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Mechanistic modeling of angiogenic factors network and cancer therapy
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Mechanistic Modeling of Angiogenic Factors Network and Cancer Therapy
by
Ding Li
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 2021
Copyright 2021 Ding Li
ii
Dedication
This dissertation is dedicated to my family,
who gave me unconditional support and unfailing love.
iii
Acknowledgements
Writing this dissertation is a reflection of my accumulated debts to many people for their
help and support along the way. Most likely, I can never pay them off. Expressing my heartfelt
gratitude is the least thing I can do, though I feel that words will fail me eventually.
I am especially indebted to my advisor Professor Stacey D. Finley, who played a huge role
in my professional and personal development. Without her never-exhausted patience and pertinent
guidance, I would never have completed this work. More importantly, she has instilled a true love
for learning and research in me, for which I am eternally grateful. The journey to obtaining a Ph.D.
can be awful, painful and frightening. The challenges on the road can make you doubt yourself,
judge yourself and even distance yourself from the best you can be. Therefore, I feel extremely
fortunate and sometimes worry that I wouldn’t make it if I didn’t have her as my advisor. I believe
that I would not have become the person I am now without her being there and believing in me.
Her affable personality, infinite enthusiasm and unwavering commitment to good science have
deeply inspired and encouraged me in different stages of my training, which ultimately help me
accomplished this manuscript that I am really proud of. I truly aspire to be able to provide the same
amount of energy she gave to me to the other people in my life.
Genuine appreciation is also expressed to other members on my supervisory committees,
Professor David Z. D’Argenio, Professor Keyue Shen, Professor Shannon M. Mumenthaler, and
Professor Adam L. MacLean, who provided me with knowledgeable guidance during my work in
the program. Prof. D’Argenio and Prof. Shen gave me essential help in my first-year study of the
program. Prof. D’Argenio patiently guided me through one lab rotation and Prof. Shen taught me
important knowledge of tumor biology in his class. Prof. Mumenthaler has been an important
collaborator on the project leading to the accomplishment of my work. She provided us with the
iv
information of the experiments, which guided the construction of my computational model. Prof.
MacLean is an excellent scientist in computational biology and helped me with his expertise from
serving on my qualifying exam committee. I am deeply grateful for the time and effort that these
professors have invested in me.
Next, I would like to thank Professor Oleg Igoshin, my research advisor during my Master
of Bioengineering program at Rice University. He was the first teacher to introduce me to the
Systems Biology. He taught me the fundamentals of computational modeling in his class, gave me
precious opportunities to work on research projects in his lab, and provided essential help in my
applications to Ph.D. program. I would not be here if it weren’t for his mentorship and support.
Many people from Finely lab were integral to the success of the research conducted in this
dissertation. They not only helped me build up my research projects, but also made my life
enjoyable. I would like to thank three lab alumni, Dr. Jennifer A. Rohrs, Dr. Mahua Roy and Dr.
Qianhui (Jess) Wu. As previous senior members in the lab, they provided insightful feedbacks and
suggestions on my projects, manuscripts and presentations. Also, as the very first three members
in Finley lab, they set a warm and inclusive lab environment for me to feel welcome and belonged.
I also want to especially thank two lab members in the same year as me, Min Song and Sahak
Makaryan. They have helped me navigate many tedious problems in and outside of my research.
I’d also like to thank Colin G. Cess and Patrick Gelbach for their support and friendship. Many
other excellent people joined the lab more recently, including Holly Huber, Ariella Simoni, Niki
Tavakoli, Vardges Tserunyan and Lynne Cherchia. Interacting with all of you in the weekly lab
meeting is an important part for me to maintain sanity in this pandemic time. Additionally, I would
like to thank Danielle Hixon from Mumenthaler Lab. She has been working on the experimental
part for the collaboration project and generously provided her insights to us.
v
I am also deeply grateful for all the ardent friendships that I have had the distinct pleasure
to have made in Los Angeles. I would like to thank Wenbo Chen, Xiwei She, Yajun Zeng, Duo
Zhang, Dechen Zeng, Jianjun Li, Chenliang Ma, Haixiang Xu, Sihao Zhang and Huailin Zhang
for their accompany and friendship, Yi Zhang, Kai Wang, and Zhiheng Wang, for bearing with
me as roommate in different years and feeding me with foods occasionally, Yuzhou Dou and
Qingyi Wang, for being my close friends and doing my haircuts in this pandemic time. I am also
benefited from many old friends I made long before my study at USC. I would like to especially
thank Xuanli Deng, a true friend from high school. He has been my emergency contact since the
day I came to USC and shared many of my ups and downs in graduate life and job-seeking.
In the end, I want to say thank you to my family for their love and support. My parents,
Zhengxin Xie and Liupu Li, raised me in one of the poorest counties in China. To ensure that I
have a bright future, they did all they can do to support my education. My sister, Yi Xie, is the
most important enabler for my graduate study in U.S. This work is made possible through her
being my ultimate supporter. I love you all and I am never not thinking of you all these years.
vi
Table of Contents
Dedication…………………………………………………………………………………………ii
Acknowledgements ……………………………………………..………………………………..iii
List of Tables …………………………………...……………………………………………….viii
List of Figures……………………………………………………………………………….........ix
Abstract………………………………………………………………………………………...…xi
Chapter 1: Introduction…………………… ………………………………………………………1
1.1 Cancer therapy targeting tumor angiogenesis……………...…………..…………..1
1.2 Angiogenic factors regulating tumor angiogenesis ………………………………..2
1.3 The interconnected network of angiogenic ……………………..…………………4
1.4 Anti-angiogenic agents targeting angiogenic signaling …….……………………..6
1.5 Therapeutic strategies targeting multiple angiogenic signals.…...…………...……7
1.6 Tumor heterogeneity and the response to anti-angiogenic therapy………………..8
1.7 Investigating anti-angiogenic therapy through computational systems biology….10
1.8 Dissertation outline ……………………………………………………………....12
Chapter 2: Modeling of angiogenic interaction network in tumor tissue…………………………16
2.1 Abstract ...…………………………..…………………………….………………..16
2.2 Introduction…………………………………….………………………………….17
2.3 Methods………………………………………….………………………………...21
2.4 Results…………………………....……………………….……………………….31
2.5 Discussion…………...…………………………………………………………….46
Chapter 3: Modeling of angiogenic interaction network in cancer patient……………………….53
3.1 Abstract ...…………………………..…………………………….………………..53
3.2 Introduction…………………………………….………………………………….54
3.3 Methods………………………………………….………………………………...57
3.4 Results…………………………....……………………….……………………….70
3.5 Discussion…………...…………………………………………………………….87
Chapter 4: Predictive model of in vivo tumor growth under anti-VEGF treatment………………94
4.1 Abstract ...…………………………..…………………………….………………..94
4.2 Introduction...………………………………….…………………………………...95
4.3 Methods …………………………………..…….………………………………….99
4.4 Results…………………………....……………………….……………………...115
4.5 Discussion…………...…………………………………………………………...130
Chapter 5: Modeling in vivo tumor growth mediated by VEGF and FGF………..…………….137
5.1 Abstract ...…………………………..…………………………….………………137
vii
5.2 Introduction...………………………………….…………………………………138
5.3 Methods …………………………………..…….………………………………..141
5.4 Results…………………………....……………………….……………………...152
5.5 Discussion…………...…………………………………………………………...156
Chapter 6: Conclusion…………………………………………………...………..…………….158
6.1 Overview ...……..…………………..…………………………….………………158
6.2 Summary...………….………………………….…………………………………158
6.3 Future direction ………………….………..…….………………………………..161
6.4 Concluding thoughts……………...……………………….……………………...163
References ……………………………...………………………………………………………164
Appendices ……………………………………………………………………………………..198
Appendix A …………………………………………………………………………….198
Appendix B ……………………………………………………………………………..214
Appendix C ……………………………………………………………………………..228
viii
List of Tables
Table 2-1: Comparison of the baseline predictions and the experimental measurements of
VEGF, FGF2, TSP1, PF4 and MMPs………………………………………………...30
Table 3-1: Comparison of predicted steady state and experimental concentrations of VEGF,
TSP1 and MMPs ……………………………………………………………………..64
Table 4-1: List of tumor geometric parameters………………………………………………….107
Table 4-2: List of VEGF ligand-receptor system parameters……………………………………107
Table 4-3: List of global cellular response parameters..………………………………………...108
Table 4-4: List of dataset-specific tumor growth kinetic parameters..……………………….....108
Table 4-5: List of the PK/PD parameters of Bevacizumab……………………………………..109
Table 4-6: List of the PK/PD parameters of Nab-paclitaxel…………………………………….110
Table 4-7: Comparison of tumor growth models……………………………………………….116
Table 5-1: List of tumor geometric parameters…………………………………………………149
