplemental Text in Appendix A. Briefly, we use the least-squares nonlinear regression
optimization algorithm lsqnonlin function in MATLAB to estimate the unknown parameters. The training data
consisted of 14 sets of time-course measurements (a total of 58 datapoints)[24], [40], [118]–[121] (Figure 2-
2a-n). Based on the parameter estimation, 19 sets of estimated parameters with the lowest errors from fitting
were selected as the best fit. We report the distribution of these parameter values in Figure 2-3. The best fit
parameter sets were validated using four datasets not used in fitting[24], [119] (Figure 2-2o-r). A list of all
model parameters and their sources, including from literature and from the model parameterization, are in
Table S1.
20
Figure 2-2. eNOS signaling model training and validation. The ODE model was trained to match in vitro experimental
measurements of HUVECs for the activated species in the VEGF-mediated eNOS signaling pathway. Fitting results
include model simulation compared to experimental datasets: (a) total R2 level; (b) membrane R2; (c) pR2 upon 50ng/ml
VEGF stimulation[118]; (d) total R2 in control condition[118]; (e) total R2 with cycloheximide treatment[118]; (f) total R2
with 50ng/ml VEGF and cycloheximide treatment[118]; (g) pSrc with 2.5ng/ml VEGF treatment[24]; (h) pAkt, (i) peNOS
with 50ng/ml VEGF treatment[118]; (j) pPLCg with 80ng/ml VEGF treatment[119]; (k) NO level with 10ng/ml VEGF
treatment[120]; concentration of (l) IP3 and (m) cytosolic Ca
2+
with 10ng/ml VEGF treatment[121]; (n) cGMP
concentration with 30ng/ml VEGF treatment[40]. (o-r) Several independent sets of data[24], [119] were used to validate
the model prediction. Solid line: mean of 19 best fits. Shaded area: standard deviation of 19 best fits. Squares: experimental
data. Error bars: standard deviation of the experimental datasets. The normalized values are relative to the highest value
for that species.
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Bruns 2010 pAkt/Akt
50ng/ml VEGF
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Ruan 2012 pSrc/Src
2.5ng/ml VEGF
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Bruns 2010 totR2
50ng/ml VEGF,CHX
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Bruns 2010 totR2
ctrl
0 10 20 30
Time (min)
0
0.25
0.5
0.75
1
1.25
normalized level
Boeldt 2017 NO
10ng/ml VEGF
0 10 20 30
Time (min)
0
1000
2000
3000
4000
concentration (nM)
Isenberg 2005 cGMP
30ng/ml VEGF
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Chabot 2009 peNOS/eNOS
80ng/ml VEGF
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Chabot 2009 pAkt/Akt
80ng/ml VEGF
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Bruns 2010 memR2
50ng/ml VEGF
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Chabot 2009 pPLCg/PLGg
80ng/ml VEGF
0 10 20 30
Time (min)
0
50
100
150
200
250
concentration (nM)
Faehling 2002 Ca
10ng/ml VEGF
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Bruns 2010 totR2
50ng/ml VEGF
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Bruns 2010 totR2
CHX
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Bruns 2010 peNOS/eNOS
50ng/ml VEGF
0 1 2 3 4
Time (min)
0
2
4
6
concentration (nM)
10
4
Faehling 2002 IP3
10ng/ml VEGF
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Chabot 2009 pR2/totR2
80ng/ml VEGF
(a) (b)
(e) (f) (g) (h)
(i) (j)
(l) (m)
(k)
(n)
0 10 20 30 40 50 60
Time (min)
0
0.2
0.4
0.6
0.8
1
normalized level
Ruan 2012 pAkt/Akt
2.5ng/ml VEGF
(o) (p) (q) (r)
Time (min) Time (min) Time (min) Time (min)
Normalized Level Normalized Level Normalized Level Normalized Level Concentration (nM)
2+
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Bruns 2010 pR2
50ng/ml VEGF
(c) (d)
21
Figure 2-3. Distribution of estimated parameters in the eNOS model. Middle line: median parameter value among
19 estimations. Box: first to third quartile (25%-75%). Whiskers: minimum and maximum of the estimated values.
Table 2-1. List of eNOS model parameters.
Index Parameter Value* Unit Source
receptor module
1 k on,TSP1.VEGF 0.03 nM
-1
min
-1
as assumed in [70]
2 k off,TSP1.VEGF 0.3 min
-1
as assumed in [70]
3 k deg,VEGF.TSP1 0.0116 min
-1
as assumed in [70]
4 k on,VEGF.R2 0.6 nM
-1
min
-1
assumed¶
5 k off,VEGF.R2 0.06 min
-1
calculated based on a k d of 100pm [130]
6 k on,TSP1.CD47 0.03 nM
-1
min
-1
as assumed in [70]
7 k off,TSP1.CD47 0.0003 min
-1
calculated based on a k d of 10pm[39]
8 k on,R2.CD47 0.0011 nM
-1
min
-1
as assumed in [107]
9 k off,R2.CD47 0.06 min
-1
as assumed in [107]
10 k inter,R2 (R2,
R2:CD47)
0.0426
[0.0421-0.0429]
min
-1
estimated in receptor module (see Appendix
A) ¶¶
11 k inter,pR2 (pR2,
R2:CD47)
4.7682
[3.0321-5.8339]
min
-1
estimated in receptor module (see Appendix
A)
12 k inter,CD47 (only
CD47)
0.5692
[0.2987-0.8321]
min
-1
estimated in full model
13 k inter,R2.CD47 0.0085 min
-1
estimated (Appendix A)
14 k inter,pR2.CD47 23.8410 min
-1
estimated (Appendix A)
15 k inter,TSP1bd (any
complex containing
TSP1)
0.5692 min
-1
assume same as k inter,CD47
16 k p,R2 0.6
[0.3251-0.8473]
min
-1
estimated in full model
17 k dp,R2 0.06 min
-1
tuned†
18 k dp,R2.CD47bd 0.01 min
-1
tuned
Icrac
10
-10
10
-9
10
-8
Oct4 lsqnonlin 23 parameters (consistent error calc.)
bounds 0.1-10x baseline
Seed bounds 0.5-1.5x baseline
best 22 fits, max-min, mean, box=0.25-0.75 percentile
kinterCD47
kpR2
kdegpR2
konSrcpR2
kdpSrc
kdpAkt
kcatPLCgDAG
kdegIP3
Iip3Ramp
Vp2
10
-2
10
-1
10
0
Oct4 lsqnonlin 23 parameters (consistent error calc.)
bounds 0.1-10x baseline
Seed bounds 0.5-1.5x baseline
best 22 fits, max-min, mean, box=0.25-0.75 percentile
kpSrc
kpAkt
kpPLCg
kdpeNOS
kclearNO
Src
CaM
eNOS
Hsp90
Akt
10
0
10
1
10
2
10
3
Oct4 lsqnonlin 23 parameters (consistent error calc.)
bounds 0.1-10x baseline
Seed bounds 0.5-1.5x baseline
best 22 fits, max-min, mean, box=0.25-0.75 percentile
KmIP3R
PIP2
10
4
10
5
10
6
Oct4 lsqnonlin 23 parameters (consistent error calc.)
bounds 0.1-10x baseline
Seed bounds 0.5-1.5x baseline
best 22 fits, max-min, mean, box=0.25-0.75 percentile
22
19 k syn,R2 0.0482
[0.0478-0.0484]
nM*min
-1
estimated in receptor module (see Appendix
A)
20 k syn,CD47 0.0899
[1.382e-4-0.1]
nM*min
-1
estimated in receptor module (see Appendix
A)
21 k deg,R2 0.0126
[0.0125-0.0210]
min
-1
estimated in receptor module (see Appendix
A)
22 k deg,pR2 0.2219
[0.1309-0.3697]
min
-1
estimated in full model
23 k deg,pR2.CD47 0.0168
[0.0059-0.0212]
min
-1
estimated in receptor module (see Appendix
A)
24 k deg,CD47 0.0063 min
-1
tuned
25 k deg,R2TSP1bd 0.0168 min
-1
assume same as #23
Src/Akt/Hsp90 module
26 k on,Src.pR2 0.06
[0.0296-0.3001]
nM
-1
min
-1
estimated in full model
27 k off,Src.pR2 25 min
-1
tuned
28 k p,Src 20
[10.9511-29.1037]
min
-1
estimated in full model
29 k dp,Src 0.4
[3080-0.5572]
min
-1
estimated in full model
30 k on,Src.Hsp90 0.5 nM
-1
min
-1
assumed
31 k off,Src.hsp90 0.5 min
-1
tuned
32 k p,Hsp90 30 min
-1
assumed
33 k dp,Hsp90 0.01 min
-1
tuned
34 k on,Src.Akt 0.06 nM
-1
min
-1
assumed
35 k off,Src.Akt 20 min
-1
tuned
36 k p,Akt 3
[1.7288-4.5689]
min
-1
estimated in full model
37 k dp,Akt 0.1
[0.0407-0.1444]
min
-1
estimated in full model
calcium module
38 k p,PLCg 10
[6.3173-15.4105]
min
-1
estimated in full model
39 k dp,PLCg 0.3 min
-1
assumed
40 K M,PIP2PLCg 193.5858 nM [104]
41 n IP3 1 Unitless;
coefficient
the hill number for generation of IP3 by
PLCγ; assumed
42 k cat,PLCg 0.3000
[0.0935-0.4366]
min
-1
estimated in full model
43 k deg,IP3 0.0200
[0.0039-0.0376]
min
-1
estimated in full model
44 k syn,PIP2 10 nM* min
-1
tuned
45 I CRAC 1.50E-09
[9.2142´10
-10
–
3.0694´10
-9
]
min
-1
estimated in full model
46 K CRAC 2492.5441
[938.1226-2492.5441]
nM estimated in fitting calcium module
(Appendix A)
47 t stim 1 min tuned
48 K M,PLCgR2 8000 nM [104]
49 n CRAC 0.6580 Unitless;
coefficient
the hill number for the steady-state CRAC
channel activation; estimated (lsqnonlin)
23
50 I IP3R 0.3910
[0.2638-0.5892]
min
-1
estimated in full model
51 K M,IP3R 20000
[10292-33382]
nM baseline assumed based on [141]; estimated
in full model
52 I PMCA 220418.4750 min
-1
calculated for calcium homeostasis (see
Appendix A)§
53 K M,PMCA 260 nM assumed based on [133]
54 Ca ext 2000000 nM assumed
55 I SERCA 435320.5900
[3.8909´10
5
-7.6429´10
5
]
min
-1
estimated in calcium module (see Appendix
A)
56 k leak,ER 6.80E-09 min
-1
calculated for homeostasis
57 K M,SERCA 150 nM [104]
58 K i,Ca 1000 nM [104]
59 CSQN 15000000 nM [104]
60 K CSQN 800000 nM [104]
eNOS module
61 k on,Ca2C 0.24 nM
-1
min
-1
[142]
62 k off,Ca2C 555 min
-1
[142]
63 k on,Ca2N 6 nM
-1
min
-1
[142]
64 k off,Ca2N 45000 min
-1
[142]
65 k on,2NeNOS 0.0081 nM
-1
min
-1
[134]
66 k on,2CeNOS 0.078 nM
-1
min
-1
[134]
67 k on,4eNOS 0.078 nM
-1
min
-1
[134]
68 k off,CaMeNOS 0.6 min
-1
[134]
69 k on,2N.eNOS.H 0.0325 nM
-1
min
-1
calculated based on [131]
70 k on,2C.eNOS.H 0.3133 nM
-1
min
-1
calculated based on [131]
71 k on,4.eNOS.H 0.3133 nM
-1
min
-1
calculated based on [131]
72 k off,CaM.eNOS.H 0.6000 min
-1
[134]
73 k on,2N.peNOS 0.0675 nM
-1
min
-1
calculated based on [131]
74 k on,2C.peNOS 0.65 nM
-1
min
-1
calculated based on [131]
75 k on,4.peNOS 0.65 nM
-1
min
-1
calculated based on [131]
76 k off,CaMpeNOS 0.6 min
-1
[134]
77 k on,2N.peNOS.H 0.1157 nM
-1
min
-1
calculated based on [131]
78 k on,2CpeNOS.H 1.1143 nM
-1
min
-1
calculated based on [131]
79 k on,4peNOS.H 1.1143 nM
-1
min
-1
calculated based on [131]
80 k off,CaM.peNOS.H 0.6 min
-1
calculated based on [131]
81 k on,Akt.eNOS 0.02 nM
-1
min
-1
assumed
82 k off,Akt.eNOS 4.0380
[3.7831-4.8589]
min
-1
estimated in eNOS module (See Appendix
A)
83 k on,pAkt.Hsp90 0.5 nM
-1
min
-1
assumed
84 k off,pAkt.Hsp90 10.2826
[2.0842-10.7935]
min
-1
estimated in eNOS module (see Appendix
A)
85 k on,Hsp90.eNOS 0.5 nM
-1
min
-1
assumed
86 k off,Hsp90.eNOS 5.7327
[0.8854-47.0715]
min
-1
estimated in eNOS module (see Appendix
A)
87 k on,Hsp90.CaMeNOS 0.5 nM
-1
min
-1
assumed
24
88 k off,Hsp90.CaMeNOS 10.0976
[1.0167-10.0976]
min
-1
estimated in eNOS module (see Appendix
A)
89 k cat,pAkt 3 min
-1
tuned
90 k cat,pAk.H 10 min
-1
tuned
91 k dp,eNOS 2.8
[1.7897-5.0371]
min
-1
estimated in full model
92 k deg,peNOS 0.001 min
-1
tuned
93 k on,beNOS.Arg 0.048 nM
-1
min
-1
[143]
94 k off,beNOS.Arg 96 min
-1
[143]
95 k on,eNOS.Arg 0.048 nM
-1
min
-1
[143]
96 k off,eNOS.Arg 2.9023
[0.3844-10.1851]
min
-1
estimated in eNOS module (see Appendix
A)
97 k on,peNOS.Arg 0.048 nM
-1
min
-1
[143]
98 k off,peNOS.Arg 4.9891
[0.4062-33.1763]
min
-1
estimated in eNOS module (see Appendix
A)
99 k on,eNOS.Arg.H 0.048 nM
-1
min
-1
[143]
100 k off,eNOS.Arg.H 6.987
[0.7341-55.1524]
min
-1
estimated in eNOS module (see Appendix
A)
101 k on,peNOS.Arg.H 0.048 nM
-1
min
-1
[143]
102 k off,peNOS.Arg.H 10.8397
[1.1183-85.2601]
min
-1
estimated in eNOS module (see Appendix
A)
103 k cat,eNOS 1.49
[1.0729-8.6044]
min
-1
estimated in eNOS module (see Appendix
A)
104 k cat,peNOS 2.682
[2.1118-16.7032]
min
-1
estimated in eNOS module (see Appendix
A)
105 k cat,eNOS.H 3.132
[1.8966-17.1657]
min
-1
estimated in eNOS module (see Appendix
A)
106 k cat,peNOS.H 4.22
[4.0505-24.2466]
min
-1
estimated in eNOS module (see Appendix
A)
sGC module
107 k clearNO 10
[5.4822-14.5019]
min
-1
baseline assumed based on [136], [144];
estimated in full model
108 k on,NO.sGC 18 nM
-1
min
-1
[135]
109 k off,NO.sGC 360 min
-1
[135]
110 k a.sGC 1680 min
-1
[135]
111 k d,sGC 1680 min
-1
[135]
112 k on,NO.NOGC 0.24 nM
-1
min
-1
[135]
113 k off,NO.NOGC 60000 min
-1
[135]
114 k f,NOGC.NO 120000 nM
-1
min
-1
[135]
115 k r,NOGC.NO 0.108 min
-1
[135]
116 k f.GC.NO 24 nM
-1
min
-1
[135]
117 k r.GC.NO 0.044 min
-1
[135]
118 k f6 60 min
-1
[135]
119 k r6 0.06 min
-1
[135]
120 k cat,sGC 31.5 min
-1
tuned
121 k on,cGMP.PDE 0.001 nM
-1
min
-1
[135]
122 k off,cGMP.PDE 7.752 min
-1
[135]
123 k a,PDE 18 min
-1
[135]
25
124 k d,PDE 7.2 min
-1
[135]
125 K M.PDE1 4000 nM [135]
126 k cat,PDE 0.2925
[0.1602-0.4325]
min
-1
estimated in full model
127 K M,PDE 1000 nM [135]
geometric parameters
128 Vol cyto 9.12´10
-13
L [133], [145]
129 Vol ext 5.00´10
-4
L assumed
130 Vol ER 3.35´10
-13
L [133]
initial condition
131 TSP1_0 0-2.2 nM Based on experimentally used exogeneous
concentrations
132 VEGF_0 0-1.1 nM Based on range of measured tissue
concentrations as compiled in [116] and
experimentally used exogenous
concentrations[40]
133 R2_0 8.971 nM [129]
134 CD47_0 199.336 nM measured‡
135 Src_0 344
[188.5609-517.2423]
nM estimated in full model
136 Ca_0 50 nM assumed
137 Ca store_0 2000000 nM assumed
138 CaM_0 30
[13.4411-41.0572]
nM baseline assumed based on [137]; estimated
in full model
139 eNOS_0 100
[46.5482-158.0576]
nM baseline assumed based on [146];
estimated in full model
140 Arg_0 100000 nM assumed based on [147]
141 Hsp90_0 500
[234.0886-687.3168]
nM estimated in full model
142 Akt_0 800
[493.1294-1182.4231]
nM baseline assumed based on [98]; estimated in
full model
143 sGC_b_0 10 nM tuned
144 GTP_0 500000 nM Assumed based on [148]
145 PIP2_0 200000
[1.4409´10
5
-3.0279´10
5
]
nM baseline assumed based on [121]; estimated
in full model
146 PLCg_0 500 nM assumed
147 Istim0 19990.3745 nM/min Initial flux through CRAC, calculated for
homeostasis§§
148 PDE_0 500000 nM tuned
Footnotes
* Value used in model. Range indicates range of estimated parameter values obtained during fitting.
¶ assumed: no data for reference unless indicated.
¶¶ estimated in module: parameters were previously estimated during model development before full model
fitting. The baseline model takes the best fit value from estimated values.
† tuned: manually adjusted.
‡ measured: species level quantified using flow cytometry (see Appendix A: Supplemental Text: Receptor
Quantification).
§ I PMCA is calculated by the equation I PMCA*(Ca_0)
1.4
/(K M,PMCA
1.4
+Ca_0
1.4
) + Istim0 = 0, to balance the initial
calcium flux across cell membrane.
§§ Istim0 is calculated by setting the initial CRAC influx to be zero, through equation ((((((Vol ext/Vol cyto)*Ca_ext)-
Ca_0)*I CRAC)*((K CRAC^n CRAC)/((K CRAC^n CRAC)+(Ca store_0^n CRAC))))/t stim)-(Istim0/t stim)=0.
26
2.3.7. Model Perturbations
To investigate the effects of perturbations on each individual parameter that is influential to the model
outputs, we use the 19 best fit sets to simulate the model and altered the values of the parameters that were
deemed to be influential in each respective condition based on eFAST analysis. We first modify the parameters
as a function of TSP1 in each simulation. For these simulations, as the TSP1 level increases, the strengths of
the perturbations increase. With these perturbations, we allow the parameters to vary two orders of magnitude
above or below the original value. We use the multiplicative factors f positive and f negative to scale up and scale down
the value of each specific parameter, respectively. Parameters that would promote overall eNOS signaling were
multiplied by f negative. Conversely, parameters that impede eNOS signaling were multiplied by f positive. We chose to
utilize the Hill equation to implement the effect of TSP1, assuming a classic Michaelis-Menten input-output
relationship[149, p.]. Thus, the values of the multiplicative factors at given by a Hill function (Figure 2-4).
Figure 2-4. Hill functions of TSP1 concentrations. The model parameter value subject to variation is multiplied by
fpositive (left panel) or fnegative (right panel) to increase or decrease its value, respectively, as a function of the TSP1 concentration.
The model simulates the time-course of species’ concentrations. We quantify the fold-change of the area
under curve (AUC) for Ca
2+
, NO, and cGMP for the first 30 min, normalized to that of the baseline model.
We use NO level as an indicator of eNOS catalytic activity because it is an important vasoregulator. We report
the mean fold-change and the standard deviation across the 19 sets of simulations of each perturbation.
10
-3
10
-1
10
1
10
2
0
20
40
60
80
100
10
-3
10
-1
10
1
10
2
0
0.2
0.4
0.6
0.8
1
10
-3
10
-1
10
1
10
2
0
20
40
60
80
100
10
-3
10
-1
10
1
10
2
0
0.2
0.4
0.6
0.8
1
Fold increase
Fold decrease
TSP1 (nM)
TSP1 (nM)
27
2.4. Results
2.4.1. Model construction
We have constructed a model of the eNOS signaling pathway in ECs, mediated by VEGF and TSP1
(Figure 2-1). Notably, we trained a detailed, novel module (termed “eNOS module”) to describe the eNOS
catalytic activity differentially regulated by Hsp90 and Akt using independent experimental measurements. We
adapted the calcium module describing the agonist-induced Ca
2+
influx and homeostatic mechanisms from
several studies[102], [132], [136], and the sGC module describing the NO/sGC-dependent cGMP synthesis is
based on work by Halvey et al.[135]. We include the known function of TSP1 where it binds to VEGF and its
receptor CD47, disrupting the coupling between CD47 and R2[49].
We investigated the sensitivity of several model outputs (species concentration) to the variations in the
model inputs (kinetic parameters and initial concentrations). Given a large number of model parameters, we
organized the parameters into seven groups. Specifically, we estimated the effects of seven groups of model
inputs: 1) receptor module, 2) Src/Akt/Hsp90 module, 3) calcium module, 4) eNOS module (activation), 5)
eNOS module (catalytic activity), 6) sGC module, and 7) the initial concentrations of signaling species (Figure
2-5). The outputs for this sensitivity analysis, namely pAkt, peNOS, Ca
2+
, NO, and cGMP, were chosen
considering that these are the key signaling species throughout the signaling pathway, and model fitting would
be conducted using experimental datasets for the dynamics of these species, in addition to data for R2 dynamics.
Before model training, we performed the global sensitivity analysis eFAST to reveal the most influential
parameters. The eFAST method enabled us to reduce the number of unknown parameters to estimate, by fixing
the non-influential parameters (see Methods). As a result of this analysis, we identified 34 influential parameters
whose values were unknown. Using results from the parameter identifiability test, we further excluded 11
parameters from fitting as they were highly correlated with one or more of the remaining parameters to be
estimated.
28
Figure 2-5. Sensitivity analysis to inform eNOS model fitting. Total sensitivity indices (Sti) of each model
parameter with respect to five signaling species in a global sensitivity analysis using the extended Fourier
Amplitude Sensitivity Test (eFAST) method. Simulations were run with the VEGF concentration of 1.1nM
(30ng/ml) and no TSP1. Due to the large size of the model, we separated the model parameters to seven
categories and conducted the sensitivity analyses within each group. These results were used to identify
the influential but unknown parameters for model fitting. White squares: the parameter sensitivity index
is not significant when compared to that of a random dummy variable (p>0.05).
We trained the model by estimating the unknown but influential model parameter values to match the
model-simulated signaling dynamics to experimental data. The trained model recapitulates the experimentally
observed signaling dynamics of key species throughout the pathway, such as phosphorylation of R2,
phosphorylation of eNOS, NO, and cGMP (Figure 2-2a-n). Furthermore, the calibrated model generated
predictions of signaling dynamics that were validated by four independent datasets not used in training[22],
[119] (Figure 2-2o-r). The distributions of all estimated parameter values are within one order of magnitude
around their respective baseline values, as shown in Figure 2-3.
konCa2C
koffCa2C
konCa2N
koffCa2N
kon2NeNOS
kon2CeNOS
kon4eNOS
koffCaMeNOS
kon2NeNOS.H
kon2CeNOS.H
kon4eNOS.H
koffCaMeNOS.H
kon2NpeNOS
kon2Cpenos
kon4peNOS
koffCaMpeNOS
kon2NpeNOS.H
kon2CpeNOS.H
kon4peNOS.H
koffCaMpeNOS.H
konAkt.eNOS
koffAkt.eNOS
konpAkt.pHsp90
koffAkt.pHsp90
konHsp90.eNOS
koffHsp90.eNOS
konHsp90.CaMeNOS
koffHsp90.CaMeNOS
kcat.pAkt
kcat.pAkt.H
kdp.eNOS
kdeg.peNOS
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konSrc.pR2
koffSrc.pR2
kp.Src
kdp.Src
konSrc.Hsp90
koffSrc.hsp90
kp.Hsp90
kdp.Hsp90
konSrc.Akt
KoffSrc.Akt
Kp.Akt
Kdp.Akt
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
R2
CD47
Src
Cacyt
CaER
CaM
eNOS
Arginine
Hsp90
Akt
sGC
GTP
cGKI
PIP2
PLCg
PDE
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kpPLCg
kdpPLCg
kmPIP2PLCg
kcatPLCgDAG
kdegip3
kPIP2gen
ICrac
Kcrac
kmPLCgR2
Iip3Ramp
Kmip3R
IPMCA
KmPMCA
Caext
ISERCA
KleakER
KmSERCA
KiCa
CSQNtot
KCSQN
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kon.beNOS.Arg
koff.beNOS.Arg
kon.eNOS.Arg
koff.eNOS.Arg
kon.peNOS.Arg
koff.peNOS.Arg
kon.eNOS.Arg.H
koff.eNOS.Arg.H
kon.peNOS.Arg.H
koff.peNOS.Arg.H
kcat.eNOS
kcat.peNOS
kcat.eNOS.H
kcat.peNOS.H
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konTSP1VEGF
koffTSP1VEGF
kdegVEGF
konVEGFR2
koffVEGFR2
konTSP1CD47
koffTSP1CD47
konR2CD47
koffR2CD47
kinterR2
kinterpR2
kinterCD47
kinterR2CD47
kinterpR2CD47
kinterTSP1bd
kpR2
kdpR2
kdpR2CD47bd
ksynR2
ksynCD47
kdegR2
kdegpR2
kdegpR2CD47
kdegCD47
kdegR2TSP1bd
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
Ca
2+
system
receptor level interactions
upstream reactions
eNOS activation
eNOS activity
sGC activity
initial concentrations
konTSP1VEGF
koffTSP1VEGF
kdegVEGF
konVEGFR2
koffVEGFR2
konTSP1CD47
koffTSP1CD47
konR2CD47
koffR2CD47
kinterR2
kinterpR2
kinterCD47
kinterR2CD47
kinterpR2CD47
kinterTSP1bd
kpR2
kdpR2
kdpR2CD47bd
ksynR2
ksynCD47
kdegR2
kdegpR2
kdegpR2CD47
kdegCD47
kdegR2TSP1bd
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konSrc.pR2
koffSrc.pR2
kp.Src
kdp.Src
konSrc.Hsp90
koffSrc.hsp90
kp.Hsp90
kdp.Hsp90
konSrc.Akt
KoffSrc.Akt
Kp.Akt
Kdp.Akt
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kpPLCg
kdpPLCg
kmPIP2PLCg
kcatPLCgDAG
kdegip3
kPIP2gen
ICrac
Kcrac
kmPLCgR2
Iip3Ramp
Kmip3R
IPMCA
KmPMCA
Caext
ISERCA
KleakER
KmSERCA
KiCa
CSQNtot
KCSQN
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kon.beNOS.Arg
koff.beNOS.Arg
kon.eNOS.Arg
koff.eNOS.Arg
kon.peNOS.Arg
koff.peNOS.Arg
kon.eNOS.Arg.H
koff.eNOS.Arg.H
kon.peNOS.Arg.H
koff.peNOS.Arg.H
kcat.eNOS
kcat.peNOS
kcat.eNOS.H
kcat.peNOS.H
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konCa2C
koffCa2C
konCa2N
koffCa2N
kon2NeNOS
kon2CeNOS
kon4eNOS
koffCaMeNOS
kon2NeNOS.H
kon2CeNOS.H
kon4eNOS.H
koffCaMeNOS.H
kon2NpeNOS
kon2Cpenos
kon4peNOS
koffCaMpeNOS
kon2NpeNOS.H
kon2CpeNOS.H
kon4peNOS.H
koffCaMpeNOS.H
konAkt.eNOS
koffAkt.eNOS
konpAkt.pHsp90
koffAkt.pHsp90
konHsp90.eNOS
koffHsp90.eNOS
konHsp90.CaMeNOS
koffHsp90.CaMeNOS
kcat.pAkt
kcat.pAkt.H
kdp.eNOS
kdeg.peNOS
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
R2
CD47
Src
Cacyt
CaER
CaM
eNOS
Arginine
Hsp90
Akt
sGC
GTP
cGKI
PIP2
PLCg
PDE
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kon.NO.sGC
koff.NO.sGC
ka.sGC
kd.sGC
kon.NO.NOGC
koff.NO.NOGC
kf.NOGC.NO
kr.NOGC.NO
kf.GC.NO
kr.GC.NO
kf6
kr6
kcat.sGC
kon.cGMP.PDE
koff.cGMP.PDE
ka.PDE
kd.PDE
KM.PDE1
kcat.PDE
KM.PDE
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
29
2.4.2. Model dynamics with physiological or exogenous VEGF levels
We first used the calibrated model to simulate the eNOS signaling dynamics stimulated with various
VEGF concentrations taken from observed ranges, including concentrations at the lower bound of the range
found in healthy tissue (0.0003nM)[150], [151], the lower and upper bounds of the range in tumor tissue
(0.008nM and 0.389nM, respectively) (as compiled in [116]); and a concentration of exogenous VEGF
concentration frequently used in experimental studies (1.1nM; 30ng/ml). Studying this wide range of VEGF
stimulation levels allows us to understand the level of signaling occurring in the ECs in different physiological
and pathological conditions. We present the signaling dynamics within 60 minutes (Figure 2-6), at the receptor
level: total R2, VEGF-bound R2, and phosphorylated R2 (pR2); for relatively upstream through intermediate
signaling: phosphorylated Src, Akt, and eNOS; and three major model outputs intermediate and downstream
species: free cytosolic Ca
2+
, NO, and cGMP. With the exception for Ca
2+
and cGMP, we report the relative
species activation normalized to the highest level achieved across the four sets of simulations, to make the
comparison more direct.
30
Figure 2-6. Signaling dynamics predicted by the eNOS model for various levels of VEGF stimulation. We compare
the levels of (a) total R2, normalized species: (b) VEGF-bound R2/R2, (c) pR2/R2, (d) pSrc/Src, (e) pAkt/Akt, (f)
peNOS/eNOS, (g) cytosolic Ca
2+
, (h) normalized NO, (i) cGMP with four different VEGF conditions selected from
healthy tissue and tumor tissue measurements, and an experimentally used exogenous VEGF concentration. For (a-f)
and (h), the species levels are normalized against the highest value across the four sets of simulations. For (g) and (i),
concentrations of species are shown. Solid line: mean of model predictions using the 19 sets of best fit parameter values.
Shaded area: standard deviation of model predictions within each simulation condition. The normalized values are
relative to the total amount of that species.
The model simulation revealed that signaling species in the receptor module, Src/Akt/Hsp90 module,
and eNOS module are more sensitive to various VEGF levels compared the signaling species in the calcium
module and sGC module. The model predicts that the lower concentration of VEGF from tumor tissue (light
green, 0.008nM VEGF), does not greatly promote eNOS signaling, in comparison to the response to the VEGF
level present in healthy tissue (dark green, 0.0003nM VEGF). On the other hand, the VEGF level present in
tumor (blue, 0.389nM VEGF), elicits a stronger signaling response that is similar to that produced by the
exogenous VEGF level (pink, 1.1nM VEGF). At these higher VEGF levels (0.389nM and 1.1nM), a transient
0 10 20 30
0
1000
2000
3000
4000
cGMP
0 10 20 30 40 50 60
0.6
0.8
1
totR2
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
totpR2
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
tot.R2.bound
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
pSrc
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
pAkt
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
peNOS
0 10 20 30
0
100
200
300
freeCac
0 10 20 30
0
0.2
0.4
0.6
0.8
1
NO
0 10 20 30 40 50 60
0
500
1000
1500
2000
2500
cGMP
0.0003nM 0.0003nM 0.008nM 0.008nM 0.389nM 0.389nM 1.11nM 1.11nM
Lower bound of normal
tissue: 0.0003-0.003nM
Lower bound of tumor
tissue: 0.008-0.389nM
Upper bound of tumor
tissue: 0.008-0.389nM
Experimentally used
exogenous level: 1.1nM
VEGF conc.:
Normalized level
Concentration (nM)
Time (min) Time (min) Time (min)
Total R2 pR2/R2 VEGF-bound R2/R2
pSrc/Src pAkt/Akt peNOS/eNOS
Calcium Nitric Oxide cGMP
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Normalized level
Normalized level
Concentration (nM)
31
increase can be observed in the levels of all the species. Compared to the signaling dynamics with 0.389nM
VEGF, the species activated in the receptor module and Src/Akt/Hsp90 module (e.g. pR2/R2, pSrc/Src,
pAkt/Akt) are depleted more rapidly with 1.1nM VEGF, whereas the Ca
2+
influx magnitudes remain quite
similar between the two cases. This could explain why there is little difference in the levels of downstream NO
and cGMP for the two higher levels of VEGF stimulation (Figure 2-6g-i), even though the magnitude of
activation are very different in the receptor module, Src/Akt/Hsp90 module, and eNOS module (Figure 2-
6b-f, blue vs. purple lines). That is, signaling differences promoted by 0.389 and 1.1nM VEGF are gradually
lost as the signal propagates downstream. In addition, the desensitization mechanism of sGC to NO level
included in our model (which is based on experimental evidence) also contributes to cGMP’s reduced sensitivity
to changes in the VEGF level. Together, these results show that the downstream output cGMP is particularly
robust to changes in the input level.
2.4.3. Simulated effects of TSP1-mediated perturbations
The modeling framework allows us to better understand experimental observations that show TSP1
affects eNOS signaling in endothelial cells in different ways. Kaur et al. identified CD47 as an R2-associated
protein, and showed that CD47 ligation by TSP1 abolishes the constitutive coupling between CD47 and R2[49].
Bauer et al. showed that TSP1 inhibits basal HUVEC eNOS catalytic activity and agonist induced Ca
2+
influx[54]. Isenberg et al. showed that TSP1 inhibits cGMP synthesis in HUVECs both in the basal condition
and when stimulated with VEGF or NO donor[40]. Together, these phenomena suggest that TSP1 has multiple
inhibition targets in endothelial cell eNOS signaling under the basal and VEGF-stimulated conditions. TSP1’s
direct effect at the receptor level has previously been studied in detail using computational modeling; however,
where the authors focused only on enhanced R2 degradation or dephosphorylation by TSP1[102]. Thus, it
remains unclear how TSP1 inhibits several downstream effectors of eNOS signaling independent of R2
inhibition.
In order to integrate existing knowledge of the eNOS signaling pathway and mechanistically explain
the experimentally observed effects of TSP1 under various VEGF- stimulated conditions, we use this model
32
to identify possible intracellular targets of TSP1. Since it is not known how or if TSP1 interacts with the
intracellular species, we simulate its effect by directly varying kinetic rate parameters and species’ initial
concentrations. Specifically, we simulated and quantified the effects of perturbations to individual reactions in
the signaling network and compared them with the experimentally observed TSP1 effects. We chose to use the
levels of intracellular Ca
2+
, NO, and cGMP as the main model outputs, as they correspond to the experimental
measurements from the TSP1 inhibition experimental studies described above.
To select the perturbation targets, we use the global sensitivity analysis on the calibrated model with
the best-fit parameter set to quantify the sensitivity of the three outputs to variations in the model inputs. We
define a parameter as influential if its global sensitivity index (S ti) value is no less than 0.1. In total, in the basal
condition (0.0003nM), 41 parameters are identified as influential (Figure 2-7a), whereas with a higher VEGF
level (0.389nM), 76 parameters are influential (Figure 2-7b).