Table 5-2: List of VEGF and FGF2 ligand-receptor system parameters………………………..150
Table 5-3: List of global cellular response parameters………………………………………….151
Table 5-4: List of dataset-specific tumor growth kinetic parameters…………………………...151
Table 5-5: List of the PK/PD parameters of VEGF-trap and FGF-trap…………………………152
ix
List of Figures
Figure 1-1: Mechanisms of the interaction between angiogenic factors…………………………...5
Figure 2-1: Schematic of the tumor tissue based model…………………………………………..20
Figure 2-2: Schematic of the extracellular network of VEGF, FGF2, TSP1 and PF4……………26
Figure 2-3: Distribution of VEGF, FGF2, TSP1 and PF4 in tumor tissue at steady state………..31
Figure 2-4: Effects of secretion of angiogenic factors on the angiogenic state of the
tumor tissue.…...…………………………………………………………………….34
Figure 2-5: Effects of PF4 secretion on the formation of specific angiogenic complexes……….37
Figure 2-6: Impact of PF4 and cHSPG on the formation of specific angiogenic complexes…….41
Figure 2-7: Effect of PF4 pulse release on VEGF signaling pathway……………………………44
Figure 2-8: The effect of PF4 pulse release on FGF2 signaling pathway………………………..45
Figure 2-9: The outcomes of anti-angiogenic factor secretion in different
microenvironments ....……………………………………………………………….49
Figure 3-1: Compartmental model of VEGF-TSP1 system in human cancer patients…………..59
Figure 3-2: The molecular interactions in the network of TSP1 and VEGF……………………..60
Figure 3-3: The comparison of model prediction and measured pharmacodynamics of
bevacizumab and ABT-510 in cancer patients………………………………………65
Figure 3-4: The sensitivity indices of model parameters…………………………………………72
Figure 3-5: The effects of one cycle of combination anti-angiogenic therapy……………………73
Figure 3-6: The effect of anti-angiogenic therapy on angiogenic complexes in tumor…….……..75
Figure 3-7: The impact of tumor receptor variability on the dynamics of VEGF, TSP1,
and the angiogenic ratio under combination therapy…………………….…………..77
Figure 3-8: The impact of tumor receptor heterogeneity on the response to anti-angiogenic
therapy……………………………………………………………………………….78
Figure 3-9: The fold-changes of the angiogenic complex under combination therapy…………..80
Figure 3-10: The impact of tumor receptor heterogeneity on the combination effect…………….82
Figure 3-11: The comparison of the predicted responses from the PLSR model and the
mechanistic model………………………………………………………………….83
Figure 3-12: The association between tumor angiogenic receptors and the response to
combination anti-angiogenic therapy………………………………………………85
Figure 3-13: The full profile of the association between angiogenic receptors and response
to combination anti-angiogenic therapy……………………………………………86
Figure 4-1: Computational model of in vivo angiogenesis and tumor growth……………………98
Figure 4-2: Schematic illustrating the process of parameter estimation and model
validation…………….……………………………………………………………..112
Figure 4-3: Distribution of estimated parameters values………………………………………..117
Figure 4-4: The total sensitivity index STi values……………………………………………….118
Figure 4-5: Cross-validation comparing the model predictions with experimental data………...120
Figure 4-6: Model validation with additional experimental datasets……………………………121
Figure 4-7: Predicted outcome of anti-VEGF treatment and hypothetical treatments
targeting tumor and endothelial cells……………………………………………….122
Figure 4-8: Predicted dynamics of tumor volume and vasculature degree with
representative combinations of dataset-specific parameter values…………………124
Figure 4-9: Impact of dataset-specific parameters on the response to anti-VEGF treatment…….125
x
Figure 4-10: Predicted synergy of anti-VEGF and chemotherapy………………………………127
Figure 4-11: Predicted outcome of the combination of anti-VEGF and chemotherapy…………128
Figure 4-12: Kaplan-Meier survival estimates for the heterogeneous virtual
mouse population ………………………………………………………………...130
Figure 5-1: Computational model of VEGF-FGF mediated angiogenesis and tumor growth…...142
Figure 5-2: The comparison of the predicted FGF-trap concentration to experimental data……153
Figure 5-3: Calibrating the model and predicting the response to the combination therapy
of VEGF-trap and FGF-trap………………………………………………………..155
xi
Abstract
Angiogenesis is the formation of new blood vessels from pre-existing vessels and is an
important hallmark of cancer. This process promotes tumor growth and progression by providing
oxygen, nutrients, and waste exchange and allowing tumor cells to establish subsequent metastasis.
Several angiogenic factors that affect the extent of tumor vascularization have been actively
studied and are commonly categorized as pro- and anti-angiogenic factors. Pro-angiogenic factors
such as vascular endothelial growth factor (VEGF) and fibroblast growth factor 2 (FGF2), bind to
specific receptors to initiate pro-angiogenic signaling promoting cell proliferation, migration and
blood vessel formation. On the other side, anti-angiogenic factors, like thrombospodin-1 (TSP1)
and platelet factor 4 (PF4), impede pro-angiogenic signaling and induce anti-angiogenic signaling
to oppose angiogenesis. Considering the importance of angiogenesis in tumor development, anti-
angiogenic therapeutics were designed to inhibit vascularization and tumor growth. However, anti-
angiogenic therapeutics to date showed limited success in the clinic side due to low efficacy, the
development of resistance, or toxicity. These drawbacks inspired the efforts to better understand
tumor angiogenesis and optimize anti-angiogenic cancer therapy. In this work, I present multiple
developed systems biology models that incorporate the interaction networks of potent angiogenic
factors (VEGF, FGF2, TSP1 and PF4) to investigate various anti-angiogenic therapies. The models
provide novel insights into the regulation of tumor angiogenesis and the observed response to anti-
angiogenic therapies tested in preclinical and clinical studies. Meanwhile, several potential
prognosis biomarkers are identified for precision medicine. Ultimately, such models can serve as
simulation tools to inform the development of effective anti-angiogenic cancer therapy.
1
Chapter 1. Introduction
1.1. Cancer therapy targeting tumor angiogenesis
Cancer is a major public health problem worldwide and is the second leading cause of
death in the United States
1
. Many different types of therapies are used for cancer treatment.
Surgical resection is often used to remove the tumor bulk from the patients. Chemotherapy and
radiotherapy are commonly used in addition to prevent the occurrence and growth of small,
unresectable tumors after surgery. However, these strategies are limited by poor specificity, where
it is difficult to distinguish normal cells from cancer cells, and result in low dose sensitivity, severe
side effects and the development of drug resistance
2
. The importance of angiogenesis in tumor
progression has been elucidated over the past several decades. The growth of the tumor relies on
the formation of new blood vessels, allowing the tumor to get oxygen and nutrients from the
environment
3
. Besides supporting the growth of the tumor, the formation of blood vessels increases
the likelihood of cancer metastasis, by enabling tumor cells to enter the bloodstream and be
transported to remote sites of the body. Highly malignant tumors are often capable of promoting
robust angiogenesis, and these tumors become fatal if no successful clinical intervention could be
made
4
. Accumulated knowledge of the importance of tumor angiogenesis gave rise to anti-
angiogenic therapy.
The study of anti-angiogenic therapy started from the 1970s when Dr. Judah Folkman
proposed cutting the blood supply off, by which cancer will be deprived of nutrients and
subsequently treated. Since then, an array of therapeutics targeting angiogenesis were developed
and tested in clinical trials. Many anti-angiogenic agents received FDA approval, and some are
recommended as the first-line therapy for certain cancer types
5
. These anti-angiogenic agents were
shown to prevent the formation of new blood vessels and normalize tumor-associated vasculature,
2
becoming an important modality in present anti-cancer therapy and complementing the therapeutic
paradigm
6
.
1.2. Angiogenic factors regulating tumor angiogenesis
With extensive studies of angiogenesis, various molecular species were identified to affect
the extent of vascularization. These molecular species have been actively studied and are
commonly categorized as pro- or anti-angiogenic factors
7
. Pro-angiogenic factors usually bind to
their respective receptors to induce signaling promoting cell proliferation, cell migration and blood
vessel formation
8,9
, while anti-angiogenic factors commonly inhibit pro-angiogenic signaling and
induce anti-angiogenic signaling to oppose angiogenesis
10,11
. In the physiological condition,
angiogenesis is tightly regulated by the balance of pro- and anti-angiogenic factors. This balance
is considered to heavily tip in favor of pro-angiogenesis in solid tumors, which leads to the
induction of the “angiogenic switch”, the strong induction of new blood vessel growth, to allow
tumor propagation and progression. Among various biochemical factors, vascular endothelial
growth factor-A (VEGF), fibroblast growth factor 2 (FGF2), thrombospondin-1 (TSP1) and
platelet factor 4 (PF4) have been investigated and identified to potently affect the extent of tumor
vascularization in different studies
12–15
.
1.2.1. Vascular Endothelial Growth Factor (VEGF)
Vascular endothelial growth factor (VEGF), originally known as vascular permeability
factor (VPF), was first described as an essential growth factor for vascular endothelial cells. One
particular form of VEGF is VEGFA, which is considered as a key regulator of angiogenesis,
promoting endothelial cell (EC) migration and proliferation. It is the most extensively studied
member in the gene family that includes five other growth factors: VEGFB, VEGFC, VEGFD,
3
VEGFE and placental growth factor (PlGF). VEGF has been implicated in various cancer types
and its contribution to tumor angiogenesis is well defined
16
. The biological functions of VEGF are
mainly mediated by two receptor tyrosine kinase (RTKs), VEGFR-1 and VEGFR-2, which are
reported to have different signaling properties
17
. Non-signaling co-receptors, including
Neuropilin-1 (NRP1) and Neuropilin-2 (NRP2), also modulate the VEGF RTK signaling
17
.
1.2.2. Fibroblast growth factor-2 (FGF2)
Fibroblast growth factor-2 (FGF2) is also known as basic fibroblast growth factor (bFGF)
and FGF-b. It belongs to the fibroblast growth factor (FGF) family that comprises at least 23
members
18,19
. Among the FGF family members, FGF2 is well-characterized and is identified as a
prominent pro-angiogenic growth factor. It promotes cell motility and proliferation, increases
tumor angiogenesis, and inhibits apoptosis
20
, all of which play an important role in tumor
progression. FGF2 interacts with four receptor tyrosine kinases (FGFR1 through FGFR4)
19
.
Additionally, FGF2 is a heparin-binding protein and can bind to the heparan sulfate
glycosaminoglycans (HSGAGs) on the surface of various cell types
18,19
, in which HSGAGs serve
as co-receptors that modulate the induced signaling of FGF2 ligand-receptor binding.
1.2.3. Thrombospondin-1 (TSP1)
TSP1 is a matricellular protein and acts as an endogenous inhibitor of angiogenesis. It binds
to various receptors to induce its biological functions
14
. The receptors for TSP1 include: CD36,
CD47, low density lipoprotein receptor-related protein (LRP), proteoglycans, integrins, integrin-
associated protein (IAP), and other unidentified receptors
21
. The role that TSP1 plays in tumor
angiogenesis is somewhat controversial. Although some studies suggest that TSP1 promotes
4
neovascularization
22
, TSP1 is commonly recognized as an anti-angiogenic factor. It can inhibit
endothelial cell migration and proliferation, stimulate endothelial cell apoptosis, regulate VEGF
bioavailability, suppress nitric oxide and VEGF signaling
23
.
1.2.4. Platelet factor 4 (PF4)
Platelet factor 4 (PF4) is a small cytokine that belongs to the CXC chemokine family. It is
also known as chemokine (C-X-C motif) ligand 4 (CXCL4). Various studies have investigated its
anti-angiogenic and anti-tumor effect
11,15,24
. It is shown to inhibit endothelial cell proliferation and
migration and angiogenesis both in vitro and in vivo
11
. It binds to a splice variant of the chemokine
receptor CXCR3, known as CXCR3B, to induce inhibitory signaling
15
. PF4 also inhibits pro-
angiogenic signaling through interactions with other angiogenic factors
15
.
1.3. The interconnected network of angiogenic factors
Angiogenesis is a systematic process regulated by a network of multiple angiogenic factors.
It is commonly accepted that the angiogenic factors interact with each other and form a regulatory
network to modulate tumor angiogenesis together. Figure 1-1 illustrates main interaction
mechanisms of angiogenic factors in tumor tissue.
Here, we present multiple reported interactions in the network of VEGF, FGF2, TSP1 and
PF4. In the network, the anti-angiogenic factors, TSP1 and PF4, can regulate the bioavailability
and activity of pro-angiogenic factors, VEGF and FGF2, via several mechanisms. Firstly, the anti-
angiogenic factors are able to regulate pro-angiogenic signaling through proteolysis and receptor
coupling
25
. In the tumor tissue, TSP1 can inhibit the activation of matrix metalloproteinase-9
(MMP9) to promote the deactivation of VEGF
26
. The ligand-bound TSP1 receptors, for example,
5
TSP1-bound CD36, can couple with VEGF receptors to inhibit the initiation of VEGF downstream
signaling
27
. Secondly, anti-angiogenic factors can affect pro-angiogenic signaling through
sequestration and heparan sulfate proteoglycans (HSPGs), important regulators of the angiogenic
signaling that facilitate the formation of VEGF and FGF2 signaling complexes
28,29
. TSP1 and PF4
both bind to VEGF and FGF2 directly to reduce the formation of pro-angiogenic signaling
complex on the surface of tumor and endothelial cells. Since PF4, TSP1, VEGF and FGF2 each
bind to heparan sulfate (HS)
30
, they will compete for binding sites in HSPGs on the cell surface
and in the extracellular matrix and basement membrane. The secretion of PF4 and TSP1 can lead
to displacement of VEGF and FGF2 from HS binding sites to regulate pro-angiogenic signaling.
Specifically, PF4 is known to interrupt the HSPG-mediated formation of pro-angiogenic
complexes to inhibit VEGF and FGF2 signaling
31,32
. In addition to the connection between pro-
and anti- angiogenic factors, FGF2 is reported to synergistically enhance the pro-angiogenic signal
with VEGF
33,34
. FGF2 can promote the secretion of VEGF, and upregulation of the FGF2 pathway
can result in resistance to anti-VEGF therapy
35
.
Figure 1-1: Mechanisms of the interaction between angiogenic factors. A. Anti-angiogenic
factors regulate the bioavailability of pro-angiogenic factors via competing for binding sites and
regulating proteolysis in interstitial space. B. Anti-angiogenic factors can bind to pro-angiogenic
factors directly. C. Anti-angiogenic receptors can couple with pro-angiogenic receptors to prevent
ligand binding or downstream signaling. D. Anti-angiogenic factors can compete for co-receptors
on cell surface to prevent the coupling of pro-angiogenic receptors. E. Angiogenic factors have
combination effect on downstream signaling.
6
1.4. Anti-angiogenic agents targeting angiogenic signaling
Based on the idea that the prevention of tumor vasculature can impede tumor growth,
various types of anti-angiogenic agent targeting the signaling of angiogenic factors were developed
for cancer therapy in past decades.
Small molecules are developed to target pro-angiogenic receptors and downstream
angiogenic signaling. For example, Sunitinib is a small molecule, multi-targeted receptor tyrosine
kinase inhibitor that was approved by FDA for the treatment of renal cell carcinoma and imatinib-
resistant gastrointestinal stromal tumor
36
. It targets VEGFR and platelet-derived growth factor
receptor (PDGFR) to inhibit tumor angiogenesis and tumor cell proliferation. Ponatinib, a drug
targeting FGFR1 and other tyrosine kinase receptors, were recently approved to treat certain
patients with chronic myeloid leukemia
37
.
Compared to small molecules, large molecule drugs, such as monoclonal antibodies,
soluble decoy receptor fusion proteins and peptide mimetics, have distinct properties and
commonly have high specificity and long half-life. Bevacizumab is a humanized monoclonal
antibody that targets VEGF to prevent neovascularization within tumor. It was the first FDA-
approved anti-angiogenic drug and is used as a monotherapy or in combination with chemotherapy
for several cancers
38
, including metastatic colorectal cancer (mCRC), non-small cell lung cancer
metastatic renal cell carcinoma, epithelial ovarian cancer and metastatic breast cancer (mBC). FP-
1039, a FGF ligand trap consisting of the extracellular domain of FGF receptor 1 (FGFR1) fused
with the Fc region of IgG1, was developed and tested in Phase I clinical trial
39
. In addition to drugs
targeting pro-angiogenic signaling, there are also agents developed to enhance anti-angiogenic
signaling. For example, ABT-510, a peptide mimetic of TSP1, reached Phase II clinical trial
40
. It
targets the TSP1 receptor, CD36, to promote endothelial cell apoptosis. Similarly, various PF4
7
variants or PF4-derived peptides have been actively investigated as anti-angiogenic drugs for
cancer therapy
41
.