33
konCa2C
koffCa2C
konCa2N
koffCa2N
kon2NeNOS
kon2CeNOS
kon4eNOS
koffCaMeNOS
kon2NeNOS.H
kon2CeNOS.H
kon4eNOS.H
koffCaMeNOS.H
kon2NpeNOS
kon2Cpenos
kon4peNOS
koffCaMpeNOS
kon2NpeNOS.H
kon2CpeNOS.H
kon4peNOS.H
koffCaMpeNOS.H
konAkt.eNOS
koffAkt.eNOS
konpAkt.pHsp90
koffAkt.pHsp90
konHsp90.eNOS
koffHsp90.eNOS
konHsp90.CaMeNOS
koffHsp90.CaMeNOS
kcat.pAkt
kcat.pAkt.H
kdp.eNOS
kdeg.peNOS
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konSrc.pR2
koffSrc.pR2
kp.Src
kdp.Src
konSrc.Hsp90
koffSrc.hsp90
kp.Hsp90
kdp.Hsp90
konSrc.Akt
KoffSrc.Akt
Kp.Akt
Kdp.Akt
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
R2
CD47
Src
Cacyt
CaER
CaM
eNOS
Arginine
Hsp90
Akt
sGC
GTP
cGKI
PIP2
PLCg
PDE
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kpPLCg
kdpPLCg
kmPIP2PLCg
kcatPLCgDAG
kdegip3
kPIP2gen
ICrac
Kcrac
kmPLCgR2
Iip3Ramp
Kmip3R
IPMCA
KmPMCA
Caext
ISERCA
KleakER
KmSERCA
KiCa
CSQNtot
KCSQN
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kon.beNOS.Arg
koff.beNOS.Arg
kon.eNOS.Arg
koff.eNOS.Arg
kon.peNOS.Arg
koff.peNOS.Arg
kon.eNOS.Arg.H
koff.eNOS.Arg.H
kon.peNOS.Arg.H
koff.peNOS.Arg.H
kcat.eNOS
kcat.peNOS
kcat.eNOS.H
kcat.peNOS.H
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konTSP1VEGF
koffTSP1VEGF
kdegVEGF
konVEGFR2
koffVEGFR2
konTSP1CD47
koffTSP1CD47
konR2CD47
koffR2CD47
kinterR2
kinterpR2
kinterCD47
kinterR2CD47
kinterpR2CD47
kinterTSP1bd
kpR2
kdpR2
kdpR2CD47bd
ksynR2
ksynCD47
kdegR2
kdegpR2
kdegpR2CD47
kdegCD47
kdegR2TSP1bd
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
Ca
2+
system
receptor level interactions
upstream reactions
eNOS activation
eNOS activity
sGC activity
initial concentrations
(a)
konTSP1VEGF
koffTSP1VEGF
kdegVEGF
konVEGFR2
koffVEGFR2
konTSP1CD47
koffTSP1CD47
konR2CD47
koffR2CD47
kinterR2
kinterpR2
kinterCD47
kinterR2CD47
kinterpR2CD47
kinterTSP1bd
kpR2
kdpR2
kdpR2CD47bd
ksynR2
ksynCD47
kdegR2
kdegpR2
kdegpR2CD47
kdegCD47
kdegR2TSP1bd
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konSrc.pR2
koffSrc.pR2
kp.Src
kdp.Src
konSrc.Hsp90
koffSrc.hsp90
kp.Hsp90
kdp.Hsp90
konSrc.Akt
KoffSrc.Akt
Kp.Akt
Kdp.Akt
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kpPLCg
kdpPLCg
kmPIP2PLCg
kcatPLCgDAG
kdegip3
kPIP2gen
ICrac
Kcrac
kmPLCgR2
Iip3Ramp
Kmip3R
IPMCA
KmPMCA
Caext
ISERCA
KleakER
KmSERCA
KiCa
CSQNtot
KCSQN
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kon.beNOS.Arg
koff.beNOS.Arg
kon.eNOS.Arg
koff.eNOS.Arg
kon.peNOS.Arg
koff.peNOS.Arg
kon.eNOS.Arg.H
koff.eNOS.Arg.H
kon.peNOS.Arg.H
koff.peNOS.Arg.H
kcat.eNOS
kcat.peNOS
kcat.eNOS.H
kcat.peNOS.H
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konCa2C
koffCa2C
konCa2N
koffCa2N
kon2NeNOS
kon2CeNOS
kon4eNOS
koffCaMeNOS
kon2NeNOS.H
kon2CeNOS.H
kon4eNOS.H
koffCaMeNOS.H
kon2NpeNOS
kon2Cpenos
kon4peNOS
koffCaMpeNOS
kon2NpeNOS.H
kon2CpeNOS.H
kon4peNOS.H
koffCaMpeNOS.H
konAkt.eNOS
koffAkt.eNOS
konpAkt.pHsp90
koffAkt.pHsp90
konHsp90.eNOS
koffHsp90.eNOS
konHsp90.CaMeNOS
koffHsp90.CaMeNOS
kcat.pAkt
kcat.pAkt.H
kdp.eNOS
kdeg.peNOS
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
R2
CD47
Src
Cacyt
CaER
CaM
eNOS
Arginine
Hsp90
Akt
sGC
GTP
cGKI
PIP2
PLCg
PDE
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kon.NO.sGC
koff.NO.sGC
ka.sGC
kd.sGC
kon.NO.NOGC
koff.NO.NOGC
kf.NOGC.NO
kr.NOGC.NO
kf.GC.NO
kr.GC.NO
kf6
kr6
kcat.sGC
kon.cGMP.PDE
koff.cGMP.PDE
ka.PDE
kd.PDE
KM.PDE1
kcat.PDE
KM.PDE
konCa2C
koffCa2C
konCa2N
koffCa2N
kon2NeNOS
kon2CeNOS
kon4eNOS
koffCaMeNOS
kon2NeNOS.H
kon2CeNOS.H
kon4eNOS.H
koffCaMeNOS.H
kon2NpeNOS
kon2Cpenos
kon4peNOS
koffCaMpeNOS
kon2NpeNOS.H
kon2CpeNOS.H
kon4peNOS.H
koffCaMpeNOS.H
konAkt.eNOS
koffAkt.eNOS
konpAkt.pHsp90
koffAkt.pHsp90
konHsp90.eNOS
koffHsp90.eNOS
konHsp90.CaMeNOS
koffHsp90.CaMeNOS
kcat.pAkt
kcat.pAkt.H
kdp.eNOS
kdeg.peNOS
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konSrc.pR2
koffSrc.pR2
kp.Src
kdp.Src
konSrc.Hsp90
koffSrc.hsp90
kp.Hsp90
kdp.Hsp90
konSrc.Akt
KoffSrc.Akt
Kp.Akt
Kdp.Akt
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
R2
CD47
Src
Cacyt
CaER
CaM
eNOS
Arginine
Hsp90
Akt
sGC
GTP
cGKI
PIP2
PLCg
PDE
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kpPLCg
kdpPLCg
kmPIP2PLCg
kcatPLCgDAG
kdegip3
kPIP2gen
ICrac
Kcrac
kmPLCgR2
Iip3Ramp
Kmip3R
IPMCA
KmPMCA
Caext
ISERCA
KleakER
KmSERCA
KiCa
CSQNtot
KCSQN
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kon.beNOS.Arg
koff.beNOS.Arg
kon.eNOS.Arg
koff.eNOS.Arg
kon.peNOS.Arg
koff.peNOS.Arg
kon.eNOS.Arg.H
koff.eNOS.Arg.H
kon.peNOS.Arg.H
koff.peNOS.Arg.H
kcat.eNOS
kcat.peNOS
kcat.eNOS.H
kcat.peNOS.H
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konTSP1VEGF
koffTSP1VEGF
kdegVEGF
konVEGFR2
koffVEGFR2
konTSP1CD47
koffTSP1CD47
konR2CD47
koffR2CD47
kinterR2
kinterpR2
kinterCD47
kinterR2CD47
kinterpR2CD47
kinterTSP1bd
kpR2
kdpR2
kdpR2CD47bd
ksynR2
ksynCD47
kdegR2
kdegpR2
kdegpR2CD47
kdegCD47
kdegR2TSP1bd
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
Ca
2+
system
receptor level interactions
upstream reactions
eNOS activation
eNOS activity
sGC activity
initial concentrations
(b)
konTSP1VEGF
koffTSP1VEGF
kdegVEGF
konVEGFR2
koffVEGFR2
konTSP1CD47
koffTSP1CD47
konR2CD47
koffR2CD47
kinterR2
kinterpR2
kinterCD47
kinterR2CD47
kinterpR2CD47
kinterTSP1bd
kpR2
kdpR2
kdpR2CD47bd
ksynR2
ksynCD47
kdegR2
kdegpR2
kdegpR2CD47
kdegCD47
kdegR2TSP1bd
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konSrc.pR2
koffSrc.pR2
kp.Src
kdp.Src
konSrc.Hsp90
koffSrc.hsp90
kp.Hsp90
kdp.Hsp90
konSrc.Akt
KoffSrc.Akt
Kp.Akt
Kdp.Akt
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kpPLCg
kdpPLCg
kmPIP2PLCg
kcatPLCgDAG
kdegip3
kPIP2gen
ICrac
Kcrac
kmPLCgR2
Iip3Ramp
Kmip3R
IPMCA
KmPMCA
Caext
ISERCA
KleakER
KmSERCA
KiCa
CSQNtot
KCSQN
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kon.beNOS.Arg
koff.beNOS.Arg
kon.eNOS.Arg
koff.eNOS.Arg
kon.peNOS.Arg
koff.peNOS.Arg
kon.eNOS.Arg.H
koff.eNOS.Arg.H
kon.peNOS.Arg.H
koff.peNOS.Arg.H
kcat.eNOS
kcat.peNOS
kcat.eNOS.H
kcat.peNOS.H
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
konCa2C
koffCa2C
konCa2N
koffCa2N
kon2NeNOS
kon2CeNOS
kon4eNOS
koffCaMeNOS
kon2NeNOS.H
kon2CeNOS.H
kon4eNOS.H
koffCaMeNOS.H
kon2NpeNOS
kon2Cpenos
kon4peNOS
koffCaMpeNOS
kon2NpeNOS.H
kon2CpeNOS.H
kon4peNOS.H
koffCaMpeNOS.H
konAkt.eNOS
koffAkt.eNOS
konpAkt.pHsp90
koffAkt.pHsp90
konHsp90.eNOS
koffHsp90.eNOS
konHsp90.CaMeNOS
koffHsp90.CaMeNOS
kcat.pAkt
kcat.pAkt.H
kdp.eNOS
kdeg.peNOS
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
R2
CD47
Src
Cacyt
CaER
CaM
eNOS
Arginine
Hsp90
Akt
sGC
GTP
cGKI
PIP2
PLCg
PDE
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kon.NO.sGC
koff.NO.sGC
ka.sGC
kd.sGC
kon.NO.NOGC
koff.NO.NOGC
kf.NOGC.NO
kr.NOGC.NO
kf.GC.NO
kr.GC.NO
kf6
kr6
kcat.sGC
kon.cGMP.PDE
koff.cGMP.PDE
ka.PDE
kd.PDE
KM.PDE1
kcat.PDE
KM.PDE
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
kclearNO
kf1
kr1
kf2
kr2
kf3
kr3
kf4
kr4
kf5
kr5
kf6
kr6
GCmax
kp1
kdp1
kp2
kdp2
Kp1
Vp2
Kp2
kcatcGMP
KmcGMP
kdpcGKI
pAkt
peNOS
Ca
Cit
NO
cGMP
0
0.2
0.4
0.6
0.8
1
34
Figure 2-7. Sensitivity analyses to inform perturbation simulations. (a) Sti of each model parameter with
respect to five signaling species in a global sensitivity analysis using the eFAST method. Simulations were
run without VEGF or TSP1. This set of results was used to identify the influential parameters for
perturbation of the basal condition. (b) Sti of each model parameter in simulation with 0.389nM VEGF and
2.2nM TSP1. This set of results was used to identify the influential parameters for perturbation of the VEGF-
stimulated condition. White squares: the parameter sensitivity index is not significant when compared to
that of a random dummy variable (p>0.05).
First, we simulated various perturbations in the basal condition by altering (increasing or decreasing)
the 41 individual parameters, as a function of the TSP1 concentration. Specifically, we used Hill functions to
characterize how the parameter value changed depending on the TPS level (Figure 2-4). The TSP1
concentrations used here correspond to those used experimentally in the study by Bauer et al., ranging from
0.00022nM to 2.2nM of TSP1. At 2.2nM TSP1, the fold-change that is applied to alter each parameter value is
approximately 100-fold, with the assumption that at such levels of TSP1, its inhibitory action achieves near
maximal strength. We quantify the area under curve (AUC) of the time-courses of the three model outputs for
the first 30 minutes, normalized to the AUC for the control condition without any perturbation.
We show the perturbations that significantly (p<0.05) reduced the level of any of the three quantified
model outputs, by at least 20% compared to unperturbed condition (Figure 2-8a & Table 2-2). A total of 19
perturbations met the criteria, and therefore the corresponding mechanisms being perturbed are predicted
candidates of TSP1’s intracellular targets of inhibition. To investigate whether these perturbations take effect
when VEGF level is high, we also simulated these 19 perturbations with stimulation using the VEGF level
found in tumor tissue, 0.389nM (Figure 2-8b). Altogether, the results show that the model outputs have dose-
dependence on TSP1. We further describe the results below.
35
Figure 2-8. Perturbations to the eNOS pathway under basal condition. (a) Perturbations that are significantly
effective in reducing the model output AUC levels by at least 20% compared to the baseline level. VEGF concentration
is 0.0003nM. (b) Effects of the same set of perturbations when VEGF is 0.389nM. Bars: mean percent difference between
perturbations and baseline level using the 19 sets of best fit parameter values with six TSP1 levels (0.0002-2.2nM). Error
bars: standard deviation of 19 sets of simulations. X-axis labels with (+) sign with black font: parameter was increased
using the left panel Hill function in Figure 3; (-) sign with gray font: parameter was decreased using the right panel Hill
function in Figure 2-4.
Table 2-2. List of Perturbations.
Altered
parameter
(direction)
Function
Reduce basal activity
(0.003nM VEGF)
Reduce 0.389nM
VEGF-stimulated
signaling
Existing therapeutic
compounds
Ca
2+
NO cGMP Ca
2+
NO cGMP
k p.R2 (-) Phosphorylation of R2 / / / Yes Yes No
TKIs (Sorafenib, Sunitinib,
etc.) [157]
k on,Src.pR2 (-) Binding of Src with pR2 / / / No Yes No
k p,Src (-) Activation of Src / / / No Yes No
Apatinib (TKI) [158],
Dasatinib, Saracatinib,
Bosutinib, KX01 [159]
k dp,Src (+) Deactivation of Src / / / No Yes No
k p,Hsp90 (-) Activation of Hsp90 / / / No Yes No
Geldanamycin and its
derived analogs, radicicol
[160]
k p,PLC! (-) Phosphorylation of PLC! / / / Yes No No Genistein [25]
k cat,PLC! (-) Catalytic activity of PLC! / / / Yes No No
U73122 and compounds
under investigation [161]
k deg,IP3 (+) Degradation of IP3 / / / Yes No No
I IP3R (-) Flux through IP3R / / / Yes No No
2-APB, caffeine [162], CAI
[163]
K M,IP3R (+) Michaelis-Menten constant of IP3R / / / Yes No No Heparin[162]
K M,PMCA (-) Michaelis-Menten constant of PMCA / / / Yes Yes No Caloxins (Pande 2011)
I CRAC (-) Flux through CRAC Yes Yes No Yes No No CAI [163]
K CRAC (-) Michaelis-Menten constant of CRAC Yes Yes No Yes No No
Ca ext (-) Extracelluar Ca
2+
Yes Yes No Yes No No
I SERCA (+) Flux through SERCA Yes Yes Yes Yes No No
K M,SERCA (-) Michaelis-Menten constant of SERCA Yes Yes Yes Yes No No Thapsigargin [164], [165]
36
k off,Ca2C (+) Dissociation of Ca
2+
from CaM C-terminus No Yes Yes No Yes No
k off,CaMeNOS (+) Dissociation of CaM and eNOS No Yes Yes No Yes No
k on,Hsp90.CaMeNOS
(-)
Binding of Hsp90 with CaM:eNOS / / / No Yes No
k off,Hsp90.CaMeNOS
(+)
Dissociation of Hsp90 and CaM:eNOS / / / No Yes No
k cat,eNOS (-) Catalytic activity of eNOS No Yes Yes No Yes No
k cat,eNOS.H (-) Catalytic activity of Hsp90-bound eNOS / / / No Yes Yes
k clear,NO (+) Clearance rate of NO No Yes Yes No Yes Yes
k off.NO.sGC (+)
Dissociation of NO from sGC distal heme;
k -1 in Halvey model
/ / / No No Yes ODQ, NS2028 [166]
k a.sGC (-) Activation of sGC; k 2 in Halvey model / / / No No Yes
k off.NO.NOGC (-)
Dissociation of NO from sGC proximal
heme; k -3 in Halvey model
/ / / No No Yes
k f.NOGC.NO (+)
Dissociation of NO from NO-bound sGC
distal heme; k4 in Halvey model
/ / / No No Yes
k r.NOGC.NO (-)
Association of NO to NO-bound sGC on
distal heme; k-4 in Halvey model
/ / / No No Yes
k cat.sGC (-) Catalytic activity of sGC No No Yes No No Yes
k on,cGMP.PDE (+) Binding of cGMP with PDE / / / No No Yes
k off.cGMP.PDE (-) Dissociation of cGMP and PDE / / / No No Yes
k a.PDE (+) Activation of the first state of PDE No No Yes No No Yes
k d,PDE (-) Deactivation of the first state PDE No No Yes No No Yes
k a2.PDE (+) Activation of the second state of PDE No No Yes No No Yes
k d2,PDE (-) Deactivation of the second state PDE No No Yes No No Yes
K M,PDE (-) Michaelis-Menten constant of PDE activity / / / No No Yes
k cat,PDE (+) Catalytic activity of PDE No No Yes No No Yes
Src (-) Src expression level / / / No Yes Yes
CaM (-) CaM expression level No Yes Yes No Yes Yes trifluoperazine[167]
eNOS (-) eNOS expression level No Yes Yes No Yes Yes
Hsp90 (-) Hsp90 expression level / / / No Yes No
PIP2 (-) PIP2 level / / / Yes No No
Triazole-based
compounds[168]
sGC (-) sGC expression level No No Yes No No Yes
GTP (-) GTP level No No Yes No No Yes
Footnote: forward slash (/): Not applicable. The parameter was not used as perturbation target, because it was not an
influential parameter in the corresponding VEGF condition.
For the basal condition, multiple perturbations in the calcium module and the eNOS module reduced
both the eNOS catalytic activity level and cGMP (Figure 2-8a). Perturbing the Ca
2+
influx mechanism CRAC,
governed by parameters I CRAC and K CRAC, and the extracellular Ca
2+
level Ca ext, reduced the Ca
2+
AUC, but only
minimally affected the downstream activity. Meanwhile, perturbing the Ca
2+
resequestration mechanism
governed by parameters I SERCA and K M,SERCA achieved strong inhibition effects on all the model outputs. As
one might expect, increasing the dissociation rate of Ca
2+
from the calmodulin C-terminus k off,Ca2C, the
37
dissociation rate of calmodulin and eNOS k off,CaMeNOS, and decreasing the catalytic rate of basal eNOS k cat.eNOS
have a strong effect on both the eNOS catalytic activity and cGMP levels. However, the effects of all the above
perturbations on eNOS catalytic activity and cGMP levels are reduced under higher VEGF stimulation (Figure
2-8b).
On the other hand, several perturbations take effect under both the low and high VEGF conditions.
Increasing the clearance rate of NO k clear,NO, resulted in reduced levels of eNOS catalytic activity and cGMP
without affecting the Ca
2+
level. Similar effects are predicted with lowered initial concentrations of CaM and
eNOS. Meanwhile, perturbations in the sGC module, including the reduced catalytic rate of sGC (k cat,sGC),
enhanced activation rates of PDE (k a,PDE, k a2,PDE), reduced deactivation rates of PDE (k d,PDE, k d2,PDE), and
enhanced PDE catalytic rate (k cat,PDE), reduced only the cGMP AUC without affecting the upstream eNOS
catalytic activity. Similar to these perturbations, lowering the levels of sGC or GTP can strongly reduce cGMP
level.
In summary, the simulated perturbations identify several parameters and initial conditions that,
depending on the TSP1 concentration, can inhibit different parts of the eNOS signaling pathway. Experimental
evidence shows that TSP1 reduces agonist induced Ca
2+
, basal eNOS catalytic activity, and both basal- and
VEGF or NO donor -induced cGMP synthesis[40], [54]. Importantly, our model predictions reveal individual
mechanisms that, when combined together, could explain these observed effects of TSP1. We present a detailed
interpretation of these results in the Discussion section.
2.4.4. Effective perturbations for high VEGF condition
In addition to investigating TSP1’s inhibitory mechanisms, we applied the model to identify strategies
that selectively target eNOS signaling in cells within the tumor microenvironment, which often exhibit higher
levels of pro-angiogenic factors. To do so, we first use the eFAST method to identify parameters that are
influential when VEGF level is high (Figure 2-7b), but not in the basal VEGF condition (Figure 2-7a). We
then simulated the effects of altering those parameters and predicted the responses of the three main model
outputs. In this set of simulations, VEGF concentration is 0.389nM and no TSP1 was simulated. The
38
perturbation was simulated by scaling the respective parameter values by the same range of values (2-to 100-
fold) as used in Figure 2-8.
From this set of simulations, (Figure 2-9), we see that most of the perturbations to parameters in the
receptor module and Src/Akt/Hsp90 module reduced eNOS catalytic activity by approximately 50%, yet
minimally affected the cGMP level. A similar result is observed for the perturbations in the eNOS module. All
of the effective perturbations in the calcium module are related to the PLCg-dependent IP3-induced Ca
2+
release mechanisms, controlled by parameters k p,PLCg, k cat,PLCg, k deg,IP3, I IP3R, K M,IP3R, with the exception of
parameter K M,PMCA. These perturbations largely reduced the Ca
2+
level but did not affect the downstream eNOS
catalytic activity and cGMP. We found eight perturbations in the sGC module that inhibit the cGMP level.
Among those eight parameters, varying the binding activity of NO with sGC’s distal and proximal binding sites
(k off,NO.NOGC, k f,NOGC.NO, k r,NOGC.NO) and increasing PDE activation via its association with cGMP (k on,cGMP.PDE,
k off,cGMP.PDE) most strongly reduced cGMP. In addition, reducing the expression levels of Src or Hsp90 inhibited
the eNOS catalytic activity, and reducing PIP2 reduced Ca
2+
level.
39
Figure 2-9. Effective perturbations in high VEGF condition. Perturbations shown are significantly effective in
reducing the model output AUC levels by at least 10% compared to the baseline level. VEGF concentration is 0.389nM
and TSP1 concentration is 0nM in all simulations. Bars: mean of model predictions using the 19 sets of best fit parameter
values with six perturbation levels (scaling parameters by 2- to -100-fold). Error bars: standard deviation of 19 sets of
simulations. Shaded areas: modules where the perturbed parameter takes effect.
Altogether, the model simulations provide detailed insight of VEGF-mediated eNOS signaling and the
effects of perturbing the network. The model reveals that the signaling response is sensitive to changing the
VEGF levels in certain upstream modules, but this sensitivity is lost as the signal propagates downstream to
cGMP synthesis. Using this model, we identified possible mechanisms of TSP1’s inhibitory function on the
eNOS signaling pathway in both basal and VEGF-stimulated conditions. Furthermore, the model predicted
alternative strategies to inhibit eNOS signaling, highlighting perturbations to the eNOS signaling network that
only affect the cells experiencing high level VEGF-induced signaling response. Moreover, it is possible to inhibit
40
distinct parts of the signaling pathway. That is, some perturbations will specifically inhibit upstream species
(such as Ca
2+
), while not altering downstream species (such as cGMP), or vice versa.
2.5. Discussion
We have developed a molecular-detailed model of the intracellular eNOS signaling pathway in ECs,
regulated by two important angiogenic factors: VEGF and TSP1. This model captures the experimentally
observed VEGF-induced eNOS signaling dynamics quantitatively (Figure 2-2). This work is complementary
to our previous work, including models that characterize the interactions of angiogenic factors present in the
extracellular space with their cell-surface receptors[70], [107], [108], VEGF-mediated pro-angiogenic signaling
through the MAPK pathway[98], and TSP1-mediated apoptotic pathway via receptor CD36[99]. With this
model, we are able to investigate the unknown intracellular mechanisms of TSP1 via receptor CD47, and
generate insight to help address the problem of systemic hypertension elicited by anti-angiogenic drugs.
This calibrated mechanistic model allows us to efficiently simulate and quantify the signaling dynamics
of the eNOS pathway under various stimulation conditions. First, we take advantage of the model to predict
the signaling dynamics in response to changes to VEGF levels. We show that the upstream signaling species
are more sensitive to different levels of VEGF signaling while downstream species are more robust to changes
in the stimulant (Figure 2-6). This hypothesis that the model generated can be validated experimentally.
Next, we used the model to hypothesize the details of possible intracellular mechanisms of TSP1 that
are currently unknown. These simulations are especially relevant in understanding TSP1’s multiple functions
and their relative importance in angiogenic inhibition. Furthermore, as the tumor vasculature is typically
comprised of highly proliferative ECs, whereas the normal vasculature is quiescent, likely due to the difference
in the growth factor levels in their respective environment, we use the model to generate predictions of effective
strategies that selectively target only the ECs experiencing high VEGF levels observed in the tumor
microenvironment. The model efficiently generates testable predictions for future experimental studies to
validate. In the following sections, we discuss these model predictions in more detail.
41
2.5.1. Model predicts intracellular target mechanisms of TSP1
We use the calibrated mechanistic model to investigate potential intracellular targets of TSP1, and
several predictions agree with the experimental observations. TSP1 has been shown to act through receptor
CD47 to reduce the levels of several intracellular signaling species in the eNOS signaling pathway[40], [49], [54];
it is expected that TSP1 acts through specific mechanisms that produce these observed effects. Because TSP1
inhibits eNOS signaling in both the basal condition and agonist-induced conditions, we present the effects of
several perturbations that are shown to be influential in the basal condition (Figure 2-8a) and compare their
effects to what happens when VEGF is present (Figure 2-8b). Note that these perturbations are in addition to
two inhibitory functions of TSP1 at the receptor-ligand level: the sequestration of VEGF by TSP1 in the
extracellular matrix and the disruption of CD47-R2 coupling once TSP1 binds to CD47.
An experimental study has shown that at the relatively upstream level, TSP1 reduced the sustained
level of Ca
2+
stimulated by ionomycin[54], which acts on internal Ca
2+
stores[169]. The sustained Ca
2+
phase is
thought to be maintained by an influx through the CRAC channel and balanced by the other homeostatic
mechanisms. Our model predicts several mechanisms through which Ca
2+
influx upon VEGF stimulation can
be reduced. Specifically, these mechanisms include perturbing of the CRAC mechanism, decreasing extracellular
Ca
2+
level, enhancing cytosolic Ca
2+
resequestration to the ER (Figure 2-8b), or sensitizing the PMCA pump
which extrudes cellular Ca
2+
(Figure 2-8a,b).
TSP1 inhibits basal eNOS catalytic activity in endothelial cells[54]. In the basal condition, the model
predicts that promoting the dissociation of Ca
2+
from CaM, or CaM from eNOS, or decreasing the basal eNOS
catalytic rate, directly inhibits the basal eNOS catalytic activity (Figure 2-8a). These three perturbations take
effect only in the basal condition and lose their inhibitory strengths when VEGF level is high (Figure 2-8b),
suggesting that TSP1 can inhibit basal eNOS catalytic activity via these mechanisms but may act through other
mechanisms to reduce VEGF-induced eNOS catalytic activity. Additionally, the model predicts that
perturbations to the SERCA mechanisms also reduce eNOS catalytic activity and subsequent cGMP synthesis;
however, without experimental data, it is difficult to know whether TSP1 disrupts Ca
2+
homeostasis in quiescent
ECs.
42
TSP1 inhibits basal and VEGF-stimulated cGMP synthesis[40]. The model predicts that increasing the
NO clearance rate, reducing sGC activity, or enhancing PDE activity achieves cGMP inhibition in both the
basal and VEGF-stimulated conditions (Figure 2-8). Comparing our results to the experimental findings,
Isenberg et al. suggest that TSP1 may increase cellular metabolism of NO, but does not selectively activate a
PDE, which helps us exclude the PDE-related perturbations as TSP1’s function. A study has shown that TSP1
inhibits sGC activity induced by sGC activators besides NO[170]. This implies that the inhibition of sGC
activation is not simply due to oxidation of the sGC heme, which agrees with our finding. Together, we have
used the model to hypothesize that TSP1 enhances the clearance rate of NO and suppresses sGC activity
independent of NO or PDE, in both the basal and VEGF-stimulated conditions. These model-generated
hypotheses can be used to guide experimentation to further investigate TSP1’s effects.
2.5.2. Relevant insights for selectively targeting VEGF-stimulated signaling
In addition to investigating the intracellular targets of TSP1, we explored alternative perturbation
strategies that can affect VEGF-stimulated eNOS signaling. We sorted the effective strategies according to
which aspect of the network that they influence. Importantly, the perturbations that strongly reduce cGMP in
this condition can serve as strategies to selectively inhibit eNOS signaling promoted by VEGF, potentially
eliminating the hypertensive effects from applying an anti-angiogenic drug that universally inhibits eNOS
catalytic activity. Below, we discuss in detail these model predictions and what they contribute to the field of
knowledge, in terms of the following aspects: 1) predictions that have been pursued in experimental studies, 2)
predictions that explain the mechanisms of agents being investigated and therefore complement existing and
ongoing studies, and 3) predictions that reveal new strategies that have not yet been pursued.
2.5.2.1. Predictions that have been pursued in experimental studies
From the simulated perturbation results, we observe that the regulation of the eNOS catalytic activity
is rather independent of the VEGF-induced Ca
2+
response through PLCg activation and IP3 generation, but
heavily relies on the Akt-Hsp90 pathway. Along this axis, inhibition of the Src and Hsp90 chaperon protein
activity prominently reduced eNOS catalytic activity but do not affect the cGMP level. In addition, the model
43
predicts that lowering the levels of Src or Hsp90 also results in similar inhibitory effects (Figure 2-9). Clinically,
both Src and Hsp90 inhibitors are being investigated as therapeutic agents to treat various types of cancer in
clinical trials[95], [159], [160], although the focus lies in their functions in cancer cells. When considering this
purpose, it is worth noting that these perturbations do not affect the basal eNOS catalytic activity and therefore
should not induce harmful effects in vasoregulation for patients receiving these drugs.
On the other hand, individually blocking IP3R channel (I IP3R and K M,IP3R) or the CRAC flux (I crac),
reduced VEGF-induced Ca
2+
influx but did not affect NO or cGMP (Figure 2-8b, Figure 2-9), and similar
results were observed when combining those perturbations (data not shown). This is likely because, as
mentioned above, the eNOS catalytic activity is regulated by the presence of Akt and Hsp90, both of which
enhance eNOS electron flow and sensitivity to CaM binding. In other words, the basal Ca
2+
level is sufficient
in supporting the activation of VEGF-induced eNOS catalytic activity, without the external Ca
2+
influx.
Meanwhile, an experimental study showed that HUVECs pretreated with carboxyamidotriazole (CAI), an
inhibitor of non-voltage operated Ca
2+
channels (cancer.gov), showed a decrease in the cGMP in response to
VEGF stimulation within two minutes[121]. However, it is possible that pretreatment has disrupted the Ca
2+
equilibrium, making direct comparison of the model simulations with the experimental results unsuitable. In
fact, for some parameter sets, our model simulations suggest that the VEGF-stimulated eNOS catalytic activity
can be inhibited by mechanisms that reduce the intracellular Ca
2+
to below the basal level (50nM) (data not
shown).
The model predicts that in addition to TSP1’s possible mechanism of directly reducing the catalytic
rate of sGC, several perturbations can reduce the VEGF-stimulated cGMP downstream of eNOS catalytic
activity. These include enhancing the dissociation of NO from the distal heme activation site of sGC (increasing
k off,NO.sGC) or reducing the activation rate of NO-bound sGC (decreasing k a,sGC) (Figure 2-9). Additionally,
directly reducing sGC level can inhibit cGMP in both the basal and VEGF-stimulated conditions (Figure 2-
8). These results agree with experimental studies using the sGC inhibitors, ODQ and NS2028, which are
effective both in vitro and in vivo[166]. These inhibitors decrease sGC activity by oxidizing the heme cofactor in
its regulatory H-NOX domain, potentially resulting in heme loss and prohibits NO from binding to sGC.
44
2.5.2.2. Predictions that complement existing/ongoing studies
The model predicts that although various perturbations to the Ca
2+
homeostatic mechanisms can
reduce the VEGF-induced Ca
2+
response (Figure 2-8b, Figure 2-9), only perturbing the PMCA mechanism
through sensitization (decreasing K M,PMCA) substantially reduced the eNOS catalytic activity. This finding is
complementary to those from an experimental study[171], showing that substantially enhancing clearance of
the intracellular Ca
2+
by PMCA does inhibit eNOS catalytic activity. In the future, researchers can expand our
model by including the binding event between PMCA and eNOS to investigate the specific mechanism and
relative significance of PMCA’s negative regulatory role via its association with eNOS.
The model predicts that inhibiting the association of Hsp90 with CaM-bound eNOS (decreasing
k on,Hsp90.CaMeNOS or increasing k off,Hsp90.CaMeNOS), or decreasing specifically the catalytic rate of Hsp90-bound eNOS
can reduce the NO level, while still only minimally affecting the downstream cGMP level. In addition, directly
reducing CaM availability or eNOS itself strongly reduced both eNOS catalytic activity and cGMP.
Experimentally, there are a large number of existing compounds that inhibit eNOS catalytic activity through
various mechanisms[172]: compounds that compete with the substrate arginine or the tetrahydrobiopterin
(BH4) cofactor (not depicted in our model); inhibitors interacting directly with the heme to prevent eNOS
dimerization (reducing the available eNOS level); and inhibitors that interacts with CaM. Interestingly, our
model predicts that in the VEGF-stimulated condition, individually altering the influential binding rates
between Ca
2+
and the two sites on CaM, between various forms of CaM and eNOS, or between various forms
of eNOS with arginine did not significantly affect eNOS catalytic activity (data not shown). However, when
we universally inhibit the binding events between Ca
2+
with all sites on CaM, binding of CaM with all forms of
eNOS, binding of all forms of eNOS with arginine, or catalytic activity of all forms of eNOS by 10-fold, these
result in a strong reduction in the VEGF-stimulated eNOS catalytic activity and cGMP (Figure 2-10).
Furthermore, these sets of universal perturbations also achieved maximal inhibition of eNOS catalytic activity
and cGMP in the basal condition (data not shown), pointing to the potential side effect of the use of generic
CaM or eNOS inhibiting compounds as they can affect the endothelium in both basal and high VEGF
45
environments.
Figure 2-10. Model predicted dynamics with combined perturbations compared to a single
perturbation. With the high VEGF level (0.389nM) (light blue), with universal perturbations on specific sets
of biochemical reactions (dark grey), compared to perturbing only one reaction (light grey). (a) Decreasing Ca
2+
binding to CaM on both N- and C-terminus (decreasing both k on,Ca2N and k on,Ca2C), versus only decreasing k on,Ca2C.
(b) Decreasing CaM binding to all eNOS forms, including eNOS (k on,CaM.eNOS), peNOS (k on,CaM.peNOS),
eNOS:Hsp90 complex (k on,CaM.eNOS.H), and peNOS:Hsp90 complex (k on,CaM.peNOS.H), versus only decreasing
k on,CaM.eNOS. (c) Decreasing Arginine binding to all forms of eNOS (k on,eNOS.Arg, k on,peNOS.Arg, k on,eNOS.Arg.H,
k on,peNOS.Arg.H) versus only decreasing k on,eNOS.Arg. (d) Decreasing eNOS catalytic activity (k cat,eNOS, k cat,peNOS,
k cat,eNOS.H, k cat,peNOS.H) versus only decreasing k cat,eNOS. Solid lines: mean of model simulations with 19 sets of
parameter values. Shaded area: standard deviation among 19 sets of simulations. All perturbed parameter values
were decreased by 10-fold.
0 10 20 30
0
1000
2000
3000
4000
cGMP
0 10 20 30
0
100
200
300
freeCac
0 10 20 30
0
0.2
0.4
0.6
0.8
1
NO
Fold-change
Concentration (nM)
Concentration (nM)
Time (min) Time (min) Time (min)
0 10 20 30
0
1000
2000
3000
4000
cGMP
0 10 20 30
0
100
200
300
freeCac
0 10 20 30
0
0.2
0.4
0.6
0.8
1
NO
Fold-change
Concentration (nM)
Concentration (nM)
Time (min) Time (min) Time (min)
Calcium Nitric Oxide cGMP
0 10 20 30
0
1000
2000
3000
4000
cGMP
0 10 20 30
0
100
200
300
freeCac
0 10 20 30
0
0.2
0.4
0.6
0.8
1
NO
Fold-change
Concentration (nM)
Concentration (nM)
Time (min) Time (min) Time (min)
Universal Perturbation
Baseline (high
tumor VEGF level)
(a)
(b)
(c)
0 10 20 30
0
1000
2000
3000
4000
cGMP
0 10 20 30
0
100
200
300
freeCac
0 10 20 30
0
0.2
0.4
0.6
0.8
1
NO
Fold-change
Concentration (nM)
Concentration (nM)
Time (min) Time (min) Time (min)
(d)
Single Perturbation
46
2.5.2.3. Predictions that reveal strategies that have not yet been pursued
Model predictions show that enhanced resequestration of intracellular Ca
2+
(increasing I SERCA or
decreasing K M,SERCA) reduces the intracellular Ca
2+
levels in both basal and VEGF-stimulated conditions
(Figure 2-8). It may be possible to implement this perturbation experimentally, as a study found that the up-
regulation of TMTC, a novel ER-resident adapter protein that associates with SERCA2B, could reduce the
Ca
2+
release from the ER[173], although the study was done with different cell types (human embryonic kidney
HEK 293T and COS).
In addition to reducing NO-dependent sGC activation as a perturbation strategy, our model predicts
that enhancing the desensitization of sGC via binding of NO on the proximal heme site (decreasing k off,NO.NOGC),
and enhancing the dissociation of NO from the distal heme activation site on sGC (increasing k f,NOGC.NO or
decreasing k r,NOGC.NO) (Figure 2-9) also achieves inhibition of cGMP, and only takes effect in the VEGF-
stimulated condition. On the other hand, sGC downregulation takes effect in both the basal and VEGF-
stimulated conditions, making healthy endothelial cells susceptible. Therefore, these perturbations may serve
as effective candidate strategies for selectively targeting eNOS signaling in the high VEGF environment.
Finally, the model predicts that enhancement of PDE activity through various mechanisms can be
effective in reducing cGMP. These include strategies that directly enhance the activation of PDE (increasing
k a,PDE or k a2,PDE , or decreasing k d,PDE or k d2,PDE) or its catalytic activity (increasing k cat,PDE), which take effect in
both the basal and VEGF-stimulated conditions (Figure 2-8), and strategies that sensitize PDE to cGMP
(increasing k on,cGMP.PDE, decreasing k off,cGMP.PDE, or decreasing K M,PDE), which are only effective in the VEGF-
stimulated condition (Figure 2-9). There are several existing non-specific and selective PDE inhibitors,
including Theophylline and Sildenafil[174]. However, the limitation of using small molecule sGC inhibitors or
PDE activators is that it is unclear whether these agents could systemically affect cGMP synthesis in other cell
types, including vascular smooth muscle cells. Our model is able to differentiate between the effects of these
specific mechanisms of action, and the model reveals that sensitizing PDE to cGMP may serve as a more
attractive strategy for cGMP inhibition, as it only affects cells in the high VEGF environment.
47
2.5.3. Model limitations
We acknowledge that the results from our work are subject to some limitations. One limitation of this
study is that model parameterization is difficult due to a lack of quantitative measurements of the kinetic
parameter. In the absence of kinetic parameter values and additional data to calibrate the model, we have to
rely on parameters from existing models. Furthermore, we did not include all the signaling events that are
related to the VEGF signaling pathway. For example, DAG is also activated by PLCg, and it activates the Ras-
Raf-MEK-ERK pathway, but we do not consider this particular signaling pathway in this model, in order to
focus on the eNOS catalytic activity. Future work can be done to expand and integrate the pathway described
in the current study with other models of the VEGF signaling pathways[98]. Another example is that not all
binding partners of eNOS are taken into account. However, a recent model of competitive eNOS tuning[134]
showed that NOS binding is the same under isolated or competitive conditions. This supports our model
assumption that eNOS-CaM binding can be isolated in the model without adding in competitive binding of
other CaM binding partners. We also acknowledge that in our model, the cGMP dynamics are loosely
constrained, due to the lack of quantitative longitudinal data of cGMP response to VEGF signaling. As
additional data becomes available, we can incorporate cGMP and downstream ERK response dynamics into
the model in order to investigate the long-term proliferative signaling in more detail.
Despite these limitations, our model provides a framework that offers mechanistic insight into the
eNOS signaling pathway that is mediated by VEGF and TSP1. Future experimental studies can be used to
verify the findings of this computational study. Ultimately, this work complements the models of VEGF
signaling pathway and will aid in our systematic understanding of the angiogenic regulation.
2.6. Conclusions
In summary, we have constructed and calibrated a mechanistic model that quantitatively describes the
VEGF-induced eNOS signaling pathway in ECs. This model provides mechanistic insight as for how TSP1
inhibits eNOS signaling at the intracellular level. This is an aspect of TSP1’s multiple inhibitory functions that
has been observed experimentally but has not been previously studied in detail. Additionally, we propose
48
alternative strategies that selectively inhibit the eNOS-dependent proliferative signaling in ECs experiencing a
higher VEGF level that is associated with the tumor microenvironment. Therefore, this work contributes to
answering a long-standing question for angiogenesis-based therapies, where systemic hypertension is often a
side effect of these treatments.
49
Chapter 3
TSP1-Mediated Endothelial Cell Apoptotic Signaling via Receptor CD36
Portions of this chapter are adapted from:
Qianhui Wu and Stacey D. Finley. Cell Communication and Signaling (2017) 15:53
3.1. Abstract
Thrombospondin-1 (TSP1) is a matricellular protein that functions to inhibit angiogenesis. An
important pathway that contributes to this inhibitory effect is triggered by TSP1 binding to the CD36 receptor,
inducing endothelial cell apoptosis. However, therapies that mimic this function have not demonstrated clear
clinical efficacy. This study explores strategies to enhance TSP1-induced apoptosis in endothelial cells. In
particular, we focus on establishing a computational model to describe the signaling pathway, and using this
model to investigate the effects of several approaches to perturb the TSP1-CD36 signaling network. We
constructed a molecularly-detailed mathematical model of TSP1-mediated intracellular signaling via the CD36
receptor based on literature evidence. We employed systems biology tools to train and validate the model and
further expanded the model by accounting for the heterogeneity within the cell population. The initial
concentrations of signaling species or kinetic rates were altered to simulate the effects of perturbations to the
signaling network. Model simulations predict the population-based response to strategies to enhance TSP1-
mediated apoptosis, such as downregulating the apoptosis inhibitor XIAP and inhibiting phosphatase activity.
The model also postulates a new mechanism of low dosage doxorubicin treatment in combination with TSP1
stimulation. Using computational analysis, we predict which cells will undergo apoptosis, based on the initial
intracellular concentrations of particular signaling species. This new mathematical model recapitulates the
intracellular dynamics of the TSP1-induced apoptosis signaling pathway. Overall, the modeling framework
predicts molecular strategies that increase TSP1-mediated apoptosis, which is useful in many disease settings.
50
3.2. Introduction
Angiogenesis, the formation of new capillaries from pre-existing blood vessels, plays a critical role in
tumor progression. Angiogenesis enables the tumor to generate its own blood supply and obtain oxygen and
nutrients from the microenvironment. This process is regulated by a dynamic interplay between the angiogenic
promoters, such as vascular endothelial growth factor (VEGF) and fibroblast growth factor (FGF), as well as
angiogenic inhibitors, such as thrombospondin-1 (TSP1) [1], [50], [175]–[177].
Due to its importance in tumor development, invasion, and metastasis, angiogenesis has become a
prominent target for cancer therapies. In addition to strategies targeting pro-angiogenic species, such as
inhibiting VEGF signaling using antibodies and tyrosine kinase inhibitors, anti-angiogenic species hold promise
in reducing tumor angiogenesis. TSP1 is a well-known, potent endogenous angiogenesis inhibitor. TSP1
expression is lost in multiple cancer types; however, its re-expression can delay cancer progression, promote
tumor cell apoptosis, and decrease microvascular density. For these reasons, it has been of interest to mimic
TSP1’s functions in regulating angiogenesis [37], [92], [175], [178], [179].
TSP1 is a multifunctional matricellular protein that acts to inhibit angiogenesis in multiple ways [45],
[50], [180], which include altering the availability of pro-angiogenic factors and promoting anti-angiogenic
signaling through its receptors CD36 and CD47. Several studies have shown that TSP1 mediates its anti-
proliferative and pro-apoptotic effects in a highly specific manner on endothelial cells. TSP1 primarily promotes
these effects by binding to the CD36 receptor [43], [48], [175], which is associated with capillary blood vessel
regression [48], [56], [180], [181]. TSP1 interaction with CD36 leads to recruitment of the Src-related kinase
Fyn, activation of p38MAPK, and processing of caspase-3, a vital protease that mediates apoptosis [48], [56],
[182]. TSP1-CD36 signaling also causes transcriptional activation of Fas ligand (FasL), a death ligand that also
promotes pro-apoptotic signaling, ultimately inhibiting angiogenesis. This apoptosis pathway is further
enhanced as pro-angiogenic factors induce increased levels of Fas receptors, sensitizing the cells to FasL [57].
Unfortunately, therapies that mimic TSP1 activity have not demonstrated definitive clinical efficacy.
For example, ABT-510, a TSP1 peptide mimetic that binds to CD36, was previously tested in a Phase II study
in 2007 for treatment of metastatic melanoma. However, the drug failed to reach its primary endpoint (18-week
51
treatment failure rate), resulting in termination of the study [78]. ABT-510 also showed little clinical effect in a
Phase II trial for advanced renal cell carcinoma [79]. These disappointing results indicate that there is a need to
better understand the effects of anti-angiogenic agents and develop effective treatment strategies. This requires
a detailed and quantitative understanding of the dynamic concentrations of the factors involved in angiogenesis
signaling.
Computational systems biology offers powerful tools for studying complex biological processes that
involve a large number of molecular species and signaling reactions that occur on multiple time- and spatial-
scales. Systems biology aims to study how individual components of biological systems give rise to the function
and behavior of the system [183]. Additionally, computational modeling aids in the development of therapeutic
strategies that specifically target tumor angiogenesis to optimally inhibit tumor progression, complementing
pre-clinical and clinical angiogenesis research [184].