1.5. Therapeutic strategies targeting multiple angiogenic signals
Tumor growth requires the formation of new blood vessels, and developed anti-angiogenic
agents show some successful results in cancer therapy. However, the limitations of traditional anti-
angiogenic agents have been gradually revealed in various studies
4,42
. None of the current anti-
angiogenic agents are effective for all cancer types
43
. Disappointing outcomes, either due to lack
of therapeutic response or toxicity issues, have been observed in several settings as well
5,43,44
. In
late 2011, the approval of Bevacizumab was revoked for the use in first-line metastatic breast
cancer
45
. Several Phase II and III clinical trials also suggested contradicting results of using
bevacizumab in neoadjuvant chemotherapy for breast cancer patients
46–50
. While the addition of
bevacizumab to neoadjuvant chemotherapy was shown to improve the response of patients
51
, the
need of the agent is also being questioned in some studies
46–50
. Sunitinib, a VEGFR inhibitor, has
also shown limited success
52
. ABT-510, a TSP1 mimetic, failed to show clear evidence of efficacy
and is no longer tested as a single-agent drug in clinical development
40,53
.
One major hurdle for anti-cancer therapy targeting angiogenesis is the fact that
angiogenesis encompasses multiple signaling pathways. The effect of anti-angiogenic therapy
targeting the signaling of a single angiogenic factor can be easily overcome and can lead to worse
outcomes in terms of disease progression and overall survival
54
. The limitations of traditional anti-
angiogenic agents prompt the development of anti-angiogenic therapy targeting multiple
angiogenic signals, which includes the combination therapy of multiple anti-angiogenic agents or
a single drug targeting multiple angiogenic pathways. The anti-angiogenic therapy strategy
8
simultaneously targeting multiple angiogenic signals is expected to achieve efficient and durable
suppression of angiogenesis by strongly shifting the relative balance of promoters and inhibitors
of angiogenesis to oppose the angiogenic switch. This strategy has been tested in both pre-clinical
and clinical studies. For instance, the ABT-510 TSP1 mimetic was clinically tested in combination
with bevacizumab in patients with advanced solid tumors to target both VEGF and TSP1
signaling
55
. Brivanib, a small molecule targeting both VEGFR2 and FGFR tyrosine kinase
inhibitor, has shown efficacy in nude mouse xenograft models that exhibit development of
adaptive resistance to anti-VEGF therapy alone
56
. Additionally, a fusion receptor protein that binds
to both VEGF and FGF2, was developed and proved to exhibit potent anti-angiogenic effects in
pre-clinical study
57
.
1.6. Tumor heterogeneity and the response to anti-angiogenic therapy
Cancer is a heterogenous disease. Tumor heterogeneity has been observed from the
molecular level to the phenotypic level in various cancers
58
. The great heterogeneity of tumor
genotypes and phenotypes drives diverse biological behavior of cancers. The tumor heterogeneity
can be categorized into inter- and intra-tumor heterogeneity
59,60
. Inter-tumor heterogeneity
comprises differences in tumors between individuals and differences in multiple tumor sites within
a single individual. The intrinsic properties of tumor cells, the surrounding microenvironment, the
location of the tumor site, and the characteristics of patients can all contribute to the inter-tumor
heterogeneity. On the other side, intratumor heterogeneity is the heterogeneity within a single
tumor site. The intratumor heterogeneity is commonly gradually developed during the course of
disease progression. Intratumor heterogeneity can be further divided into spatial and temporal
heterogeneity
60
. Spatial heterogeneity are the differences between different subpopulations within
9
a single tumor site, while temporal heterogeneity refers to the dynamic shift of tumor cells with
genetic alterations and phenotypic changes within tumors over time
60
. Tumor heterogeneity greatly
affects the outcome of cancer therapy. As a result of intratumor heterogeneity, tumors comprised
of a diverse collection of cells harboring distinct molecular signatures can develop significant
resistance to therapeutic treatment after the selective process
60–62
; For inter-tumor heterogeneity,
tumors with distinct properties could have differential levels of sensitivity to treatment and can
respond to the same treatment in highly different ways
60,61
.
The impact of tumor heterogeneity on the response to anti-angiogenic therapy is observed
in various pre-clinical and clinical studies
5,63,64
. Anti-VEGF is currently the most successful anti-
angiogenic strategy. However, although VEGF inhibitors are effective at reducing
neovascularization, they do not produce consistent and enduring clinical benefit in a great number
of patients
65,66
. The heterogeneous response is also observed in the anti-angiogenic therapy
targeting the signaling of multiple angiogenic factors. The ABT-510, a TSP1 mimetic, was
clinically tested in combination with bevacizumab in patients with advanced solid tumors.
However, patients displayed a heterogeneous response to this combination therapy
55
: one patient
had a partial response (Tumor shows significant reduction, but is not fully eliminated) and only
32% of the patients had prolonged stable disease (≥6 months). Furthermore, angiogenesis
inhibitors are reported to lead to countertherapeutic effect in some conditions. Anti-angiogenic
agents have been shown to make some tumors more aggressive in animal models
67,68
, which
changes the natural development of tumors, induces resistance to therapy and increases invasion
and metastasis. For example, bevacizumab is observed to lead to an increase of VEGF levels in
some patients
69,70
, which makes the effects of administration of anti-VEGF drugs on systemic
levels controversial.
10
1.7. Investigating anti-angiogenic therapy through computational systems biology
Computational systems biology serves as a useful tool to study angiogenesis and anti-
angiogenic therapy, complementing experimental and clinical studies. Various modeling
approaches have been applied to investigate tumor angiogenesis and anti-angiogenic therapy,
including differential equation based models, Boolean network models, multi-compartment
models, hybrid cellular automaton models, multiscale agent-based models, image-based models
and bioinformatics-based modeling
71
. These models provide quantitative insights, at different
levels of detail and scales, ranging from intracellular signaling to whole-body dynamics. Models
of intracellular signaling of angiogenic factors characterize the biochemical events inside the cell
initiated by ligand binding to signaling receptors on the cell surface. They help in the identification
of new intracellular drug targets
72
. At the extracellular level, models of the extracellular species’
reaction network are used to understand the distribution of angiogenic factors in tumor tissue
73
and
in the whole body
74
. By linking to the kinetics of anti-angiogenic drugs, models that capture
extracellular interactions can be used to study therapeutics that modulate the distribution of
angiogenic factors, which directly affects angiogenic signaling
70,75
. Specifically, the effects of anti-
VEGF agents on VEGF and its receptors have been intensively investigated with computational
modeling. Targeting VEGF binding, VEGF secretion and VEGFR signaling as anti-angiogenic
strategy have been illustrated in different studies
71
. For example, a computational model has been
used to illustrate the counterintuitive increasing of VEGF after anti-VEGF treatment
70
. Recently,
mathematical modeling was used to understand the impact of the cross-talk between tumor cells
and endothelial cells
76
and the vascular phenotypes
77
on the effects of anti-angiogenic treatment,
which generates new insights into anti-angiogenic therapy with mathematical modeling.
11
Overall, the computational systems biology models have been actively used to generate
mechanistic understanding of tumor angiogenesis and anti-angiogenic therapy and help explain
experimental observations. However, there are still several important questions and emerging
needs in the field, which greatly motivates the works in this dissertation.
Firstly, most previous modeling studies only focus on illustrating the functions of single
angiogenic factors, and the models of multiple angiogenic factors are not well-developed. As
introduced in Section 1.3, the angiogenic factors interact with each other and form an
interconnected regulatory network. A computational model that captures a holistic view of
multiple angiogenic factors can better reflect the systematic dynamics and provide novel
understanding into how tumor angiogenesis is regulated by multiple angiogenic factors.
Additionally, to improve therapeutic outcome, the development of anti-angiogenic therapy is
moving from targeting single angiogenic factors to simultaneously targeting multiple angiogenic
species. Thus, there is an emerging need for models incorporating multiple angiogenic factors,
which can provide insights into how the vasculature can be effectively and optimally targeted at
the systems level.
Secondly, the heterogenous responses to anti-angiogenic therapy remain a major challenge
in anti-angiogenic therapy. Although clinical studies based on population average response might
implicate positive impacts of anti-angiogenic therapy, the individual responses are highly variable
and can even show undesired countertherapeutic outcomes. Depending on the cancer type and the
specific anti-angiogenic agents, the responses to anti-angiogenic therapies can be quite
contradictory
66
. The mechanisms of how heterogeneity influences anti-angiogenic therapy remain
unclear. A computational model explaining the observed ranges of responses, including
12
counterintuitive effects, could greatly advance our understanding of anti-angiogenic therapy and
guide the future practice of anti-angiogenic therapy development.
Thirdly, it is difficult to develop biomarkers for anti-angiogenic therapy with experimental
methods alone. The observed heterogenous response in cancer patients have inspired the
development of prognosis biomarkers. The use of biomarkers could provide a way to circumvent
the drawbacks of anti-angiogenic therapy by identifying the patients with highest likelihood for a
positive response to treatment. However, although many efforts have been made and have
generated some promising preliminary results, there is no reliable biomarker that can be used in
the clinic so far to help select patients with a positive prognosis for anti-angiogenic therapy.