Substantial research has focused on the pro-angiogenic factors and their extracellular interactions [107],
[109], [184]. However, a consideration of the intracellular mechanisms of anti-angiogenic factors is also needed
in order to fully understand the dynamics of the signaling networks regulated by angiogenesis promoters and
inhibitors. In this study, we focus on TSP1-mediated apoptosis signaling through the CD36 receptor. Although
some aspects of the TSP1-CD36 pathway have been studied experimentally, the signaling network has not been
quantitatively and systematically analyzed. We constructed the first computational model that describes the
intracellular signaling network induced by TSP1-CD36 binding in endothelial cells, a complex network
comprised of biochemical reactions that lead to cell apoptosis. We apply the model to predict the effects of
modulating protein expression and enzyme activity on apoptosis signaling. The model quantifies the effects of
these perturbations and predicts promising targets, both in terms of the averaged response of a population of
endothelial cells and individual cells within the population. Thus, the model is a quantitative framework to
predict strategies to enhance TSP1-mediated apoptosis. Ultimately, the model can be used to identify novel
pharmacologic targets and optimize therapeutic strategies that promote apoptosis and, subsequently, inhibit
angiogenesis.
52
3.3. Methods
3.3.1. Mathematical model.
We constructed a computational model of TSP1-mediated apoptosis signaling via the CD36 receptor
in endothelial cells. The molecular interactions depicted in Figure 3-1 were translated into biochemical reaction
equations, with the assumption that the reactions follow well-established kinetic laws, including mass-action or
Michaelis-Menten kinetics. A system of nonlinear ordinary differential equations (ODEs) was formulated to
describe the rate of change of the species’ concentration. The model is comprised of 53 ODEs to predict the
concentrations of the 53 species in the signaling network over time. The Simbiology toolbox (MATLAB) was
used to implement the biochemical reaction equations, and the MATLAB stiff solver ODE15s was used the
numerically solve the system of ODEs.
Solving the set of ODEs with the baseline initial conditions provides the averaged response of a
population of cells. Additionally, we account for heterogeneity in a population of cells by solving the ODE
model 2,000 times, each with a different set of initial conditions. We refer to this as the “population-based
model”.
Cytosolic and nuclear compartments. The model is comprised of two compartments, cytosolic and
nuclear, both assumed to be well mixed. Specific molecules, such as NF-kB, may move from one compartment
to another at a defined translocation rate. The volume of the nuclear compartment is estimated to be 14.32%
of the cytosolic compartment [185], and the concentrations of species transported between the two
compartments is converted using this ratio.
Initial protein concentrations. The initial conditions used in the model are given in Table 3-1 Very
few references for initial concentrations of proteins are available. Therefore, we adapted values from a
previously published model [186] and adjusted the initial concentrations of several species in order for the
model to match experimental measurements. For the CD36 and Fas receptors, we used flow cytometry to
quantify the average numbers of receptors on cultured human microvascular endothelial cells (data not shown;
similar to previous work [187], and converted the receptor numbers to concentrations using the total cell
volume of 1 picoliter [145].
53
When simulating the population-based model, we randomly select the initial conditions from a gamma
distribution. The gamma distribution is characterized by two parameters: the shape factor, a, and the scale
parameter, b. These parameters are related to the mean, m, and standard deviation, sd, of the distribution: 1/a
= sd
2
/m
2
; b = sd
2
/m. Thus, a×b = m. We set m to be the baseline value of the initial condition for each species
(given in Table 3-1) and assume a shape factor of 5.5 (based on previous work [188]).
Figure 3-1. Model schematic of TSP1-mediated apoptosis signaling via receptor CD36. TSP1 binding to the CD36
receptor recruits p59fyn, which induces activation of the caspase-3 cascade. The kinase p38MAPK is subsequently
phosphorylated and translocated to the nucleus. NF-kB translocates into the nucleus and is activated in presence of
phosphorylated p38MAPK. This leads to transcriptional activation of FasL. FasL protein binds to its receptor Fas, forming
the DISC complex, which binds to c-FLIP (FL) and procaspase-8 (pro8) to form the p43-FLIP complex. This complex
activates IKK, which releases NF-kB from its inhibitor IkB. Blue arrows indicate transport reactions.
54
Table 3-1. CD36 model initial concentrations.
Species I.C. (mM) Reference
CD36 3.32E-01 ‡
p59 3.40E-01 *
pro8 6.47E-02 ^
pro3 1.44E-03 ^
p38cyt 1.50E-01 *
Ptase_cyt 1.70E-02 *
XIAP 1.70E-01 *
PARP 1.70E+00 *
Fas 1.49E-02 ‡
MEKK1 2.50E-02 *
FL 7.40E-03 ^
FS 5.08E-03 ^
IKK 5.77E-03 ^
NFkB_IkB 4.74E-03 ^
Ptase_nuc 1.70E-02 *
NFkB_cyt 8.00E-04 *
‡: measured; *: manually adjusted; ^: Neumann et al.
Rate constants.
Production of soluble species. The basal rate at which each species is synthesized (K syn_all) is set to be 10
-4
µM/min,
with the exception of FasL, procaspase-8, and procaspase-3, whose production rates are described below.
The model accounts for FasL production mediated by TSP1, and we described the production of FasL
mRNA production (DNA transcription) using Michaelis-Menten kinetics:
V = V max_FasL* NF-kB_p/(K m_FasL+ NFkB_p)
where V max_FasL and K m_FasL and the Michaelis-Menten kinetic rate constants for FasL mRNA production, and
NF-kB_p is the activated transcriptional factor that catalyzes this process. The molecular details involved in
FasL protein production encompass the mRNA translocation and translation, and protein secretion. The rates
involved in these reactions are not readily available in published literature. Therefore, we estimated the values
in model fitting in order to match experimental data.
55
The synthesis rate of procaspase-8 and procaspase-3 were assumed to be dependent on the
concentration of DISC present in the system, as a partial effect of Fas ligation. The synthesis rate is described
as:
V = F*DISC + K syn_all
where F is a hand-tuned coefficient, DISC is the complex formed by FasL binding to Fas, and K syn_all is the basal
level synthesis rate assigned to all the other species except for FasL.
Protein degradation. Protein species are assumed to be degraded at the same rate, 10
-3
min
-1
, unless there
was a degradation rate available in the literature or from a previous model. This allows the system to balance
and reach steady-state in the absence of TSP1 stimulation. The degradation rates of caspase-8, caspase-3, the
p43:FLIP:IKK_a complex, and cytosolic NF-kB have unique values adapted from previous modeling work by
Neumann et al. [186].
Receptor-ligand interactions. The affinity of TSP1 and its receptor CD36 has been measured experimentally:
the K d value is 230 nM [189]. We assume that FasL binds to Fas with an affinity of 0.4 nM. In all cases, the
dissociation rate for the receptors is 1.2×10
-2
min
-1
. Receptors are internalized and inserted at the cell membrane
such that the total number of receptors (ligated plus unbound) is constant.
FasL cascade. The model includes DISC formation upon FasL binding with Fas, and the downstream
caspase-8 and NF-kB activation reactions. The molecular details were adapted from the model established by
Neumann et al. [186]. We altered this portion of their model by adding reversible binding reactions to ensure
the reaction network is consistent with the other parts of our model. We tuned the universal dissociation rate
K off to be 1.2×10
-2
min
-1
to match the data presented in their paper. The simulations of the implemented minimal
model are shown in Figure 3-2.
56
Figure 3-2. Comparison of minimal model of FasL signaling to experimental data. We implemented a minimal
based on the work of Neumann et al. We included reversible reactions to mirror how other binding interactions are
implemented in our full model. Predictions from the minimal model (lines) matches the original data (squares). FasL
concentration used in model simulations: 1500ng/ml (black), 500ng/ml (blue), and 250ng/ml (red).
Sensitivity analysis. There is limited quantitative experimental data available to specify the values of
the kinetic parameters. However, the parameters must be set to appropriate values in order for the model to
generate reliable predictions. We first used sensitivity analysis to reduce the number of parameters to be
estimated. Specifically, to identify the influential kinetic parameters before each step of model fitting, we
conducted global sensitivity analysis using the extended Fourier Amplitude Sensitivity Test (eFAST) method
[190], as we have done in previous work [184], [107]. All inputs were allowed to vary simultaneously one order
of magnitude above and below the baseline value, and the effects of multiple inputs on the model outputs of
individual inputs were quantified. An additional global sensitivity analysis was performed after model training,
0 100 200 300
0
0.5
1
pro8(sum1)
0 100 200 300
0
0.5
1
casp8
0 100 200 300
0
0.5
1
pro3
0 100 200 300
0
0.5
1
casp3
0 100 200 300
0
0.5
1
NFkB:IkB
0 100 200 300
0
0.5
1
NFkB:IkB:p
0 100 200 300
0
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1
p43p41
0 100 200 300
0
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1
pro8(sum1)
0 100 200 300
0
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1
casp8
0 100 200 300
0
0.5
1
pro3
0 100 200 300
0
0.5
1
casp3
0 100 200 300
0
0.5
1
NFkB:IkB
0 100 200 300
0
0.5
1
NFkB:IkB:p
0 100 200 300
0
0.5
1
p43p41
0 100 200 300
0
0.5
1
pro8(sum1)
0 100 200 300
0
0.5
1
casp8
0 100 200 300
0
0.5
1
pro3
0 100 200 300
0
0.5
1
casp3
0 100 200 300
0
0.5
1
NFkB:IkB
0 100 200 300
0
0.5
1
NFkB:IkB:p
0 100 200 300
0
0.5
1
p43p41
0 100 200 300
0
0.5
1
pro8(sum1)
0 100 200 300
0
0.5
1
casp8
0 100 200 300
0
0.5
1
pro3
0 100 200 300
0
0.5
1
casp3
0 100 200 300
0
0.5
1
NFkB:IkB
0 100 200 300
0
0.5
1
NFkB:IkB:p
0 100 200 300
0
0.5
1
p43p41
Time (min)
Time (min)
Fold-Change Fold-Change Fold-Change Fold-Change
57
in order to quantify the robustness of the model with respect to varying the kinetic parameters (Figure 3-3
panels A-C). Sensitivity analysis was also used to determine the effects of initial protein concentrations to
inform perturbation simulations (Figure 3-3 panel D).
Caspase casecade
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
30 min 60 min
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
300 min 720 min
A
p38 signaling
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 5
0
0.2
0.4
0.6
0.8
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 4
0
0.2
0.4
0.6
0.8
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 2
0
0.2
0.4
0.6
0.8
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 3
0
0.2
0.4
0.6
0.8
1
30 min 60 min
300 min 720 min
B
58
Figure 3-3. Global sensitivity analysis of parameters in the CD36 model. An eFAST sensitivity analysis was
performed to identify which parameters most significantly influence the cPARP concentration predicted by the model
for different simulated timepoints. The total sensitivity index is shown for each parameter. (A-C) x-axis: parameters
(inputs); y-axis: model species (outputs). A) Parameters involved in upstream signaling (“Caspase cascade”). B)
Parameters involved in intermediate signaling (“p38 signaling”). C) Parameters involved in downstream signaling (“FasL
signaling”). (D) Global sensitivity analysis of non-zero initial concentrations. x-axis: non-zero initial concentrations
(inputs), y-axis: model species (outputs).
D
FasL signaling
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kon-dephos
Kdephos
Ki-casp3-XIAP
Ktrsp-cyt-nuc
Kinter
Vmax-FasLm
Km-FasLm
Kexp-FasLm
Ksyn-FasL
Kexp-FasL
Kon-Fas-FasL
Kon-DISC-pro8
Ksyn-all
Kdeg
Kon-casp3-MEKK1
Kp-p38 = params
Kc-MEKK1 = params
Kon-cMEKK1-p38
FasLsyn-factor
Kon-DISC-FL
Kon-DISC-FS
Kp43p41
Kp43FLIP
Kon-DISC2-FS
K-casp8
Kc-casp3
Kr-casp8
Ka-IKK
Kp-NFkBIkB
Ka-NFkB
Kdeg-IKKa
Kdeg-NFkBcyt
Kdeg-casp8
Kdeg-casp3
Kon-pp38-NFkB
Kdeg-pp38cyt
Kon-TSP1-CD36
Kon-TSP1-CD36-p59
Kp-p59
Kp-NFkB
Kon-casp3-PARP
Kc-PARP
Ksyn-Ptase
Kdeg-Ptase
Kc-casp8
Kinser
koff
Koff-dephos
Koff-casp3-MEKK1
Koff-cMEKK1-p38
Koff-pp38-NFkB
Koff-TSP1-CD36
Koff-TSP1-CD36-p59
Koff-casp3-PARP
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
30 min 60 min
300 min 720 min
C
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
TSP1
CD36
TSP1:CD36
p59
TSP1:CD36:p59
TSP1:CD36:pp59
pp59:Ptase
pro8
casp8
pro3
casp3
caspase3 activity
XIAP
casp3(u)
PARP
casp3:PARP
cPARP
casp3:MEKK1
cMEKK1
MEKK1
Timepoint 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
cMEKK1:p38(cyt)
p38(cyt)
pp38(cyt)
Ptase(cyt)
pp38cyt:Ptase
pp38(nuc)
p38(nuc)
Ptase(nuc)
pp38nuc:Ptase
pp38:NFkB
NFkB-p
NFkB:IkB
NFkB:IkB-p
NFkB(cyt)
NFkB(nuc)
Timepoint 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD36
p59
pro8
pro3
p38(cyt)
Ptase(cyt)
XIAP
PARP
Fas
MEKK1
FL
FS
IKK
NFkB:IkB
NFkB(cyt)
Ptase(nuc)
FasLm(nuc)
FasL(cyt)
FasLm(cyt)
Fas
FL
DISC
FasL
DISC:pro8
DISC:FL
FS
DISC:FS
p43p41
p43:FLIP
DISC:pro8:FS
DISC:FL:FL
DISC:FL:FS
DISC:FS:FS
IKK
p43:FLIP:IKK-a
Timepoint 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
30 min 60 min 300 min 720 min
Caspase
casecade
p38 signaling FasL signaling
59
3.3.2. Quantification of experimental data
The experimental data used in model fitting and validation are extracted from previously published
studies [48], [56]. Jimenez et al. stimulated human microvascular endothelial cells (HMVECs) with 10 nM TSP1
and used immunoblotting of cell lysates to measure TSP1-induced association of activated p59fyn with CD36
over 30 minutes (TSP1:CD36:p59fyn complex and activated p59Fyn, pp59), and activated p38 (pp38) over 60
minutes. We analyzed the Immunoblots using ImageJ (https://imagej.nih.gov) and extracted quantitative data
needed for model fitting and validation. The local background from bands was subtracted and their intensity
was quantified. The intensities of subject species were normalized to the corresponding control band intensities.
One data point (TSP1:CD36:p59fyn concentration at 30 minutes) was excluded due to low image quality.
Two sets of data for caspase-3 activity upon TSP1 stimulation measured with fluorescence assays were
extracted: from Jimenez et al. and Nor et al.. HMVECs stimulated with 5 nM TSP1 over 5 hours (300 minutes),
and human dermal vascular endothelial cells (HDMECs) stimulated with 0.388 nM TSP1 over 12 hours (720
minutes) were measured in these studies, respectively. We quantified the caspase-3 activity at each timepoint
directly from the published figures using ImageJ.
3.3.3. Receptor Quantification
We measured CD36 and Fas receptor numbers on HMVECs, following methods previously
established [129]. Briefly, HMVECs from Lonza were cultured in flasks and maintained in Endothelial Cell
Growth Media-2 (EGM-2) supplemented by the EGM-2 Single Quot Kit (Lonza). Cells were maintained at
37 °C in 95% air and 5% CO 2, and we only use cells at passage numbers 2-4. To dissociate cells from the
culture plate, cells were incubated with a non-enzymatic cell dissociation solution, CellStripper (Corning), for 5
min at 37 °C. Cells were centrifuged at 500×g for 5 min to obtain a final concentration of 4x10
6
cells/mL in
stain buffer (PBS, bovine serum albumin, and sodium azide).
Aliquots of cells (25 µL, ~10
5
cells) were labeled with phycoerythrin (PE)-conjugated monoclonal
antibodies (Biolegend) and allowed to incubate on ice for 45 minutes. The volumes of antibody solution used
(15 µL for CD36 receptor; 10 µL for Fas receptor) were the optimal volumes as determined by saturation
60
experiments. Cells were then washed with ice-cold stain buffer, centrifuged twice at 500×g and re-suspended
in 200 µL stain buffer prior to single-cell analysis via flow cytometry to quantify the number of receptors per
cell.
Flow cytometry was performed on a MACSQuant flow cytometer (Miltenyi), and FlowJo (BD
Biosciences) software was used to analyze the data. To identify dead cells, 5 µg/mL Sytox Blue (Thermofisher)
was added to all samples, and tubes were vortexed immediately prior to placement in the flow cytometer. Cells
exhibiting very low Sytox Blue fluorescence were identified as live cells, and gating was performed to collect
10,000 live cells for each sample. Finally, the gated cells were examined in a plot of forward scatter area (FSC-
A) versus side scatter area (SSC-A) to identify the single-cell population.
To determine the number of receptors per cell, the fluorescence of Quantibrite PE beads (BD
Biosciences) was measured. We measured the fluorescence for beads with different numbers of binding sites
(as specified by the manufacturer). We applied linear regression to the fluorescence measurements, constructing
a calibration curve to convert the geometric mean of PE fluorescence to the number of bound molecules. The
average number of receptors on a cell in the population was then calculated using the linear regression and the
cell fluorescence data. For each experiment, two biological replicates were used, and the experiments were
repeated for 3-4 times. We report the mean and standard error of the mean of the measurements of all samples:
CD36 = 24,372±2,365 receptors/cell and Fas = 7,860±395 receptors/cell. The receptor distributions of
representative samples of each receptor are shown in Figure 3-4.
3.3.4. Parameter estimation
The estimation of the kinetic parameters was achieved using the “lsqnonlin” function in MATLAB, as
done in our previous work [107], [116], [191]. This algorithm solves the nonlinear least squares problem using
the trust-region-reflective optimization algorithm, minimizing the weighted sum of the squared residuals
(WSSR). The minimization is subject to the upper and lower bounds of the free parameters. One hundred runs
were performed in each fitting step, and a global sensitivity analysis was performed with the best fit parameter
values (the parameters that produce the lowest WSSR). The step-wise iteration was repeated four times to
61
ensure fine-tuning of the parameter values. Parameter values used in the implemented model are from the best
fit (lowest WSSR) from the last step.
Figure 3-4. Receptor number distributions of CD36 and Fas. Histogram showing distributions of CD36 receptor
(blue) and Fas receptor (red) on HMVECs. Two representative samples of each receptor quantification measurement are
shown (a total of 12,286 cells for CD36 and 11,013 cells for Fas). Grey: unstained control (3,840 cells).
3.3.5. Definition of apoptotic cells
Cleaved poly(ADP-ribose) polymerase (cPARP) is the output of the model used as an indicator of
apoptosis, since loss of intact PARP results in failure to repair DNA damage. Our model simulations show that
the dynamics of cPARP follows a switch-like action; however, the range of cPARP varies widely depending on
the initial concentration of PARP. Previous study [192] has shown that low doxorubicin (DXR) dosage with
10 nM TSP1 stimulation resulted in approximately 50% of the cells becoming apoptotic in 24 hours. Therefore,
we simulated this treatment condition using the population-based model, and determined the cPARP
concentration that results in 50% cell apoptosis. We then use this concentration, 1.05 nM, as the defined
threshold that needs to be reached for cell apoptosis to occur. Thus, the definition of which cells are apoptotic
is based on literature evidence.
3.3.6. Simulated perturbations to TSP1-mediated apoptosis.
We apply the model to simulate seven specific perturbations to the intracellular signaling network, to
find strategies that enhance apoptosis signaling. Below, we list the motivation and literature evidence for each
100 1000 10000 100000
0
0.5
1
1.5
2
2.5
3
3.5
Number of Receptors per HMVEC
% HMVECs
control
CD36
Fas
62
of the seven perturbations. We also describe how the perturbation was simulated in our mathematical model.
The abbreviations listed in parentheses are also used in the results figures. Generally, perturbations are
simulated in the ODE model by adjusting the baseline initial conditions and parameter values.
1. XIAP downregulation (“XIAP”): Experimental studies show that downregulation of X-linked inhibitor
of apoptosis protein (XIAP) can promote the apoptotic signaling [193]–[196]. We simulated this effect
by reducing XIAP concentration to 0.5-fold of the baseline value.
2. Low dosage doxorubicin treatment (“DXR”): Experimental studies [192], [197] have shown that a low
dose of doxorubicin upregulates the expression of Fas receptor and other protein species. We
simulated this effect by increasing the initial Fas receptor level by 3-fold and K syn_all by 10-fold.
3. Phophatase inhibition (“Ptase”): Studies have shown that inhibiting MAPK phosphatase (MKP)
activity can promote apoptosis signaling [198], [199]. We simulated this effect by decreasing the
association rate (K on_dephos) of the phosphatase with phosphorylated p38MAPK (pp38) and the
dephosphorylation rate (K dephos) by 10-fold.
4. Kinase promotor (“Kp”): Literature evidence suggests that the tumor microenvironment likely
upregulates many kinase’s activity in the tumor-related endothelial cells [200]–[202]. We simulated the
kinase promoter by increasing the phosphorylation rates of p59fyn, p38MAPK, and IkB by 10-fold.
5. Procaspase-3 upregulation (“pro3”): Global sensitivity analysis (Figure 3-2D) and baseline model
simulations indicate that upregulation of procaspase-3 increases the cPARP level upon TSP1
stimulation. Therefore, we investigate the effect of procaspase-3 upregulation by increasing
procaspase-3 concentration by 3-fold.
6. Fas upregulation (“Fas”): Experimental investigation by Quesada et al. suggests that upregulation of
the receptor Fas promotes TSP1-induced apoptosis [192]. We simulated the effect of Fas upregulation
by increasing Fas concentration by 3-fold.
7. Translocation rate increase (“Ktrsp”): Based on the structure of the signaling network, we hypothesized
that increasing the cytoplasm-to-nucleus transport would enhance apoptosis. We simulated the effect
of faster cytosol-to-nucleus translocation by increasing the translocation rate (K trsp) by 10-fold.
63
3.3.7. Analysis of sensitivity and specificity of a cPARP-based classifier
Here, we consider binary classification of the cells’ response to TSP1 stimulation based on cPARP
levels at 24 hours: apoptotic or non-apoptotic. We aim to classify the cells as apoptotic or non-apoptotic using
certain model variables as predictors (i.e., the initial species’ concentrations). The goal is to determine whether
the initial amounts of one or more species are accurate predictors of what the response to TSP1 stimulation
would be. That is, whether the cell will become apoptotic or not. We construct the ROC curve to determine
which model variables are accurate predictors. Here, the “actual response” is the classification of a cell as
apoptotic or non-apoptotic based on its cPARP level predicted by the mechanistic model of TSP1-mediated
apoptosis signaling presented above.
For a binary classification system such as this, there are four possible predicted outcomes for a given
cPARP cutoff value: true positive, a cell predicted to be apoptotic is actually apoptotic; false positive, a cell predicted
to be apoptotic is actually non-apoptotic; true negative, the predicted and actual response are both non-apoptotic;
false negative, a cell predicted to be non-apoptotic is actually apoptotic. This analysis determines the fraction of
positives predicted correctly (sensitivity or the true positive rate) and the fraction of true negatives predicted
(specificity or the true negative rate) for different cutoff values of cPARP.
To evaluate tradeoffs between sensitivity and specificity, we constructed a receiver operator
characteristic (ROC) curve for cPARP. The ROC curve plots the true positive rate versus the false positive rate
(1-specificity). An ideal input maximizes true positives, with minimal false positives (i.e., the (0,1) point on the
ROC graph). An ROC curve that lies on the 45-degree angle line indicates that the input does not classify the
output any better than a random guess, where the area under the ROC curve (AUC) is 0.5. Thus, having an
AUC value significantly greater than 0.5 indicates that the input can be used to classify the data. We performed
the ROC analysis using the custom “roc” function in MATLAB.
64
3.4. Results
3.4.1. Model training and validation.
We constructed a model of the signaling network of TSP1-mediated apoptosis in endothelial cells
based on literature evidence. TSP1 binds to CD36, activating caspase-3, the core executioner protease. Caspase-
3 promotes apoptosis by cleaving PARP in endothelial cells. Activation of caspase-3 also mediates intracellular
signaling leading to the production of FasL, a death ligand that binds to its receptor Fas on endothelial cells
and further promotes apoptosis through activation of caspase-3 [48], [56], [57]. The signaling network,
illustrated in Figure 3-1, includes several important feedback loops involved in TSP1-mediated apoptosis,
including the caspase cascade (caspase-3 activates its activator, caspase-8) and Fas signaling (TSP-1 promotes
the production of Fas, which also activates caspase-3). We implemented the signaling network mathematically
to generate an ODE model, assuming that the reactions follow mass-action or Michaelis-Menten kinetics rate
laws.
The model was trained using quantitative experimental data and validated with an independent set of
measurements. We extracted experimental data from the literature in order to calibrate the model and estimate
the kinetic parameters. Specifically, the fold-changes in the caspase-3 activity and the levels of three intracellular
species (TSP1:CD36:p59fyn, pp59fyn, and p38MAPK) upon TSP1 stimulation were quantified from Western
blot data and used to train the ODE model.
We used a step-wise strategy comprised of global sensitivity analysis and parameter estimation to ensure
that the model could match the training data (see Methods). As a result of this approach, we obtained 12 sets
of parameters that enable the model to closely reproduce the training data (Table 3-2, Figure 3-5A-E).
65
Table 3-2. CD36 model estimated parameter values.
Set ktrsp kinter Vmax_fasl Km kexp_fasl
koff_casp3_mek
k1
kp_p38
1 4.38E-02 1.21E-03 7.87E-04 5.15E-04 7.73E-03 4.10E-01 2.60E+02
2 1.13E-01 4.57E-03 6.69E-04 1.63E-04 1.36E-02 1.36E-01 1.73E-01
3 4.34E-02 2.18E-03 7.87E-04 5.15E-04 7.46E-03
1.39E+02
4 3.75E-02 1.56E-05 7.87E-04 5.15E-04 7.67E-03
2.25E+02
5 4.21E-02 2.51E-04 7.87E-04 5.15E-04 7.62E-03
8.82E+01
6 4.40E-02 5.11E-04 7.87E-04 5.15E-04 7.77E-03
1.35E+02
7 3.22E-02 3.13E-04 7.87E-04 5.15E-04 6.62E-03
2.38E+04
8 6.67E-02 1.19E-03 9.98E-04 5.15E-04 4.89E-03 1.88E+01 9.12E-01
9 4.58E-02 7.00E-05 2.41E-02 5.15E-04 9.74E-05 2.29E+01 4.53E+02
10 5.26E-02 5.53E-06 4.56E-03 5.15E-04 5.36E-04 4.59E-02 3.68E+02
11 3.12E-02 1.26E-03 9.73E-04 5.15E-04 4.39E-03 1.08E-02 7.50E+03
12 4.10E-02 4.67E-06 7.90E-04 5.15E-04 8.31E-03 1.72E+01 1.31E+02
Mean 4.94E-02 9.65E-04 4.70E-03 3.39E-04 6.39E-03 8.49E+00 2.76E+03
Standard
deviation
2.20E-02 1.33E-03 8.68E-03 2.49E-04 3.62E-03 1.05E+01 6.96E+03
Figure 3-5. CD36 Model training and validation. The ODE model was trained to match experimental measurements
of activated species in the TSP1-mediated apoptosis signaling pathway. A) TSP1:CD36:p59fyn [12]; B) pp59fyn [12]; C)
pp38MAPK [12]; D) caspase-3 activity [12]; and E) caspase-3 activity [15]. F) An independent set of data for caspase-3
activity under the condition of p38MAPK inhibition [12] was used to validate the model prediction. Solid line: mean of 12
best fits. Shaded area: 95% confidence interval. Squares: experimental data.
Fold-change
Fold-change
Time (min)
Time (min)
D E
Time (min)
caspase-3 activity
(Jimenez 2000)
caspase-3 activity
(Nor 2000)
Fold-change
Time (min)
F
caspase-3 (p38i)
Time (min)
Fold-change
B pp59
Fold-change
Time (min)
C pp38
0 20 40 60
0
0.2
0.4
0.6
0.8
1
1.2
Time (min)
Fold-change
A TSP1:CD36:p59
66
After fitting the model to the experimental data, we used a separate set of measurements to validate
the model predictions. Here, we applied the trained model to predict the dynamics of caspase-3 activity when
p38MAPK is inhibited, mimicking an experimental study from Jimenez et al. [48]. This inhibitory effect on
p38MAPK is simulated by setting the phosphorylation rate of NF-kB by active p38MAPK (pp38MAPK) to be
zero. The 95% confidence interval of the model predictions produced with all 12 sets of parameters shown in
Figure 2F is not visible. This indicates that the parameter sets produce similar dynamics of caspase-3 activity
with p38MAPK inhibition. The model qualitatively matches this independent set of data (Figure 3-5F), where
caspase-3 activity is reduced at 300 minutes, compared to the case without p38 MAPK inhibition (Figure 3-
5D). Overall, the model fitting and validation produces a trained model that generates reliable predictions
related to the dynamics of TSP1 simulation. Results from a representative set of parameter values are shown in
Supplemental Figure S6, where the baseline model is simulated to produce the dynamics of all 53 species upon
24-hour simulation with 10 nM TSP1. Notably, TSP1 decays rapidly, and cPARP has a sigmoidal shape.
A global sensitivity analysis was performed to reveal the robustness of the trained model. The
sensitivity of all 53 species in the model with respect to changes in the parameter values (Figure 3-3A-C) and
species with non-zero initial concentrations (Figure 3-3D) was computed. These results show that the model
output, cPARP, is largely influenced by the concentrations of its immediate effectors (procaspase-3, XIAP, and
PARP), as well as critical parameters identified and estimated during model training. Upstream or intermediate
species, such as those involved in p38 signaling and FasL signaling (Figure 3-3D, middle and bottom panels),
are sensitive to changes in a variety of initial concentrations and parameters values.
3.4.2. Altering the concentrations of intracellular signaling species influences the apoptotic
response
We first applied the trained and validated model to investigate the effects of varying the concentrations
of cell surface receptors and intracellular signaling species, in combination with different TSP1 stimulation
levels. In this study, we specifically focus on predicting the concentration of cleaved PARP (cPARP) as an
indicator of cell apoptosis. Caspase-3 promotes apoptosis by cleaving PARP, and cleavage of PARP by caspases
67
is considered a hallmark of apoptosis [203]. Sensitivity analysis revealed that the concentrations of procaspase-
3, XIAP, and PARP most significantly influence the cPARP level throughout the simulated time course (Figure
3-3D). This analysis suggests that varying the concentrations of those intracellular species can impact TSP1-
mediated apoptosis signaling. Since the receptor concentration influences the initial dynamics of TSP1
stimulation, we also hypothesized that increasing the receptor’s availability (i.e., increasing the receptor:ligand
ratio) can amplify the signaling induced by ligand-receptor binding. Therefore, we ran the model and
individually altered the expression level (initial conditions) of the CD36 or Fas receptors, or intracellular species
procaspase-3, XIAP, and PARP, by 10-fold above and below the baseline values. We applied this relatively
large alteration in the protein expression levels to explore the extent of changes in the model output. The initial
conditions were varied for each of the 12 fitted parameter sets, and we compared the cPARP level at various
time points for each case.
Across the simulated time points, there is a dose-dependent response to TSP1, where increasing the
concentration of TSP1 increases the predicted cPARP concentration. Interestingly, altering the expression
levels of the CD36 or Fas receptors does not affect the cPARP level, compared to the baseline model (Figure
3-6A-B). This result holds true for all TSP1 concentrations investigated, and is in accordance with the findings
from the global sensitivity analysis, which identified CD36 and Fas as non-influential to the cPARP level
(Figure 3-3D).
In contrast, varying the initial concentrations of the influential species led to significant changes in
cPARP levels. Increasing the amount of procaspase-3, the unprocessed form of caspase-3, by 10-fold leads to
increased cPARP level at every simulated time point, as compared to the baseline model (Figure 3-6C, right
panel). Downregulation of procaspase-3 to 0.1-fold of the baseline value slightly decreased cPARP level at
intermediate time points (6 to 12 hours), but did not affect the cPARP level at 24 hours, compared to the
baseline model.
Regulation of the caspase-3 inhibitor XIAP reduces apoptosis signaling. That is, increasing the level of
XIAP by 10-fold dramatically decreased cPARP concentration to less than 20% of the baseline level, as shown
in the right panel of Figure 3-6D. However, decreasing XIAP by 0.1-fold results in a larger and faster increase
68
in cPARP level compared to the baseline model (Figure 3-6D, left panel). For example, after 24 hours, the
decreased XIAP resulted in 41% and 34% more cPARP than the baseline level, with 0.1 nM and 100 nM TSP1,
respectively.
Lastly, the model predicts that increasing PARP levels significantly influences cPARP levels (Figure
3-6E). When PARP is increased by 10-fold, the cPARP level at all time points is approximately nine times
higher than the amount produced in the baseline model. In summary, the apoptotic response stimulated by
TSP1 is sensitive to varying the concentrations of certain intracellular species.
69
Figure 3-6. Dose-dependent response of apoptosis signaling with varied initial concentrations. Initial
concentrations of A) CD36, B) Fas, C) procaspase-3, D) XIAP, and E) PARP were varied 10-fold above (right column)
and below (left column) the baseline values (center column). The model was used to simulate cPARP level in response to
four different TSP1 concentrations: 0.1, 1, 10, and 100 nM. The predicted cPARP level at 24 hours was generated using
the 12 best sets of parameter values for each condition. The mean cPARP concentration is plotted; error bars show the
standard deviation.
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
cPARP (µM)
0.1-fold
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
cPARP (µM)
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
cPARP (µM)
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
1.5
cPARP (µM)
1 2 4 6 12 24
0
2
4
6
8
10
Time (hr)
cPARP (µM)
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
Baseline
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
1.5
1 2 4 6 12 24
0
2
4
6
8
10
Time (hr)
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
10-fold
TSP1 0.1nM
TSP1 1nM
TSP1 10nM
TSP1 100nM
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
1 2 4 6 12 24
0.0
0.3
0.6
0.9
1.2
1.5
1 2 4 6 12 24
0
2
4
6
8
10
Time (hr)
A
B
C
D
E
Varying
CD36
Varying
Fas
Varying
pro3
Varying
XIAP
Varying
PARP
70
3.4.3. Perturbing the signaling pathway influences the population response to TSP1 stimulation
Next, we implemented perturbations in the model and predicted the response of individual cells in a
population. We accounted for heterogeneity in the cell population by varying the initial concentrations of
protein species. Cellular heterogeneity is observed for multiple dimensions of single cell measurements, and
detailed molecular differences can be used to distinguish cell-to-cell variation [204]. In this population-based
model, the initial concentrations of all starting species are drawn from a gamma distribution [188], [205] (see
Methods for details). Here, we focus on extrinsic noise (i.e., variability in the protein levels), as opposed to
intrinsic variations (fluctuations in the rates of the biochemical reactions), since several studies have
demonstrated that the experimentally-observed cell-to-cell heterogeneity is largely due to extrinsic rather than
intrinsic noise [188], [206]–[209]. We perform the simulations with the baseline model and the parameter set
that best fit the data out of the 12 parameter sets obtained from model training. We then ran the model 2,000
times, representing 2,000 independent cells, and analyzed the population-level response to TSP1 stimulation.
We simulate the response to seven conditions (as described in the Methods) at two TSP1 concentrations (0.1
and 10 nM). Particularly, we investigated whether the predicted results from solving the deterministic model
with the fixed initial conditions (Figure 3-6) hold true when accounting for heterogeneity at the population
level.
We characterized the population-level response based on the cells’ cPARP concentration. We extracted
predicted intracellular cPARP concentrations for the 2,000 cells at distinct time points up to 24 hours of TSP1
stimulation, and generated histograms. This provides a direct visualization of the distribution of cPARP levels
in the cell population. Based on literature data, we defined the threshold of intracellular cPARP required for
apoptosis to occur within each cell to be 1.05 µM (see Methods). We used the model to predict the percentage
of apoptotic cells, based on the predicted cPARP concentrations. Cells that have high cPARP level (greater
than 1.05 µM) are classified as apoptotic, since their cPARP level exceeds the threshold value. Cells whose
intracellular cPARP concentration is below the threshold value are classified as non-apoptotic. We also analyzed
when cells that have high cPARP level appear at the simulated time points.
71
In the baseline model, the apoptotic response initiates within six hours after 10 nM TSP1 stimulation
(Figure 3-7A). The size of the cPARP-positive population increases throughout the 24-hour stimulation. By
24 hours, the apoptotic cells make up 41% of the total population (Figure 3-7E). Below, we compare the
population-level response for the baseline model to the response when particular species in the intracellular
signaling network are perturbed.
Figure 3-7. Distribution of cPARP concentration in population-level model. (A)-(D): Histogram showing the
percentage of the 2,000 cells with a given cPARP concentration, in response to 10 nM TSP1 stimulation. A) Baseline
model; B) XIAP downregulation; C) DXR treatment; and D) Increased nuclear translocation rate. A different color is
assigned to each time point. The cPARP threshold is marked by a solid line and the region in the x-y plane beyond the
threshold is shaded as light purple. (E)-(H): The predicted percentage of non-apoptotic (black) and apoptotic (purple) cells
in response to 10 nM TSP1 stimulation. E) Baseline model; F) XIAP downregulation; G) DXR treatment; and H) Increased
nuclear translocation rate.
According to the model with fixed initial conditions, downregulation of XIAP strongly promotes
apoptotic signaling (Figure 3-6D, left panel). To explore whether this conclusion still holds with a
heterogeneous cell population, we decreased XIAP expression level by 0.5-fold, a physiologically reasonable
change to the protein expression, and simulate the population-based response to 10 nM TSP1 stimulation under
this condition. The results show that with XIAP downregulation, cells with high cPARP level appear at four
hours (Figure 3-7B,F). By 24 hours, 57% of the cell population is apoptotic. Additionally, the apoptotic
population exceeds the non-apoptotic population by 0.4-fold (Figure 3-7F).
1.2
24 0
0
2
16
4
12
0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12
0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12
0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12
0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
% Cells % Cells
Time (hours)
Time (hours)
Time (hours)
Time (hours)
cPARP ( M)
cPARP ( M)
cPARP ( M)
cPARP ( M)
Time (hours) Time (hours) Time (hours) Time (hours)
2 4 6 8 10 12 16 24 0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
baseline XIAP DXR Ktrsp
A B C D
E F G H
72
We also considered the effect of doxorubicin (DXR) on the apoptosis signaling network. A published
experimental study suggest that a low dosage of DXR sensitizes cells to pro-apoptotic signaling [192].
Specifically, Quesada and coworkers observed that Fas receptor expression increases approximately 3-fold
following DXR treatment. Thus, we simulated the effect of such a DXR treatment by increasing Fas expression
by 3-fold. Additionally, we increased the synthesis rates of certain intracellular species, as DXR has been shown
to increase protein expression [197]. Here, we increased K syn_all by 10-fold. Under this simulated DXR treatment
condition, cells with high cPARP level appear within two hours, a faster apoptotic response than in the baseline
model or with XIAP downregulation (Figure 3-7C). However, the population of cells with high cPARP is
52%, which is not as large as what is predicted with XIAP downregulation (57%). Additionally, with DXR
treatment, the progressive increase in the percentage of apoptotic cells through 24 hours is more gradual than
with XIAP downregulation (Figure 3-7F, G). By 24 hours, 52% of the cells are apoptotic, and there are 0.2-
fold more apoptotic cells than non-apoptotic cells.
Upon examining structure of the signaling network, we hypothesized that increasing the translocation
rate of phosphorylated p38MAPK (pp38) and NF-kB into the nucleus can promote apoptotic signaling.
Therefore, we simulated the model with K trsp increased by 10-fold. The apoptotic response is slower and smaller
in scale than in the baseline model (Figure 3-7D). Additionally, the positive population does not appear until
10 hours after starting TSP1 stimulation, and by 24 hours, less than 30% of the cells are apoptotic (Figure 3-
7H).
We also simulated the population response with procaspase-3 upregulation, increased Fas expression,
phosphatase inhibition, and kinase-activity upregulation. The results are shown in Figure 3-8. These
perturbations to the signaling network do not dramatically affect the population response. That is, the speed
and magnitude of the response in each case are similar to the baseline model (Figure 3-7, panels A and E).
Apoptotic cells begin to appear by six hours, and after 24 hours of TSP1 stimulation, at least 40% of the cells
are apoptotic (Figure 3-8). Additionally, we predicted the population-based response for the baseline model
and the seven network perturbations when the cells are stimulated with 0.1 nM TSP1. These results are shown
73
in Supplemental Figure 3-9. Next, we present our detailed analysis of the predicted results for the two TSP1
stimulation levels and compare the apoptotic response.
Figure 3-8. Population-level response to TSP1 stimulation. (A)-(D): Histogram showing the percentage of the 2,000
cells with a given cPARP concentration, in response to 10 nM TSP1 stimulation with A) procaspase-3 overexpression; B)
Fas overexpression; C) phosphatase inhibition; and D) increasing kinase activity. A different color is assigned to each time
point, and shading on the x-y plane indicates the threshold cPARP concentration for classifying cells as apoptotic (1.05
nM). (E)-(H): The predicted percentage of non-apoptotic (black) and apoptotic (purple) cells in response to 10 nM TSP1
stimulation with E) procaspase-3 overexpression; F) Fas overexpression; G) phosphatase inhibition; and H) increasing
kinase activity.
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
A B C D
% Cells
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
Time (hours) Time (hours) Time (hours) Time (hours)
% Cells
E F G H
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
pro3 Fas Ptase Kp
74
Figure 3-9. Population-level response to 0.1 nM TSP1 stimulation. (A)-(D): Histogram showing the percentage of
the 2,000 cells in response to 0.1 nM TSP1 stimulation. A) Baseline model; B) XIAP downregulation; C) DXR treatment;
and D) Increased nuclear translocation rate. A different color is assigned to each time point. (E)-(H): The predicted
percentage of non-apoptotic (black) and apoptotic (orange) cells in response to 0.1 nM TSP1 stimulation. E) Baseline
model; F) XIAP downregulation; G) DXR treatment; and H) Increased nuclear translocation rate. (I)-(L): Histogram
showing the percentage of the 2,000 cells in response to 0.1 nM TSP1 stimulation with I) procaspase-3 overexpression; J)
Fas overexpression; K) phosphatase inhibition; and L) increasing kinase activity. (M)-(P): The predicted percentage of
non-apoptotic (black) and apoptotic (orange) cells in response to 0.1 nM TSP1 stimulation with M) procaspase-3
overexpression; N) Fas overexpression; O) phosphatase inhibition; and P) increasing kinase activity. In (A)-(D) and (I)-
(L), shading on the x-y plane indicates the threshold cPARP concentration for classifying cells as apoptotic (1.05 nM).
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
1.2
24 0
0
2
16
4
12 0.2
6
10
0.4
8
8
10
0.6 6
12
14
0.8 4
16
2 1
18
1
20
0
% Cells
A B C D
% Cells
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
Time (hours) Time (hours) Time (hours) Time (hours)
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
% Cells % Cells
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
Time (hours)
cPARP (µM)
Time (hours) Time (hours) Time (hours) Time (hours)
E F G H
I J K L
M N O P
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100 non-apoptotic
apoptotic
pro3 Fas Ptase Kp
baseline XIAP DXR Ktrsp
75
3.4.4. Strategies to enhance apoptotic response have differential effects on the magnitude and time
scale of TSP1-mediated signaling
We applied the model to distinguish the effects of possible strategies to promote TSP1-induced
apoptosis under different levels of TSP1 stimulation. Here, we compared three quantities: the percentage of
cells that have reached the cPARP threshold by 24 hours, the maximum cPARP level reached in each cell, and
the time to reach the threshold cPARP concentration (T t) within the 24-hour simulation time. Combined with
the results shown in Figure 3-10, these quantities provide insight into TSP1-mediated apoptosis signaling.
Below, we compare the results to the baseline case.
Figure 3-10. Predicted population-based response to TSP1 stimulation. Comparison of three quantities that
characterize the population-level response: A) the percentage of cells that have reached the cPARP threshold by 24 hours,
B) the maximum cPARP level reached in each cell, and C) the time to reach threshold (T t). Asterisks in panels (B) and (C)
indicates the p-value from ANOVA: ****, p<0.0001; ***, p<0.001; **, p<0.01; *, p<0.1; ns, not significant.
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
0
20
40
60
% apoptotic cells
0.1 nM
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
0
500
1000
1500
Tt (min)
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
Tt
max cPARP
baseline
XIAP
Ptase
DXR
pro3
Kp
Fas
Ktrsp
0
20
40
60
10 nM
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
0
1
2
3
4
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
0
500
1000
1500
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
-4
Tt
max cPARP
-3
-2
-1
log
10
(p-value)
(*)
(**)
(***)
(****)
baseline
XIAP
Ptase
DXR
Kp
pro3
Fas
Ktrsp
0
1
2
3
4
Max cPARP (µM)
A
B
C
D
****
ns ns ns
**** *** ** **** **
ns ns
**** **** ****
**** ****
ns
* **** **** **** **** **
ns ns
**** **** ****
76
In the baseline model, 0.1 nM TSP1 stimulation leads to 37% of the cells being apoptotic at 24 hours.
The model predicts that 49% more cells are apoptotic with XIAP downregulation than the baseline (Figure 3-
10A, left panel). Additionally, phosphatase inhibition and DXR treatment increased the apoptotic population
by 14% and 9%, respectively, compared to the baseline model. Upregulation of procaspase-3 or kinase activity
both increase the apoptotic population by approximately 7%. Increasing Fas expression did not have an effect
on the percentage of apoptotic cells, while increasing the translocation rate decreased the apoptotic cells by
27%.
With 0.1 nM TSP1 stimulation, the median values for the maximum cPARP attained under each
simulated condition follow the same order of effectiveness as observed with the percentage of apoptotic cells
(Figure 3-10B, left panel). Additionally, we performed statistical analyses to compare the maximum cPARP
between the baseline model and each perturbation (Figure 3-10B, left panel, asterisks above each column).
The maximum cPARP reached is highly significantly different from the baseline model when XIAP is
downregulated (the maximum cPARP is higher; p<0.0001) or when the translocation rate is increased (cPARP
decreases; p<0.0001). Notably, the effects of altering XIAP or the nuclear translocation rate are more
significantly different from the baseline than all of the other strategies.
Interestingly, the effectiveness of the approaches on time to reach threshold does not follow the same
order as that of the percentage of apoptotic cells or of maximum cPARP (Figure 3-10C, left panel). Based on
our statistical analysis, compared to the baseline level, the time to reach threshold is significantly shorter (with
high significance level) with XIAP downregulation, phosphatase inhibition, DXR treatment or procaspase-3
over-expression (Figure 3-10C, left panel, asterisks above each column). In contrast, the time to reach
threshold is significantly longer when the translocation rate is increased by 10-fold.
With 10 nM TSP1 stimulation, XIAP downregulation leads to 40% more apoptotic cells than the
baseline model (Figure 3-10A, right panel). Phosphatase inhibition and DXR treatment also lead to a strong
response, with 17% and 27% more apoptotic cells, respectively. Increasing procaspase-3 or kinase activity both
increased the relative size of the apoptotic population by approximately 10%, compared to the baseline.
77
XIAP downregulation, phosphatase inhibition, DXR treatment, and increase of procaspase-3
expression significantly increased the maximum cPARP level and shortened the time to reach threshold (Figure
3-10B-C, right panels). Increasing the translocation rate significantly decreased the maximum cPARP reached,
and prolonged the time to reach threshold.
In summary, these results show that XIAP downregulation is more effective than the other approaches
in both increasing the maximum cPARP level attained in the cell population and shortening the time to reach
the cPARP threshold. This holds true when cells are stimulated with either 0.1 nM or 10 nM TSP1. Increasing
the level of TSP1 stimulation to 10 nM makes all of the pro-apoptotic strategies more effective. However, it is
interesting to note that the ordering of the strategies from most effective to least effective changes with the
level of TSP1 stimulation.
3.4.5. Initial protein expression levels influence apoptosis response
In order to explore the cause for the different responses to the apoptosis signaling within the
population of 2,000 cells, we compared the initial conditions of the apoptotic cells and non-apoptotic cells at
24 hours. Statistical analysis of the distributions of the initial protein concentrations (normalized to their
baseline values) indicate that XIAP concentration in the apoptotic population is significantly lower than in the
non-apoptotic population (p<0.0001), while PARP concentration is significantly higher in the apoptotic
population (p<0.0001) (Table 3-3). In fact, the relationship between the apoptotic response and the XIAP and
PARP initial conditions is easily visualized (Figure 3-11). This illustrates that apoptotic cells (Figure 3-11A,
purple markers) have higher PARP and lower XIAP than non-apoptotic cells (Figure 3-11A, black markers).
The NF-kB concentration in the cytosolic compartment is also significantly lower in the apoptotic population
compared to apoptotic cells (p=0.04). Thus, statistical analysis shows that the initial concentrations of certain
species distinguish apoptotic from non-apoptotic cells. Moreover, the distribution of the initial concentrations
of XIAP and PARP are significantly different for apoptotic versus non-apoptotic cells (Figure 3-11B,C; Table
3-3).
78
Figure 3-11. Relationship between initial conditions and predicted apoptotic response. A) Initial concentrations of
PARP and XIAP for apoptotic cells (purple) and non-apoptotic cells (grey). The difference between the initial amounts of
PARP and XIAP is larger for apoptotic cells, which reach higher cPARP levels. B) Histogram showing distribution of
initial XIAP concentration for apoptotic cells (purple) and non-apoptotic cells (grey). The apoptotic cells have relatively
lower initial XIAP concentrations. C) Histogram showing distribution of initial PARP concentrations for apoptotic cells
(purple) and non-apoptotic cells (grey). The apoptotic cells have higher initial PARP concentrations.
Table 3-3. Comparison of XIAP and PARP levels between non-apoptotic and apoptotic populations.
0.01
0.1
1
10
Concentration (µM)
Non-apop Apoptotic Non-apop Apoptotic
XIAP PARP
0.0 0.2 0.4 0.6
0
50
100
150
Initial XIAP [µM]
Number of cells
0 2 4 6
0
50
100
150
200
Initial PARP [µM]
Number of cells
Non-apoptotic
Apoptotic
A B C
Unpaired t test with Welch's
correction (non-parametric)
XIAP concentration in non-
apoptotic cells vs. apoptotic cells
PARP concentration in non-
apoptotic cells vs. apoptotic cells
P value <0.0001 <0.0001
P value summary **** ****
Significantly different (P < 0.05)? Yes Yes
One- or two-tailed P value? Two-tailed Two-tailed
Welch-corrected t, df t=12.33 df=1871 t=45.96 df=1311
How big is the difference?
Mean ± SEM of column A 0.1472 ± 0.002221, n=795 1.261 ± 0.01174, n=1205
Mean ± SEM of column B 0.185 ± 0.002113, n=1205 2.344 ± 0.02043, n=795
Difference between means 0.03781 ± 0.003066 1.083 ± 0.02356
95% confidence interval 0.0318 to 0.04382 1.037 to 1.129
R squared (eta squared) 0.07518 0.6171
F test to compare variances
F, DFn, Dfd 1.372, 1204, 794 1.998, 794, 1204
P value <0.0001 <0.0001
P value summary **** ****
Significantly different (P < 0.05)? Yes Yes
79
Building on the results from the statistical analysis of the initial concentrations, we investigated whether
the initial concentrations can be used to classify cells as apoptotic or non-apoptotic upon 24 hours of TSP1
stimulation. Here, we generated a receiver operator characteristic (ROC) curve. The ROC curve illustrates the
ability of an input descriptor to classify a response with high sensitivity and specificity (see Methods). For
inputs, we used the initial concentration of each species that does not start at zero (16 species), the ratios of
XIAP and PARP concentrations ([XIAP]/[PARP] and [PARP]/[XIAP]), and the absolute value of the
difference between the concentrations of PARP and XIAP] (i.e., |[PARP]-[XIAP]|). Thus, we considered 19
total inputs that may possibly predict the response to TSP1-mediated apoptosis. We use the area under the
ROC curve (AUC) to compare the ability of the inputs to predict the response to TSP1.
Constructing the ROC curve for the 19 inputs shows that the absolute difference between the initial
concentrations of XIAP and PARP predicts which cells will be apoptotic. Specifically, the difference between
XIAP and PARP can classify the cells with high sensitivity and specificity (Figure 3-12). In this case, the AUC
is 0.97, with a 95% confidence interval of [0.96 – 0.98], providing a quantitative measure of the predictive ability
of the difference between the XIAP and PARP concentrations. This AUC is significantly different than 0.5
(p<0.0001), which indicates that using the difference between the concentrations of XIAP and PARP is more
predictive than classifying cells as apoptotic or not based purely on chance. The AUC values for classifying the
apoptotic response using the initial concentration of XIAP or PARP alone are 0.65 and 0.95, respectively, and
in both cases, the AUC values are significantly different from 0.5 (p<0.0001). Thus, although using the
concentration of XIAP or PARP alone is better than randomly guessing which cells will respond, these
concentrations are less reliable predictors when considered individually. The AUC values for the remaining 16
inputs range from 0.48 to 0.54, and are not significantly different than randomly selecting which cells will be
apoptotic. Quantitative results from constructing the ROC curve for all of the inputs are provided in Table 3-
4. Overall, the results of this analysis demonstrate that the initial concentrations of PARP and XIAP, and
especially the difference between their concentrations, can be used to predict which cells will respond to TSP1
signaling.
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Table 3-4. Results from ROC analysis.
Input AUC AUC confidence interval Significance level
initial conditions
CD36 0.501 [0.467 - 0.535] 0.482
p59 0.483 [0.449 - 0.517] 0.898
pro8 0.509 [0.475 - 0.543] 0.247
pro3 0.516 [0.482 - 0.550] 0.109
p38cyt 0.491 [0.457 - 0.525] 0.745
Ptase_cyt 0.506 [0.472 - 0.540] 0.330
XIAP 0.648 [0.615 - 0.681] < 0.0001
PARP 0.955 [0.941 - 0.968] < 0.0001
Fas 0.499 [0.465 - 0.533] 0.541
MEKK1 0.508 [0.474 - 0.542] 0.273
FL 0.499 [0.465 - 0.532] 0.545
FS 0.488 [0.454 - 0.522] 0.820
IKK 0.521 [0.487 - 0.555] 0.060
NFkB_IkB 0.497 [0.463 - 0.531] 0.578
Ptase_nuc 0.511 [0.477 - 0.545] 0.202
NFkB_cyt 0.540 [0.506 - 0.574] 0.001
ratio XIAP/PARP 0.920 [0.902 - 0.938] < 0.0001
ratio PARP/XIAP 0.920 [0.902 - 0.938] < 0.0001
difference |PARP-XIAP| 0.971 [0.961 - 0.982] < 0.0001
Figure 3-12. ROC curves for classifying the apoptotic response. Blue: ROC curve for the difference between the
initial concentration of PARP and XIAP input; AUC is 0.97. Purple: ROC curve for the initial PARP concentration input;
AUC is 0.95. Cyan: ROC curve for the initial XIAP concentration input; AUC is 0.65. All of three AUC values are
significantly different than 0.5 (given by the gray dashed line, p<0.0001), indicating that these inputs are reliable predictors
of the cells’ response to TSP1 stimulation.
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
False positive rate
(1-sensitivity)
True positive rate
(Specificity)
[XIAP]
[PARP]
|[XIAP]-[PARP]|
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3.5. Discussion
We have developed a molecular-detailed model of the TSP1-induced apoptotic signaling. The model
represents the reaction network of interactions involved in the intracellular signaling pathway and includes
multiple feedback loops. Our model captures the feedback from transcriptional regulation by NF-kB onto Fas
signaling, which allows us to expand the dynamics of the network to a longer time scale. Predictions from the
trained model match experimental data. We further validated the model using a separate set of experimental
measurements. We implement the model using ODEs, which can be solved once to simulate the average
response of a population of cells. We also account for randomness in the protein concentrations by solving the
ODEs 2,000 times with varied initial conditions to predict the individual responses of 2,000 cells. In this case,
the cells each have different initial concentrations of the molecular species, representing heterogeneity of the
cell population. This heterogeneity influences the responses to TSP1 treatment and the effectiveness of
strategies aiming to increase apoptosis signaling.
The model provides mechanistic and quantitative explanations of the effects of several approaches to
promote TSP1-mediated apoptosis. Using the model, we proposed and simulated the effects of perturbing the
signaling network, including altering receptor and protein levels, rates of protein synthesis and transport, the
activity of specific phosphatases, and the overall kinase activity within the cells. These simulations exploit the
power of mathematical modeling to generate quantitative predictions that would otherwise be time- and cost-
consuming to explore experimentally. Overall, our model provides quantitative insight into the effects of
targeting particular aspects of the TSP1-mediated apoptosis signaling pathways.
Global sensitivity analyses reveal insight into the robustness of the structure of the signaling network.
We find that the model output cPARP is most significantly influenced by the concentrations of its immediate
effectors, procaspase-3, XIAP, and PARP. Cleaved PARP is insensitive to changes in the initial conditions of
upstream signaling species in the network; however, its effectors are influenced by the upstream signaling
molecules. One such example is procaspase-8. The species cFLIP-L (FL) forms a complex with procaspase-8
involving DISC, and promotes activation of caspase-8 or NFkB. Caspase-8 then cleaves caspase-3, which in
turn cleaves PARP. Therefore, cPARP is indirectly influenced by upstream signaling. However, the multiple
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feedback loops regulating this network appear to attenuate or buffer the effects of the upstream signal on the
end output cPARP.
The model predicts that downregulation of XIAP is a promising strategy to enhance TSP1’s apoptotic
signaling effect, sensitizing cells to low-dosage TSP1 treatment. XIAP is a potent inhibitor of caspase activity
[193]. Experimental studies have shown that specific over-expression of XIAP can rescue cells from apoptosis,
and antisense downregulation of XIAP led to a dramatic decrease in resistance to radiation-induced cell death
[194]–[196], [210]. Our model simulation shows that in TSP1-mediated apoptotic signaling, modulating XIAP
level also has a similar effect. Importantly, the model provides quantitative and mechanistic insight into the
effects of targeting XIAP. Downregulation of XIAP directly leads to an increased level of active caspase-3, a
crucial mediator in the apoptosis signaling network. Our simulation results demonstrated that this approach is
the most effective in promoting endothelial cell apoptosis. The further analysis based on the ROC curve
supports the model simulations showing the importance of XIAP in influencing the dynamics of TSP1-
mediated apoptosis. Interestingly, the ROC curve reveals a relationship between XIAP and PARP that we had
not identified using model simulations alone. The difference between the initial concentrations of those proteins
can accurately predict which cells will undergo apoptosis in response to TSP1 stimulation, even before the cells
are exposed to TSP1. This highlights one potential clinical application of our work, to predict the response to
pro-apoptosis signaling. With our model, it may be possible to determine whether a TSP1-based anti-angiogenic
treatment that targets tumor endothelial cells would be effective. For example, endothelial cells isolated from a
tissue sample obtained from a cancer patient’s tumor biopsy can be analyzed to determine the intracellular
XIAP and PARP levels. Those measurements can be input into the model and used to inform whether the
treatment would be effective. Although validating the model for this purpose is beyond the scope of this study,
our work provides a foundation to pursue such investigation.
In another example, a strategy to increase apoptosis signaling is supported by experimental studies. We
used the model to quantify the effect of inhibiting MAPK phosphatase (MKP) activity. We simulated the effect
of this approach by decreasing the binding affinity between the phosphatase and its substrate, pp38, and the
dephosphorylation rate. Therefore, the active pp38 level remains high as the phosphatase activity is inhibited,
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enabling downstream signaling. The results indicate that this approach can effectively promote the apoptotic
response. Our predictions agree with experimental results that show that modulating MKPs is a viable option
to promote apoptosis mediated by p38MAPK [198], [199].
The model also generates non-intuitive results. The simulations show that increasing the rate of
translocation from the cytosol to the nucleus delayed and attenuated the apoptotic response. This observation
is counterintuitive, as faster translocation of species immediately upstream of FasL production is expected to
accelerate signal transduction. However, the model simulation suggests that with faster translocation, the pool
of caspase-3 and p38MAPK is depleted in upstream signal transduction, before DISC formation occurs (data
not shown). The effect of a pan-kinase activity promoter is another example of non-intuitive predictions. We
simulated the kinase promoter by increasing the phosphorylation rates of p59fyn, p38MAPK, and IkB by 10-
fold. Intriguingly, this approach did not affect either the response time (time to reach apoptosis threshold) or
the percentage of apoptotic cells. The explanation is that increased kinase activity depleted certain species before
their accumulation is achieved, in a similar manner to the faster cytosol-to-nucleus translocation case.
In addition to proposing strategies to increase apoptosis signaling, the model provides mechanistic
insight into experimental observations. At low dosages, doxorubicin treatment has been shown to promote
TSP1-mediated apoptosis. Using our model, we propose the potential mechanism of action of this effect. A
study by Quesada et al. showed that endothelial cell apoptosis was due to a synergistic effect of the upregulation
of FasL induced by TSP1 and upregulation of Fas by doxorubicin [192]. Our model simulations show that
altering Fas receptor expression level alone does not affect the apoptotic response; rather, the availability of
intracellular signaling species significantly influences apoptosis signaling as well. Specifically, the model
simulations show that increasing the synthesis of particular molecular species is required to qualitatively match
the effects of DXR observed experimentally. Based on these modeling results, we hypothesize that the low
dosage doxorubicin treatment not only regulates the protein expression of Fas, but also other species. Our
predictions agree with other experimental studies that show translation of multiple proteins increases when the
cells are exposed to stress [25,30]. Our model simulation demonstrates the effect of a low dosage of doxorubicin
through the proposed mechanism of action, which can be further tested with experiments.
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This work provides a biophysically realistic network that generates reliable predictions of the
population-level responses. We incorporated variability into the ODE model to represent a heterogeneous
population of cells. This implementation provides a framework to test how molecular-targeted strategies
influence individual cells in a population. Solving the ODE model only once for a single set of initial conditions
indicates that upregulation of procaspase-3 greatly increases the magnitude of the apoptotic response, while
procaspase-3 downregulation does not affect cPARP level. This implies that a threshold value of procaspase-3
expression may be needed in order to enhance apoptosis signaling. On the other hand, the population-based
model simulations showed that overexpressing procaspase-3 by 3-fold has only a mild effect of increasing the
apoptotic response. These conflicting results demonstrate the importance of accounting for heterogeneity
within a cell population. Therefore, we emphasize the utility of the population-based model to make
predictions, as the deterministic model that represents the dynamics of an average single cell can be misleading
in certain cases.
To our knowledge, this is the first mechanistic model to investigate TSP1-mediated apoptosis. The
apoptotic signaling in this study is essential to the inhibitory effect of TSP1 [56]. Notably, TSP1 not only induces
apoptosis through the CD36 receptor, but also has many other anti-angiogenic functions, possibly making it
more potent than a single apoptosis inducer for regulation of angiogenesis. The framework established in our
study can be readily adapted and combined with models describing other interactions of TSP1 [104], or pro-
angiogenic signaling networks [22,23] for future modeling studies. The model can also be expanded to include
cell-cell interactions with both exogenous and endogenous FasL signaling. Future work can improve the model
framework in various ways, for example, by adding the downstream function of PARP to address the balance
between survival and apoptotic effects as PARP loses its repair function in its cleavage; specifying initial
concentrations from different cell types; including more detailed reaction mechanisms (such as NF-kB
activation by p38MAPK); or accounting for the mitochondrial feed-forward loop, which provides the link to
the intrinsic apoptotic pathway. Finally, we note that strategies to increase apoptosis of diseased cells may also
impact normal endothelial cells. We can expand the model to study both normal and diseased cells, which may
85
have differential receptor expression levels, as observed for VEGF receptors in normal versus tumor cells [187],
[212]. In this way, we can predict strategies that more specifically target the diseased population of cells.
Our model complements other studies that focus on apoptosis signaling promoted by death ligands
and their receptors [185], [186], [213]. We adapted the model for Fas-mediated apoptotic and NF-kB signaling
established by Neumann et al., which served as a foundation for the FasL signaling cascade in our work. In
other work, Albeck et al. established a model to describe TNF-related apoptosis-inducing ligand (TRAIL)
induced apoptosis in HeLa cells (an ovarian cancer cell line), with a focus on the “variable-delay, snap-action”
switching mechanism of extrinsic apoptosis. Both the Albeck model and our model exhibit the cells’ response
of switching to a high apoptotic response. However, one key difference between our model and theirs is how
the switching arises. In the Albeck model, all-or-none switching of the cell death response is achieved by a
network that does not include feedback. They concluded that this snap-action arises from interplay between
the biochemistry of protein-protein interaction and translocation between the cytosol and mitochondria. We
have simplified this extrinsic apoptosis pathway in our model; however, the snap-action behavior of apoptosis
is still evident, shown by the fast accumulation of cPARP. This switching is a direct result of the reaction
between caspase-3 and PARP, amplified by the feedback loops. Another difference between the two models
is how stochasticity is implemented. The time to reach threshold (T t) in our model is analogous to the delay
time (T d) in Albeck model. Albeck and co-workers impose a distribution in the delay time by randomly selecting
T d from a defined range. In contrast, in our model, cell-to-cell differences in the switching delay emerge solely
based on the variation in intracellular protein concentrations. This is a more realistic framework that represents
an actual population of cells. Thus, our model is a tool to analyze the population-level responses to TSP1
stimulation and perturbations to the signaling network.
3.6. Conclusion
In summary, our model quantitatively describes the TSP1-mediated intracellular signaling via the CD36
receptor, which leads to endothelial cell apoptosis. This model predicts that downregulation of XIAP is the
most promising way to effectively promote TSP1-mediated apoptosis. In addition, we propose an alternative
86
mechanism of action for the effect of low dosage doxorubicin treatment in sensitizing cells to TSP1 stimulation.
This model framework can be ultimately used to generate and optimize TSP1-based therapeutic strategies for
promoting apoptosis.
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Chapter 4
INTEGRATION OF MODELS OF TSP1-MEDIATED INTRACELLULAR SIGNALING
4.1. Introduction
As introduced in Chapter 1, the multi-domain protein TSP1 acts potently to inhibit angiogenic signaling
in endothelial cells through multiple mechanisms. At nanomolar concentrations, it triggers apoptotic signaling
via receptor CD36, while at a picomolar concentration, it associates with CD47 with high affinity to suppress
VEGF-induced eNOS signaling. Both pathways seem to inhibit angiogenesis, but the former signaling response
demands higher concentrations of TSP1, while the latter antagonizes pro-angiogenic signaling with
physiological ranges of TSP1[74]. From a systems biology perspective, it is of great interest to investigate the
influence of each signaling pathway on the cell response. With a calibrated model, we can perform simulations
to predict the cells’ signaling response under various stimulation conditions, which will allow us to better
understand and exploit the functions of TSP1. More importantly, we aim to identify the most efficient target
of angiogenic inhibition, whether it is a receptor or an intracellular component, using an integrated anti-
angiogenic signaling network model.
Furthermore, as numerous studies have demonstrated, the heterogeneity in a population of cells can
largely influence the signaling response to a stimulant ([70], [99], [185] and as reviewed in [214]). Previously, we
have conducted flow cytometry quantification of receptors CD36, CD47, and Fas expressed on human
microvascular endothelial cells (Table 4-1). Here, we utilize this integrated model to investigate the influence
of variation in the levels of these particular receptors on the cell signaling response in the CD36 and CD47
pathways upon TSP1 stimulation. Furthermore, we can investigate the influence of intracellular heterogeneity,
assuming that the protein concentrations vary within certain ranges, as we have demonstrated in Chapter 3 with
the CD36 pathway model.
Table 4-1. Quantification of average receptor numbers on HMVECs.
Receptor Avg. # /cell concentration (nM)
CD47 120,000 199.336
CD36 20,000 33.222
Fas 8,000 13.289
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We have constructed two mechanistic models for TSP1’s anti-angiogenic effects: the TSP1-mediated
apoptotic signaling via receptor CD36, and the TSP1-mediated inhibition of eNOS signaling via receptor CD47.
It is interesting to learn whether TSP1’s multiple functions take effect simultaneously via both receptors to
inhibit angiogenic signaling in endothelial cells, and whether one pathway dominates the other. In order to gain
quantitative understanding of the relative importance of the two intracellular signaling pathways mediated by
TSP1, in this study, we integrate the abovementioned two mechanistic models, and use the integrated model to
predict the endothelial cell population response for a range of ligand stimulation and the influence of cellular
heterogeneity on the population response to treatment.
4.2. Methods
4.2.1. Model integration in BioNetGen
The TSP1-CD36 model described in Chapter 3, which was originally constructed using the Simbiology
toolbox in MATLAB, was first re-written in a rule-based fashion using BioNetGen. This converted CD36
model was then combined with the CD47 model in BioNetGen. TSP1 is allowed to bind to both CD36 and
CD47 simultaneously, as studies have shown that the two receptors associate with the ligand at different binding
sites[92]. For simplicity, TSP1:CD36:CD47 trimer follows the same kinetic rate parameters used for the
TSP1:CD36 complex.
4.2.1. Model parameterization
Due to differences in model implementation for the original CD36 model and CD47 model, the
reaction rules for CD36 model were slightly modified to be consistent with the latter. With the presence of all
relevant receptors (CD36, CD47, R2) in the integrated model, new unknown parameters from the modification
were estimated by fitting the model to the CD36 pathway datasets. We re-estimated parameters that were
previously estimated in the CD36 model that are influential to the species dynamics in the integrated model,
(k i,casp3, factor FasLksyn, V max,FasL, k off,FasFasL), parameters that were added during model integration (k dp,p38,p59), and
parameters that were previously assigned to multiple species to share one rate constant (e.g. internalization rate
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for all receptor TSP1:CD36 and DISC complexes, degradation rate for all species) but now we assign to
complexes formed with each receptor a separate set of internalization rate and degradation rate parameters
(k inter,DISC, k inter,TSP1CD36, k deg,DISC, k deg,TSP1CD36), which need to be estimated. The lsqnonlin parameter optimization
function in MATLAB was used to estimate nine unknown parameter values. All the other parameters were
fixed at their original best fit values from previous studies. The fitting procedure was performed 100 times, and
a total of nine sets of estimated parameters resulted in the lowest fitting errors. The fitting results with these
nine sets of parameters are shown in Figure 4-1A-E. The estimated parameters and the fitness of the model
compared to the CD36 datasets are reported in Table 4-2.
Figure 4-1. Integrated model training and validation using apoptosis pathway datasets. The integrated model was
trained to match experimental measurements of activated species in the TSP1-mediated apoptosis signaling pathway. A)
TSP1:CD36:p59fyn [48]; B) pp59fyn [48]; C) pp38MAPK [48]; D) caspase-3 activity [48]; and E) caspase-3 activity [56].
F) An independent set of data for caspase-3 activity under the condition of p38MAPK inhibition [48] was used to validate
the model prediction. Solid line: mean of nine best fits. Shaded area: standard deviation of model best fits. Squares:
experimental data.
The model prediction for 5nM TSP1-induced caspase-3 activity with p38 inhibition, using the newly
estimated best fit parameters were validated against the dataset of caspase-3 activity under 5nM TSP1
stimulation and p38 inhibition, as shown in (Figure 4-1F). We also show that the predicted CD47 pathway
0 20 40 60
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(A) (B)
(E) (F)
(C)
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TSP1 Complex pp59
Caspase-3 activity
pp38
Caspase-3 activity
(Nor et al. 2000)
Caspase-3 activity
p38 inhibition
90
dynamics still reproduce the experimental datasets without additional fitting (Figure 4-2). For subsequent
simulations, we used the best fit parameter values that yielded the lowest error during fitting.
91
Table 4-2. Estimated parameters for integrated model using CD36 pathway datasets.
set kinter,DISC kinter,TSP1CD36 factor,fasLksyn ki,casp3 Vmax,FasL kdp,p38,p59 kdeg,TSP1CD36 kdeg,DISC koff,FasFasL error
1 1.8227 0.6368 3318.3820 0.0495 0.0109 1.5997 0.0062 95.0889 9.2470 64.3889
2 0.7760 0.6368 4905.6170 0.0525 0.0123 2.9413 0.0062 61.8365 8.9924 64.6360
3 1.5853 0.6368 1700.6367 0.0499 0.0463 2.8198 0.0062 74.7597 13.5615 64.6426
4 0.6856 0.6369 936.6938 0.0579 0.0973 3.5445 0.0063 68.0623 7.6060 64.7084
5 0.9137 0.6369 1684.7518 0.0584 0.0956 4.4424 0.0062 57.7930 9.4170 64.7940
6 1.0391 0.6378 971.0658 0.0444 0.0751 3.3148 0.0062 146.1060 16.0342 64.8590
7 0.5387 0.6368 518.3477 0.0295 0.4093 5.7663 0.0062 99.4406 51.6511 66.0875
8 0.4795 0.6369 1081.9426 0.0352 0.2095 7.3522 0.0067 24.6315 23.2125 66.3525
9 0.2866 6.1403 29.9470 0.0348 2.9471 5.2947 0.0011 0.0929 3.9256 85.8510
mean 0.9030 1.2484 1683.0427 0.0458 0.4337 4.1195 0.0057 69.7568 15.9608
standard
deviation
0.5106 1.8345 1523.7348 0.0105 0.9507 1.7696 0.0017 42.5370 14.5054
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Figure 4-2. Integrated model dynamics compared to datasets of the eNOS signaling pathway. Model generated
dynamics for the activated species in the VEGF-mediated eNOS signaling pathway remain unchanged with the newly
estimated nine parameters. Model simulation compared to normalized experimental datasets: (A) total R2 level; (B)
membrane R2; (C) pR2 upon 50ng/ml VEGF stimulation[118]; (D) total R2 in control condition[118]; (E) total R2 with
cycloheximide treatment[118]; (F) total R2 with 50ng/ml VEGF and cycloheximide treatment[118]; (G) pSrc with
2.5ng/ml VEGF treatment[24]; (H) pAkt, (I) peNOS with 50ng/ml VEGF treatment[118]; (J) pPLCg with 80ng/ml
VEGF treatment[119]; (K) NO level with 10ng/ml VEGF treatment[120]; concentration of (L) IP3 and (M) cytosolic
Ca
2+
with 10ng/ml VEGF treatment[121]; (N) cGMP concentration with 30ng/ml VEGF treatment[40]. Solid line: mean
of nine best fits. Shaded area: standard deviation of nine best fits. Squares: experimental data. Error bars: standard deviation
of the experimental datasets.
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Boeldt 2017 NO
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(A) (B)
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(K)
(N)
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Time (min)
Normalized Level Normalized Level Normalized Level Concentration (nM)
2+
(C) (D)
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4.2.3. Simulation of population response
To simulate the apoptotic response of a population of cells to treatment with a variety of ligand
concentrations, we first vary only the species concentrations along the CD36 pathway. For this set of
simulations, we focus on the CD36 pathway dynamics, and therefore only varied initial conditions in the CD36
pathway while keeping the CD47 pathway initial conditions fixed at their baseline values.We use the initial
conditions of 2000 cells that were used in Chapter 3, where each cell has a unique set of species concentrations
randomly generated from gamma distributions centered around the initial species’ baseline values.
We also simulated the population response to TSP1, with variation of CD36 and CD47 receptor levels.
Particularly, we scaled both of the receptors by 50%, 100%, and 150% of their baseline levels that we have
quantified using flow cytometry. Therefore, a total of nine combinations of CD36 and CD47 levels were used.
Additionally, we varied the intracellular species along the CD36 pathway in the same manner as described
above.
4.3. Preliminary Results
4.3.1. Implementation of TSP1/CD47 intracellular mechanisms
After parameterizing the integrated model and comparting to training and validation data, we first
applied the model to predict the effects of TSP1-mediated inhibitory effects on angiogenic signaling. As
informed by our study on the eNOS signaling pathway in Chapter 2, there are multiple mechanisms by which
TSP1 can inhibit the intracellular species, NO and cGMP. Furthermore, we discovered that combined
mechanisms that inhibit components of the signaling pathway is necessary to achieve effective inhibitory
effects, as demonstrated in Chapter 2 Figure 10. Here, we simulate two of those mechanisms, which are shown
to significantly inhibit signaling (Chapter 2, Figure 2-9): 1) TSP1 directly reduces R2 kinase activity in
phosphorylating its two substrates, Src and PLCγ by affecting the rate parameters kp,Src and kp,PLCg, respectively,
and 2) TSP1 increases the clearance rate of NO by affecting the rate parameter kclear. The first mechanism is in
accordance with the experimental observations that TSP1 inhibits R2 kinase activity. The second mechanism,
through our own analysis of the eNOS signaling pathway, was identified as an effective and potential
mechanism that achieves basal and agonist-induced cGMP production. We use the same method as presented
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in Chapter 2, where we scale each parameter by the perturbation strength calculated using a Hill function with
TSP1 concentration as the input.
Figure 4-3 shows the inhibition effects on various eNOS pathway species dynamics when the
abovementioned two perturbations are implemented with 10nM TSP1 stimulation (orange curves). Notably,
the eNOS signaling induced by VEGF stimulation (Figure 4-3A) is suppressed at both the upstream (pSrc/Src,
peNOS/eNOS, calcium influx) and downstream (NO, cGMP) levels, whereas in the basal condition without
VEGF stimulation (Figure 4-3B), the upstream dynamics remain the same, while the basal NO and cGMP
levels are suppressed. These results are in agreement with the experimentally observed effects of TSP1 (Bauer,
Isenberg). Given model parameterization described in Section 4.2.1 and these simulations that also match
experimental results, we have established a predictive integrated model of TSP1 signaling through the CD36
and CD47 receptors. We next used the model to generate novel insight as to the effects of TSP1 at the
population level.
Figure 4-3. Model simulated effects of TSP1’s inhibitory effects on eNOS signaling dynamics. (A) Model simulated
signaling dynamics with high tumor VEGF level (0.389nM), with 10nM TSP1-mediated inhibition (orange) or without any
TSP1 (blue). (B) Model simulated basal signaling dynamics of the eNOS pathway with 10nM TSP1-mediated inhibition
(orange) or without any TSP1 (blue).
Fold-change
Concentration (nM)
Fold-change
Fold-change
Concentration (nM)
pSrc/Src peNOS/eNOS Calcium NO cGMP
(A)
(B)
Time (min) Time (min) Time (min) Time (min) Time (min)
Fold-change
Concentration (nM)
Fold-change
Fold-change
Concentration (nM)
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4.3.2. Population response to TSP1-mediated apoptosis
With the integrated model, we first focus on whether it can reproduce our predictions of the population
apoptotic response to TSP1 treatment, as shown in Chapter 3. In order to identify a cPARP threshold value
above which the cells would be defined as “apoptotic”, we simulated the effect of low dosage treatment of
doxorubicin by directly increasing Fas initial condition by three-fold and increasing the synthesis rates of CD36
pathway species by 50-fold (Figure 4-4A,E). Following the same procedure for identifying the cPARP
threshold as described in Chapter 3, we identify that the new cPARP threshold must be 1.6306 µM in order to
have 50% of the cells be apoptotic after 24 hours of doxorubicin treatment. This is a higher threshold value
than the original 1.0537 µM, but still within the same scale. This difference between the two thresholds is likely
a result of the adjustments made to the model reaction rules during model integration as well as the newly
estimated parameter values. For example, the newly estimated internalization rate of TSP1:CD36 complex is
larger than in the original study (best fit values 6.39e-1/min vs. 4.67e-6/min). We then applied this threshold
value to the simulated population response to baseline treatment with 10nM TSP1 (Figure 4-4B,F). For this
condition, approximately 31% of cells become apoptotic within 24 hours. Thus, TSP1 treatment alone is not
as potent as the chemotherapeutic agent.
In another study, Volpert et al. showed that VEGF sensitizes endothelial cells to TSP1-induced
apoptosis by up-regulating Fas expression[57], the receptor for FasL which is upregulated by TSP1 via its
receptor CD36. Therefore, we sought to implement this mechanism, as it is another connection between VEGF
and TSP1. As a first step to simulate this effect by VEGF, I directly increased the synthesis rate of the receptor
Fas. I then simulated the population response to 15nM TSP1 stimulation, the same concentration used in the
experimental study. For this condition, the model predicts that 32.2% of cells become apoptotic after 24 hours.
However, our simulation result suggests that increasing the synthesis rate of Fas by 100-fold alone was not
effective in enhancing the population apoptotic response, as 32.7% of cells are apoptotic after 24 hours (data
not shown). By examining the simulated results, we found only increases Fas synthesis has a minimal effect on
apoptosis because Fas is still rapidly internalized and degraded upon FasL binding (data not shown). To test
other potential mechanisms that allow for Fas upregulation, I simulated the effect of reducing Fas degradation
by 10-fold and increasing the synthesis rate of all the other species by 10-fold, combined with the 100-fold
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increase in Fas synthesis. Together, these three changes allowed a slight increase of apoptosis from 32.2% to
37.8% of the 2000 cell population by 24 hours (Figure 4-4C-D,G-H). Thus, additional effects besides
increasing Fas levels are required to sensitize the cells to TSP1 treatment.
Figure 4-4. Integrated model simulated apoptotic response to TSP1 stimulation as flow-cytometry like data.
cPARP response to TSP1 treatment in 2000 cells with varied initial conditions in the CD36 pathway species were simulated.
(A) baseline model response to 10nM TSP1 stimulation. (B) simulated effect of low dosage DXR in addition to 10nM
TSP1, as informed by Quesada et al. (2000) [192]: increase in Fas initial concentration by 3-fold and synthesis rate of all
model species by 10-fold. (C) baseline model response to 15nM TSP1 stimulation. (D) simulated effect of 3.704pM VEGF
in addition to 15nM TSP1 stimulation: increased Fas synthesis rate by 100-fold, synthesis rate of all other model species
by 10-fold, and decreased Fas degradation rate by 10-fold.