Computational models provide a great platform to help precision and optimized personal therapy.
By taking advantage of computational modeling, it is possible to predict the optimal anti-
angiogenic treatment strategies for individuals and identify biomarkers for patient screening in an
extremely time-saving and cost-efficient manner.
With these motivations, we pursued mechanistic modeling of the angiogenic factors
network and cancer therapy.
1.8. Dissertation outline
In this work, I use computational systems biology to study tumor angiogenesis and anti-
angiogenic therapy to achieve three main goals: illustrate the regulation mechanism of the network
of angiogenic factors, improve the understanding of the response to anti-angiogenic therapy, and
explore potential biomarkers for anti-angiogenic therapy. Multiple novel models were constructed
and applied to generate new predictions and to provide mechanistic insights.
In Chapter 2, I present a molecularly detailed model describing the extracellular interaction
network of four angiogenic factors in tumor tissue, which include two pro-angiogenic factors
13
(VEGF and FGF2) and two anti-angiogenic factors (TSP1 and PF4). Compared to previous models,
this model provides a more comprehensive view of the angiogenic networks. The model was used
to explore the localization of pro- and anti-angiogenic factors and how their distributions are
affected by tissue angiogenic factor secretion and the presence of heparan sulfate proteoglycans.
The model simulation provides a better understanding of how the tumor angiogenic proteins are
regulated in the extracellular space. Specifically, it produces valuable predictions on how the
numbers of angiogenic signaling complexes are changing under the variation of angiogenic factor
level in the tumor interstitial space, which provides insights into the changes of tumor angiogenic
signaling under common physiological activities (e.g., platelets activation) and treatment
interventions (e.g., the administration of anti-angiogenic agents).
In Chapter 3, I extend the tumor tissue model into a multi-compartment model integrating
the reaction networks of VEGF and TSP1 in human cancer patients. This model characterized the
distribution of VEGF and TSP1 in tumor tissue, blood, and normal tissue, which provides a
platform to study the clinically tested drug combination targeting these two potent angiogenic
factors. The values of physiologically relevant parameters were varied to represent the interpatient
tumor heterogeneity. The numbers of angiogenic signaling complex in tumor are used to quantify
the response to the anti-angiogenic therapy. With the model, we generated predictions for the
impact of tumor receptor heterogeneity on the response to a clinically tested combination anti-
angiogenic therapy targeting both VEGF and TSP1 signaling. In addition to the mechanistic
modeling, we applied partial least square regression (PLSR), a data-driven analysis, to identify
potential tissue biomarkers for anti-angiogenic therapy. Overall, the model predictions provide
mechanistic explanations of several important results reported in clinical trials of anti-angiogenic
14
therapy, including the heterogeneous response to treatment and the importance of CD36, CD47,
and VEGFR1 as predictive biomarkers.
In Chapter 4, I focus on constructing a model predicting the tumor volume change under
anti-angiogenic treatment. I present a predictive model that links the biochemical network of
VEGF ligand-receptor binding to the in vivo tumor growth dynamic of mouse xenografts. In the
preclinical studies of anti-angiogenic cancer therapy, the mouse xenograft model is widely used
for the evaluation of drug efficacy and safety. After injecting cancer cells into a mouse, the tumor
will develop over weeks and the response to the therapy can be studied in vivo. Multiple datasets
of tumor volume dynamics are available in the published anti-VEGF studies using the mouse
xenograft model. The experimental datasets were used to calibrate and validate a computational
model. With the constructed computational model, I generate a series of predictions to investigate
the effect of anti-VEGF on endothelial cells and tumor cells, the impact of tumor growth properties
on the response to anti-VEGF, and the synergy of anti-angiogenic therapy and chemotherapy. The
predictions indicate that the variation of tumor cell growth rate can be a main reason for the
experimentally observed heterogeneous response to anti-VEGF therapy. Specifically, the tumors
with lower tumor cell growth rate and higher carrying capacity are predicted to have a stronger
response to anti-VEGF treatment. In addition, the simulation results suggest a new synergy
mechanism where anticancer therapy can enhance anti-VEGF simply through reducing the tumor
cell growth rate.
In Chapter 5, I present the work extending the model from chapter four to study the anti-
angiogenic therapy targeting both VEGF and FGF signaling. FGF plays an important role in the
development of the resistance to anti-VEGF therapy. Therefore, the molecular details of the FGF2
system are further incorporated into the model in addition to our model of the VEGF system. The
15
constructed model is able to predict in vivo tumor growth under anti-VEGF, anti-FGF or the
combination therapy targeting both angiogenic factors. This model provides a computational
platform to study tumor angiogenesis and tumor xenograft growth mediated by multiple pro-
angiogenic factors, which is applied to investigate the dose-response and the combination therapy
of anti-VEGF and anti-FGF in my work.
Altogether, my work focuses on using computational systems biology approach to study
tumor angiogenesis regulated by multiple angiogenic factors and the effects of cancer therapy
targeting angiogenic signals. This work provides a series of computational models that generate
much needed systems-level insight into the function of multiple angiogenic factors in tumor
progression. As such, this work is an important advance in the field of modeling tumor
angiogenesis and cancer therapy. The completed work generates novel insights into the dynamics
of angiogenic factors and experimental observations, which help to fundamentally understand
tumor biology and anti-angiogenic therapy. The models could serve as simulation tools to explore
optimal cancer therapy targeting multiple angiogenic factors and guide the practice of anti-
angiogenic therapy in pre-clinical and clinical settings.
16
Chapter 2. Modeling of angiogenic interaction network in tumor tissue
Portions of this chapter are adapted from:
Ding Li and Stacey D. Finley. Frontiers in Physiology, 2019; 10: 823
2.1. Abstract
Tumor angiogenesis is regulated by pro- and anti-angiogenic factors. Anti-angiogenic
agents target the interconnected network of angiogenic factors to inhibit neovascularization, which
subsequently impedes tumor growth. Due to the complexity of this network, optimizing anti-
angiogenic cancer treatments requires detailed knowledge at a systems level. In this study, I
construct a tumor tissue-based model to better understand how the angiogenic network is regulated
by opposing mediators at the extracellular level. I consider the network comprised of two pro-
angiogenic factors: vascular endothelial growth factor (VEGF) and basic fibroblast growth factor
(FGF2), and two anti-angiogenic factors: thrombospondin-1 (TSP1) and platelet factor 4 (PF4).
The model’s prediction of angiogenic factors’ distribution in tumor tissue reveals the localization
of different factors and indicates the angiogenic state of the tumor. I explored how the distributions
are affected by the secretion of the pro- and anti-angiogenic factors, illustrating how the angiogenic
network is regulated in the extracellular space. Interestingly, I identified a counterintuitive result
that the secretion of the anti-angiogenic factor PF4 can enhance pro-angiogenic signaling by
elevating the levels of the interstitial and surface-level pro-angiogenic species. This
counterintuitive situation is pertinent to the clinical setting, such as the release of anti-angiogenic
factors in platelet activation or the administration of exogenous PF4 for anti-angiogenic therapy.
The work included in this chapter provides mechanistic insights into this counterintuitive behavior
of angiogenic signaling network and highlights the role of heparan sulfate proteoglycans (HSPG)
in regulating the interactions between angiogenic factors. This work complements previous studies
17
aimed at understanding formation of angiogenic complexes in tumor tissue and helps in the
development of anti-cancer strategies targeting angiogenesis.
2.2. Introduction
Angiogenesis, the growth of new blood microvessels from pre-existing microvasculature,
plays a crucial role in tumor development
78
. Tumor growth relies on angiogenesis to enable waste
exchange and provide oxygen and nutrients from the surrounding environment. Several angiogenic
factors that affect the extent of tumor vascularization have been identified and are commonly
categorized as pro- and anti-angiogenic factors. Pro-angiogenic factors, including vascular
endothelial growth factor-A (VEGF) and fibroblast growth factor 2 (FGF2), bind to their
respective receptors to induce pro-angiogenic signaling promoting cell proliferation, cell migration
and blood vessel formation
8,9
. On the other side, anti-angiogenic factors, like thrombospodin-1
(TSP1) and platelet factor 4 (PF4), inhibit pro-angiogenic signaling and induce anti-angiogenic
signaling to oppose angiogenesis
10,11
. Considering the importance of angiogenesis in tumor
development, anti-angiogenic therapies are designed to target the signaling of angiogenic factors
to inhibit neovascularization and tumor growth
5
. Single-agent anti-angiogenic therapies that target
a particular angiogenic factor in the network were the first angiogenesis-inhibiting therapies
studied. These include antibodies or small molecules targeting pro-angiogenic factors
43
and
peptide mimetics of anti-angiogenic factors
79
. However, these single-agent anti-angiogenic
therapies showed limited success in the clinic due to toxicity, low efficacy, or the development of
resistance
5,52
. These drawbacks have promoted efforts to develop combination therapies
administering multiple anti-angiogenic agents and other therapeutic agents that simultaneously
target various angiogenic species in the network
54,55,80,81
.
18
Due to the intrinsic complexity of the network regulating tumor angiogenesis, optimizing
anti-angiogenic cancer treatment, specifically anti-angiogenic therapy targeting multiple
angiogenic factors, requires detailed knowledge and a holistic view at a systems level.
Computational systems biology models offer powerful tools to systematically study tumor
angiogenesis and optimize anti-angiogenic tumor therapy. Various types of systems biology
models have been constructed to investigate new anti-angiogenic therapies
71
. However, the vast
majority of previous modeling efforts have focused on the function of single pro-angiogenic
factors. Therefore, these models do not provide insights into the angiogenic regulation involved
multiple angiogenic factors, such as the balance of pro-angiogenic and anti-angiogenic signal and
the synergy between angiogenic factors. More importantly, angiogenesis is a system process and
is not regulated by a single angiogenic factor. Modulating the level of a single angiogenic factor
will result to a systematic change in the network. To better understand the effects of targeting
angiogenic factors in the tumor, we built a new tissue-based systems biology model characterizing
the extracellular network that involves four main angiogenic factors regulating tumor angiogenesis,
including VEGF, FGF2, TSP1 and PF4 (Figure 2-1).
Our modeling work expanded previous models by incorporating angiogenic factors that
were previously omitted from the models, as well as other significant mediators. Thus, our model
enables a systematic study of the extracellular regulation of multiple angiogenic factors. The
extracellular distribution of VEGF alone was firstly investigated in a computational setting with a
tissue-based model
73
. Then this physiologically relevant and molecularly detailed model was
extended to include TSP1, a potent endogenous anti-angiogenic factor, to explore the balance of
pro- and anti-angiogenic factor in tumor tissue
25
. In the work presented in this chapter, we further
expand the model to include the pro-angiogenic factor, FGF2, and an additional anti-angiogenic
19
factor, PF4. These species are reported to interact with VEGF and TSP1 and significantly impact
on tumor angiogenesis. FGF2 is reported to synergistically enhance the pro-angiogenic signal with
VEGF
33,34
. On the other hand, upregulation of the FGF2 pathway can result in resistance to anti-
VEGF therapy
54,81
. PF4, like the other anti-angiogenic factor TSP1, binds to VEGF and FGF2 to
reduce pro-angiogenic signaling
15,82
.Therefore, incorporating FGF2 and PF4 provides a more
complete view of the angiogenic interaction network and a more comprehensive understanding of
tumor angiogenic state, as compared to previous models. In addition, PF4, TSP1, VEGF and FGF2
each bind to heparin, competing for the heparan sulfate (HS) binding sites in heparan sulfate
proteoglycans (HSPG) on the cell surface and in the extracellular matrix and basement membrane
30
.
The secretion of PF4 and TSP1 leading to displacement of VEGF and FGF2 from HS binding sites
is an important mechanism of tumor angiogenesis regulation. Specifically, PF4 is known to
interrupt the HSPG-mediated formation of pro-angiogenic complexes to inhibit VEGF and FGF2
signaling
31,32
. To account for the regulation of HSPG, our model includes two distinct species with
HS binding sites, one of which, the surface-level HSPG, is not explicitly accounted for in previous
tumor tissue-based models
25,73
. The previous tissue-based model of VEGF and TSP1 has 120
species that was generated with 27 seeding species and 78 reaction rules
25
. After incorporating
FGF2, PF4, HSPGs, and their binding partners, the novel model presented in this study is
comprised of 168 species, generated with 40 seed species and 127 reaction rules.
With the newly constructed model, we firstly profiled the distribution of these four
angiogenic factors in tumor tissue and systematically investigated how the secretion of different
angiogenic factors affects the balance of pro- and anti-angiogenic signaling. Furthermore, we
generate insights explaining two specific counterintuitive phenomena: (1) the secretion of PF4
increases the levels of free VEGF and FGF2 in tumor tissue and (2) the secretion of PF4 promotes
20
the formation of VEGF signaling complexes. We found HSPG’s level directly affects these
counterintuitive results in different ways, emphasizing the important role of HSPGs in the
regulation of angiogenic factor signaling. Lastly, we apply the model to simulate a controlled
release of PF4 in tumor tissue, and our results indicate that the HSPG level in the tumor
microenvironment might affect the response to platelet activation and recombinant PF4 anti-
angiogenic therapy. Overall, the work in this chapter establishes a new computational framework
to understand the extracellular distribution of angiogenic factors in tumor tissue and generate new
insights into the regulation of the angiogenic factors’ interaction network, which are difficult to
examine through experimental study alone.
Figure 2-1: Schematic of the tumor tissue based model. The compartmental model describes
the reaction network of four major angiogenic factors (VEGF, FGF2, TSP1 and PF4) in the
extracellular space of tumor tissue. Angiogenic receptors are expressed on the cell surfaces.
Soluble angiogenic factors exist in the interstitial space, and they bind to cell surface receptors to
form signaling complexes. Two different heparan sulfate proteoglycans are included in the model,
including cell surface HSPG (cHSPG) and interstitial HSPG (iHSPG).
21
2.3. Methods
2.3.1. The tumor tissue model of angiogenic factors
We constructed a molecularly detailed model that describes the extracellular network of
four main angiogenic factors in tumor tissue (Figure 2-1). The modeling approach is consistent
with various previous works
25,73
. The system is represented by a set of coupled nonlinear ordinary
differential equations (ODEs) to characterize a well-mixed tumor tissue. For the model structure,
the extracellular spaces in tumor tissue are divided into three regions: the surface of endothelial
cells, the surface of tumor cells and interstitial space. The interstitial space between tumor and
endothelial cells is comprised of extracellular matrix (ECM) and the basement membranes
surrounding the tumor cells (TBM) and the endothelial cells (EBM). The soluble species are
secreted by both cell types and can be removed from the system through degradation in the
interstitial space or internalization with receptors at the cell surface.
Ten soluble species are present in the model (Figure 2-2, Legend I). Physiologically, in
tumor tissue, VEGF121, VEGF165, FGF2, TSP1, MMP3 and proMMP9 are mainly produced
through the secretion from tumor cells and endothelial cells, while PF4 is stored in the a-granules
of the platelets and is released through platelet activation. Thus, in the model, the source of PF4 in
tumor tissue is represented by a generic production rate. In addition, VEGF114, inactive TSP1 and
active MMP9 are formed through cleavage. Nine relevant receptors are present on the cell surface
(Figure 2-2, Legend II), including VEGF receptors (VEGFR1, VEGFR2, Neuropilin-1), TSP1
receptors (CD47, CD36, LRP1, αxβ1 integrins), FGF2 receptor (FGFR1) and PF4 receptor
(CXCR3). Receptors are assumed to be uniformly distributed on the cell surface and are recycled
back to surface to maintain a constant total number for each type of receptor. In addition, we
include the heparan sulfate proteoglycans (HSPGs) in the model, which are important modulators
22
of angiogenic signaling. HSPGs are glycoproteins, which have a protein core and one or more
covalently attached heparan sulfate (HS) chains. Two types of HSPGs are present in the model
(Figure 2-2, Legend III). One is the interstitial heparan sulfate proteoglycans (iHSPG) that are
present in the ECM, EBM and TBM. The other one is the cell-surface heparan sulfate
proteoglycans (cHSPG). The iHSPG serves as a reservoir for angiogenic factors, while the cHSPG
mainly functions as a co-receptor participating in the formation of complexes to modulate
angiogenic signaling.
2.3.2. Network of reactions
The principles of mass action kinetics are used to characterize the species’ dynamics. The
defined rules that govern the molecular interactions are showed in Figure 2-2, and the detailed
reactions are given in Appendix A Table A-1.
VEGF-Receptor axis (Figure 2-2 A): Previous work modeling VEGF ligand-receptor
interactions did not explicitly include the surface-level HSPGs (cHSPG)
83
, assuming the presence
of abundant HSPGs on the cell surface. To investigate the impact of HSPG on VEGF signaling,
we extended previous VEGF-VEGFR modeling to incorporate the cHSPG-facilitated VEGF
binding reactions. Previous works have detailed documentation of estimating the kinetic for two
VEGF isoforms (VEGF165 and VEGF121) binding to VEGF receptors
73,83
, and we use those
parameter values in our model. Below, we present how we have adapted previous works to include
cHSPG regulation.