4.3.3. Influence of heterogenous receptor expression on inhibitory effects of TSP1
Previously with our baseline CD36 model that does not incorporate cell-to-cell heterogeneity, varying
receptor CD36 or Fas alone did not affect the cPARP response (Chapter 3, Figure 3-6). However, it is of
interest to investigate whether the receptors influence the signaling outcome differently now that both CD36
and CD47 are available as TSP1’s binding partners. As a proof of concept, we simulated the cPARP levels of
2000 cells at 24 hours in response to 0.0003nM VEGF (low healthy tissue VEGF level) with 10nM TSP1
treatment (Figure 4-5A); 0.389nM VEGF (high tumor VEGF level) with 10nM TSP1 treatment (Figure 4-
5B); 0.0003nM VEGF with 0.1nM TSP1 treatment (Figure 4-5C); and 0.389nM VEGF with 0.1nM TSP1
treatment (Figure 4-5D). Here, we simulated the sensitization effect by the VEGF treatment by assuming that
VEGF increases Fas synthesis rate by 100-fold, decreases Fas degradation rate by 10-fold, and increase synthesis
baseline 10nMT
31.1%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
dxr50 10nMT
52.5%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
baseline 15nM TSP1
32.2%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
Volpert1e3 koff
37.8%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
non-apoptotic
apoptotic
baseline 10nMT
31.1%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
dxr50 10nMT
52.5%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
baseline 15nM TSP1
32.2%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
Volpert1e3 koff
37.8%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
non-apoptotic
apoptotic
baseline 10nMT
31.55%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
dxr50 10nMT
52.45%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
Volpert1e3
38.05%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
Volpert1e3 koff
37.15%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
non-apoptotic
apoptotic
15nM TSP1
15nM TSP1+ 3.704pM VEGF
(Fas upregulation,
low degradation)
10nM TSP1 + DXR
(3xFas IC,
high synthesis rates)
Baseline 10nM TSP1
non-apoptotic
(A) (B)
(E) (F) (G) (H)
(C) (D)
% cells % cells
baseline 10nMT
31.1%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
dxr50 10nMT
52.5%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
baseline 15nM TSP1
32.2%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
Volpert1e3 koff
37.8%
0 1 2 4 6 8 10 12 16 24
0
20
40
60
80
100
non-apoptotic
apoptotic
apoptotic
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rates of all other non-zero species by 10-fold (since this was required to see an effect of TSP1 stimulation on
the apoptotic response.
Figure 4-5. Population apoptosis with varied receptor levels in response to treatments. The apoptotic response of
2000 cells were simulated for 24hrs with each combination of receptor CD36 and CD47 as 50%, 100%, and 150% of their
baseline levels. (A) 10nM TSP1 with 0.0003nM VEGF treatment; (B) 10nM TSP1 with 0.389nM VEGF; (C) 0.1nM TSP1
with 0.0003nM VEGF; (D) 0.1nM TSP1 with 0.389nM VEGF.
The results show that, at high TSP1 concentration (10nM), the apoptotic response does not depend
on either CD36 or CD47 levels (Figure 4-5A,B), even with the addition of VEGF-induced upregulation of
Fas. Meanwhile, at low concentration of TSP1 (0.1nM), the cells become more resistant to apoptosis at a higher
CD47 level (approximately 300nM), whereas CD36 levels did not apparently influence the apoptotic response
(Figure 4-5C,D). Interestingly, in the low-TSP1 condition, high VEGF dramatically sensitized the cells (Figure
4-5D), yielding apoptotic levels close to that under the high TSP1 and low VEGF condition (Figure 4-5A).
Future investigation should focus on understanding the dependence of the apoptotic response to TSP1
concentrations; furthermore, since this preliminary set of simulations reveal that receptor levels may be more
10000 20000 30000
CD36 (nM)
180000
120000
60000
CD47 (nM)
% change in apoptotic cells
23.15
25.95
26.8
22.65
25.75
26.7
22.55
25.55
26.6
0
10
20
30
40
50
60
10000 20000 30000
CD36 (nM)
180000
120000
60000
CD47 (nM)
% change in apoptotic cells
14.25
17.65
18.8
13.5
16.85
18.45
13.15
16.4
18.2
0
10
20
30
40
50
60
10000 20000 30000
CD36 (avg #/cell)
180000
120000
60000
CD47 (avg #/cell)
% change in apoptotic cells
29.5
29.9
29.95
29.45
29.85
29.95
29.45
29.85
29.9
0
10
20
30
40
50
60
10000 20000 30000
CD36 (nM)
180000
120000
60000
CD47 (nM)
% change in apoptotic cells
38.2
38.55
38.6
38.15
38.55
38.6
38.2
38.6
38.6
0
10
20
30
40
50
60
High VEGF (0.389nM) Low VEGF (0.0003nM)
High TSP1 (10nM) Low TSP1 (0.1nM)
CD36 (avg. #/cell) CD36 (avg. #/cell)
CD47 (avg. #/cell) CD47 (avg. #/cell)
A B
C D
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influential at a low TSP1 concentration, it would be of interest to continue model analysis with a low range of
TSP1 concentration.
4.4. Discussion
4.4.1 Preliminary insight given by the integrated model
In this chapter, we have integrated the two intracellular pathway models of TSP1, focusing on ensuring
the consistency in the biochemical reaction rules that we defined in this model. We re-calibrated a small number
of parameters in the CD36 pathway so that the integrated model still recapitulates the apoptotic signaling
dynamics. As a first step, we use this integrated model to generate preliminary simulations to test the signaling
response to TSP1 stimulation.
Previous experimental studies suggest that endothelial cells can be sensitized to TSP1-induced
apoptosis through Fas receptor upregulation[57], [192]. However, the model simulation of the population
response to TSP1 stimulation indicates that the response is quite robust to strategies to induce Fas upregulation,
unless other mechanisms that promote signal transduction, such as increased synthesis rate for all other species,
are also incorporated (Figure 4-4). In the single baseline model, cPARP reaches its maximum level within 4
hours of simulation in response to various levels of TSP1 above 1nM (data now shown). Together, these results
suggest that simply increasing Fas level is not sufficient to sensitize the cells to TSP1-induced apoptotic
signaling through FasL production; rather, increased synthesis rate of other species seems to play a more
important role in the apoptotic response. A more thorough analysis of which model parameters influences
sensitivity of the cells to endogenous FasL stimulation can be done in the near future. For example, the
influence of the parameters in the integrated model on the cPARP output can again be further investigated
through a sensitivity analysis.
Besides the apoptotic response induced by TSP1, its inhibitory effect on eNOS signaling has also been
our interest. With the integrated model, we can conduct the sensitivity analysis with both TSP1 and VEGF
treatment, to understand the influential components of the model to the NO production. Furthermore, we can
generate a population response, in a similar manner as previously described, exploring the effects of various
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VEGF and TSP1 stimulation levels, to predict how the endothelial NO production is regulated by these
angiogenic factors. Cautious simulation design needs to be made in order to appropriately simulate a population
of cells that is undergoing both partial apoptosis and NO production.
4.4.2. Future simulations of relevant therapeutic agents
As mentioned in the Introduction (Chapter 1), TSP1 mimetics and its derived antagonists of the
receptors CD36 and CD47 have been developed and tested in preclinical and clinical studies [76-80] and
previously reviewed by Henkin and Volpert [215]. For example, the C-terminal 4N1 and 7N3 peptides bind to
CD47, while a series of optimized peptide mimetics ABT -510,526, and 898 have been developed that bind to
CD36 and yield high potency in blocking angiogenesis in preclinical models. Furthermore, a peptide named
TAX2 is found to block TSP1-CD47 interaction, which is believed to potentiate TSP1 engagement with
receptor CD36 and therefore suppressed tumor angiogenesis and progression[216].
With information available to characterize the specific drug-target interactions (e.g. binding sites and
affinities), we can use the integrated pathway model as a platform to efficiently simulate the downstream
signaling response when these therapeutic agents are applied. This work can be immediately carried out once a
thorough literature search regarding these molecules of interests is done. This will allow us to generate relevant
and quantitative insight on how these therapeutic agents may influence the intracellular signaling network, and
point out directions where candidate molecules can be selected or optimized for future preclinical investigation.
Similarly, for existing modalities that hold promise in angiogenic blockade, whether it engages the target
receptor or acts on the intracellular components depicted in the model network, we can utilize this integrated
model as the platform to predict their effects. Therefore, besides investigating the biological question of how
TSP1 mediates angiogenesis, we establish this model to be used as a framework that can be easily adapted to
investigate the effects of candidate molecules to facilitate preclinical drug discovery.
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4.4.3. Further implementation of the integrated model
There are several interactions between components of both pathways that are not currently included
in the model. Below, I discuss the consideration of several potential crosstalk mechanisms and additional
mechanisms to be incorporated in the model integration step.
Consideration 1: upregulation of Fas expression by VEGF stimulation. As mentioned above,
Volpert et al. have shown that low dosage VEGF stimulation induces Fas upregulation within two to four hours,
which sensitizes endothelial cells to TSP1-induced apoptosis[57]. As our preliminary simulation results suggest,
the upregulation of Fas alone does not accomplish this sensitization, as Fas receptor is subject to fast
internalization and degradation upon FasL binding (DISC formation). However, it is important to incorporate
this mechanistic detail discovered experimentally into the computational model. Therefore, analysis of the
baseline model robustness, especially the sensitivity of the cPARP response to the model parameters needs to
be conducted. Currently, the module in the CD36 pathway model that describes DISC formation, caspase
amplification, and NF!B activation is a direct adaptation from the model developed by Neuman et al. [186]. If
necessary, this module could be modified and calibrated with endothelial cell line data, such that the FasL-
induced apoptosis is more sensitive to the changes in Fas receptor, as suggested by the experimental study.
Consideration 2: inhibition of myristate update by CD36. In addition to its role in TSP1’s pro-
apoptotic signaling, CD36 is an integral membrane fatty acid translocase (FAT). Myristic acid is a common
saturated fatty acid that can be taken into vascular cells via CD36[217]. Myristoylation is critical for membrane
association of Src family kinases (SFKs), which in turn is crucial for cellular functions mediated by SFKs. Non-
myristoylated forms of Src are cytoplasmic and cannot induce cellular transformation[218]. Myristoylation is
shown to positively regulate c-Src kinase activity in COS (a monkey kidney fibroblast-like cell line) and SYF
cells (mouse embryotic fibroblasts lacking Src family kinases), potentially inducing a conformation of the c-Src
molecule that is more optimal for its kinase activity[58].
The SFK Fyn is one of the myristoylated proteins and is a target of CD36 signaling in ECs[48]. Cell
culture growth medium containing serum provided adequate myristate to maintain full Fyn association with the
membrane fraction in HUVECs. However, in serum free medium, Fyn primarily localizes in the cytosolic
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fraction. Under this condition, exogenous myristate stimulated rapid translocation of Fyn from the cytosol to
the cell membrane in HUVECs, and increased Tyr416 phosphorylation of SFKs.
Exogenous myristate also increased cGMP production in serum-starved HUVECs at 5 min in a dose
dependent manner, with a maximum response occurring at a dose of 10 µM. Inhibiting myristate uptake via
CD36 with 1-10 nM TSP1 prevented eNOS-dependent cGMP synthesis, a concentration adequate to inhibit
NO-stimulated cGMP accumulation[40]. Furthermore, the study showed that myristate induced EC and VSMC
adhesion on type I collagen via the NO/cGMP pathway, and TSP1 inhibits this response by simultaneously
inhibiting myristate uptake via CD36, and downstream cGMP signaling indirectly via CD47.
However, it is unclear whether CD36 globally limits protein myristoylation or acts specifically to
regulate trafficking of certain targets, such as Fyn. In addition, the role of CD36 in eNOS regulation has not
been clearly understood. As described in Aim 1, c-Src is an important upstream regulator of eNOS activity that
associated with and activated by active VEGFR2[22]. I hypothesize from the relevant studies that TSP1
inhibition on myristate uptake via receptor CD36 negatively impacts the activation of both c-Src and Fyn. In
our published CD36 model, this mechanism was not included, because the experimental conditions we referred
to did not exclude or add exogenous myristate. Now, because active c-Src is an important component in eNOS
signaling as described in Aim 1 CD47 model, it is important to include the effect of CD36-mediated myristate
uptake on c-Src activation, as the first convergence point for the crosstalk between the CD36 and CD47-
mediated pathways. This will help us understand the relative importance of these two receptors in TSP1-
mediated inhibitory signaling. We can also use the model to explore the relative importance of VEGF and
myristate on pro-angiogenic signaling.
Consideration 3: TSP1-CD36 mediated phosphatase (SHP-1) recruitment to R2. An
experimental study showed that in HMVECs, CD36 can associate with R2, and TSP1 engagement with CD36
recruits SHP-1 to the CD36-R2 complex[42]. This recruitment of SHP-1 dephosphorylates R2, resulting in
suppression of R2 signaling. This study also confirmed that CD36 is necessary in the TSP1 inhibition of R2
phosphorylation through CD36 knockdown study. Interestingly, Kaur et al. has shown that in HUVECs, TSP1
disrupts the CD47-R2 association and therefore suppresses R2 signaling[49], a mechanism that both Bazzazi et
102
al. and our group have attempted to recapitulate with computational models primarily calibrated with HUVEC
data [102], [104]. Furthermore, Bazzazi et al. have used their model to demonstrate that enhanced
dephosphorylation of R2 can reduce the downstream phosphorylation of eNOS[102].
In our present model, a complex of R2 and CD36 can be formed indirectly through CD47 coupling
with R2 and TSP1, followed by binding of TSP1 with CD36, which is independent of TSP1-CD47 binding.
Our fitted model parameters suggest that while CD47 associates with R2, R2 dephosphorylation is slow, and
without CD47’s stabilization of R2, the dephosphorylation rate of R2 is faster. We can incorporate the effect
of increased R2 dephosphorylation when it is associated with CD36. However, it seems more pressing to use
one consistent cell line to first confirm the role of CD36 and CD47 in association with VEGFR2, and only
with quantitative data that characterize the activity through either receptor, we would be able to accurately
describe the exact TSP1 mechanisms regulating R2 phosphorylation with certainty.
Consideration 4: interaction between Akt and cFLIP. TSP1 antagonizes pro-angiogenic signaling
induced by VEGF-R2. The decrease in phosphorylation of R2 correlates with increased association of the
phosphatase SHP-1 with the R2 complex[42]. This in turn results in a decrease in Akt phosphorylation, which
can promote the activity of caspase-8 through modulation of cFLIP[219], [220]. Specifically, Akt interacts with
cFLIP, and this interaction possibly regulates Akt’s ability to bind and phosphorylate its substrates.
Furthermore, this interaction functionally regulates apoptosis, but the exact mechanisms remain unclear[221].
R2 and Akt are components of the CD47 pathway model (Chapter 2), whereas cFLIP and caspase-8 are both
components of the CD36 pathway model. Thus, a next step would be to add the interaction between Akt and
cFLIP. This serves as a second convergence point for the crosstalk between the TSP1-mediated signaling
pathways via receptors CD36 and CD47.
4.4.4. Potential need for model reduction
The model generates a large number of molecules and complexes, based on the user-defined reaction
rules. Certain initial conditions, such as one with low dosage VEGF or TSP1 treatment, can result in low
concentrations for many of these molecules, in the range of near-zero picomolar concentrations. Although
103
more often than not, we use the total sum of various forms of a molecule whether it is engaged with other
molecules, for example, all forms of active caspase-3, as a specific model output; having a large number of
ODEs while many of the resulting concentrations remain negligible during the course of simulation, can
generate computational inefficiency. Therefore, to better utilize such a large platform model, reductions can be
made informed by correlation analyses, such as sensitivity analysis and PLSR analysis. Importantly, reducing
the complexity of the model will require an understanding of the relative importance of component of the
model in relation to the specific question to address.
4.5. Conclusion
In this work, we have integrated the mechanistic models of TSP1’s intracellular functions through its
association with receptors CD36 and CD47. To our knowledge, this is the first time that a molecularly detailed,
quantitative, comprehensive network model of TSP1 that has been established. The integrated model
recapitulates the experimentally observed signaling dynamics of both the apoptotic and eNOS pathways
individually. Preliminary simulation results show that useful insight can be generated using this model, serving
to guide optimization of angiogenic treatment strategy. Furthermore, this comprehensive model provides a
much-needed framework to investigate the effects of other angiogenic regulators that impact various
components of this network.
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Chapter 5
Model of Human Breast Cancer Tumor-Bearing Mice Receiving Anti-VEGF Treatment
Portions of this chapter are adapted from:
Thomas D. Gaddy, Qianhui Wu, Alyssa D. Arnheim, and Stacey D. Finley. PLoS Computational
Biology (2017) 13(12): e1005874
5.1. Abstract
Tumors exploit angiogenesis, the formation of new blood vessels from pre-existing vasculature, in
order to obtain nutrients required for continued growth and proliferation. Targeting factors that regulate
angiogenesis, including the potent promoter vascular endothelial growth factor (VEGF), is therefore an
attractive strategy for inhibiting tumor growth. Computational modeling can be used to identify tumor-specific
properties that influence the response to anti-angiogenic strategies. Here, we build on our previous systems
biology model of VEGF transport and kinetics in tumor-bearing mice to include a tumor compartment whose
volume depends on the “angiogenic signal” produced when VEGF binds to its receptors on tumor endothelial
cells. We trained and validated the model using published in vivo measurements of xenograft tumor volume,
producing a model that accurately predicts the tumor’s response to anti-angiogenic treatment. We applied the
model to investigate how tumor growth kinetics influence the response to anti-angiogenic treatment targeting
VEGF. Based on multivariate regression analysis, we found that certain intrinsic kinetic parameters that
characterize the growth of tumors could successfully predict response to anti-VEGF treatment, the reduction
in tumor volume. Lastly, we use the trained model to predict the response to anti-VEGF therapy for tumors
expressing different levels of VEGF receptors. The model predicts that certain tumors are more sensitive to
treatment than others, and the response to treatment shows a nonlinear dependence on the VEGF receptor
expression. Overall, this model is a useful tool for predicting how tumors will respond to anti-VEGF treatment,
and it complements pre-clinical in vivo mouse studies.
105
5.2. Introduction
Angiogenesis is the formation of new blood vessels from pre-existing vasculature and is important in
both physiological and pathological conditions. Numerous promoters and inhibitors regulate angiogenesis. One
key promoter of angiogenesis is the vascular endothelial growth factor-A (VEGF-A), which has been
extensively studied and is a member of a family of pro-angiogenic factors that includes five ligands: VEGF-A,
VEGF-B, VEGF-C, VEGF-D, and placental growth factor (PlGF). VEGF-A (or simply, VEGF) promotes
angiogenesis by binding to its receptors VEGFR1 and VEGFR2 and recruiting co-receptors called neuropilins
(NRP1 and NRP2). The VEGF receptors and co-receptors are expressed on many different cell types, including
endothelial cells (ECs), cancer cells, neurons, and muscle fibers [222]. Together, VEGF and its receptors and
co-receptors initiate the intracellular signaling necessary to promote vessel sprouting, and ultimately, the
formation of fully matured and functional vessels. The new vasculature formed following VEGF signaling
enables delivery of oxygen and nutrients and facilitates removal of waste products [223].
Regulating angiogenesis presents an attractive treatment strategy for diseases characterized by either
insufficient or excessive vascularization. In the context of excessive vascularization seen in many types of
cancer, inhibiting angiogenesis can decrease tumor growth. Anti-angiogenic treatment targeting tumor
vascularization is a particular focus area within cancer research [224]. One anti-angiogenic drug is bevacizumab,
a recombinant monoclonal antibody that neutralizes VEGF (an “anti-VEGF” drug). Bevacizumab is approved
as a monotherapy or in combination with chemotherapy for several cancers, including metastatic colorectal
cancer, non-small cell lung cancer, and metastatic cervical cancer [225]. In 2008, the drug gained accelerated
approval for treatment of metastatic breast cancer (mBC) through the US Food and Drug Administration
(FDA), based on evidence from pre-clinical studies and early phase clinical trials. Though initial clinical trials
initially showed that bevacizumab improved progression-free survival (PFS), subsequent results revealed that
bevacizumab failed to improve overall survival (OS) in a wide range of patients and that the drug elicited
significant adverse side effects [226]. Consequently, the FDA revoked its approval for the use of bevacizumab
for mBC in late 2011 [227].
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The case of bevacizumab illustrates that although anti-angiogenic therapy can be effective, not all
patients or cancer types respond to the treatment. This underscores the need for biomarkers that can help select
patients who are likely to respond to anti-angiogenic treatment. Numerous studies have sought to identify
biomarkers for anti-angiogenic treatment. Biomarkers can be used to determine which tumors will respond
prior to any treatment being given (“predictive”), or to evaluate efficacy following treatment (“prognostic”)
[228]. Biomarkers can also be used to determine optimal doses, to design combination therapies, and to identify
resistance to therapies [229]. The concentration range of circulating angiogenic factors (CAFs), and VEGF in
particular, is one possible predictor of the response to anti-angiogenic therapy [228]. Alternatively, expression
of angiogenic receptors such as NRP1 and VEGFR1 on tumor cells, in the tumor interstitial space, or in plasma
can serve as biomarker candidates [226], [230]. Unfortunately, though some of these candidates are promising,
a marker that predicts bevacizumab treatment outcome has not yet been validated [226], [228]. In fact, relying
on the concentrations of CAFs has produced inconclusive and inconsistent results [228], [229], [231]. Tumor
growth kinetics have also been investigated as prognostic biomarkers of the response to anti-angiogenic
treatment [232]–[236]. The most recent studies take advantage of improved imaging technology that can assess
tumor volume, rather than only providing two-dimensional information [232]. The imaging analyses show that
tumor growth kinetics may be a reliable indicator of treatment efficacy and are in good agreement with
standardized approaches for assessing response treatment. However, utilizing tumor growth kinetics as a
predictive biomarker has not been extensively studied.
Mouse models present a useful platform for cancer research, including biomarker discovery. Despite
differences in the mouse and human anatomy and immune system, pre-clinical mouse studies are useful in
understanding human cancer progression and response to therapy [237]. Advances in molecular biology
techniques have generated relevant mouse models (i.e., patient-derived tumor models and genetically
engineered models). These mouse models enable biomarker discovery for early detection of cancer [238], to
identify non-responders to a particular treatment [239], and to classify tumors as being drug-sensitive or drug-
resistant [240]. Excitingly, computational analyses are being combined with pre-clinical models to identify
biomarkers for early detection and progression [238], [240].
107
There is a substantial and productive history of applying computational modeling to study cancer at multiple
scales, from initiation through metastasis [241]–[243]. The model predictions provide testable hypotheses that
have been experimentally and clinically validated. Given the multiple cell types, molecular species and signaling
pathways involved in angiogenesis, systems biology approaches are used to understand the dynamic ligand-
receptor interactions that mediate angiogenesis and tumor growth. Systems biology studies how individual
components of biological systems give rise to the function and behavior of the system and aims to predict this
behavior by combining quantitative experimental techniques and computational models [244]. Our previous
work and the work of others demonstrates that mathematical models complement pre-clinical and clinical
angiogenesis research [245], [246]. These models have been used to identify prognostic biomarkers that can
predict which patients will benefit from anti-angiogenic therapies [246]–[248].
In this work, we use a computational systems biology model to investigate the utility of tumor growth
kinetics in predicting response to anti-VEGF treatment. We make use of quantitative measurements from pre-
clinical mouse studies and use those data to train the computational model. This work builds upon our previous
computational model of VEGF distribution and kinetics in tumor-bearing mice [249] by changing the dynamic
tumor volume to be dependent on the pro-angiogenic complexes involving VEGF-bound receptors (the
“angiogenic signal”). This new element of the computational model allows us to simulate anti-VEGF treatment
and predict the effect of the treatment on tumor volume. We apply the new model to identify conditions and
characteristics of tumor growth that may be predictive of a favorable response to anti-angiogenic treatment.
Our work contributes to the identification of validated biomarkers that could be used to determine tumors that
are sensitive to anti-angiogenic treatment.
5.3. Methods
5.3.1. Computational Modeling
Compartmental model. In this work, we expand on our previous three-compartment model [249] by
including VEGF-mediated tumor growth. We briefly describe the full model and detail the new additions that
are the focus of this work. The model is comprised of three compartments representing the whole mouse:
108
normal tissue (assumed to be skeletal muscle), blood, and tumor (Figure 5-1). The model includes human and
mouse VEGF isoforms: human isoforms (VEGF121 and VEGF165) are secreted by tumor cells, and mouse
isoforms (VEGF120 and VEGF164) are secreted by endothelial cells in the normal, blood, and tumor
compartments and muscle fibers in the normal tissue. VEGF receptors (VEGFR1 and VEGFR2) and co-
receptors (neuropilins) are expressed on the surface of muscle fibers, endothelial cells, and tumor cells.
VEGFR1 and VEGFR2 are the primary receptors to which VEGF binds. The neuropilins (NRP1 and NRP2)
are co-receptors for VEGF, to which VEGF can directly bind. Additionally, NRPs can couple to VEGF
receptors VEGFR1 or VEGFR2, and then VEGF can bind to the VEGFR-NRP complex. The interactions
between VEGF and its receptors and co-receptors occur in all three compartments. By binding to its receptors
on endothelial cells in the tumor compartment, VEGF is able to initiate pro-angiogenic signaling that mediates
the formation of new blood vessels. We account for VEGF-mediated tumor growth by incorporating the
concentration of VEGF-bound receptors into the tumor volume equation (described in more detail below).
Parameters characterizing the compartment geometry, receptor densities, kinetic rates, and transport rates are
given in [249].
109
Figure 5-1. Tumor growth model schematic. The computational model includes three compartments:
normal tissue, blood, and tumor volume. The compartments are connected via lymphatic flow from the
interstitial space in the normal tissue to the blood and transendothelial macromolecular permeability. Molecular
species include human and mouse VEGF isoforms, VEGF receptors and co-receptors (including the soluble
receptor VEGFR1, sR1), and the protease inhibitor α-2-macroglobulin (a2m). Glycosaminoglycan (GAG)
chains represent the extracellular matrix. The volume of the tumor depends on the concentration of receptor-
bound VEGF complexes on tumor endothelial cells (denoted as [rec-VEGF]).
Tumor volume and growth. Previously, we assumed the tumor volume increased exponentially with
time, based on measurements from tumor xenografts [249]. Under that assumption, cancer treatment, including
anti-angiogenic therapy, has no effect on tumor growth. In the present study, we address that limitation by
introducing an equation for tumor growth wherein the volume of the tumor compartment is dependent on the
“angiogenic signal” (Ang) produced when VEGF binds to its receptors on endothelial cells in the tumor. By
including the concentration of VEGF-bound receptors directly into the tumor volume equation, we account
for VEGF-mediated tumor angiogenesis and subsequent tumor growth.
110
The tumor compartment is assumed to consist of cancer cells, endothelial cells (vascular volume) and
interstitial space, each of which has a defined volume fraction (i.e., volume relative to the total tumor volume).
Our previous model assumed that as the total tumor volume increased, the relative proportions of cancer cells,
vascular space, and interstitial space remain constant. Here, we still have the volume fraction for the vascular
space remaining constant, based on a range of experimental data [250]–[252]. However, we used results from a
recent imaging study to account for an increase in the relative volume of cancer cells as the tumor volume
increases. Christensen and coworkers measure how tumor cell density increases as the tumor grows by tracking
cancer cells in xenograft tumors in rats using near near-infrared (NIR) fluorescence dyes [253]. The authors
quantify the fluorescence intensity in a tumor and use it to estimate the number of cancer cells as the tumor
grows over time. The estimated cell count was normalized by the tumor volume to obtain the number of cancer
cells per unit volume of tumor tissue as the tumor grows. We extracted the values obtained by Christensen and
coworkers for MDA-MB-231 tumors and converted them to the cancer cell volume fraction using the volume
of tumor cells, as we have done in our previous work [249]. Therefore, we have been able to incorporate into
our model an increase in the cancer cell volume fraction over time. Assuming a tumor cell volume of 905 µm
3
,
based on our previous examination of the literature [249], we developed expressions describing the decay of
interstitial space during tumor growth. We found that the relative decrease in interstitial space during tumor
growth was adequately modeled by exponential decay. The equations for how the relative volume of the
interstitial space varies with total tumor volume are given in Table 5-1.
Table 5-1. Equations describing change in relative volume of the interstitial space.
Dataset Relative volume of interstitial space (cm3/cm3 tissue)
Roland
!"#
!"
= 0.8323∙+
#$%.'() ∙+(-)/
Zibara
!"#
!"
= 0.8247∙+
#$%.%0)∙+(-)/
Tan
!"#
!"
= 0.8343∙+
#$%.%0'∙+(-)/
Volk (2008)
!"#
!"
= 0.8628∙+
#$%.%01∙+(-)/
Volk (2011a)
!"#
!"
= 0.8557∙+
#$%.%12∙+(-)/
Volk (2011b)
!"#
!"
= 0.8536∙+
#$%.%01∙+(-)/
111
5.3.2. Data Extraction
Data from six independent in vivo published experimental studies of MDA-MB-231 xenograft tumors
in mice were used for parameter fitting and validation [254]–[258]. The six datasets included growth profiles
for untreated tumors (control), as well as tumors treated with the anti-VEGF agent bevacizumab. Experimental
data was extracted using the WebPlotDigitizer program (http://arohatgi.info/WebPlotDigitizer).
The extended Fourier amplitude sensitivity test (eFAST), a global variance-based sensitivity analysis,
was used to understand how different parameters (“model inputs”) affect model predictions (“model outputs”).
In this method, the inputs are varied together within specific ranges at different frequencies, and the model
outputs are calculated. The Fourier transform of a model output is then calculated to identify which inputs have
the most influence based on the amplitude of each input’s frequency, where greater amplitudes indicating more
sensitive parameters. By varying the inputs at the same time, this method allows for the calculation of the total
FAST index, STi, for each input i. The total index is a measure of the global sensitivity, accounting for second
and higher-order interactions between multiple inputs.
We implemented the eFAST method using MATLAB code developed by Kirschner and colleagues.
We analyzed the effects of the tumor growth parameters (k0, k1, y, and Ang0) on one model output (the tumor
volume without anti-VEGF treatment). The parameter values were allowed to vary at least one order of
magnitude (10
-8
to 10
-2
for k0 and k1, 0.1 to 50 for y, and 10
-16
to 10
-14
for Ang0) to account for potentially large
uncertainty in the model parameters. These are the same ranges used for the parameter estimation (described
below). The parameters for which the total FAST index is large are considered to be influential parameters, and
their values are estimated in the model fitting.
112
5.3.3. Parameter estimation
Model training. We fit the influential tumor growth parameters (“free parameters”) using the control
tumor growth profiles for each dataset. Each of the six datasets provides measurements of the tumor volume
in the mouse xenograft in vivo model, where MDA-MB-231 cells were injected into mice. However, there are
significant differences between the six studies, as outlined in Table 5-2. These include differences in the mouse
strains used, the number of cancer cells injected to initiate tumor growth, whether the cancer cells were injected
alone or with matrigel, and the site of the cancer cell injection. Additionally, the equation used to calculate the
tumor volume influences the reported volume, and papers use different volume equations. Given all of these
differences, we treat each dataset individually. This is analogous to determining patient-specific tumor growth
parameters, even for patients with the same type of tumor.
Fitting was performed using the lsqnonlin function in MATLAB to minimize the sum of squared
residuals (SSR):
Min%%&(Θ)=+,-∑ /0
!"#,%
−0
&%',%
(Θ)2
(
)
%*+
[1]
where Vexp,i is the ith experimentally measured tumor volume, Vsim,i is the ith simulated volume at the
corresponding time point, and n is the total number of experimental measurements. The minimization is subject
to Θ, the set of upper and lower bounds on each of the free parameters. We found that weighting the residual
by the experimental measurement biased the error towards early data points and reduced the model’s ability to
fit the full course of tumor growth. Therefore, we minimized the residual, with no weighting, to fit the model
to the experimental data.
We performed the parameter fitting 30 times for each dataset. To attempt to arrive at a global minimum
for the error, we initialized each fitting run by randomly selecting a value for the free parameters within the
specified upper and lower bounds. The bounds were set such that the range for each parameter was at least one
order of magnitude: 10
-8
to 10
-2
for k0 and k1 and 10
-16
to 10
-14
for Ang0. After performing the model fitting, we
used the SSR to identify the optimal parameters. Parameter sets with the smallest errors were taken to be the
“best” fits and were used for subsequent statistical analysis. The number of “best” parameter sets varied
between datasets and ranged from 11 to 20 parameter sets. We first tested to see whether there were significant
113
effects of the experimental data being fit on the estimated parameters values using one-way non-parametric
ANOVA. This method makes no assumptions about the distributions of parameter values and tests whether
samples originate from a common distribution. We then performed post-hoc analyses to make pairwise
comparisons using the Kruskal-Wallis test. We corrected for multiple comparisons by controlling the false
discovery rate. All statistical analyses were performed using GraphPad Prism.
114
Table 5-2. Experimental treatment from published papers.
Author Year Mouse
# cells
injected
Injection site of tumor cells
Drug injection
route
Treatment
Start
Dosage Interval Duration
# of
Doses
Roland 2009 NOD/SCID 5.00E+06 mammary fat pad Subcutaneous Day 26 10 mg/kg 2x per wk 3 weeks 6
Zibara 2015
NSG
immunodeficient
2.00E+06 or
1.00E+06
subdermally or IV IP Day 0 10 mg/kg 2x per wk 4 weeks 8
Tan 2015 Balb/ Slc-nu/nu 1.00E+07
per 100uL, subcutaneous
into bilateral flank
IP Day 14 5 mg/kg 2x per wk 2 weeks 2
Volk 2008
nu/nu (Harlan
Sprague-Delaney)
4.00E+06
cells + matrigel into
mammary fat pad
IP Day 10 4 mg/kg 2x per wk 5.5 weeks 11
Volk 2011 SCID mice (NCI) 4.00E+06
cells + matrigel into
mammary fat pad
IP Day 19 4 mg/kg 2x per wk 6 weeks 12
Volk 2011 SCID mice (NCI) 4.00E+06
cells + matrigel into
mammary fat pad
IP Day 21 4 mg/kg 2x per wk 3 weeks 6
115
Two of the experimental datasets contained at least three data points prior to administration of
treatment [254], [258]. These points were used in a separate model fitting to see whether limiting the data used
for model training to only pre-treatment measurements could generate a fitted model that still accurately
predicts the response to anti-angiogenic treatment.
Model validation – anti-VEGF drug treatment. After fitting the control data, we validated the
estimated parameters with data not used in the fitting. We applied the fitted model to simulate anti-angiogenic
treatment (bevacizumab, a monoclonal antibody that binds to the human VEGF isoforms) and compared the
predicted tumor growth profile to the experimental measurements for the treatment cases. Here, we simulated
the dosing regimens used in each experiment with the same optimized parameters obtained by fitting the control
data. For each dataset, we simulated intravenous injections lasting for one minute (as in our previous model).
More specifically, this means that there is a net rate of secretion of the drug directly into the blood compartment.
All six experimental studies administered bevacizumab bi-weekly; however, the dosage varied between the
studies. The dosing regimens are given in Table 5-2. The binding affinity and clearance rate for bevacizumab
were obtained from experimental studies in which VEGF was immobilized on a flow cell (FC) and bevacizumab
was injected over the FC at varying concentrations [259]. Based on those measurements, the binding affinity
was set to 4456 pM (kon = 5.4×10
4
M
-1
s
-1
; koff = 2.19×10
-5
s
-1
), and 5.73×10
-7
s
-1
was used for the anti-VEGF
clearance rate.
5.3.4. Partial least squares regression analysis
Partial least squares regression (PLSR) modeling was used to determine the relationship between the
fitted parameters characterizing tumor growth kinetics (inputs) and the response to treatment given by the RTV
value (output). PLSR modeling seeks to maximize the correlation between the inputs and outputs. To
accomplish this, the inputs and outputs are recast onto new dimensions called principal components (PCs),
which are linear combinations of the inputs. The regression coefficients estimated by PLSR describe the relative
importance of each input. Quantitative measures from the PLSR modeling, including the loadings and scores,
provide some insight into the biological meaning of the PCs [260]. Additionally, we use the estimated regression
116
coefficients to determine each input’s contribution across all responses. This metric is given by the “variable
importance of projection” (VIP) for each predictor. The VIP value is the weighted sum of each input’s
contribution to all of the responses. As such, the VIP values indicate the overall importance of the predictors.
VIP values greater than one indicate variables that are important for predicting the output response.
In the final PLSR model we selected, the input matrix was 6 rows x 4 columns, where the 6 rows
correspond to the best fit for each of the six datasets, and the 4 columns consisted of the estimated free
parameters (k0, k1, and Ang0) and the calculated ratio of k 0/k 1. The output matrix was 6 rows x 2 columns,
where the rows corresponds to the predicted RTV using the best fit for each of the six datasets, and the columns
are the two treatment doses (2 and 10 mg/kg). We used two metrics to evaluate the model fitness: R
2
Y and
Q
2
Y, which each have a maximum value of 1. The R
2
Y value indicates how well the model fits the output data.
The Q
2
Y metric specifies how much of the variation in the output data the model predicts [261], and values
greater than 0.5 indicate that the model can predict data not used in the fitting. We performed PLSR modeling
using the nonlinear iterative partial least squares (NIPALS) algorithm [262], implemented in MATLAB
(Mathworks, Inc.). We implemented many other PLSR models, using various combinations of the four model
inputs.
5.3.5. Numerical implementation
All model equations were implemented in MATLAB using the SimBiology toolbox. The final model
is provided as the SimBiology project file, as SBML, and as a MATLAB m-file (S2 Dataset). Parameter fitting
was performed using the lsqnonlin function MATLAB. GraphPad Prism was used to run statistical analyses on
parameter values.
5.4. Results
5.4.1. Model construction.
We have previously developed compartmental models to investigate the kinetics and transport of
VEGF, a key regulator of angiogenesis [263]–[267]. In our previous computational model, the dynamic tumor
117
volume was given by an exponential function and was not linked to the concentrations of pro-angiogenic
species. We now address this limitation of our previous work. Specifically, we expand our previous
computational model of VEGF distribution in tumor-bearing mice [263] to incorporate the effect of VEGF
on tumor growth. Having the dynamic tumor volume be a function of the concentration of VEGF bound to
receptors on tumor endothelial cells is a significant improvement and generates a more physiologically relevant
computational tool to investigate anti-angiogenic treatment strategies.
Details regarding the model structure and molecular species are provided in the Methods Section. Here,
we detail the equation for tumor growth. Tumor growth is given by an adapted Gompertz model focusing on
the exponential and linear phases of the tumor, as previously described [229], [268]. Thus, the differential
equation for the tumor volume (termed “Tumor Growth Model 1”) is:
!"($)
!$
=
&
!
∗"($)
()*+
"
!
"
#
∗"($),
$
-
#
$
∙#1−
./0
!
1./0($)
./0
!
& [2a]
We note that equation [2a] simplifies to:
!"($)
!$
=
&
!
∗"($)
()*+
"
!
"
#
∗"($),
$
-
#
$
∙#
./0($)
./0
!
& [2b]
Here, V(t) is the tumor volume in cm
3
at time t, k0 and k1 are parameters describing the rate of
exponential and linear growth, respectively. The units of k0 and k1 are s
-1
and cm
3
tissue/s, respectively. The y
parameter represents the transition from exponential to linear tumor growth and is unitless. The Ang0 parameter
represents the basal angiogenic signal (at time t = 0), and Ang(t) is the angiogenic signal at time t. The value of
Ang at any time is calculated as the total concentration of pro-angiogenic VEGF-receptor complexes on tumor
endothelial cells. This includes VEGFR1 and VEGFR2 bound to either mouse or human VEGF isoforms,
with or without the NRP1 co-receptor. Thus, Ang(t) and Ang0 have units of concentration (mol/cm
3
tissue).
The values of the tumor growth parameters were estimated by fitting the model to experimental data, as
described in the following section.
118
5.4.2. Model fitting.
We fit the model to control data from published experimental datasets quantifying tumor volume in
mice bearing MDA-MB-231 xenograft tumors without any anti-VEGF treatment [254]–[258]. Although all of
the datasets use the same breast cancer cell line, tumor growth is variable in each case, with the final tumor
volume ranging from 0.8 – 2.5 cm
3
. Additionally, the tumors follow different growth profiles. These differences
in the final volume and growth kinetics can be attributed to differences in the experimental methods from each
dataset, including the mouse strain used, number of tumor cells injected, and the location of the tumor cell
injection. Finally, the researchers quantify tumor volume using different equations. We aim to identify tumor
growth kinetic parameters for individual tumors; therefore, we fit each dataset individually in the parameter
estimation. This allows us to determine tumor-specific growth parameters, even for mice with the same type of
tumor.
We used nonlinear least squares optimization to fit the model and estimate the optimal parameter
values, minimizing the error between the model predictions and the experimental measurements. Before
pursuing model optimization, we first performed a global sensitivity analysis to identify which of the four tumor
growth kinetic parameters most significantly influence the predicted tumor volume. We utilize the eFAST
approach (described in the Methods), which we have routinely used in our previous work [263], [269], [270], to
guide the model fitting. Results from the sensitivity analysis indicate that k0, k1, and Ang0 are influential
parameters across all six data sets, where the total sensitivity index is greater than 0.4 (Figure 5-2). Therefore,
we estimated the values of these three tumor growth parameters, and we hold y constant at a value of 20 [245].
We performed the model fitting 30 times for each of the six datasets (see Methods section for more details),
obtaining 30 sets of optimized parameter values per dataset. Overall, the model does a good job of recreating
the growth dynamics of untreated tumors (Figure 5-3, blue shading). One limitation is the fit to data from
Volk et al. [258], where the model fails to capture the sigmoidal shape of the experimental tumor growth curve
(Figure 5-3).