VEGFR2 and co-receptors (first two rows of Figure 2-2 A): According its structure,
VEGF165 binds to VEGFR2 via the exon 4 encoded domain and to NRP1 and HSPG via the exon
7 encoded domain to form a ternary complex
83,84
. It is commonly assumed that VEGFR2 does not
23
directly interact with NRP1, but is bridged by the VEGF165
85
. For the HSPG, in a recent study,
VEGFR2 was shown not to interact with heparin directly, and that VEGF165 also mediates the
interactions between VEGR2 and heparin
29
. Therefore, in our model, we assume HSPG does not
directly interact with VEGFR2, and the impact of HSPG on VEGFR2 signaling is mediated
through supporting the VEGF165-mediated bridging of VEGFR2 with NRP1. For the interactions
between HSPG and NRP1, it is reported that heparin could bind to the b1b2 domain of NRP1
directly, greatly enhancing the binding of VEGF165 to NRP1
86
. This suggests that VEGF165 binds
to NRP1 in an HSPG-dependent way. To include this knowledge, we allow HSPG to pre-couple
with NRP1 before interacting with VEGFR2. The other isoform of VEGF, VEGF121, lacks the
exon 7 coded region; thus, it does not bind to NRP1 or HSPG
29,84
.
VEGFR1 and co-receptors (second two row of Figure 2-2 A): Following our previous
modeling
73,83
, VEGFR1 can couple with NRP1, while the binding with VEGF121 is not affected by
the coupling. Since VEGR1 was shown to bind to heparin directly and VEGFR1 does not show a
heparin-aided VEGF binding as VEGR2 does
29
, we assume HSPG can couple with VEGR1 and
does not affect its binding to VEGF. In addition, we assume VEGFR1 can couple with the NRP1
pre-coupled with HSPG to form a ternary complex and that then binds with VEGF. Following our
previous model, VEGF165 does not bind to VEGFR1 pre-coupled with NRP1
73,83
. In addition, since
it is reported that the presence of heparin does not significantly change the binding of VEGF165 to
VEGFR1
29
, we assume the pre-coupling of VEGFR1 with HSPG does not affect VEGFR1’s
binding with VEGF165.
TSP1-Receptor axis (Figure 2-2 B-C): The reaction involving interactions between TSP1
and its receptors are taken from previous works
25
, in which TSP1 regulates angiogenic signaling
in different ways. TSP1 binds to its own receptors to induce anti-angiogenic signaling (Figure 2-
24
2 B). TSP1 binds to CD47 and LRP1 directly. The complex of VEGF bound TSP1 also binds to
LRP1. TSP1 contains a binding region in its N-terminal end which enable the binding to HSPG
21
.
TSP1 binds to CD36, integrin b1 and the coupled complex of them. TSP1 and TSP1 receptors can
also interact with VEGFR2 to inhibit the signaling of VEGF (Figure 2-2 C). It is reported that
TSP1 inhibits VEGFR2 signaling by disrupting its association with CD47
87
. Additionally, TSP1
receptors CD36 and β1 integrin can associate with the VEGFR2 to regulate the angiogenic
signaling
88
. These interactions are included in the model.
FGF2-Receptor axis (Figure 2-2 D): The reactions for the FGF2-receptor axis are adapted
from the extracellular part of an in vitro whole cell FGF2 signaling model
89
, which defines the
formation of FGF2 signaling trimeric complexes that then dimerize. FGF2 binds to HSPG to form
a complex, which binds to the FGFR1 monomer to form a trimeric complex. Then, dimerization
of the trimeric complex leads to the formation of the full FGF2 signaling complex. The choice of
this ordering is based on several observations from experimental studies
28,89
: FGF2 shows a lower
affinity to FGFR1 than to heparin; the interaction of FGFR1 and heparin has a very weak affinity;
and FGF2 dramatically increases the association of FGFR1 with heparin. Alternative orders of the
binding reactions are possible; however, they are reported to not conform well with the
experimental data
28
.
PF4-Receptor axis (Figure 2-2 E): PF4 regulates angiogenesis through various
mechanisms. On the cell surface, PF4 binds to cell surface receptors (CXCR3 and LRP1) to induce
anti-angiogenic signaling
90,91
and binds to cHSPG to control pro-angiogenic signaling
32,82
. We
include these interactions in the model. PF4 and TSP1 both are reported to bind to LRP1
91,92
, and
we have TSP1 and PF4 compete for LRP1 with different affinities.
25
Interactions between angiogenic factors (Figure 2-2 F): The angiogenic factors also
interact either by direct binding or through HSPGs in the interstitial space(iHSPG). TSP1
associates with VEGF and FGF2 to reduce pro-angiogenic signaling
25,93
, and it mediates VEGF
cleavage through MMP activity
25
. In addition, TSP1 can compete for the HS binding sites on
cHSPG and iHSPG to release HS-bound angiogenic factors. Similarly, FGF2 can be trapped by
TSP1, PF4 and iHSPG. Additionally, PF4 directly binds to VEGF165 and FGF2, reducing the
available pro-angiogenic factors
15,82
. Lastly, PF4 competes for the HS binding sites on the iHSPG.
26
27
Figure 2-2: Schematic of the extracellular network of VEGF, FGF2, TSP1 and PF4. (A)
Molecular interactions of two active VEGF isoforms (VEGF165 and VEGF121), receptors
(VEGFR1, VEGFR2 and NRP1) and heparan sulfate proteoglycans on the cell surface (cHSPG).
(B) Molecular interactions of TSP1 binding to its receptors (CD36, CD47, LRP1 and αxβ1 integrins)
and cHSPG. (C) Molecular interactions of the coupling between VEGFR2 and TSP1 receptors. (D)
Molecular interactions of FGF2 binding to FGFR1 and cHSPG and the formation of the full
signaling complex through dimerization. (E) Molecular interactions of PF4 binding to receptors
(CXCR3 and LRP1) and cHSPG, as well as MMP9 binding to LRP1. (F) The molecular
interactions of angiogenic factors binding to one another and heparan sulfate proteoglycans in the
interstitial space (iHSPG), as well as the proteolysis and degradation of soluble species. Numbers
for each interaction correspond to the list of reactions in Appendix A Table A-1. One interaction
on the schematic may represent multiple reactions (i.e. the same species can bind through different
binding sites). In total, the details of 89 reaction rules are listed in Appendix A Table A-1.
2.3.3. Parameterization
The model parameter values are reported in Appendix A Table A-2 with literature references.
Here, we describe the derivation of inherited values and the rationales for the parameterization of
newly introduced values in the model.
Geometric parameters: The tumor tissue is parameterized as a 33 cm
3
breast tumor, which
is modeled as a spatially averaged compartment in the model (Figure 2-1). The geometric
parameters define the volume of the compartment, the interstitial space volume fraction, and the
tissue surface areas of endothelial cells and tumor cells. These geometric parameters enable the
conversion of concentration from moles per cm
3
tissue to standard units (pmol/l), where the
derivations are thoroughly documented in previous works
73,74
.
Production and degradation of soluble species: The production and degradation rates of
VEGF, TSP1, MMP3 and proMMP9 are estimated in our previous work
25
. The baseline production
rates of PF4 and FGF2 are set to match an intermediate level within the range of experimental
measurements (Table 2-1). The degradation rates of PF4 and FGF2 are set according to their half-
life (t1/2): the rate of degradation is ln(2)/t1/2. Since a wide range of reported values for the FGF2
half-life is found in literature
94,95
, we assume it has a half-life of 60 minutes, similar to VEGF,
28
which is within the reported range. PF4 is reported to be rapidly cleared in human body, where the
half-life is assumed to be 5 minutes
96
.
Receptor Numbers: The receptor densities for VEGF receptors, TSP1 receptors, FGFR1
and HSPGs are taken from previous modeling works
25,89
. There is a paucity of measurements for
the PF4 receptor, CXCR3. Thus, we referred to the qualitative measurements in Human Protein
Atlas
97
, assuming ‘‘low’’, ‘‘medium’’, and ‘‘high’’ expression levels correspond to 2500, 5000,
and 10,000 receptors per cell. CXCR3 has a low expression, which is set to be to be 2,500 receptors
per cell accordingly.
Kinetic Parameters: For the VEGF axis, the kinetic parameters have been estimated in
previous work, based on experimental measurements
83
and assuming an abundant level of HSPGs.
We adopted these values in our current model by incorporating several experimentally observed
synergistic interactions in the presence of heparin. Since the previous model is calibrated in
condition with abundant HSPGs, we assume the NRP1 in the previous model is already coupled
with HSPGs. Therefore, the parameters of VEGF165 binding to NRP1 in the previous model is used
for VEGF165 binding to the NRP1:HSPG complex in our model. Then, we assume the VEGF165
binding to NRP1 alone is 20-fold weaker than binding to the NRP1:HSPG complex, according to
a study showing that the presence of heparin significantly increases VEGF binding to NRP1
86
.