119
Figure 5-2. Sensitivity indices of tumor growth parameters. The sensitivity indices estimated using the extended
Fourier Amplitude Sensitivity Test (eFAST) quantifying the variance in the model output (tumor volume without
treatment) with respect with covariances in combinations of model inputs: the tumor growth parameters k0, k1, , and
Ang0 at distinct times for each dataset. A, Roland [34]. B, Zibara [35]. C, Tan [36]. D, Volk [37]. E, Volk 2011a [38]. F,
Volk 2011b [38]. The sensitivity indices for the growth parameters are compared to a dummy variable that is not included
in the model. Indices that are significantly different from the dummy variable influence the model output. We used a cutoff
of 0.4 to select which parameters to fit in the parameter estimation.
k0
k1
psi
Ang0
dummy
0
0.2
0.4
0.6
0.8
1
k0
k1
psi
Ang0
dummy
0
0.2
0.4
0.6
0.8
1
k0
k1
psi
Ang0
dummy
0
0.2
0.4
0.6
0.8
1
k0
k1
psi
Ang0
dummy
0
0.2
0.4
0.6
0.8
1
k0
k1
psi
Ang0
dummy
0
0.2
0.4
0.6
0.8
1
k0
k1
psi
Ang0
dummy
0
0.2
0.4
0.6
0.8
1
Total eFAST index (Sti)
A
D F
C
E
B
Total eFAST index (Sti)
Parameter Parameter Parameter
Time
k0
k1
psi
Ang0
dummy
0
0.2
0.4
0.6
0.8
1
120
Figure 5-3. Model fit and validation using full tumor growth time course for fitting. The whole-body mouse model
was used to fit measurements of tumor xenograft volumes, and the tumor growth kinetic parameters were estimated. The
predicted tumor volume over time is shown for the six datasets. A, Roland [34]. B, Zibara [35]. C, Tan [36]. D, Volk [37].
E, Volk 2011a [38]. F, Volk 2011b [38]. The model is able to reproduce experimental data for tumor growth without
treatment and predict validation data not used in parameter fitting. Blue triangles and purple squares are control and
treatment experimental data points, respectively. Shading indicates the 95% confidence interval. Note different scales on
both axes.
We also explored an alternate equation for predicting tumor growth. In this case, we augment equation
(1) to include a coefficient (CAng) that describes how dependent the tumor growth is on the concentration of
the VEGF-VEGFR species (termed “Tumor Growth Model 2”):
!"($)
!$
=
&
!
∗"($)
()*+
"
!
"
#
∗"($),
$
-
#
$
∙#1−
./0
!
12
%&'
∙./0($)
./0
!
& [3]
We again applied the eFAST global sensitivity analysis to determine which of the five tumor growth
kinetic parameters (k0, k1, y, Ang0, and CAng) significantly influence the predicted tumor volume. This analysis
shows that the influence of CAng on the tumor volume is comparable to the effects of k0, k1, and Ang0. However,
we find that the CAng parameter is tightly correlated to Ang0 (based on parameter identifiability analysis used in
our previous work [270], [271]). This means that it is not appropriate to fit both CAng and Ang0 at the same time,
121
as their values may not be estimated with tight confidence intervals. Therefore, we moved forward with Tumor
Growth Model 1, which includes four parameters that characterize the kinetics of tumor growth (equation [2]),
with three of the parameter values estimated in the model fitting described above. The estimated parameter
values are shown in Figure 5-4.
Figure 5-4. Estimated model parameters obtained from fitting. The whole-body mouse model was used to fit
measurements of tumor xenograft volumes, and the tumor growth kinetic parameters were estimated. The estimated
parameter values from the best fits are plotted for each dataset. A, k0. B, k1. C, Ang0. D, k0/k1. Horizontal bar indicates
the median of the best fits obtained from fitting the model to each dataset; error bars indicate the 95% confidence interval.
Statistical comparison of the estimated parameter sets is given in Figure 5-6.
5.4.3. Model validation.
We validated the model with data not used in the fitting. Using the same fitted kinetic parameters as
the control case, we simulated the treatment regimens described in the in vivo mouse studies. The model does
an excellent job of matching the experimental data (Figure 5-3, purple shading), capturing the effect of anti-
VEGF treatment on tumor growth for the majority of datasets. Based on these results, the model is in
agreement with experimental data of untreated tumor growth and can be appropriately validated using
treatment data. Thus, our model is able to recreate the growth dynamics of untreated breast tumor xenografts
in mice and can predict the tumor volume in response to anti-angiogenic treatment.
122
5.4.4. Model fitting to early tumor growth data.
We investigated whether it is possible to accurately predict the response to anti-VEGF treatment when
the model fitting only includes the initial tumor growth data. We selected the datasets that included at least
three tumor volume measurements prior to administration of bevacizumab (two out of the six datasets fit this
criterion). We fit those initial experimental data points for the control (no anti-VEGF treatment) and validated
the fitted model using the anti-VEGF treatment data. We again performed the model fitting 30 times for each
dataset. The optimized model fit using only the initial tumor growth data was able to predict the tumor volume
following treatment (Figure 5-5). Although the 95% intervals were wider in this fitting as compared to the
results obtained when all of the data points were used for model fitting (see Figure 5-3), the newly optimized
model still predicted reasonable values for the tumor size and the confidence intervals contained the
experimental data points for validation (tumor volume with treatment), as shown in the right panels of Figure
5-5. These results demonstrate that the model can recreate treatment dynamics even when parameter fitting is
performed using a limited number of experimental measurements. However, the estimated parameter values
varied widely when fitting to the pre-treatment measurements only compared to fitting to all of the available
control data. Therefore, we only used the model obtained by fitting the full set of control data to make
meaningful comparisons amongst the parameter values from each dataset.
123
Figure 5-5. Model validation after fitting initial tumor growth data. Predicted tumor volume over time for the two
datasets with at least three pre-treatment measurements for tumor volume. A, Roland [254]. B, Volk 2011a [258].
Experimental data points: triangles are control (left panel) and squares are treatment (right panel). Only the triangles
outlined in blue are used for fitting. Shading shows the 95% confidence interval on the best fits. Note different scales on
both axes.
5.4.5. Analysis of the estimated parameter values.
We evaluated the optimized parameters estimated from fitting the model to all of the available control
data. The estimated parameter values for the fits with the lowest errors are given in Figure 5-4. For all of the
fitted parameters, the estimated 95% confidence intervals are within one order of magnitude or less, and there
are few outliers. This indicates that the parameter values can be determined with high confidence, and allows
statistical analysis to compare the parameter values obtained from fitting each dataset. Visual inspection shows
that when fitting to the datasets from Volk et al., the model fitting and parameter estimation showed higher
k0/k1 ratios than the other three datasets (Figure 5-4). Since there appear to be other differences in the
estimated parameter values, we wanted to determine if the differences in the parameter values influence the
predicted response to anti-angiogenic treatment. Below, we present simulations obtained using the optimized
parameter sets estimated from fitting the control data and compare the response to treatment.
124
5.4.6. Predicting the response to anti-VEGF treatment.
Having validated our model, we used the optimized parameter sets to predict the tumor volume in
response to anti-VEGF treatment. We ran the model for each of the six datasets, using all 30 sets of optimized
parameter values. For each set of parameters, the model was simulated for three cases: no treatment (control)
and two treatment conditions (2 and 10 mg/kg bevacizumab). For the treatment cases, twice-weekly injections
were simulated, starting when the tumor volume reached 0.1 cm
3
(termed “Tstart”). We selected this volume,
since it is established that this is the critical time at which tumors typically start secreting higher levels of
angiogenic factors in order to recruit the vasculature necessary to support further growth (~1-2 mm in
diameter). For all cases, the model was simulated for 6 weeks after Tstart. We used the model to predict the
relative tumor volume (RTV), the ratio of the final tumor volume for the control and treatment cases:
RTV=
"
()*+(,*&(
"
-.&()./
[3]
where Vtreatment and Vcontrol are the tumor volumes at the end of the simulation with treatment and without
treatment, respectively. Thus, the RTV represents the fold-change in tumor size due to treatment, where an
RTV value less than one indicates that the treatment reduced the tumor volume, compared to the control. We
use the RTV value to characterize the response to anti-VEGF treatment. The predicted responses to
bevacizumab treatment at a dose of 2 or 10 mg/kg using the best fit parameter values are shown in Figure 5-
6. The range of predicted RTV values indicates that certain tumors are more responsive to anti-VEGF
treatment than others (Figure 5-6). In particular, the predicted RTV values obtained using fitted parameter
values from fitting to data from Volk are higher than the predicted response for the other datasets for the 10
mg/kg dose. Interestingly, the ordering of the most responsive tumors differs for the two dosage levels,
indicating nonlinear effects of the drug that vary with the amount administered. We next performed a thorough
statistical comparison of the RTV and the estimated parameter values obtained in the fitting.
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Figure 5-6. Predicted response to anti-VEGF treatment. The whole-body mouse model, including the dynamic
tumor compartment whose volume is predicted using equation [2], was used to simulate bevacizumab treatment at a
dose of A, 2 mg/kg or B, 10 mg/kg. The relative tumor volume (RTV) predicted by the model is shown. Horizontal bar
indicates the median of the predicted RTV for the best fits from each dataset.
Our statistical analysis indicates a relationship between particular kinetic parameters that characterize
tumor growth and the effectiveness of treatment. We used to statistical analyses to determine whether the sets
of estimated parameters or the predicted RTV values were statistically significantly different (p < 0.05) across
the six datasets (Figure 5-7). Based on this analysis, we found that all datasets with significantly different
predicted RTV values had significantly different k0, k1 or k0/k1 ratios. Interestingly, there was no statistically
significant difference in the estimated Ang0 values, the “basal angiogenic signal”, between any of the datasets.
Overall, the statistical analysis reveals that certain kinetic parameters (particularly, k0/k1) varied considerably
between datasets and corresponded to significantly different treatment response (as indicated by the RTV
value). The values of those parameters, which characterize the kinetics of tumor growth, may be used to predict
the response to treatment.
126
Figure 5-7. Statistical analysis of the optimized parameter sets. Standard ANOVA analysis followed by pairwise
comparisons was used to determine whether the sets of optimized parameter values were statistically different. A, upper
triangle: k0; lower triangle: k1. B, upper triangle: Ang0; lower triangle: k0/k1. C, upper triangle: RTV for bevacizumab dose
of 2 mg/kg; lower triangle: RTV for dose of 10 mg/kg. The color and asterisks indicate log10(p-value): ***, (p-value ≤
0.001); **, (0.001 < p-value ≤ 0.01); *, (0.01 < p-value < 0.05).
5.4.7. Determination of relationship between tumor growth parameters and response to treatment.
We applied PLSR, a multivariate regression analysis, to further quantify the importance of specific
tumor growth characteristics in predicting the response to anti-VEGF treatment. We used the values of k0, k1,
Ang0, and k0/k1 as inputs (predictors) and the RTV at the two dosage levels for bevacizumab (2 and 10 mg/kg)
as the responses. We determined the optimal PLSR model by varying the number of components from one to
four and calculating the fitness metrics R2X, R2Y, and Q2Y values (see Methods section). We also varied the
number of inputs, using different combinations of the estimated parameters. The final PLSR model (i.e., the
model that best predicted the responses without over-fitting) had two components and included four inputs
(k0, k1, Ang0, and k0/k1). This PLSR model is able to accurately predict the RTV at both dosage levels (Figure
5-8A), captures the variance in the inputs and output (high R2X and R2Y, respectively), and performs well with
leave-one-out cross validation (Q2Y = 0.89). All PLSR models that included the k0/k1 ratio but excluded k0,
k1, or Ang0 performed equally well in the cross validation analysis; however, the fitness metrics are the same,
and we cannot objectively select one model over another. Therefore, we moved forward with the model that
included all four inputs.
We analyzed the PLSR model to obtain insight regarding how the four inputs relate to the outputs.
The variable importance of projection (VIP) scores for the four model inputs indicate that the value of k0/k1
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is the largest contributor to predicting the RTV (Figure 5-8B). This suggests that the value of k0/k1 could be
used to distinguish tumors that will respond to therapy or not.
Figure 5-8. Results from multivariate analysis. PLSR analysis quantifies how the tumor growth parameters
influence the response to treatment (RTV). A, PLSR model to predict RTV for two dosage levels of the anti-
VEGF. The optimal PLSR model includes two components. Decreasing in component 1 or increasing in
component 2 corresponds to higher efficacy of the anti-VEGF treatment. B, VIP scores for the model inputs;
a score greater than one indicate variables that are important for predicting the RTV. C, Scores of the model
output, revealing how tumors from each dataset compare in their responsiveness to treatment. D, Loadings of
the model inputs, indicating how the model inputs (fitted parameters) correspond to sensitivity to anti-VEGF
treatment.
Although the PLSR components do not explicitly correspond to a physiological variable, plotting the
loadings for the inputs and outputs provides some insight into the meaning of each component. A plot of the
loadings for the outputs (Figure 5-8C) reveals that both components capture the treatment efficacy. Here, we
consider both components, as together, they account for 99% of the variance in the output. Decreasing in
component 1 and increasing in component 2 corresponds to increased efficacy of the anti-VEGF treatment.
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The datasets in which anti-VEGF treatment is the least effective in reducing tumor growth (collectively, across
the two drug doses) compared to the other datasets, have the highest loading in component 1 and lowest
loading in component 2 (i.e., appearing in the lower right portion of the plot). In comparison, measurements
from tumors in which anti-VEGF treatment leads to more growth inhibition appear in the upper left quadrant
of the plot.
A plot of the loadings for the inputs reveals how the estimated tumor growth parameters are associated
with treatment efficacy. We focus first on the loadings for component 1, as this component accounts for 94%
of the variance in the inputs. We find that k0/k1 is positively correlated with low treatment efficacy, as it has a
positive loading in component 1 (Figure 5-8D). The k0/k1 ratio also has the highest loading in component 2.
Together, these results suggest that a high value of k0/k1 is associated with low treatment efficacy. In summary,
the multivariate analysis provides a regression model that accurately predicts the relative tumor volume
following anti-VEGF treatment, given the tumor growth parameters. Additionally, the analysis confirms the
importance of k0/k1 as a key predictor of the tumor’s response to anti-VEGF treatment.
5.4.8. Effect of tumor receptor number on the response to treatment.
After validating the model and investigating relationships between kinetic parameters describing tumor
growth and response to treatment, we sought to investigate the effects of tumor-specific properties. In
particular, we examined the effect of neuropilin and VEGF receptor levels on relative tumor volume. VEGF
receptor levels were varied from 0 to 10,000 receptors/cell, and NRP levels were varied from 0 to 100,000
receptors/cell. Using a representative set of parameters from the best fits for each dataset, we used the model
to determine Tstart for each combination of receptor levels. We then ran the model to simulate the tumor growth
for six weeks past Tstart to obtain the baseline control volumes. Treatment volumes were obtained by simulating
twice-weekly bevacizumab injections at a dose of 10 mg/kg for six weeks after Tstart. The RTV values were
calculated for each combination of the tumor receptor densities. The model predicts that higher neuropilin
levels led to increased treatment efficacy, especially for high VEGFR2 levels (Figure 5-9). The predicted RTV
values obtained using the estimated parameters from certain datasets show that neuropilin expression has a
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noticeable impact on the response to treatment (Figure 5-9A-B). In comparison, neuropilin levels seem to
have a diminished impact for the Volk dataset, indicated by contour plots that are very similar, even with drastic
changes in neuropilin receptor levels (Figure 5-9C). In summary, the model can be used to study tumor-specific
conditions that are favorable for anti-angiogenic treatment. Higher receptor expression is predicted to increase
anti-VEGF efficacy, although the relationship was not uniform across all datasets, indicating the importance of
accounting for specific tumor settings.
Figure 5-9. Effect of VEGF receptor expression on tumor cells. Relative tumor volume (RTV) predicted
by the model using optimized parameter values obtained from fitting: A, Roland [254]. B, Zibara [255]. C, Volk
2008 [257], for different VEGF receptor levels on tumor cells. Neuropilin density varies: 0 receptors/cell (left),
20,000 receptors/cell (center), and 100,000 receptors/cell (right). Contour plots reveal the relationship between
RTV and VEGFR1, VEGFR2, and neuropilin receptor density on tumor cells. The colorbar indicates the RTV
value, with the same range for all panels. Red color indicates higher RTV, representing tumor conditions that
are less favorable for anti-VEGF treatment.
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5.5. Discussion
We have developed a compartmental model representing tumor-bearing mice in which the tumor
volume is responsive to changes in VEGF concentration. The tumor volume explicitly depends on the
“angiogenic signal”, which is the signal produced when VEGF binds to its receptors on tumor endothelial cells.
In this way, the model can be applied to analyze the effect of anti-VEGF treatment on xenograft tumor growth,
aiding in the analysis of pre-clinical data. Tumor growth kinetic parameters are obtained by fitting the model to
experimental data of breast xenograft tumor growth in mice for control conditions (no anti-angiogenic
treatment) and are validated with treatment data. By including a dynamic tumor volume that explicitly depends
on the concentration of VEGF-bound receptors, we address a primary limitation of our previous work.
Our approach of training the model using control data and using the optimized model to predict
treatment data is a significant advantage over previous modeling work. For example, in model fitting performed
by other groups, tumor growth parameters were estimated by simultaneously fitting both control and treatment
groups [268] or adopted parameter values from previous models [272]. In other work [229], [268], the tumor
growth equation includes coefficients that characterize the killing effect of cancer drugs, including anti-
angiogenic agents, on tumor growth. In contrast, our computational model is able to accurately predict response
to anti-VEGF treatment, data not used in the fitting. This is a significant feature of our model – it is trained
using control data and can reproduce the response to anti-VEGF treatment simply by introducing the drug into
the blood compartment, mimicking pre-clinical mouse studies.
The model provides unique insight into how certain kinetic parameters that characterize tumor growth
correlate with response to anti-angiogenic treatment. Our results demonstrate how the parameters describing
tumor growth could be used as a predictive biomarker for treatment response. In comparison, other studies
have used volume-based growth tumor kinetics as a prognostic biomarker. Lee and coworkers found that the
time to progression (defined as the time it takes the tumor to grow from its nadir in volume after treatment to
a progressive disease state) was significantly correlated with overall survival [232]. In other work, researchers
used tumor growth kinetics to determine the efficacy of anti-angiogenic treatment [233]–[236]. Excitingly, our
approach is highly predictive, where volumetric measurements performed prior to treatment can give insight
131
into how the tumor might respond to an anti-VEGF agent such as bevacizumab. This work is particularly useful
in the pre-clinical setting – the model parameters can be systematically varied, and the tumor volume can be
predicted for each case. Thus the model serves as a quantitative tool to perform in silico pre-clinical trials, guiding
in vivo pre-clinical studies. It may be possible be extend the model to simulate human tumor growth in the
future.
We performed various analyses to quantify how the tumor growth kinetic parameters influence the
response to treatment. The PLSR and statistical analyses reveal that higher k0/k1 values are related to decreased
treatment efficacy. In nearly all cases of the pairwise comparisons, datasets with significantly different responses
to anti-VEGF treatment, the k0/k1 ratio is also significantly different. Our statistical analyses indicate a direct
relationship between the k0/k1 ratio and effectiveness of treatment. Simeoni et al. posit that k0 and k1 may be
indicative of the initial aggressiveness of the cell line and of the response of the animal to tumor progression
(i.e., immunological or anti-angiogenic response), respectively [268]. According to this interpretation, treatment
would be least effective for tumors with aggressive initial growth (high k0) combined with a strong response
from the animal (low k1). Additionally, we find that the basal angiogenic signal, Ang0, is not predictive of anti-
angiogenic treatment response. This agrees with experimental results indicating that the ability of basal levels
of circulating angiogenic factors to predict treatment efficacy is limited [228].
We used the model to investigate how the number of VEGF receptor and co-receptors on tumor cells
influences the response to treatment. Currently, modified expression of VEGF receptors (VEGFR1, VEGFR2,
or NRP1) appears to be among the most promising markers for bevacizumab treatment, though this has not
consistently been replicated across different studies involving various cancer types [226]. In particular, low
levels of soluble VEGFR1 expression in plasma and NRP1 expression on tumor cells are characteristics of a
bevacizumab-responsive tumor [226]. Therefore, we wanted to use our model to predict the influence of tumor-
specific properties on treatment efficacy. The model predicts that low levels of NRP1 or VEGFR lead to
increased treatment efficacy for all datasets. The treatment is predicted to be most effective when tumor NRP
levels are high. These results are in agreement with other biomarker studies [230], [273]. Although there was a
consistent relationship between receptor levels and treatment efficacy, the extent to which receptor numbers
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influenced the predicted relative tumor volume was not identical for all tumors. Datasets for tumors with higher
k0/k1 ratios had higher RTV (i.e., the treatment was less effective), even for a wide range of receptor expression
levels. This may indicate that intrinsic characteristics of the tumor related to its growth kinetics make anti-
angiogenic treatment less effective, regardless of microenvironmental tumor conditions. As a result, solely using
receptor expression as a predictive biomarker could lead to inconsistent results across tumor types.
The focus of our model is on the molecular level interactions occurring between VEGF and its
receptors. In our model, the number of VEGF-receptor (pro-angiogenic) signaling complexes formed directly
influences tumor growth. We acknowledge that this representation of tumor growth omits the intracellular
signaling pathways and corresponding cellular-level responses (i.e., proliferation and migration) involved in new
blood vessel formation. However, the model does indeed capture the dynamics of tumor growth, providing a
mechanistic understanding of the growth kinetics that contribute to the response to anti-VEGF treatment.
We acknowledge some assumptions and limitations that may be addressed as more quantitative data become
available. We do not account for changes in tumor vascularity relative to the tumor volume. The tumor volume
consists of interstitial space, vascular volume, and tumor cells. We account for tumor growth by assuming the
tumor cell volume fraction increases, while the interstitial space volume fraction decreases, and the relative
proportion of the vascular volume is constant (see Methods section for more detail). This means that the tumor
vascularity does change as the overall tumor volume grows, but it remains in the same proportion relative to
the whole tumor volume. Furthermore, we do not simulate remodeling of the blood compartment or changes
in vascular permeability in response to anti-VEGF treatment. However, experimental data show a decrease in
microvessel density following bevacizumab treatment [274], and incorporating this observation would enhance
the model. Additionally, anti-angiogenic treatment promotes normalization of the vasculature, which allows for
more efficient delivery of chemotherapy to the tumor [275]. Accounting for changes in the microvascular
density would allow us to simulate combination treatments that include chemotherapy and anti-angiogenic
agents. Unfortunately, there is a lack of robust time-series data that can be used to predict changes in vascular
density with treatment. This limitation may be addressed as additional quantitative measurements are published.
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The model is highly successful in capturing the growth kinetics of exponential or linear growth curves.
However, the model does not accurately predict sigmoidal tumor growth. The equation governing tumor
growth used in our model is based on the foundational work of Simeoni et al., who adapted a Gompertz model
of tumor growth to investigate both the exponential and linear phases of growth [268]. Although this makes
the tumor growth equation more flexible, it also limits the ability to simulate an eventual plateau in growth. The
model’s inability to capture sigmoidal growth was particularly apparent when fitting the Volk datasets [257],
[258]. However, we have focused on exponential growth, as it has been implemented in many other
mathematical models [276], [277] and shown to accurately fit tumor growth data [278]. Expansion of the tumor
growth equation can be added in future studies.
5.6. Conclusion
We constructed a computational model that simulates the kinetics of VEGF binding to its receptors
and the influence of VEGF-bound receptor complexes on tumor volume in tumor-bearing mice. The validated
model accurately predicts the tumor growth upon administration of anti-angiogenic treatment that targets
VEGF. The fitted parameter values estimated in the present study point to the possibility of using tumor growth
kinetics as a predictive biomarker for anti-angiogenic treatment. Additionally, this model also helps to elucidate
why biomarker candidates such as expression of VEGF receptors on tumor cells may not be reliable for all
tumors. Although the model predicts that receptor levels influence response to treatment, the effects are not
uniform across all of the experimental datasets we analyzed. Thus, our modeling work lays the foundation for
future studies to investigate the importance of tumor growth kinetics as a predictive and specific biomarker and
can accelerate the discovery of biomarker candidates in pre-clinical studies.
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Chapter 6
Tumor Growth Kinetics as Biomarkers to Predict Anti-VEGF Treatment Outcome
Portions of this chapter are adapted from:
Qianhui Wu, Alyssa D. Arnheim, and Stacey D. Finley. Journal of The Royal Society Interface (2018)
15:20180243
6.1. Abstract
Angiogenesis is a crucial step in tumor progression, as this process allows tumors to recruit new blood
vessels and obtain oxygen and nutrients to sustain growth. Therefore, inhibiting angiogenesis remains a viable
strategy for cancer therapy. However, anti-angiogenic therapy has not proved to be effective in reducing tumor
growth across a wide range of tumors, and no reliable predictive biomarkers have been found to determine the
efficacy of anti-angiogenic treatment. Using our previously established computational model of tumor-bearing
mice, we sought to determine whether tumor growth kinetic parameters could be used to predict the outcome
of anti-angiogenic treatment. A model trained with datasets from six in vivo mice studies was used to generate a
randomized in silico tumor-bearing mouse population. We analyzed tumor growth in untreated mice (control)
and mice treated with an anti-angiogenic agent and determined the Kaplan-Meier survival estimates based on
simulated tumor volume data. We found that the ratio between two kinetic parameters, k0 and k1, which
characterize the tumor’s exponential and linear growth rates, as well as k1 alone, can be used as prognostic
biomarkers of population survival outcome. Our work demonstrates a robust, quantitative approach for
identifying tumor growth kinetic parameters as prognostic biomarkers and serves as a template that can be used
to identify other biomarkers for anti-angiogenic treatment.
6.2. Introduction
Tumor angiogenesis results in the vascularization of a tumor. This process facilitates tumor growth by
allowing tumor cells to obtain oxygen and nutrients through the newly formed blood vessels. As excessive
vascularization is often seen in many types of cancer, inhibiting angiogenesis is thought to decrease tumor
135
growth. Therefore, anti-angiogenic treatment is pursued as an attractive therapeutic strategy in oncology [17],
[88].
Bevacizumab is a humanized monoclonal antibody against vascular endothelial growth factor A
(VEGF), a key angiogenic promoter in tumors [17]. This drug has been approved as a monotherapy or in
combination with chemotherapy for many cancers, including renal cell carcinoma, metastatic colorectal cancer,
non-small cell lung cancer, and metastatic cervical cancer [279]. It also gained accelerated approval for treatment
of metastatic breast cancer through the US Food and Drug Administration (FDA) in 2008. However,
subsequent results showed that bevacizumab failed to improve overall survival and that the drug elicited
significant adverse side effects. Consequently, the FDA revoked its approval for use of bevacizumab for first-
line metastatic breast cancer in late 2011 [63], [72]. Several Phase II and III clinical stage studies have also
revealed contradicting results regarding the benefit of add-on bevacizumab in the neoadjuvant treatment setting
for breast cancer patients [64]–[69]. Altogether, these studies illustrate that angiogenic therapy may not be
effective across a wide range of patients. Indeed, breast cancer is a genetically and clinically heterogeneous
cancer type, which makes identifying optimal therapies a challenge [280].
More broadly, there is a need for biomarkers to predict the response to treatment and identify the
tumors for which anti-angiogenic treatment will be effective. A number of mechanistic biomarkers have been
investigated for their ability to predict response to anti-angiogenic treatment and to determine an optimal
treatment strategy. Promising biomarker candidates include the concentration ranges of circulating angiogenic
molecules (such as plasma levels of VEGF) [281], [282], tissue markers (tumor microvessel density) [283]–[286],
and imaging parameters (MRI-measured K
trans
) [71], [283], [287]. However, currently no validated and robust
biomarkers are available that can guide selection of patients for whom anti-angiogenic therapy is most beneficial
[72], [283]].
As an alternative, tumor growth kinetics may be used as biomarkers. There is a body of work that
investigates how tumor growth kinetics can serve as prognostic biomarkers of the response to anti-angiogenic
treatment [288]–[292]. Recently, a study showed that volume-based tumor growth kinetics may be a reliable
indicator of treatment efficacy, and are in good agreement with standardized approaches for assessing response
136
treatment [288]. Moreover, we developed a computational systems biology model to further investigate the
relationship between tumor growth kinetics and the response to anti-angiogenic therapy [111]. The model
predicts VEGF distribution and kinetics in tumor-bearing mice, where the dynamic tumor volume is a function
of the pro-angiogenic complexes involving VEGF-bound receptors (the “angiogenic signal”). By fitting the
model to in vivo experimental data, we estimated the kinetic parameters that characterize tumor growth. We
then used the trained model to predict the effect of anti-VEGF treatment on tumor volume, using only the
estimated parameter values. The model predictions of tumor growth in response to anti-VEGF treatment
closely matched experimental data. In this study, we concluded that there is a strong correlation between
particular intrinsic kinetic parameters and the response to anti-VEGF treatment in terms of the end relative
tumor volume (RTV).
Taking advantage of our established model framework and its strong predictive power, we now use
this model to further investigate the utility of tumor growth kinetics to serve as a biomarker for anti-angiogenic
treatment outcome. We performed an in silico randomized mouse study and estimated the survival of tumor-
bearing mice in response to anti-VEGF treatment. Here, we introduced variability in the mouse population by
allowing the tumor growth kinetic parameter values to vary within defined ranges. A total of 2,400 mice with
different tumor growth profiles were simulated in this study. By generating these large, heterogeneous in silico
population of tumor-bearing mice, we can eliminate the likely bias caused by animals dropping out of
experimental xenograft studies due to high tumor burden. In general, the average tumor size, particularly in the
control group, can be underestimated in an experimental study, thereby underestimating the treatment effect,
because large tumors are excluded from the analysis [293]. In contrast, computational modeling avoids these
limitations and enables performance metrics (e.g., survival estimates) to be calculated [294]. Furthermore,
computational systems biology is a powerful tool for studying how individual components contribute to the
function and behavior of a large system, and has been applied to study cancer at multiple scales [295]–[297].
Such computational models have been used to identify predictive biomarkers and to enhance the efficacy of
anti-angiogenic therapies [60], [281], [298].
137
In our previous work, we did not explore how tumor growth parameters affect the response to
treatment for individual tumors, nor did we examine time-based tumor growth inhibition. Therefore, in this
study, we simulate the tumor volume over time in a heterogeneous population of mice and use more reliable
and appropriate readouts. Specifically, we performed time-to-event analysis [299] by determining the Kaplan-
Meier survival curves based on the in silico population tumor growth data. We examined tumor growth kinetic
parameters as prognostic biomarkers to distinguish the tumor response to anti-angiogenic treatment amongst
the stratified groups.
6.3. Methods
6.3.1. Computational model
We use our previously calibrated and validated model of a VEGF binding and distribution in tumor-
bearing mouse [111]. Briefly, the model is comprised of three compartments representing the whole mouse
(Figure 6-1): normal tissue, blood, and tumor tissue. We include human VEGF isoforms (VEGF 121 and
VEGF 165) secreted by tumor cells, as well as mouse isoforms (VEGF 120 and VEGF 164) secreted by endothelial
cells and muscle fibers. The model includes cell surface VEGF receptors, VEGFR1 and VEGFR2 and soluble
VEGFR1 (sVEGFR1). We include neuropillin co-receptors (NRP1 and NRP2) that bind VEGF directly and
also form tertiary complexes with the VEGFRs. The protease inhibitor α-2-macroglobulin binds VEGF in
blood plasma. We consider the luminal and abluminal endothelial surfaces at the interface between the blood
and each tissue compartment. The VEGF isoforms and sVEGFR1 are transported between compartments via
transendothelial macromolecular permeability and lymphatic flow. Additionally, species are removed via
clearance.
VEGF binding to its receptors on endothelial cells promotes intracellular signaling that mediates
angiogenesis. Thus, we explicitly account for VEGF-mediated tumor growth by incorporating the
concentration of ligated receptors localized on tumor endothelial cells into the tumor volume equation (see
Figure 6-1). We simulate anti-VEGF treatment as intravenous injections lasting for one minute by adding a
net rate of secretion of the drug (bevacizumab) directly into the blood compartment.
138
6.3.2. Numerical implementation
Model equations were implemented in MATLAB using the SimBiology toolbox. Parameter fitting was
performed using the lsqnonlin function in MATLAB. Kaplan-Meier survival estimation was performed using the
kmplot function in MATLAB, and GraphPad Prism was used for statistical survival analyses.
139
Figure 6-1. Schematic and overview of computational model of tumor-bearing mice. The three-compartment
mouse model predicts VEGF binding kinetics and distribution in normal tissue, blood, and tumor tissue. The model
includes human (VEGF121 and VEGF165) and mouse (VEGF120 and VEGF164) VEGF isoforms, VEGF receptors
(VEGFR1, sVEGFR1, and VEGFR2), and the protease inhibitor α-2-macroglobulin. The VEGF isoforms and sVEGFR1
can be transported between compartments via transendothelial macromolecular permeability and lymphatic flow. Species
are also removed from the body via clearance. The pro-angiogenic signal (Ang(t)) is calculated as the summation of the
concentrations of VEGF-bound receptor complexes in the tumor endothelium. The dynamic tumor volume is a function
of the angiogenic signal, explicitly accounting for VEGF-mediated tumor growth. We previously estimated the tumor
growth parameters (k0, k1, ψ, and Ang0) by fitting the model to experimental data. In this study, we randomly varied tumor
growth parameters within specified ranges to simulate tumor growth of several heterogeneous mouse populations. The
anti-VEGF agent bevacizumab is used to simulate anti-angiogenic treatment via intravenous injections into the blood
compartment. Bevacizumab inhibits the formation of pro-angiogenic complexes.
Endothelial cells
Endothelial cells
Blood
h
m
R1 R2 N1
R2 R1 N1
Secretion
Secretion
m
!2m
sR1
Muscle fibers
Normal
m
h
R1 R2 N1
N1
GAG
Secretion
Secretion
m
sR1
Endothelial cells
Endothelial cells
Dynamic Tumor
m h
GAG
R2 R1 N1
R1 R2 N1
Secretion
Secretion
sR1
Lymphatic flow
Permeability
Permeability
Clearance
Tumor cells
Bevacizumab
In silico mouse population
Dynamic Tumor Volume
Varying k0 , k1
(informed by PLSR model)
Ang(t)
R1
m-V164
R2
m-V120
Angiogenic Signal Ang(t): tumor endothelium
R1
m-V120
R2
m-V164
N1
R1
m-V120
N1
R2
m-V164
R1
h-V165
R2
h-V121
R1
h-V121
R2
h-V165
N1
R1
h-V121
N1
R2
h-V165
m-V164
sR1
m-V120
sR1 N1
m-V120
sR1
h-V165
sR1
h-V121
sR1 N1
h-V121
sR1
Bevacizumab in blood
+ h h
LEGEND
Bevacizumab
GAG
human VEGF
isoforms
h
mouse VEGF
isoforms
m
VEGFR1
R1
VEGFR2
R2
NRP1,2
N
α2M
!2m
sR1
soluble
VEGFR1
Reduces
VEGF levels
N2
140
6.3.3. Simulation of in silico mouse population
We previously fit the model to six independent control datasets to estimate the growth kinetic
parameters (k 0, k1, and Ang 0). The parameter ψ was held constant, as it was not shown to significantly influence
tumor growth, compared to the other parameters. The model-predicted tumor growth curves match closely to
the experimental data (fitting error range: 0.0405 – 0.1833).
Here, we generated 400 sets of values for k0 and k1, randomly selected from a uniform distribution
within the range of the best-fit parameter sets from our previous study. The Ang0 value is set to be the median
of the best fits in each case. These sets were used to calculate tumor growth with or without anti-VEGF
treatment, simulating a population of mice for each datasets. In order to keep tumor growth profiles realistic,
tumors that do not reach 0.1 cm
3
within 10 days upon tumor engraftment (assuming initial tumor volume of
0.004 cm
3
) were excluded from the analyses.
We simulated anti-VEGF treatment for each dataset. Treatment protocol A is simulated universally
across the six cases. In this protocol, weekly treatment starts when the tumor volume reached 0.1 cm
3
, as the
switch where angiogenesis is more strongly promoted occurs when the tumor reaches 1-2 mm in diameter. The
treatment dosage is 10 mg/kg. The model was simulated for 12 weeks after treatment started. We also simulated
alternate treatment protocols: Z, denotes biweekly treatment at dosage of 10 mg/kg starting when tumor
volume is 0.004 cm
3
; V11a, denotes biweekly treatment (twice a week) at a dosage of 10 mg/kg, starting when
the tumor volume is 0.5 cm
3
; and V11a-D, denotes biweekly treatment at a dosage of 20 mg/kg, starting when
tumor volume is 0.5 cm
3
. Information for all treatment protocols is shown in Table 6-1.
Table 6-1. Treatment protocols used in model simulations.
Protocol
Treatment start at
tumor volume =
Frequency Dosage (mg/kg) Duration (weeks)
Protocol A 0.1 cm3 biweekly 10 12
Protocol Z 0.004 cm3 biweekly 10 12
Protocol V11a 0.5 cm3 biweekly 10 12
Protocl V11a-D 0.5 cm3 biweekly 20 12
141
6.3.4. Relative tumor volume (RTV)
Based on the model-generated tumor growth data, the relative tumor volume (RTV) is calculated at
any simulated time point:
RTV=
*
$456$75/$
*
89/$49:
An RTV value less than one indicates that the treated tumor volume is smaller than the control.
6.3.5. Kaplan-Meier survival estimation
We applied time-to-event analysis to determine the survival of each mouse population [299]. An in silico
mouse is recorded as “sacrificed” when its tumor reaches 2 cm
3
within the simulated time. Alternatively, a
mouse is recorded as “censored” at a particular time point, t, if its tumor volume simulation remains below 2
cm
3
but ended before that time t. All other mice are retained in the study and recorded as “alive”. Survival
curves were estimated by the Kaplan-Meier method using the kmplot function in MATLAB [300], and compared
using the Mantel-Cox log rank test and Mantel-Haenszel hazard ratio in GraphPad Prism.
The hazard ratio (HR) compares the rate of death in two groups, with the assumption that the
population hazard ratio is consistent over time. It is calculated using the Mantel-Haneszel approach, which is
more accurate than the log rank approach [301]. As an example, an HR of 0.5 between two groups means that
the death rate of the first group is half of that of the second group.
6.3.6. Determination of threshold values
In order to determine threshold values for the k0/k1 ratio, we ordered the simulated mouse tumor
volume data for each of the six populations according to the k0/k1 ratio. Then, we systematically tested each
k0/k1 ratio (called “ratiothresh”) value to see if there is a significant difference between the survival estimates for
the mice with k0/k1 ratio above and below “ratiothresh” in the log rank test (p<0.05). We performed a similar
analysis for k0 and k1 individually to determine any k0,thresh and k1,thresh values.
6.3.7. Validation of the predicted biomarker
142
Upon identifying a potential predictive biomarker for the efficacy of anti-VEGF treatment, we
validated our findings using an independent set of data that was not used to determine the range of the threshold
value. To do so, we fit the control tumor growth for the independent data set and generated an in silico mouse
population based on the fitted parameters.
Data extraction. For threshold validation, data from the published in vivo experimental study of MDA-
MB-231 xenograft tumor growth in mice by Mollard et al. were used for parameter estimation and validation
[302]. Experimental data was extracted using the WebPlotDigitizer program [122] and is shown in Table 6-2.
Parameter estimation. We trained the model to fit the control tumor growth dataset from [302] using
the same approach as described in our previous work [111]. The values of tumor growth parameters k0, k1, and
Ang0 were estimated. In their study, Mollard and coworkers only reported the tumor volumes relative to day
eight. However, the absolute tumor volumes are needed to determine how the tumor interstitial volume varies
as a function of the total tumor volume. Therefore, we compared the relative tumor volume at each time point
in the work by Mollard and coworkers to that of all the available control datasets (Figure 6-2). We then chose
to use the interstitial volume equation from the Zibara data, given that the relative tumor volume closely
matches that of the data in Mollard. Finally, we fit our tumor growth model to the Mollard control dataset.
Figure 6-2. Comparison of normalized experimental data. Control tumor volume on day eight is extrapolated from
an exponential fit to the experimental data [303]–[307], and used to calculate the relative tumor volumes for the models
fit to the control tumor volume from each of the six datasets. The resulting normalized control tumor volume datasets are
compared to that from the Mollard study.
Time (days)
0 10 20 30 40 50 60
Normalized tumor volume
0
50
100
150
200
250
raw data normed to day8 (extrapolated)
Mollard
Roland
Zibara
Tan
Volk 2008
Volk 2011a
Volk 2011b
Mollard
Roland
Zibara
Tan
Volk 2008
Volk 2011a
Volk 2011b
Normalized Tumor Volume
250
200
150
100
50
0
0 10 20 30 40 50 60
Time (days)
143
Table 6-2. Estimated parameter values from fitting tumor growth model to Mollard dataset.
set 1 set 2 set 3 set 4 set 5 set 6 set 7 set 8 set 9 set 10 set 11 set 12
Estimated
parameter
values
k0 (s-1) 1.16E-05 1.37E-05 1.10E-05 1.39E-05 1.39E-05 4.92E-06 4.89E-06 2.58E-06 9.24E-06 8.32E-06 6.67E-06 7.32E-06
k1 (cm3
tissue/s)
1.78E-07 1.95E-07 1.57E-07 1.98E-07 1.98E-07 7.02E-08 6.97E-08 3.69E-08 1.32E-07 3.16E-07 4.16E-06 1.15E-06
Ang0
(mol/cm3
tissue)
1.00E-04 9.97E-05 7.96E-05 1.00E-04 9.97E-05 3.53E-05 3.51E-05 1.85E-05 6.60E-05 9.97E-05 8.38E-05 9.12E-05
Estimated
errors
error (total)
1.45E+0
4
1.97E+0
4
2.01E+0
4
2.04E+0
4
2.04E+0
4
2.06E+0
4
2.06E+0
4
2.07E+0
4
2.08E+0
4
2.49E+0
4
2.78E+0
4
2.99E+0
4
error (ctrl)
1.05E+0
4
1.30E+0
4
1.32E+0
4
1.33E+0
4
1.34E+0
4
1.35E+0
4
1.35E+0
4
1.35E+0
4
1.35E+0
4
1.85E+0
4
2.10E+0
4
2.32E+0
4
error (tx)
3.97E+0
3
6.74E+0
3
6.93E+0
3
7.05E+0
3
7.06E+0
3
7.13E+0
3
7.14E+0
3
7.19E+0
3
7.24E+0
3
6.39E+0
3
6.86E+0
3
6.78E+0
3
144
Fitting was performed using the lsqnonlin function in MATLAB to minimize the sum of squared
residuals (SSR):
min$$%(Θ)=*+,- ./
!"#, %
−/
&%', %
(Θ)1
(
)
%*+
where Vexp,I is the ith experimental data point of tumor volume, Vsim,I is the ith simulated volume at the
corresponding time point, and n is the total number of experimental data points. The minimization is subject
to Θ, the set of upper and lower bounds on each of the free parameters.
The bounds for each parameter spanned at least two orders of magnitude: 10
-8
to 10
-2
for k0 and k1
and 10
-16
to 10
-14
for Ang0. After fitting to the control data, we validated the estimated parameters with data not
used in the fitting for model validation. Specifically, we applied the fitted model to simulate anti-angiogenic
treatment (bevacizumab) and compared to the experimental measurements for the treatment case. We
simulated the dosing regimen used by Mollard et al.: three cycles of weekly intravenous injections lasting for
one minute starting from day five. We used the combined SSR for the relative tumor volume between model
prediction and the experimental data (both control and treatment) to identify the optimal parameters. Twelve
parameter sets with the smallest errors were taken to be the “best” sets (Table 6-2) and the ranges of the
estimated parameter values were used for subsequent model simulations (Table 6-3).
We extracted the absolute tumor volume at day 8 from previously reported data from Mollard and
coworkers [308] to determine the survival estimates for a mouse population simulated based on the fitted
growth kinetics parameter values.
Table 6-3. Parameter bounds and values used in mice population simulations.
k 0 (s
-1
) k 1 (cm
3
tissue/s) Ang 0 (mol/cm
3
tissue)
Roland [2.85e-6 1.62e-5] [4.00e-7 2.10e-6] 5.22E-15
Zibara [3.36e-6 2.96e-5] [5.51e-7 5.61e-6] 9.91E-15
Tan [2.68e-6 3.09e-5] [3.72e-6 6.28e-6] 8.59E-15
Volk2008 [1.96e-6 8.83e-5] [9.59e-8 3.98e-6] 7.22E-15
Volk2011a [2.80e-6 5.95e-5] [1.52e-7 3.22e-6] 7.84E-15
Volk2011b [2.69e-6 6.16e-5] [1.63e-7 3.77e-6] 8.05E-15
Mollard [2.58e-6 1.39e-5] [3.69e-8 4.16e-6] 8.75E-15
145
6.4. Results
6.4.1. In silico mouse population tumor growth in the whole-body model
We performed an in silico randomized mouse study using our whole-body mouse model (Figure 6-1).
The model was previously fitted to each of six independent experimental datasets of control tumor volume in
mice bearing MDA-MB-231 xenograft tumors and validated with a separate dataset [111]. The values of k0 and
k1 (the rates of exponential and linear growth, respectively), and Ang0 (the basal angiogenic signal at time, t=0)
were estimated. A global sensitivity analysis indicated that ψ did not significantly influence tumor volume; thus,
it was held constant. Here, we simulated the tumor growth of the six in silico populations of mice (henceforth
referred to as “Roland”, “Zibara”, “Tan”, “Volk2008”, “Volk2011a”, and “Volk2011b”), with and without anti-
VEGF treatment, in mice with different tumor growth kinetic parameters. For each population, the values of
parameters k0 and k1 are randomly varied simultaneously with a uniform distribution within the ranges of their
estimated values from our previous model fitting. Previously, a sensitivity analysis showed that the Ang0
parameter was an influential parameter to the model output when the model was fitted; however, further
analysis using partial least squares regression (PLSR) indicated that Ang0 was not a strong predictor of response
to treatment [111]. Therefore, in each case, Ang0 is set as the median of the range of its estimated values. We
generated 400 in silico mice for each of the six cases.
Our simulations show that among the six cases, the anti-VEGF treatment has differential effects in
reducing the tumor growth, as compared to the control group (Figure 6-3). For all cases, we used a single
treatment protocol different from protocols used in each of the six experimental studies, in order to compare
the predicted results without bias (termed “protocol A”). For Roland, Tan, Volk2008, and Volk2011b (Figure
6-3A,C,D,F), the treated tumor volumes are less than the untreated tumors. Meanwhile, for Zibara and
Volk2011a (Figure 6-3B,E), there is no apparent difference in the tumor volumes for the treated and control
groups. Thus, the model simulations reveal distinct differences in the effect of anti-VEGF treatment.
146
Figure 6-3. Model-simulated tumor growth data of in silico mouse populations. The whole-body mouse
model previously fit to each of the six datasets individually was used to simulate tumor volume over time. To
generate the simulated tumors, the tumor growth kinetic parameters k0 and k1 were randomly varied within the
range of the estimated values. A total of 400 simulations were run for each case. The mean and 95% confidence
interval at each time point are shown. A, Roland. B, Zibara. C, Tan. D, Volk2008. E, Volk2011a. F, Volk2011b.
Asterisks indicate that the difference between the control and treatment group tumor volumes is statistically
significant (p<0.05).
We further studied the effect of anti-VEGF treatment on tumor growth using RTV, the ratio between
the mean tumor volumes of the treated and control groups. We calculated the RTV at each time point for all
simulated tumors, and determined the RTV at the end of treatment (Figure 6-4). The RTV values in all cases
are smaller than one, indicating that the anti-VEGF treatment limits tumor growth, similar to what has been
observed experimentally [303]–[307]. For Zibara and Volk2011a, the endpoint RTV values are just slightly less
than one (Figure 6-4B,E), which is an expected result based on the similar tumor growth curves between the
control and treated groups (Figure 6-3B,E). Comparing the endpoint RTV among all six cases, the effect of
anti-VEGF treatment in limiting tumor growth is the strongest for Volk2011b (RTV = 0.459 ± 0.054), followed
by Roland (0.454 ± 0.096), Volk2008 (0.615 ± 0.066), and Tan (0.638 ± 0.049). This treatment effect is the
least significant in Zibara (0.979 ± 0.009) and Volk2011a (0.987 ± 0.013).
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
V08 004 sT1 nocut
control
treatment
*
*
*
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
R 004 sT1 nocut
control
treatment
*
*
*
*
*
*
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
Z 004 sT1 nocut
control
treatment
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
V11b 004 sT1 nocut
control
treatment
*
*
*
*
*
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
V11a 004 sT1 nocut
control
treatment
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
T 004 sT1 nocut
control
treatment
0 4 8 12
0
1
2
3
4
5
Time (weeks)
Tumor Volume (cm
3
)
T 004 sT1 nocut
control
treatment
A
D
B C
E F
Roland Zibara
Volk2008 Volk2011a Volk2011b
Tan Control
Treatment
147
Figure 6-4. Scatter plot of RTV at the end of simulations versus tumor growth kinetic parameters. Left to right
columns: k0, k1, and k0/k1 ratio. A, Roland. B, Zibara. C, Tan. D, Volk2008. E, Volk2011a. F, Volk2011b. Color gradient
represents the range of RTV values (from 0 to 1).
k
0
(s
-1
)
10
-6
10
-5
10
-4
RTV
0
0.2
0.4
0.6
0.8
1
k
1
(cm
3
tissue/s)
10
-7
10
-6
10
-5
RTV
0
0.2
0.4
0.6
0.8
1
k
0
/k
1
10
0
10
2
10
4
RTV
0
0.2
0.4
0.6
0.8
1
k
0
(s
-1
)
10
-6
10
-5
10
-4
RTV
0
0.2
0.4
0.6
0.8
1
k
1
(cm
3
tissue/s)
10
-7
10
-6
10
-5
RTV
0
0.2
0.4
0.6
0.8
1
k
0
/k
1
10
0
10
2
10
4
RTV
0
0.2
0.4
0.6
0.8
1
k
0
(s
-1
)
10
-6
10
-5
10
-4
RTV
0
0.2
0.4
0.6
0.8
1
k
1
(cm
3
tissue/s)
10
-7
10
-6
10
-5
RTV
0
0.2
0.4
0.6
0.8
1
k
0
/k
1
10
0
10
2
10
4
RTV
0
0.2
0.4
0.6
0.8
1
k
0
(s
-1
)
10
-6
10
-5
10
-4
RTV
0
0.2
0.4
0.6
0.8
1
k
1
(cm
3
tissue/s)
10
-7
10
-6
10
-5
RTV
0
0.2
0.4
0.6
0.8
1
k
0
/k
1
10
0
10
2
10
4
RTV
0
0.2
0.4
0.6
0.8
1
k
0
(s
-1
)
10
-6
10
-5
10
-4
RTV
0
0.2
0.4
0.6
0.8
1
k
1
(cm
3
tissue/s)
10
-7
10
-6
10
-5
RTV
0
0.2
0.4
0.6
0.8
1
k
0
/k
1
10
0
10
2
10
4
RTV
0
0.2
0.4
0.6
0.8
1
k
0
(s
-1
)
10
-6
10
-5
10
-4
RTV
0
0.2
0.4
0.6
0.8
1
k
1
(cm
3
tissue/s)
10
-7
10
-6
10
-5
RTV
0
0.2
0.4
0.6
0.8
1
k
0
/k
1
10
0
10
2
10
4
RTV
0
0.2
0.4
0.6
0.8
1
A
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.2
0.4
0.6
0.8
1
B
C
D
E
F
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
RTV
Roland
Zibara
Tan
Volk 2008
Volk 2011a
Volk 2011b
k0 (1/s) k1 (cm
3
tissue/s) k0/k1 ((cm
3
tissue)
-1
)
k0 (1/s) k1 (cm
3
tissue/s) k0/k1 ((cm
3
tissue)
-1
)
k0 (1/s) k1 (cm
3
tissue/s) k0/k1 ((cm
3
tissue)
-1
)
k0 (1/s) k1 (cm
3
tissue/s) k0/k1 ((cm
3
tissue)
-1
)
k0 (1/s) k1 (cm
3
tissue/s) k0/k1 ((cm
3
tissue)
-1
)
k0 (1/s) k1 (cm
3
tissue/s) k0/k1 ((cm
3
tissue)
-1
)
148
6.4.2. Kinetic parameters as potential predictor for stratified population response
We investigated the relationship between the parameters that characterize tumor growth kinetics and
the effect of the anti-VEGF treatment. Previously, our PLSR analysis indicated that for nearly all pairwise
comparisons, if the RTV values for two datasets were significantly different, their k0/k1 ratios were also
significantly different. This implies that the k0/k1 is a large contributor in predicting the endpoint RTV [111].
Additionally, plotting the RTV versus k0, k1, and k0/k1 shows some relationship between the endpoint RTV
and the tumor growth parameters (Figure 6-4). Therefore, we investigated whether these tumor growth
parameters could stratify the simulated mouse populations, and distinguish their tumor growth and survival
estimates. To address this question, we used our simulated tumor growth data for each case, noting the number
of in silico mice at each time point. We record the time at which a mouse is “sacrificed”, which happens when
the tumor volume reaches 2 cm
3
, as typically done in experimental studies [309]. This approach for modeling
population survival allows us to closely mimic the practice in preclinical animal studies, and provides easily
interpretable insights for researchers and clinicians.
We used the simulated population survival data to determine if k0, k1, or k0/k1 can be used to
discriminate between tumors for which anti-VEGF treatment is effective or not. We found that in each case, a
range of k0/k1 ratios, as well as k1, can be used to distinguish the population response to the anti-VEGF
treatment (Figure 6-5B,C). We term these “ratiothresh” and “k1,thresh”, the values of the growth kinetic parameters
that separate the simulated mouse population into groups with significantly different survival estimates. In
contrast, we did not find any values of k0 alone that could be used to separate the simulated mouse population
into groups whose survival estimates are statistically different for Roland, Zibara, and Volk2011b cases. For
Tan and Volk2008, we only found one such k0 value in each case (Figure 6-5A).
Interestingly, although the ranges of generated k0/k1 ratios and k1 were different for each of the six
sets of tumor growth data, we found that there is an overlap among the potential ratiothresh or k1,thresh values found
in each of the six cases. The common range of ratiothresh is 9.757 to 17.982, and that of k1,thresh is 1.391×10
-6
to
1.931×10
-6
. This means that separating the treatment group by any k1,thresh or ratiothresh value within its respective
range will produce two groups of treated mice that have statistically different survival estimates. Specifically,
149
the treated group with k0/k1 ratios larger than ratiothresh has a better survival estimate than the treated group with
smaller ratios. The treated group with k1 smaller than k1,thresh has a better survival estimate than the treated group
with larger k1.
Figure 6-5. Range of kinetic parameter and threshold values. In each of the six cases, values of k1,thresh and ratiothresh
were found among all of the randomly generated values of k1 or k0/k1 ratio used in the simulations. A, k0. B, k1. C, k0/k1
ratio. Bars: the ranges of all generated parameter values in each case. Boxes: the ranges of possible threshold values in each
case. Shading: the common range of threshold values among the six cases.
We used the median ratiothresh value (13.689) to illustrate this distinction. We compare the survival
estimates for a total of six groups: 1) all mice in the control group; 2) all mice in the treatment group; 3) control
group with k0/k1 < ratiothresh; 4) control group with k0/k1 > ratiothresh; 5) treatment group with k0/k1 < ratiothresh;
and 6) treatment group with k0/k1 > ratiothresh. We generated the Kaplan-Meier survival curves for these groups
for each of the six cases investigated (Figure 6-6). We also estimated the median survival of the six groups in
each case (Table 6-4), the Mantel-Haenszel hazard ratio (HR), with 95% confidence interval (CI), and the p-
values from the Mantel-Cox log rank test for the survival curve comparison (Table 6-5). When comparing two
groups, if the HR is less than one, the first group has a lower death rate (see Methods). Together these analyses
emphasize that mice with larger k0/k1 ratios survive for longer, with p-value < 0.05. Interestingly, for Zibara
and Volk2011a, although the anti-VEGF treatment does not significantly reduce tumor growth and therefore
does not yield a better survival estimate for the treated groups compared to their control groups (Figures 6-
3B,E and Figure 6-6B,E), the stratified groups yield significantly different survival estimates. That is, the
control and treated groups with k0/k1 ratios larger than ratiothresh have better survival estimates than those with
smaller k0/k1 ratios.
D1_analyse
k0 (1/s x 10
-5
) k1 (cm
3
tissue/s x 10
-6
)
A B
k0/k1 ratio ((cm
3
tissue)
-1
)
C
0 2 4 6 8 10
Volk2011b
Volk2011a
Volk2008
Tan
Zibara
Roland
k0 1 k0 2
0 2 4 6 1 3 5 7
Volk 2011b
Volk 2011a
Volk 2008
Tan
Zibara
Roland
k1 1 k1 2
0 50 100 150
Volk 2011b
Volk 2011a
Volk 2008
Tan
Zibara
Roland
ratio 1 ratio 2
0 2 4 6 8 10
Volk2011b
Volk2011a
Volk2008
Tan
Zibara
Roland
k0 1 k0 2
0 2 4 6 8 10
Volk2011b
Volk2011a
Volk2008
Tan
Zibara
Roland
k0 1 k0 2
150
Figure 6-6. Kaplan-Meier curves for the six simulated groups of tumor-bearing mice using ratio threshold. Here,
the ratiothresh value is taken as the median from the common range found among the six cases (13.8693). A, Roland. B,
Zibara. C, Tan. D, Volk2008. E, Volk2011a. F, Volk2011b. The estimated survival curves of in silico mice subgroups within
each group are shown in each plot: all mice, mice with ratio above or below the median ratiothresh in the control setting or
with treatment.
Table 6-4. Summary of median survival of population separated by median ratio thresh.
Median survival
(days)
Roland
†
Zibara
†
Tan
†
Volk
2008
†
Volk
2011a
†
Volk
2011b
†
Zibara
§
Volk
2011a
¶
Volk
2011a
¶¶
Mollard
†
Control (All) 53 55 58 64 69 68 55 69 69 85
Control
(k0/k1 < ratiothresh)
44 44.5 45 40 44 42.5 44.5 42.5 44 77
Control
(k0/k1 > ratiothresh)
86.5 84 Un* 89.5 87 88 84 80 87 96
Treatment
(All)
Un* 63 77.5 Un* 69 Un* 63 71 Un* Un*
Treatment
(k0/k1 < ratiothresh)
74 46 50 50 44 79 46 42.5 78.5 Un*
Treatment
(k0/k1 > ratiothresh)
Un* Un* Un* Un* 87 Un* Un* 87 Un* Un*
*Un: Undefined. The median survival cannot be estimated if the survival estimation does not reach below 50%;
†
protocol A: biweekly treatment at a dosage of 10 mg/kg, starting when tumor volume reaches 0.1 cm
3
;
§
protocol Z: biweekly treatment at a dosage of 10 mg/kg, starting when tumor volume is 0.004 cm
3
(upon engraftment of
tumor);
¶
protocol V11a: biweekly treatment at a dosage of 10 mg/kg, starting when tumor volume reaches 0.5 cm
3
;
¶¶
protocol V11a-D: biweekly treatment at a dosage of 20 mg/kg, starting when tumor volume reaches 0.5 cm
3
.
A
D
B C
E F
Roland Zibara
Volk2008 Volk2011a Volk2011b
Tan
0 20 40 60 80 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 20 40 60 80 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 20 40 60 80 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 20 40 60 80 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 20 40 60 80 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 20 40 60 80 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 20 40 60 80 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
151
Table 6-5. Statistics comparing the Kaplan-Meier survival curves of population separated by median ratio thresh:
hazard ratio (95%CI) and log rank test p-values.
HR
(95% CI)
p-value
Roland
†
Zibara
†
Tan
†
Volk2008
†
Volk2011a
†
Treatment
(k0/k1 > ratiothresh) vs.
Treatment
(k0/k1 < ratiothresh)
0.2073
(0.1059-0.4057)
p<0.0001
0.2005
(0.0991-0.4055)
p<0.0001
0.1623
(0.0872-0.3021)
p<0.0001
0.0576
(0.0237-0.1399)
p<0.0001
0.0216
(0.0098-0.0476)
p<0.0001
Control
(k0/k1 > ratiothresh) vs.
Control
(k0/k1 < ratiothresh)
0.1214
(0.06974-0.2144)
p<0.0001
0.1627
(0.0866-0.3056)
p<0.0001
0.1445
(0.0808-0.2582)
p<0.0001
0.0422
(0.0173-0.1035)
p<0.0001
0.0296
(0.0098-0.0476)
p<0.0001
Treatment
(k0/k1 > ratiothresh) vs.
Control
(k0/k1 > ratiothresh)
0.0675
(0.0234-0.1949)
p<0.0001
0.1191
(0.01194-1.188)
p=0.0697
0.101
(0.0249-0.4103)
p=0.0013
0.5683
(0.33490.9643)
p=0.0362
0.9921
(0.6117-1.609)
p=0.9742
Treatment
(k0/k1 > ratiothresh) vs.
Treatment (All)
0.2562
(0.1239-0.5299)
p=0.0002
0.2538
(0.1191-0.5408)
p=0.0004
0.239
(0.1236-0.4621)
p<0.0001
0.6138
(0.3732-1.01)
p=0.0546
0.576
(0.3863-0.8588)
p=0.0068
Treatment (All) vs.
Control (All)
0.2307
(0.1548-0.3438)
p<0.0001
0.6742
(0.4384-1.037)
p=0.0726
0.5845
(0.3934-0.8684)
p=0.0079
0.6481
(0.4331-0.9699)
p=0.0350
0.9959
(0.7038-1.409)
p=0.9815
Treatment
(k0/k1 < ratiothresh) vs.
Treatment (All)
1.569
(0.9721-2.41)
p=0.0549
1.558
(0.9714-2.5)
p=0.0658
1.794
(1.158-2.778)
p=0.0089
6.405
(2.971-13.81)
p<0.0001
7.657
(4.065-14.42)
p<0.0001
Table 6-5 (Continued)
HR (95% CI)
p-value
Volk2011b
†
Zibara
§
Volk2011a
¶
Volk2011a
¶¶
Mollard
†
Treatment
(k0/k1 > ratiothresh) vs.
Treatment
(k0/k1 < ratiothresh)
0.0673
(0.0288-0.157)
p<0.0001
0.2332
(0.1191-0.4566)
p<0.0001
0.01104
(0.0039-0.0315)
p<0.0001
0.358
(0.0157-0.0815)
p<0.0001
0.1862
(0.1043-0.3327)
p<0.0001
Control
(k0/k1 > ratiothresh) vs.
Control
(k0/k1 < ratiothresh)
0.0368
(0.01750-0.0778)
p<0.0001
0.1655
(0.0925-0.2962)
p<0.0001
0.0110
(0.0039-0.0315)
p<0.0001
0.0418
(0.0204-0.0857)
p<0.0001
0.6573
(0.5219-0.8029)
p<0.0001
Treatment
(k0/k1 > ratiothresh) vs.
Control
(k0/k1 > ratiothresh)
0.1592
(0.0817-0.3102)
p<0.0001
0.1707
(0.0557-0.5226)
p=0.002
0.7027
(0.4718-1.047)
p=0.0825
0.0842
(0.0452-0.1568)
p<0.0001
0.0782
(0.0561-0.1089)
p<0.0001
Treatment
(k0/k1 > ratiothresh) vs.
Treatment (All)
0.3364
(0.1662-0.6806)
p=0.0024
0.2513
(0.1294-0.4881)
p<0.0001
0.7306
(0.5008-1.066)
p=0.1033
0.2524
(0.126-0.5058)
p=0.0001
0.317
(0.176-0.571)
p=0.0001
Treatment (All) vs.
Control (All)
0.266
(0.1733-0.4083)
p<0.0001
0.6742
(0.4384-1.037)
p=0.0726
0.7766
(0.5543-1.088)
p=0.1416
0.2016
(0.1343-0.3027)
p<0.0001
0.0940
(0.0762-0.1159)
p<0.0001
Treatment
(k0/k1 < ratiothresh) vs.
Treatment (All)
3.938
(1.985-7.811)
p<0.0001
2.119
(1.294-3.47)
p=0.0005
15.64
(6.536-37.41)
p<0.0001
5.074
(2.653-9.705)
p<0.0001
0.5152
(0.3481-0.8458)
p=0.0035
†
protocol A,
§
protocol Z,
¶
protocol V11a,
¶¶
protocol V11a-D
152
We performed a similar analysis using the median k1,thresh value (1.661×10
-6
) to show the distinction
between the survival estimates (Figure 6-7). The control and treated groups with k1 smaller than k1,thresh have
better survival estimates than those with larger k1 values. We also estimated the median survival of the six
groups separated using the median k1,thresh (Table 6-6), the Mantel-Haenszel HR, and the p-values from the
Mantel-Cox log rank test for the survival curve comparison (Table 6-7). From these analyses, mice with smaller
k1 survive longer than those with larger k1, and the HR is smaller than one (p<0.05).
Figure 6-7. Kaplan-Meier curves for the six simulated groups of tumor-bearing mice using k 1 threshold. Here,
the k1,thresh value is taken as the median from the common range found among the six cases (1.661×10
-6
). A, Roland. B,
Zibara. C, Tan. D, Volk2008. E, Volk2011a. F, Volk2011b. The estimated survival curves of in silico mice subgroups within
each group are shown in each plot: all mice, mice with k1 smaller or larger than the median k1,thresh, in the control setting or
with treatment.
Table 6-6. Summary of median survival of population separated by median k 1,thresh.
Median survival
(days)
Roland
†
Zibara
†
Tan
†
Volk
2008
†
Volk
2011a
†
Volk
2011b
†
Zibara
§
Volk
2011a
¶
Volk
2011a
¶¶
Mollard
†
Control (All) 53 55 58 64 69 68 55 69 69 87
Control
(k1 < k1,thresh)
59.5 84 86 Un* 87 Un* 84 87 87 92
Control
(k1 > k1,thresh)
35 45 43 41 44 45 45 44 44 72
Treatment
(All)
Un* 63 77.5 Un* 69 Un* 63 71 Un* Un*
Treatment
(k1 < k1,thresh)
Un* Un* Un* Un* 88 Un* 108 108 Un* Un*
Treatment
(k1 > k1,thresh)
55 46 46 47.5 44 82 44 44 78.5 Un*
†
protocol A,
§
protocol Z,
¶
protocol V11a,
¶¶
protocol V11a-D
Roland Zibara
Volk 2008 Volk 2011a Volk 2011b
Tan
0 50 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (k
1
< k
1,thresh
)
Treatment (k
1
< k
1,thresh
)
Control (k
1
> k
1,thresh
)
Treatment (k
1
> k
1,thresh
)
0 50 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 50 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 50 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 50 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 50 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 50 100
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
A
D
B C
E F
153
Table 6-7. Statistics comparing the Kaplan-Meier survival curves of population separated by median k 1,thresh:
hazard ratio (95%CI) and log rank test p-values.
HR (95% CI)
p-value
Roland
†
Zibara
†
Tan
†
Volk2008
†
Volk2011a
†
Treatment
(k1 < k1,thresh) vs.
Treatment
(k1 > k1,thresh)
0.0012
(0.0004-0.0041)
p<0.0001
0.0904
(0.0456-0.1793)
p<0.0001
0.0794
(0.0422-0.1491)
p<0.0001
0.0241
(0.0118-0.0493)
p<0.0001
0.0138
(0.0063-0.0301)
p<0.0001
Control
(k1 < k1,thresh) vs.
Control
(k1 > k1,thresh)
0.5882
(0.3549-0.9751)
p<0.0001
0.0832
(0.0421-0.1643)
p<0.0001
0.0809
(0.0430-0.152)
p<0.0001
0.0241
(0.0118-0.0492)
p<0.0001
0.01376
(0.0063-0.0301)
p<0.0001
Treatment
(k1 < k1,thresh) vs.
Control
(k1 < k1,thresh)
0.134
(0.0805-0.2231)
p<0.0001
0.0927
(0.0258-0.3324)
p=0.0003
0.0843
(0.0287-0.2471)
p<0.0001
0.1775
(0.0682-0.462)
p=0.0004
0.9909
(0.5909-1.662)
p=0.9724
Treatment
(k1 < k1,thresh) vs.
Treatment (All)
0.5033
(0.2978-0.8505)
p=0.0103
0.2096
(0.1054-0.4169)
p<0.0001
0.2076
(0.1112-0.3874)
p<0.0001
0.2094
(0.1143-0.3839)
p<0.0001
0.515
(0.3422-0.7749)
p=0.0015
Treatment (All) vs.
Control (All)
0.2307
(0.1548-0.3438)
p<0.0001
0.6742
(0.4384-1.037)
p=0.0726
0.5845
(0.3934-0.8684)
p=0.0079
0.6481
(0.4331-0.9699)
p=0.0350
0.9959
(0.7038-1.409)
p=0.9815
Treatment
(k1 > k1,thresh) vs.
Treatment (All)
30.33
(12.08-76.16)
p<0.0001
2.553
(1.538-4.239)
p=0.0003
2.759
(1.728-4.405)
p<0.0001
5.824
(3.356-10.1)
p<0.0001
8.024
(4.379-14.7)
p<0.0001
Table 6-7 (Continued)
HR (95% CI)
p-value
Volk2011b
†
Zibara
§
Volk2011a
¶
Volk2011a
¶¶
Mollard
†
Treatment
(k1 < k1,thresh) vs.
Treatment
(k1 > k1,thresh)
0.0662
(0.0301-0.1456)
p<0.0001
0.0904
(0.0456-0.1793)
p<0.0001
0.0138
(0.0063-0.0301)
p<0.0001
0.0265
(0.0118-0.0595)
p<0.0001
0.1265
(0.0619-0.2588)
p<0.0001
Control
(k1 < k1,thresh) vs.
Control
(k1 > k1,thresh)
0.0254
(0.0126-0.0513)
p<0.0001
0.0832
(0.0421-0.1643)
p<0.0001
0.0138
(0.0063-0.0301)
p<0.0001
0.0138
(0.0063-0.0301)
p<0.0001
0.6814
(0.5175-0.8971)
p=0.0063
Treatment
(k1 < k1,thresh) vs.
Control
(k1 < k1,thresh)
0.0960
(0.0410-0.2244)
p<0.0001
0.0927
(0.0258-0.3324)
p=0.0003
0.5917
(0.3641-0.9618)
p=0.0342
0.0636
(0.0329-0.1233)
p<0.0001
0.0781
(0.0611-0.0999)
p<0.0001
Treatment
(k1 < k1,thresh) vs.
Treatment (All)
0.1959
(0.0899-0.4268)
p<0.0001
0.2096
(0.1054-0.4169)
p<0.0001
0.5129
(0.3404-0.7728)
p=0.0014
0.1783
(0.0858-0.3702)
p<0.0001
0.5779
(0.3567-0.9361)
p=0.0259
Treatment (All) vs.
Control (All)
0.266
(0.1733-0.4083)
p<0.0001
0.6742
(0.4384-1.037)
p=0.0726
0.7766
(0.5543-1.088)
p=0.1416
0.2016
(0.1343-0.3027)
p<0.0001
0.0940
(0.0762-0.1159)
p<0.0001
Treatment
(k1 > k1,thresh) vs.
Treatment (All)
3.248
(1.77-5.959)
p=0.0001
2.168
(1.336-3.516)
p=0.0003
8.024
(4.379-14.7)
p<0.0001
3.518
(1.913-6.472)
p<0.0001
3.444
(1.863-6.365)
p<0.0001
†
protocol A,
§
protocol Z,
¶
protocol V11a,
¶¶
protocol V11a-D
154
6.4.3. Alternative treatment strategies to improve survival estimates
We next sought to understand whether alternative treatment protocols can effectively reduce tumor
volume for the Zibara and Volk2011a cases, since the baseline protocol did not significantly affect tumor
volume. For the Zibara case, we simulated the original treatment protocol used in the experimental study
(termed “protocol Z”). This protocol starts the 10 mg/kg biweekly treatment upon tumor engraftment
(assuming the initial tumor volume to be 0.004 cm
3
) [304]. The predicted tumor volumes are smaller in the
treated group (Figure 6-8A), recapitulating the findings from the published experimental study. The predictions
may suggest that in this case, starting the treatment earlier is more effective in limiting the tumor growth. For
mice with k0/k1 ratios larger than the median ratiothresh, or with k1 smaller than the median k1,thresh, the HR between
the treated and control groups is smaller than one, and the survival curves are significantly different (p<0.0001)
(Tables 6-5 and 6-7).
Figure 6-8. Model-simulated tumor growth data with alternative treatment protocols. The mean and 95%
confidence interval at each time point are shown. A, Zibara case with treatment protocol Z. B, Volk2011a case with
treatment protocol V11a. C, Volk2011a case with treatment protocol V11a-D (see Methods). Asterisks indicate that the
difference between the control group and the treatment group tumor volumes is statistically significant (p<0.05).
For Volk2011a, we simulated treatment termed “protocol V11a”, which starts the 10 mg/kg biweekly
treatment when the tumor volume reaches 0.5 cm
3
, a start time extracted from the published preclinical study
[307]. After 12 weeks, the simulated mean tumor volumes in the treated group are significantly smaller than the
control tumors (Figure 6-8B). However, the survival estimates were not significantly different (p>0.05). Again,
the treated group with k0/k1 ratios larger than the median ratiothresh, or with k1 smaller than the median k1,thresh,
has a significantly better survival estimate than the opposite group (p<0.0001) (Tables 6-5 and 6-7). This
phenomenon is similar to that observed in the Volk2011a case using protocol A, where the two groups
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
) V11a 004-1 sT5 filter nocut 20mg/kg biwkly
control
treatment
*
*
*
*
*
*
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
V11a 004-1 sT5 nocut
control
treatment
*
*
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
)
Z sT004 nocut
control
treatment
A
Zibara (protocol Z)
B
Volk 2011a (protocol V11a)
C
Volk 2011a (protocol V11a-D)
Control
Treatment
0 4 8 12
0
2
4
6
Time (weeks)
Tumor Volume (cm
3
) V11a 004-1 sT5 filter nocut 20mg/kg biwkly
control
treatment
*
*
*
*
*
*
155
separated according to the k0/k1 ratio or k1 have distinct survival estimates, but there is no significant difference
between the treated and control groups.
Finally, we explored whether another treatment protocol could significantly improve the survival
estimates for the treated group compared to the control. We simulated protocol V11a-D, where biweekly
treatment starts when the tumor volume reaches 0.5 cm
3
, and the drug dosage is doubled to 20 mg/kg. This
treatment protocol significantly limits the tumor growth (Figure 6-8C), and the survival curves are significantly
better for the treated group compared to the control (p<0.0001). Overall, the treated and control groups have
an HR of 0.2016 (95% CI: 0.1343-0.3027) (Table 6-5).
6.4.4. Validation of thresholds using an independent dataset
To validate the use of the range of ratiothresh and k1,thresh values that we found, we used a recently published
independent set of data that measures tumor growth in mice with MDA-MB-231 xenografts, with or without
bevacizumab treatment [302]. First, we fit the model to the measured tumor volumes without treatment. We
obtained 12 sets of estimated parameter values for k0, k1, and Ang0 that allow the model to best fit to the control
data. We then validated the fitted model by simulating anti-VEGF treatment and comparing to the experimental
measurements. The predicted tumor growth with treatment matches closely to the experimental data (Figure
6-9A).
Using the same approach as described above, we generated 400 sets of tumor volumes for an in silico
mouse population with and without treatment (referred to as “Mollard”). To do so, we randomly varied k0 and
k1 from the ranges of the 12 sets of estimated parameter values from model fitting to the Mollard dataset, with
Ang0 held constant at the median of its estimated values. The simulated tumor volumes for the control and
treated groups are shown in Figure 6-9B.
We generated the population survival data based on the simulated tumor growth profiles. We tested
whether the common range of ratiothresh and k1,thresh values identified using the six datasets described above are
able to separate the population survival data for this validation case (Mollard). For all ratiothesh values within the
range, the survival estimate of the treated mice with k0/k1 ratios larger than the threshold is better than those
156
with smaller k0/k1 ratios. Examples using the median ratiothresh and the median k1,thresh are shown in Figure 6-
9C-D. We calculated the HR values, as well as the p-value from the Mantel-Cox log rank test among the treated
and control groups, separated using the median of the common ratiothresh range (Table 6-5) or the common
k1,thresh range (Table 6-7). Thus, we were able to validate the threshold values.
Figure 6-9. Validation of ratio thresh and k 1,thresh values with an independent set of data. A, Model fit to control data
and validation with treatment data from [302]. The model was fit to normalized tumor volume, and the tumor growth
kinetic parameters were estimated. The model is able to reproduce experimental data in the control group and predict the
treatment data. Line: mean of best fits. Shading: range of standard deviation. Squares: experimental data. Error values: SSR
for mean of the best fits. B, Model-simulated tumor growth of an in silico mouse population, with tumor growth kinetic
parameters k0 and k1 for each simulation randomly varied within the range of their estimated values. The mean and 95%
confidence interval at each time point are shown. Asterisks indicate that the difference between the control and treatment
group tumor volumes is statistically significant (p<0.05). C and D, Estimated Kaplan-Meier survival curves of the
simulated mouse population obtained using the model that was fitted to Mollard data. The population is separated using
the median of the range of C, ratiothresh values (13.8693), or D, k1,thresh values (1.661×10
-6
).
6.4.5. Tumor growth dynamics among stratified populations
We explored the dynamics of the tumor growth for the groups separated by the threshold values to
better understand why the anti-VEGF treatment has differential effects in the simulated mouse populations.
As researchers have pointed out, log-transformation of tumor growth data provides information on the tumor
growth rates (given by the slope of the curve) and is more suitable for detecting a transient biological or
therapeutic effect [309]–[311]. Therefore, we compared the mean RTV time courses (Figure 6-10) and the
0 4 8 12
0
2
4
6
8
Time (weeks)
Tumor Volume (cm
3
)
M_Z sT1 00452 12picks
control
treatment
*
*
*
*
*
0 50 100 150
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
B A
C
Time (weeks) Time (weeks)
0 50 100 150
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (k
1
< k
1,thresh
)
Treatment (k
1
< k
1,thresh
)
Control (k
1
> k
1,thresh
)
Treatment (k
1
> k
1,thresh
)
D
Time (weeks)
0 3 6 9
Normalized Tumor Volume
0
50
100
150
200
250
300 300
250
200
150
100
50
0
Normalized Tumor Volume
Tumor Volume (cm
3
)
0 50 100 150
0
50
100
Time (days)
Survival (%)
Control (All)
Treatment (All)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
0 50 100 150
0
50
100
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Survival (%)
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Treatment (All)
Control (k
1
< k
1,thresh
)
Treatment (k
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1,thresh
)
Control (k
1
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1,thresh
)
Treatment (k
1
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1,thresh
)
Control
Treatment
error (ctrl):1.5x10
4
error (tx): 6.71x10
3
error (total): 2.17x10
4
157
mean tumor volume data plotted on the log-scale (Figure 6-11) of the groups stratified by the median ratiothresh
(13.869) in each case.
Figure 6-10. Time course of relative tumor volume (RTV). The mean RTV levels of all in silico mice and the groups
with k0/k1 smaller or larger than the median ratiothresh (13.8693) are shown. A, Roland. B, Zibara. C, Tan. D, Volk2008. E,
Volk2011a. F, Volk2011b.
Figure 6-11. Tumor volume data plotted on the log-scale for all in silico mice and populations separated by
ratio thresh value of 13.8693. A, Roland. B, Zibara. C, Tan. D, Volk2008. E, Volk2011a. F, Volk2011b.
day
0 20 40 60 80
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Time (days) Time (days)
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E F
Roland Zibara Tan
Volk 2008 Volk 2011a Volk 2011b
RTV
RTV
RTV
RTV
RTV
RTV
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R 004 sT1 nocut
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thresh
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ctrl_above
tx_above
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tx_below
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3
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V11a 004 sT1 nocut
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treatment
ctrl_above
tx_above
ctrl_below
tx_below
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0.001
0.01
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10
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3
)
V11b 004 sT1 nocut
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ctrl_above
tx_above
ctrl_below
tx_below
A
D
B C
E F
0 20 40 60 80
0.001
0.01
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1
10
Time (days)
Log Tumor Volume (cm
3
)
Z 004 sT1 nocut
Control (All)
Treatment (All)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
Roland Zibara
Volk2008 Volk2011a Volk2011b
Tan
Tumor Volume (cm
3
)
Tumor Volume (cm
3
)
Tumor Volume (cm
3
)
Tumor Volume (cm
3
)
Tumor Volume (cm
3
)
Tumor Volume (cm
3
)
158
For Roland, Tan, and Volk2008, the mean RTV of the group with larger k0/k1 ratios (Figure 6-
10A,C,D) is initially larger, and then becomes smaller relative to the opposite group. This switch occurs because
in the group with larger k0/k1 ratios, the difference between the treated and control tumor volumes is smaller
at early times, and then becomes larger (Figure 6-11). Meanwhile, the actual tumor volumes for this group are
both relatively low. As a result, this group survives longer (Figure 6-6). For the Mollard case, the differences
between the treated and control tumor volumes in the group with larger k0/k1 ratios are larger (Figure 6-12B,
dotted curves), giving rise to the larger mean RTV (Figure 6-12A). However, the group with larger k0/k1 ratios
still survives longer because the actual tumor volumes are relatively low (Figure 6-9C).
Figure 6-12. Dynamics of tumor volume. A, Time course of relative tumor volume (RTV) for the Mollard case. The
mean RTV for all in silico mice and mice with tumors whose k0/k1 ratio is smaller and larger than the median ratiothresh
(13.8693) are shown. B, Tumor volume data plotted on the log-scale for all in silico mice and mice separated according to
the tumor’s k0/k1 ratio.
The tumor volume data plotted on the log-scale also reveal that the tumor growth rates of control and
treated groups diverge at different time points. For Roland, the gap between the control and treated groups
continually increases when plotted on a linear scale (Figure 7A). However, the tumor volumes on the log-scale
show that their growth rates mostly differentiate during days 14-40. The growth rates become similar during
the later stage (after 40 days), as evidenced by the parallel curves on the log-scale (Figure 7B). Therefore, the
increasingly large gap between the tumor volumes is a result of early differences in the tumor growth rates. A
similar phenomenon is observed for Volk2011b, where the tumor growth rate of the treated group is suppressed
transiently at early times but not in the later stage (Figure 6-11). In Zibara, Tan and Volk2008, the growth rates
start to differentiate between day 30 and day 45, and only gradually become similar towards the end of the
simulated time. Overall, analysis of the growth curves plotted on the log-scale reveals that the anti-VEGF
treatment has differential effects in limiting tumor growth, and the effects occur at different stages for the
day
0 20 40 60 80
RTV
0
0.5
1
ratio thresh=13.8693
all
ratio < ratio
thresh
ratio > ratio
thresh
Time (days)
0 20 40 60 80
0.001
0.01
0.1
1
10
Time (weeks)
Log Tumor Volume (cm
3
)
M_Z sT1 00452 12picks
control
treatment
crtrl_above
tx_above
ctrl_below
tx_below
A B
Time (days)
0 20 40 60 80
0.001
0.01
0.1
1
10
Time (days)
Log Tumor Volume (cm
3
)
Z 004 sT1 nocut
Control (All)
Treatment (All)
Control (ratio > ratio
thresh
)
Treatment (ratio > ratio
thresh
)
Control (ratio < ratio
thresh
)
Treatment (ratio < ratio
thresh
)
159
simulated cases. The treatment effect appears to be stronger for the group with k0/k1 ratios larger than the
median ratiothresh.
Figure 6-13. Mean tumor growth. We plot the mean tumor volume for all in silico mice in control and treatment groups
using the model fitted to Roland data. A, Linear scale and B, Log scale.
6.5. Discussion
In this study, we focus on identifying tumor growth kinetic parameters as potential biomarkers for the
outcome of anti-VEGF treatment. We developed a computational approach that incorporates model training,
simulation of tumor growth within a heterogeneous population, and estimation and analysis of population
response.
We simulated anti-VEGF treatment and compared the effect of treatment across tumor-bearing mice
generated from our previous fitting to six independent preclinical studies. For most simulated tumors, the anti-
VEGF agent significantly reduces tumor volume compared to control. However, our simulations for Zibara
and Volk2011a show that these populations do not respond to the treatment (Figure 6-3B,E), which is
different than the effect seen experimentally. This difference occurs for two reasons. First, our simulated
treatment protocol A is universal across the six cases, and is different from what was used in each of the original
six experimental studies. Second, in our simulations, k0 and k1 are varied simultaneously and independently of
each other, possibly resulting in more variability than what occurs experimentally .
Our study demonstrates that the k0/k1 ratio or k1 alone can be utilized to stratify the population
response with or without anti-VEGF treatment. This finding agrees with our previous finding through PLSR
analysis that the ratio is a key predictor of the tumor response to anti-VEGF treatment [111]. Building on that
framework, we found that the survival estimate of mice with larger k0/k1 ratios or smaller k1 is better compared
0 20 40 60 80
0
2
4
6
Time (days)
Tumor volume (cm
3
)
R 004 sT1 nocut
control
treatment
A B
0 20 40 60 80
0.001
0.01
0.1
1
10
Time (days)
Log tumor volume (cm
3
)
R 004 sT1 nocut
Control (All)
Treatment (All)
0 20 40 60 80
0
2
4
6
Time (days)
Tumor volume (cm
3
)
R 004 sT1 nocut
control
treatment
160
to those with smaller ratios or higher k1. Interestingly, the result for the ratio is the opposite of the conclusion
we drew previously (that a larger ratio correlates with a poorer response to treatment). However, in that work,
we focused only on whether the final RTV value was low. This highlights the fact that only evaluating the
endpoint RTV of the treated and control group and neglecting the actual tumor volume data over time can lead
to misinterpretation of the treatment effect. Indeed, researchers have recognized that while most preclinical
studies focus on the end points of tumor growth, monitoring tumor growth kinetically may be more insightful
[310], [311].
We found that in two cases (Volk2011a simulated with protocols A and V11a), no significant difference
is observed in the survival estimates between the treated and control groups. However, even for these cases,
two populations with significantly different survival estimates can be identified based on their k0/k1 ratios
(Figure 6-6B,E) or k1 value (Figure 6-7B,E). This indicates that even when the treatment is not effective in
reducing tumor volume, there is still a difference in tumor growth dynamics between the two populations
stratified based on the tumor’s growth kinetic parameters. Thus, we believe that the k0/k1 ratio or k1 may be
prognostic biomarkers to stratify populations for their survival estimate without the anti-angiogenic treatment.
Interestingly, the parameters provide mechanistic insight into tumor growth. In particular, they highlight that
slower linear growth (larger ratio or smaller k1) results in less aggressive overall tumor growth (Figure S5) and
therefore, better survival outcome.
Another interesting aspect is the utility of k1 to serve as a prognostic biomarker. Although k1 was not
revealed as a strong predictor of the final RTV previously in the PLSR analysis, it is inversely correlated with
the k0/k1 ratio, and therefore in our study, it also can be used to stratify the population survival outcome. Here,
performing the survival analysis addresses one limitation from our previous PLSR analysis, where we were able
to identify which parameters were related to treatment efficacy, but could not identify the specific relationship
between the kinetic parameter values and effectiveness of the treatment.
Compared to the mean RTV data, the tumor volume data provide more useful insight into the tumor
growth characteristics of the stratified population. In particular, the tumor volume plotted on the log-scale
more clearly illustrates the source of the differences in the population survival estimates. Specifically, we found
161
that larger k0/k1 ratios often yield slower tumor growth in a population, and therefore, lead to a better survival
estimate of the population. This conclusion could not be made if we were to only analyze the RTV data. In
addition, the tumor volumes on the log-scale reveal that the effect of anti-VEGF treatment in tumor growth
can be relatively transient or gradual.
Our study uses a predictive computational model of tumor growth. This is a pharmacokinetics-
pharmacodynamics model with mechanistic detail that goes beyond what is found in other models. However,
in the future, this model can be expanded to address limitations that are not currently accounted for. For
example, we do not account for changes in tumor vascularity relative to tumor volume. We assume the vascular
volume relative to total tumor volume remains constant, given the lack of robust quantitative data needed to
develop a mathematical function describing how tumor vascularization changes over time. In addition, vascular
normalization is an important process that has been shown to affect tumor growth and can be regulated by
anti-VEGF agents [60]; however, this process is not included in our model. These aspects can be implemented
into the model as more quantitative data become available and enable us to characterize the dynamics of vessel
normalization. The model can then be further extended to account for other characteristics of tumor
progression, including tumor perfusion and metastatic potential. The model can also be adapted to simulate the
effect of cytotoxic drugs that target tumor cells, which in turn will affect the tumor volume. Furthermore, the
range of threshold values for tumor stratification is constrained by the estimated parameter values from model
training to each experimental dataset. It is possible that artifacts from experimental data quantification led to
bias in the range of the fitted parameter values. This can be improved when more quantitative experimental
data become available for additional model training. We note that the biomarker candidates identified in this
study are best used to stratify populations for their survival outcome, whether the mice receive treatment or
not, rather than to predict treatment efficacy. This is primarily because the datasets used for model training
were tumor volumes measured over several weeks. Our results would be of broader applicability if only pre-
treatment data were adequate to train the model. We attempted such an approach in previous work [111];
however, the simulated volumes varied widely, preventing us from making conclusive predictions. Despite this
162
perceived limitation, our modeling approach generates hypotheses about potential biomarkers, and spurs on
experimental validation to ensure the utility of the biomarkers identified.
Our study demonstrates a time- and cost-effective way to generate large in silico mouse populations, predict
anti-VEGF treatment outcome, and stratify the populations. This approach provides useful information that
could facilitate efficient experimental design, such as predicting the effect of different treatment protocols
(varying the dosage and the timing of the injections). Additionally, our modeling approach can be adapted for
analysis of patient treatment outcome in clinical studies. With data from a small patient population, we can
develop a patient-specific model and generate a larger in silico population. Analysis of the simulated tumor
growth and survival data can be used to identify biomarkers that predict responders versus non-responders to
anti-VEGF treatment, stratify the predicted population survival, and test the response to various treatment
schedules.
6.6. Conclusion
We examined tumor growth kinetic parameters as potential biomarkers of anti-angiogenic treatment
outcome. Using a computational model that simulates VEGF-dependent tumor growth in tumor-bearing mice,
we generated an in silico mouse population and related the kinetic parameters that characterize tumor growth to
the response to anti-VEGF treatment. We found that the ratio between two tumor growth kinetic parameters,
k0 and k1, as well as k1 alone, can be prognostic biomarkers and that the simulated treatment protocol may have
a better outcome for mice whose tumors have smaller linear growth rates. In fact, we found ranges of threshold
values for the k0/k1 ratio and k1 that distinguish tumors’ response to the anti-VEGF treatment. This study
demonstrates an approach for identifying tumor growth kinetic parameters as potential biomarkers, and this
model framework can be adapted to predict the efficacy of other anti-angiogenic strategies.
163
Chapter 7
Conclusions
7.1 Overview
In this work, I have developed a detailed mechanistic model of the eNOS signaling pathway which
generated testable hypothesis on TSP1’s inhibitory mechanisms via receptor CD47, and established the first
mechanistic model to describe the TSP1-mediated apoptosis signaling pathway via receptor CD36. The
integrated intracellular network model will enable quantitative understanding of the relative importance of the
two pathways that regulates angiogenesis.
7.2. Summary
The modeling work for TSP1’s intracellular signaling pathways described in Chapter 2-4 provides new
quantitative, mechanistic understanding of the anti-angiogenic functions of TSP1. We first sought to identify
potential intracellular mechanisms of TSP1 via receptor CD47, by constructing a model of the eNOS signaling
pathway. This model is extensively detailed to capture various mechanisms that regulates eNOS activity, and it
is calibrated using in vitro datasets that constrained parameters throughout the signaling pathway. We use the
model to simulate signaling dynamics in cells experiencing various physiologically relevant VEGF levels. The
simulations show that while upstream dynamics are rather sensitive to changes in the VEGF input, downstream
response in the NO and cGMP levels remain quite robust. We then used the model to simulate various
perturbations to predict possible mechanisms of TSP1 through receptor CD47, by comparing the predicted
inhibitory effects to experimental datasets. Furthermore, perturbations that are exclusively effective in a high
VEGF condition but not in the basal condition serve as new strategies for selective targeting of cells that are
experiencing high local VEGF levels, likely in tumor microenvironments, while avoiding harming the normal
tissue vasculature where VEGF is typically at a lower level.
Next, we establish a mechanistic model for the TSP1-mediated apoptosis pathway via receptor CD36.
This model was trained and validated using in vitro datasets of species dynamics upon TSP1 activation of CD36.
We implemented the model with quantified the receptor numbers for CD36 and Fas on HMVECs. Motivated
164
by the understanding that heterogeneity in expression levels can impact the response to extrinsic apoptotic
signaling, we used the model to simulate the apoptotic response of a heterogeneous cell population. We also
simulated the population response to TSP1 treatment in combination with various perturbation strategies, in
order to identify effective strategies to enhance the population apoptotic response. This work provides a
quantitative understanding of the TSP1-mediated endothelial cell apoptosis signaling, and provides insight into
how cell killing can be improved by applying additional perturbations along with the TSP1 treatment.
As a final step, we integrated the two pathway models to investigate the influence of receptor
expression profile on the signaling response to TSP1 and VEGF, and the relative importance of the two
pathways in a single deterministic model. Ultimately, this integrated model of TSP1’s intracellular signaling
network in endothelial cells can serve as a framework to predict treatment effects of pro- and anti-angiogenic
agents, and predict patient-specific treatment strategies that achieves optimal angiogenic inhibition based on
the specific information for that patient.
In Chapter 5 and 6, I present the modeling work using the established whole-body model of tumor-
bearing mouse. We first expand the model to account for the effects of the pro-angiogenic signal and anti-
VEGF treatment on tumor volume, by incorporating the angiogenic signal as a new factor in the calculation of
the tumor growth rate. We estimated the unknown tumor growth kinetic parameters by fitting the tumor growth
model to in vivo datasets of control mice bearing human breast-cancer xenograph, and validated the model
predictions of treatment response using the treatment datasets. For each experimental study, we kept the
estimated parameter sets separate to account for the differences between the experimental setting and animal
model handling and treatment protocols. We use the trained model to generate the treatment response to the
anti-VEGF treatment, in a population of mice with unique tumor growth profiles. Then, we sought to
determine whether a kinetic parameter can be used to stratify the survival estimate of each virtual mouse cohort.
We identified threshold values in two such parameters that can serve this purpose, and validate their utility
using an independent set of data. This work demonstrates a computational approach to investigate the utility
of tumor-growth kinetics as biomarkers to predict population response.
165
7.3. Future directions
The integrated TSP1 signaling model can be used to predict the cell signaling response to a variety of
angiogenic regulators, such as VEGF itself, other pro-angiogenic factors that stimulate the eNOS pathway, as
well as TSP1 and its mimetics. It would be of interest to investigate whether TSP1 takes effect in simultaneously
inducing endothelial cell apoptosis and suppression of eNOS signaling. Furthermore, variation of cellular
signaling species expression levels can be incorporated to predict the optimal treatment strategy to inhibit the
angiogenic functions of a population of endothelial cells.
As described in Chapter 4, to further enhance the utility of the integrated intracellular signaling model
for TSP1, several crosstalk mechanisms between the CD36, CD47, and R2 pathways can be taken into account.
Particularly of interest are the VEGF-induced upregulation of Fas receptor, TSP1-mediated SHP-1 recruitment
to R2 via CD36, its inhibition of myristate uptake via CD36 and the subsequent effect on myristylation of Src
family kinases, and the interaction between Akt and cFLIP. Certainly, as existing experimental evidence seems
to be contradictory or unclear, new experiments designed to verify that these mechanisms hold true for the
same HMVECs cell line, and to generate quantitative data of human endothelial cells would be extremely
helpful in validating these mechanisms. This information can then be implemented into the mechanistic model.
Generally, the computational systems biology approach should be an iterative process involving
incorporating experimental data to calibrate the model, using the model to generate new testable hypothesis,
and again using the experiments to verify the model predictions. Additionally, a predictive model can effectively
reduce the cost of experimental studies as it can be used to inform efficient experimental design. For instance,
in Chapter 2, our model predictions points to a set of intracellular mechanisms that achieves potent angiogenic
inhibition in a high VEGF environment. We then conducted a search for the existing compounds that
correspond to these mechanisms of action, which helps to identify agents that can potentially be repurposed
and tested in the experimental setting.
166
7.4. Concluding thoughts
This work provides a framework for understanding the effects of anti-angiogenic agents in endothelial
cells. It can be extended to investigate the subsequent regulation of vascular activity following the drug effect
on the endothelium. It can also be combined with pathway models of pro-angiogenic signaling to build a
comprehensive reaction network, and predict the system’s response to a larger variety of signals that exist in
the tumor microenvironment. Furthermore, these models can be linked with agent-based models that accounts
for receptor heterogeneity across tissue and cell types. The information from this model can ultimately be used
to inform effective anti-angiogenic treatment design.
167
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191
Appendices
Appendix A. Supplemental Text: eNOS Model Development
Generation of the reaction network using BioNetGen:
We used BioNetGen, a rule-based approach to formulate the reaction network. BioNetGen enables
automated generation of the reaction network using a set of defined reaction rules[117]. This approach is
particularly useful in models that involve dynamic assembly of multi-protein complexes, which occurs in our
model, for example, in the case of complexes involving calcium, calmodulin, eNOS, Akt, and Hsp90. The
baseline model includes 18 seed species that can participate in 102 reaction rules that we defined. BioNetGen
applies the reaction rules first to the seed species, and then in successive generations, to species formed due to
the application of the reaction rules. In total, 734 reactions were generated based on the reaction rules, forming
a total of 160 molecular species. The generated model is comprised of 160 non-linear ordinary differential
equations (ODEs) that describes the changes in the species’ concentrations over time. We note that two of the
species are used a placeholders to keep track of newly formed or degraded species. Thus, there are 158
biochemical species. The equations were implemented in MATLAB (The MathWorks, Natick, MA, USA).
Receptor Quantification:
We quantified the CD47 receptor number on the surface of human microvascular endothelial cells
(HMVECs) using the quantitative flow cytometry (qFLOW) technique previously described[129]. Briefly,
HMVECs from Lonza were cultured in flasks and maintained in Endothelial Cell Growth Media-2 (EGM-2)
supplemented by the EGM-2 Single Quot Kit (Lonza). Cells were maintained at 37 °C in 95% air and 5% CO 2,
and we only use cells at passage numbers 2-4. To dissociate cells from the culture plate, cells were incubated
with a non-enzymatic cell dissociation solution, CellStripper (Corning), for 5 min at 37 °C. Cells were
centrifuged at 500×g for 5 min to obtain a final concentration of 4x10
6
cells/mL in stain buffer (PBS, bovine
192
serum albumin, and sodium azide).Aliquots of cells (25 µL, ~10
5
cells) were labeled with phycoerythrin (PE)-
conjugated monoclonal antibodies (Biolegend) and prepared for single-cell analysis via flow cytometry.
Flow cytometry was performed on a MACSQuant flow cytometer (Miltenyi), and FlowJo (BD
Biosciences) software was used to analyze the data. To determine the number of receptors per cell, the
fluorescence of Quantibrite PE beads (BD Biosciences) was measured. We followed the procedure as specified
by the manufacturer and constructed a calibration curve to convert the geometric mean of PE fluorescence to
the number of bound molecules. The average number of receptors on a cell in the population was then
calculated. For each experiment, two biological replicates were used, and the experiments were repeated for 3-
4 times. We report an average of 120,000 CD47 receptors/cell, which converts to a concentration of 199.336nM
assuming a total cell volume of 1pL.
Ligand-receptor interactions:
R2 concentration is calculated based on the receptor number measured in HUVECs[129], assuming
they are all active dimers. R2 dimerization has been omitted for simplicity. Therefore, we assume binding
between VEGF and R2 dimers follows a 1:1 stoichiometry. The dissociation constant between VEGF and R2
is set to be Kd of 0.150nM (150pM) based on experimental measurements[130], and assuming the association
rate, kon,R2 is 0.6/nM-min.
For TSP1-CD47 binding, it is assumed that TSP1 only binds to CD47 that is not coupled with R2. The
association rate, kon,TSP1CD47 is taken from our previous model 0.03/nM-min[70], and the dissociation rate
koff,TSP1CD47 is calculated to be 0.0003/min based on measured Kd of 0.01nM (10pM)[39].
Ligand-ligand binding:
As in our previous tissue model[70], TSP1 binds to free VEGF, and the TSP1:VEGF complex has a
degradation rate of 0.01158/min (0.000193/s). In the present model, the synthesis and degradation of the
exogenous ligands (TSP1 and VEGF) are neglected, as was assumed in previous modeling works[102], [104].
193
Receptor coupling:
As mentioned above, TSP1 only binds to CD47 that is uncoupled with R2. Once ligated, the CD47
receptor cannot couple with R2. But, the VEGF:R2 complex can still couple with free CD47 receptor. Our
handling of CD47-R2 coupling is different from Li and Finley, where no coupling is allowed for any ligated
receptor. We adjusted this assumption based on the evidence[49] that TSP1 disrupts R2 and CD47 coupling,
and that in the absence of TSP1, coupling between R2 and CD47 should be undisrupted upon R2 ligation.
To exclude the possibility that TSP1 only takes effect by directly forming a complex with
VEGF:R2:CD47, we derived another model version where TSP1 and VEGF can both bind to their respective
receptors even when CD47 and R2 are coupled. We then altered the trafficking parameters for the TSP1-
containing R2 complexes. However, the model simulation showed that varying these parameters did not
influence the VEGFR2 signaling dynamics, and the TSP1-containing R2 complexes are of negligible level (data
not shown). Therefore, we assume that TSP1’s inhibitory function via receptor CD47 does not solely depend
on its direct involvement with the ligated R2 species.
R2 phosphorylation:
In this model, we assume R2 phosphorylation upon ligation occurs for both cell surface and
internalized receptors. Since it is possible that CD47 coupling may stabilize R2 signaling in the absence of
TSP1[49], we assume the dephosphorylation rate of the CD47-coupled pR2 is slower than that of the uncoupled
pR2 (0.01/min vs. 0.06/min).
Receptor dynamics:
Internalization: free CD47 has its own internalization rate (kinter,CD47). TSP1:CD47 complex has its own
internalization rate kinter,TSP1bd; however, due to lack of data, we set the baseline value of kinter,TSP1bd to be the same
as kinter,CD47 and investigated the effect of altering its value in the perturbation simulations. Receptor R2
internalization depends on its activation (phosphorylation) status and whether it has coupled with CD47. We
distinguish the internalization rates of inactive R2 (kinter,R2), active R2 (kinter,pR2), inactive R2:CD47 complex
194
(kinter,R2CD47), and active R2:CD47 complex (kinter,pR2CD47). This distinction is different from the model by Bazzazi
et al.[102], where the R2 internalization rate depends on the presence of NRP1 but not CD47.
Experimental data show that there is a decrease in the receptor levels over time in the control condition
(without ligand stimulation). To account for this, since only the internalized receptors are degraded, we assume
that inactive R2 is also internalized. All of the aforementioned internalization rates are estimated in model
fitting. All parameter estimation in this study is done using the least squares nonlinear (lsqnonlin) optimization
function in MATLAB, which minimizes the sum of the squared (SSE) of the model predicted dynamics
compared to the experimental data.
Degradation rate parameters: For simplicity, the unbound ligands, TSP1 and VEGF, are not subject to
degradation. Instead, their disappearance occurs due to being bound to receptors that can be internalized (same
as in the model by Bazzazi). Internalized (cytosolic) receptors, free CD47, the TSP1:CD47 complex, and the
inactive R2:CD47 complex are assumed to have the same degradation rate kdeg,CD47, which is the lowest among
all the degradation rates. We estimate the value of kdeg,CD47 by fitting to the total R2 data in the Cycloheximide
(CHX) treatment condition[118] (see below). For other R2 species, we again assign individual degradation rates
based on the R2 activation status and whether it is coupled with CD47.
Rate parameters for receptor internalization and synthesis: Receptor synthesis is implemented by specifying the
rate at which new receptors appear at the cell membrane. First, the values of receptor internalization (kinter,R2,
kinter,CD47, kinter,R2:CD47, kdeg,R2 and kdeg,CD47) were estimated in model fitting in order to match with CHX treatment
data, where CHX blocks cellular protein synthesis)[118]. Then, the synthesis rates of R2 and CD47 were
estimated to match control data (no CHX). Lastly, the degradation rates of pR2 species were estimated to fit to
the datasets with VEGF stimulation (with or without CHX) while the previously estimated parameter values
were fixed.
In parameter estimation, we allow the internalization rates or the degradation rates to vary across the
same ranges respectively. We observed from the estimated values that kinter,pR2CD47> kinter,CD47 (=kinter,TSP1bd)>
kinter,pR2> kinter,R2> kinter,R2CD47, suggesting that the CD47-coupled pR2 internalizes the fastest while the CD47-
coupled inactive R2 internalizes the slowest. In addition, parameter fitting showed that kdeg,pR2> kdeg,pR2CD47>
195
kdeg,R2> kdeg,CD47 (for both CD47 and CD47:R2). This trend is in line with the observation that R2 level decreases
faster upon VEGF stimulation than the control[118]. The R2:CD47 degrade more slowly than their CD47-free
R2 counterparts. This agrees with the hypothesis that CD47 facilitates the maintenance of active R2
signaling[49]. Importantly, we note that we did not impose that the values of the degradation and internalization
parameters follow a specific order; rather, this result naturally emerged from the model optimization.
Src-Hsp90-Akt activation
VEGF activates c-Src (herein abbreviated as Src) in a T cell-specific adaptor molecule (TSAd)-
dependent manner[21]. Active Src (pSrc) engages the receptor tyrosine kinase Axl, which promotes association
with PI3K and activation of Akt[24]. Additionally, c-Src phosphorylates Hsp90 on Tyrosine 300 in response to
R2 activation[27].
To simplify this activation process, we model that pR2 engages and activates Src, which then binds
and activates Akt and Hsp90. However, as a chaperone protein, Hsp90 is assumed to bind to its partners,
including Src, at a much faster rate (0.5/nM-min) than the assumed generic binding rate for most signaling
proteins (0.06/nM-min). This assumption is based on the evidence that Hsp90 acts as a chaperone protein and
may facilitate protein interactions by bringing multiple signaling proteins into close vicinity[312]. Additionally,
large binding rates are possible[139]. Both Hsp90 and Akt are activated through phosphorylation by active Src.
The kinetic rate parameters governing the activation and binding reactions of Src, Akt, and Hsp90 were
specified based on existing models from literature[98], [106], [313] to match with experimental data.
R2-induced Ca
2+
influx
R2 stimulates phosphoinositol metabolism through their activation of phospholipase C-γ (PLCγ) and
phosphoinositide-3 kinase (PI3K). Activation of PLCγ results in hydrolysis of phosphatidylinositol biphosphate
(PIP2) to form diacylglycerol (DAG) and 1,4,5-trisphosphate (IP3), which promote PKC and Ca
2+
signaling,
respectively, to their downstream cellular targets[314]. In this study, we focus on PLCγ activation by pR2 and
IP3 formation and its effect on eNOS signaling, omitting the dynamics of DAG and its downstream effect in
196
the PKC/ERK pathway. We assign a synthesis rate of PIP2 (10/min), as PIP2 synthesis can be upregulated to
compensate for its hydrolysis[315].
The IP3 can be degraded by phosphatases and kinases (the degradation rate, kdeg,IP3, is assumed to be
0.06/min), and binds to its receptor IP3R on the endoplasmic reticulum (ER) membrane[315], triggering the
IP3R channel to open. A slower inactivation process also pertains to this channel. As Ca
2+
level in the ER
depletes, store-operated Ca
2+
entry (SOCE) occurs through the store-operated Ca
2+
release-activated Ca
2+
(CRAC) channels (reviewed in Shim 2015 and refs). Finally, Ca
2+
is pumped back into the ER by the sarco-
endoplasmic reticulum Ca
2+
ATPase (SERCA) pump. Ca
2+
can also be extruded from the cell by a number of
exchange and pump, which we modeled as the plasma membrane Ca
2+
ATPase (PMCA) pump. In addition, a
passive leak of Ca
2+
from the ER to the cytosol is included, balanced by SERCA for Ca
2+
equilibrium in the
unstimulated cells. The rate equation to calculate the intracellular and ER Ca
2+
levels based on the fluxes
through these channels and pumps are adapted from Wiesner et al.[132] and Bazzazi et al.[104].
Because it has been shown that the elevated Ca
2+
plateau phase post VEGF-stimulation is dependent
on the presence of extracellular Ca
2+
[121], we modified the established Ca
2+
model to include the dependence
of the CRAC influx on the dynamic extracellular Ca
2+
level. We describe the flux of Ca
2+
from the extracellular
space into the cytosol using the following equation:
,-
!"#!
,.
=
/
!"#!
0-
!"#!
1
!"#!
[4]
3
2342
=(45
!".
∗
567
$%&
567
'(&
−45
89.
)∗
/
!"#!
:
!"#!
*
!"#!
:
!"#!
*
!"#!
;2<
+"
*
!"#!
[5]
Consequently, we estimated the values of n CRAC, I CRAC, and K CRAC after this modification. Several
parameters were calculated to balance the fluxes across the cell and ER membranes for steady state Ca
2+
equilibrium. For example, the rate of Ca
2+
leak from the ER into the cytosol is balanced by the rate of SERCA
resequestration of Ca
2+
from cytosol back into the ER. We tuned and estimated the unknown model parameters
in this module by fitting the simulated IP3 activation and intracellular Ca
2+
dynamics upon VEGF stimulation
197
to the datasets of HUVEC cells from Faehling et al.[121]. As the single cell datasets from this study exhibit large
cell to cell heterogeneity, as is the case with other papers presenting EC Ca
2+
influx data[316], [317], we
estimated the averaged levels of Ca
2+
and IP3 from the datasets, representing an average cell, and used these
values in model training. We assume the basal level of intracellular Ca
2+
to be 50nM[121], [317]. For IP3 levels,
we used data from Faehling et. al. Fig. 4[121], taking the average value at each timepoint for all three sets of
single cell data.
eNOS module
1. Ca-CaM-eNOS interactions
Free intracellular Ca
2+
binds to and activates CaM. We adapt a four-state Ca
2+
-CaM binding model
from previous models[134], [142], in which it is assumed that binding of two Ca
2+
at each CaM terminus can
be treated as a single event due to the highly cooperative binding of Ca
2+
at each terminus. The Ca
2+
-saturated
or partially saturated CaM binds and activates eNOS, and no eNOS-CaM binding was observed in Ca
2+
-free
solution (EDTA)[318]. Based on values from both the experimental study and computational models, we set
the forward binding rate of eNOS with the C-terminus saturated CaM and fully saturated CaM to be 0.078/nM-
min, the binding rate of eNOS with the N-terminus saturated CaM to be 0.0081/nM-min, and the dissociation
rate of eNOS from all forms of CaM to be 0.6/min (0.01/s). Additionally, a 2017 study by Chen et al. revealed
that different conformational edits to the eNOS can enhance its affinity with CaM[131]. Based on the levels of
enhancement as shown in their datasets, we adjusted the affinity of various forms of eNOS with CaM (Table
2).
We acknowledge that not all binding partners of eNOS are taken into account. However, a recent model
of competitive eNOS tuning[134] showed that NOS binding is the same under isolated or competitive
conditions. This supports our model assumption that eNOS-CaM binding can be isolated in the model without
adding in competitive binding of other CaM binding partners.
2. eNOS catalytic activity
198
Compelling evidence shows that both Akt and Hsp90 regulate eNOS catalytic activity. A study by McGabe
et al. suggests that eNOS phosphorylation at the S1179 site by Akt decreases the dissociation of CaM from
eNOS and increases the eNOS catalytic activity[319]. Another study showed that as a scaffolding protein,
Hsp90 facilitates CaM binding to eNOS, and a synergistic effect on eNOS activation where Hsp90 enhances
the extent of eNOS phosphorylation by Akt[320]. Furthermore, Chen et al. (2014) demonstrated that eNOS
predominantly exists in the dimeric form and is stabilized by Hsp90, whereas the eNOS monomer is less stable
and is subject to ubiquitination[321]. The dimeric eNOS form is responsive to regulation (such as
phosphorylation) on its activity. In addition, destabilization of eNOS dimers results in eNOS degradation by
proteasome, accompanied by its dephosphorylation. For simplicity, we assume that all eNOS in this model is
in the form of a dimer. To account for the function of Hsp90 on maintaining the eNOS level, we assign a non-
zero degradation rate for peNOS (phosphorylated eNOS dimer) when it is unassociated with Hsp90.
eNOS binds to its substrate L-Arginine in a reversible manner. Kinetic studies of eNOS binding with its
substrates[143] reported the binding rate of eNOS and Arg to be 0.012~0.048/nM-min, and dissociation rate
4.8~96/min (as summarized in an article by Chen and Popel[146]). Meanwhile, the eNOS catalytic rate varies
largely across experimental and modeling studies[143], [146], [322]. Therefore, we fit the catalytic rates by fitting
to experimental data.
Given the evidence that Ca-CaM, Akt, and Hsp90 can influence the affinity of eNOS with its substrate and
eNOS catalytic activity differently, we used an iterative approach in constructing and training this model. The
experimental data that we used for training this minimal model include a dataset from Takahashi and
Mendelsohn[320] showing Hsp90 influencing eNOS phosphorylation by Akt, and a dataset from Chen et
al.[131] showing eNOS catalytic activity dependence on CaM, Hsp90, and its phosphorylation status. We
started with a relatively simple system, where the various forms of the eNOS species share the same affinity
with the substrate L-Arginine, only distinguishing the catalytic rates for basal eNOS, phosphorylated eNOS,
and Hsp90-bound eNOS. As fitting results reveal inadequacy of the module structure, we modified the module
several times to incorporate differences in the eNOS catalytic activity levels for the various species (Figure A1).
199
Figure A1. eNOS module fitting and AIC test. Each version of the eNOS model was trained using the lsqnonlin algorithm
to match with four sets of experimental data of eNOS activity. The AIC score was computed taking into account the total
number of parameters in fitting and the sum of squared error (SSE) for each model version. The difference of each model
AIC score compared to the final version, !AIC, was computed.
Briefly, we first tested Michaelis-Menten kinetics for the biochemical reactions in module version 1,
and then tested mass-action reaction kinetics in module version 2. Based on the model fitting and analysis, we
found that the various forms of eNOS must have both different affinities and catalytic rates in order for the
predicted eNOS activities to match the experimental data. We further evaluated the adequacy of the model
structure by seeing which structure could achieve the observed dynamics from a separate dataset. We
determined that Hsp90’s effect on eNOS catalytic activity includes not only a faster reaction for Akt-mediated
phosphorylation of eNOS via increased affinity between eNOS and CaM (version 3), but also another layer of
enhanced activity. Therefore, we further altered the model structure by assigning separate catalytic rates for the
Hsp90-bound eNOS forms (version 4). In version 5, in order to match with the datapoints with the lowest
CaM level, we let peNOS be active independently from CaM. When we discovered that only assigning a
different catalytic rate is not sufficient to separate the two initial data points (control vs. Hsp90-present) in the
Chen dataset, we further assigned different affinities to the Hsp90-bound eNOS with L-Arginine to allow the
model to fit to the two different levels of eNOS catalytic activity used experimentally (version 6).
0 50 100 150 200
CaM (nM)
0
0.2
0.4
0.6
0.8
1
1.2
Citrulline Production
version 10
Sim. Control
Sim. S1179D
Sim. Hsp90
Sim. Hsp90+S1179D
Exp. Control
Exp. S1179D
Exp. Hsp90
Exp. Hsp90+S1179D
0 50 100 150 200
CaM (nM)
0
0.2
0.4
0.6
0.8
1
1.2
Citrulline Production
version 9
Sim. Control
Sim. S1179D
Sim. Hsp90
Sim. Hsp90+S1179D
Exp. Control
Exp. S1179D
Exp. Hsp90
Exp. Hsp90+S1179D
0 50 100 150 200
CaM (nM)
0
0.2
0.4
0.6
0.8
1
1.2
Citrulline Production
version 6
Sim. Control
Sim. S1179D
Sim. Hsp90
Sim. Hsp90+S1179D
Exp. Control
Exp. S1179D
Exp. Hsp90
Exp. Hsp90+S1179D
0 50 100 150 200
CaM (nM)
0
0.2
0.4
0.6
0.8
1
1.2
Citrulline Production
version 5
Sim. Control
Sim. S1179D
Sim. Hsp90
Sim. Hsp90+S1179D
Exp. Control
Exp. S1179D
Exp. Hsp90
Exp. Hsp90+S1179D
0 50 100 150 200
CaM (nM)
0
0.2
0.4
0.6
0.8
1
1.2
Citrulline Production
version 2
Sim. Control
Sim. S1179D
Sim. Hsp90
Sim. Hsp90+S1179D
Exp. Control
Exp. S1179D
Exp. Hsp90
Exp. Hsp90+S1179D
0 50 100 150 200
CaM (nM)
0
0.2
0.4
0.6
0.8
1
1.2
Citrulline Production
version 1
Sim. Control
Sim. S1179D
Sim. Hsp90
Sim. Hsp90+S1179D
Exp. Control
Exp. S1179D
Exp. Hsp90
Exp. Hsp90+S1179D
model version 1 2 3 4 5 6
# parameters 12 12 12 10 13 14
error (SSE) 19.98 6.83 7.08 12.44 5.19 4.24
AIC 21.02 8.91 9.30 11.67 7.80 7.51
∆AIC 13.51 1.40 1.79 4.16 0.29 0.00
0 50 100 150 200
CaM (nM)
0
0.2
0.4
0.6
0.8
1
1.2
Citrulline Production
version 10
Sim. Control
Sim. S1179D
Sim. Hsp90
Sim. Hsp90+S1179D
Exp. Control
Exp. S1179D
Exp. Hsp90
Exp. Hsp90+S1179D
Ver. 1 Ver. 2 Ver. 3 Ver. 4 Ver. 5 Ver. 6
CaM (nM) CaM (nM) CaM (nM) CaM (nM) CaM (nM) CaM (nM)
eNOS activity
1.2
1
0.8
0.6
0.4
0.2
0
1.2
1
0.8
0.6
0.4
0.2
0
1.2
1
0.8
0.6
0.4
0.2
0
1.2
1
0.8
0.6
0.4
0.2
0
1.2
1
0.8
0.6
0.4
0.2
0
1.2
1
0.8
0.6
0.4
0.2
0
0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200
200
Since we trained the eNOS module using the experimental datasets from purified protein mixture
studies[131], [320], we assumed that phosphatases, ubiquitin, and proteasomes do not exist in the mixture.
Therefore, the dephosphorylation and degradation rates were set as zero. We then estimated their values during
full model training using in vitro cell culture datasets.
3. AIC test
We compared the quality of the various eNOS module versions using the Akaike Information Criterion
(AIC), which measures the quality of a model to represent a given set of data while accounting for the number
of parameters estimated[323] (Figure A1). Specifically, we calculate the AIC score for each best fitted eNOS
module version using the following equation, as used in a previous study[324].
734 =,×9:;(
==>
)
)+2> [6]
where n is the number of data points, SSE is the sum of the squared error between the data and the
model predictions, and k is the number of parameters used to fit the model. The module version with the
smallest AIC is assumed to be the best version. We also calculate and report the change in the AIC value for
each module version, relative to the version with the smallest AIC. This provides insight into how changing the
complexity of the module and the number of fitted parameters influences the fit.
sGC-PDE activity
We adapted the model by Halvey et al. for downstream sGC activity[135]. This model describes the
kinetic of NO-cGMP signaling in rat platelets and was adapted for rat cerebella cells as well. sGC is activated
by NO binding distally to the heme prosthetic group, and then the proximal coordinating histidine bond breaks,
resulting in an sGC conformational change. A second NO can bind to the vacant proximal heme site with a
very low dissociation rate, desensitizing sGC to the NO level (kon,NO.NOGC). When the distal NO dissociates from
sGC (kf,NOGC.NO), this results in a NO-bound inactive state of sGC. Active sGC generates cGMP from GTP,
201
which binds to PDE on the agonist site and PDE hydrolyzes cGMP at its catalytic site. All forms of PDE, the
free form and two cGMP-bound states are assumed to hydrolyze cGMP, as depicted in the Halvey model.
In this part of the signaling pathway, we must also account for NO clearance. The half-life of NO is
30 s in physiological buffers (corresponding to a decay constant of 1.38/min)[325]. However, NO has a much
shorter half-life (~4 s) under physiological conditions (corresponding to a decay constant of 10.4/min)[326].
In a more recent study, the clearance rate of NO under flow condition was estimated to be 20-30/min[136].
Therefore, we allow the NO clearance rate parameter kclearNO to vary within the range of 5~15 min in training
the full model.
To match model simulations with the endothelial cell data, we estimated two unknown model
parameters, the catalytic rate of activated sGC, kcat,sGC, and the catalytic rate of activated PDE5, kcat,PDE5a, by
fitting to experimental data of cGMP level at 10 min in HUVECs stimulated by 30 ng/ml VEGF[40]. Our
model-simulated cGMP synthesis exhibits a transient increase, similar to that observed in a previous study using
VEGF-stimulated bovine aortic endothelial cells[86].
Abstract (if available)
Abstract
Tumor angiogenesis is a critical step in tumor progression. By instructing vascular cells to form new blood vessels from pre-existing ones, tumor cells continue to obtain nutrients and oxygen for growth. The newly formed vessels also enable subsequent metastasis. Vascular endothelial growth factor (VEGF) is a crucial angiogenesis promoter. VEGF binds with its major receptor VEGFR2 on endothelial cells (ECs) and promotes signal transduction that induces long-term responses including cellular proliferation, survival, migration, and vascular permeability, as well as an acute response including nitric oxide (NO) release. This pro-angiogenic signal is balanced by angiogenesis inhibitors, such as thrombospondin-1 (TSP1), an endogenous matricellular glycoprotein. TSP1 can directly bind to and sequester VEGF. At picomolar concentrations, this multi-domain molecule also binds to its receptors CD47 and CD36 to redundantly inhibit VEGFR2-mediated endothelial nitric oxide (eNOS) activity and other downstream pro-angiogenic signaling. Furthermore, TSP1 can induce endothelial cell apoptosis via receptor CD36 at nanomolar concentrations. Meanwhile, existing anti-VEGF agents often elicit systemic hypertension as an adverse side effect. In addition, responses to anti-VEGF agents may be limited by parallel activation of the downstream pathways by additional angiogenic factors (such as fibroblast growth factor) independent of the VEGF receptor. Therefore, inhibitors similar to TSP1 that act on essential downstream pathways may be more effective than the existing VEGF/VEGFR antagonists for controlling tumor angiogenesis. ❧ To design treatments that achieve optimal anti-angiogenic outcome, we need to quantitatively understand the dynamics of such a complex network that regulates angiogenesis itself. In this work, I present a series of quantitative mechanistic models that examine the effects of a potent endogenous angiogenic inhibitor TSP1. The models predict TSP1-mediated inhibition of the eNOS signaling pathway and activation of apoptotic signaling in endothelial cells. Additionally, I present a model of tumor-bearing mice receiving anti-angiogenic treatment, and demonstrate the utility of tumor growth kinetics in stratification of the animal survival outcome. Ultimately, such model frameworks can be used to inform development of effective anti-angiogenic strategies for cancer therapy.
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Asset Metadata
Creator
Wu, Qianhui (Jess)
(author)
Core Title
Understanding anti-angiogenic signaling and treatment for cancer through mechanistic modeling
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
07/16/2020
Defense Date
04/24/2020
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
angiogenesis,Biomedical Engineering,computational systems biology,mechanistic modeling,OAI-PMH Harvest,oncology
Language
English
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Electronically uploaded by the author
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Advisor
Finley, Stacey Deleria (
committee chair
), D'Argenio, David Z. (
committee member
), Fraser, Scott (
committee member
), McCain, Megan Laura (
committee member
), Wang, Pin (
committee member
)
Creator Email
jessswooo@gmail.com,qianhuiw@usc.edu
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Tags
angiogenesis
computational systems biology
mechanistic modeling
oncology