Likewise, the rates for VEGFR2 coupling to VEGF165-bound NRP in the previous model are used
for the VEGFR2 coupling to the VEGF165-bound NRP:HSPG complex in our model, while the
previous rates for VEGF165-bound VEGFR2 coupling to NRP1 are used for the VEGF165-bound
VEGFR2 coupling to NRP:HSPG complex in our model. To our knowledge, there are no available
measurements to estimate the coupling rates of NRP1 to HSPG. Therefore, we assume the rates of
NRP1 coupling to HSPG are the same as rates of VEGFR2 coupling to NRP1, which are taken
29
from previous modeling
73
. Previous experimental study shows a VEGF165-mediated synergistic
binding between NRP1 and heparin
29
, and we accordingly assume the coupling of VEGF165:NRP
to HSPG and the coupling of VEGF165:HSPG to NRP are an order of magnitude stronger than the
coupling between NRP and HSPG. Following previous works
73,75
, the coupling of VEGFR1 to
NRP is set to be an order of magnitude weaker than VEGFR2-NRP coupling. According to the
measured binding constants
29
, the coupling of VEGFR1 to HSPG is assumed to be 5-fold stronger
than NRP-HSPG coupling.
For the TSP1 axis, we followed the values used in previous works
25
. For the kinetic rates
governing the FGF2 axis, we used the values estimated from experimental data in a previous
study
89
. For the PF4 axis, the Kd values of PF4 binding to CXCR3 and LRP1 are estimated to be
1.85 nmol/l
90
and 238 nmol/l
98
, respectively. These are used to set the dissociation rate, with the
association rate held at 5×10
5
M
-1
s
-1
, based on molecular dynamics studies of biomolecular
reaction kinetics
99,100
. In the model, VEGF, TSP1, PF4 and FGF2 each have a different affinity to
HSPG. Their affinities to iHSPG are set according to their binding constants (Kd values) measured
with heparin. The Kd values of heparin binding to VEGF165, FGF2, TSP1 and PF4 are 80, 39, 41
and 20 nmol/l
21,28,101–103
, respectively. The rates for FGF2 binding to cHSPG (association rate, Kon,
and dissociation rate, Koff,) are estimated in previous work
89
, and this provides the FGF2 affinity
to cHSPG. We derive the affinities of VEGF165, TSP1 and PF4 binding to cHSPG by scaling the
FGF2-cHSPG affinity according to their relative affinity to heparin, assuming the measured
heparin affinity reflects their relative binding affinity to cHSPG. We first make VEGF, TSP1, PF4
all have the same association rates (Kon) as FGF2, and set the dissociation rates (Koff) according to
their corresponding affinities. For the associations between pro- and anti-angiogenic factors, PF4
binds to VEGF165 and FGF2 with Kd values of 5 and 37 nmol/l
82
, respectively. The Kd values of
30
TSP1 binding to VEGF and FGF2 are 10 and 10.8 nmol/
32,87
. The parameters for the protease
activity are taken from previous works
25,75
.
2.3.4. Model implementation and simulation
The model ODEs are generated using BioNetGen
104
, a rule-based modeling framework.
BioNetGen produces all possible molecular species and the corresponding ODEs by specifying a
set of starting molecular species and defining reaction rules. Given 40 seed species and 127
reaction rules, the model produced by BioNetGen consists of 168 species. The set of 168 ODEs is
implemented in MATLAB (The MathWorks, Natick, MA, USA), which we used to generate the
dynamic results, as well as steady state predictions (i.e., when the model outputs change less than
0.01%).
Table 2-1: Comparison of the baseline predictions and the experimental measurements of
VEGF, FGF2, TSP1, PF4 and MMPs.
Species
Range of Experimental
Measurements
†
Predicted
Concentration
Source and References
VEGF unbound 8.0 - 389 pM 180.2 pM Multiple
105
TSP1 total
‡
1.0 - 6.2 nM (2.0) 3.0 nM Breast cancer
22
PF4 unbound 1.0 - 11.3 nM 4.7 nM Multiple
106–109
FGF2 total 0.2 - 11.1 nM 3.9 nM Prostate cancer
110
MMP3 total 1.8 - 65.1 nM (5.1) 5.0 nM Oral squamous cell carcinoma
111
MMP9 total 1.0 - 287.8 nM (9.0) 9.2 nM Oral squamous cell carcinoma
111
MMP9 active 0 - 22.4 nM (0.8) 0.2 nM Oral squamous cell carcinoma
111
†
Median value is shown in parentheses, if provided in literature. If the experimental data reflects
the total concentration in tissue, we assume 50% of the total protein amount is localized in
extracellular space.
‡
TSP1 concentration includes both the active TSP1 and the cleaved TSP1.
31
2.4. Results
2.4.1. Baseline prediction of the angiogenic factors’ distribution in tumor tissue
The baseline secretion rates of angiogenic factors were tuned in order to obtain
concentrations within the range of available experimental measurements. We report the predicted
species’ concentrations (for VEGF, TSP1, PF4, FGF2, MMP3 and MMP9) and compare with
experimental measurements in the Table 2-1.
Figure 2-3: Distribution of VEGF, FGF2, TSP1 and PF4 in tumor tissue at steady state.
The percentages of each angiogenic species in its various forms are shown. Species are grouped
and labeled with different colors. The sum of the forms bound to the cell surface or in the interstitial
space is also indicated.
With the baseline secretion rates, the model predicts that the pro-angiogenic factors (VEGF
and FGF2) and anti-angiogenic factors (TSP1 and PF4) have significantly different distribution
patterns in tumor tissue (Figure 2-3). The majority of each pro-angiogenic factor in the tumor
32
(~81% of VEGF and ~50% of FGF2) is bound to the cell surface, while only a small percentage
of the anti-angiogenic factors (~16% of PF4 and ~12% of TSP1) exists on the cell surface. The
cell surface bound ligands can be further categorized into non-signaling and signaling forms. The
non-signaling forms include complexes with cHSPG and non-signaling receptors, and signaling
forms include ligated receptors that promote intracellular signaling. Most of the cell-surface bound
VEGF is in a signaling form, where VEGFR1-, VEGFR2-and NRP1-bound VEGF comprise 35%,
17% and 29% of the total VEGF in the tumor, respectively. Only 0.4% of total VEGF is bound to
cHSPG. The model predicts that 23% of total FGF2 is in a signaling form bound to FGFR1:cHSPG
dimers. The balance of the cell-surface FGF2 is non-signaling, bound to either cHSPG or FGFR1
monomers, which comprise 6% and 22% of total FGF2, respectively. In comparison to the
distributions of the pro-angiogenic factors, most of the cell-surface bound anti-angiogenic factors
are in non-signaling forms. The model predicts that 11% of total TSP1 and 16% of total PF4 are
bound to cHSPG. Only 1% of total TSP1 is bound to signaling receptors, including CD47, CD36,
LRP1 and β1. In the case of PF4, an even smaller fraction (0.4%) is bound to anti-angiogenic
receptors, including CXCR3 and LRP1. However, it is worth noting that the ratio of the number
of VEGF and FGF2 signaling complexes to the number of TSP1 and PF4 signaling complexes is
approximately 1.7. This means that the number of anti-angiogenic complexes is still in the same
order of magnitude as the number of pro-angiogenic complexes.
In the interstitial space, there are three forms of angiogenic factors, including the unbound
form, iHSPG-bound form, and the form bound to other angiogenic factors. Approximately 12%
of total VEGF is in an unbound active form, including VEGF121 and VEGF165, and 0.1% of VEGF
is present as the inactive isoform VEGF114. The percentages of VEGF bound to iHSPG or other
angiogenic factors are 6% and 0.7%, respectively. Unlike VEGF, most FGF2 in the interstitial
33
space is trapped by iHSPG. That is, 46% of total FGF2 is bound to iHSPG, while the unbound and
angiogenic factor-bound forms only comprise 3% and 0.3% of the total FGF2, respectively. In
contrast, the two anti-angiogenic factors, PF4 and TSP1, both have a larger portion in the
interstitial space. In the case of PF4, 81% is bound to iHSPG, while the unbound and angiogenic
factor-bound forms comprise only 2% and 0.01% of the total PF4, respectively. Finally, most of
TSP1 in the interstitial space is bound to iHSPG (48%) or in the cleaved, inactive form (35%). The
balance of TSP1 is unbound or bound to other angiogenic factors, comprising 3% and 0.6% of the
total TSP1, respectively.
To summarize these results, the model predicts that most of VEGF and FGF2 is bound to
the cell surface and in signaling forms, while most of TSP1 and PF4 is in the interstitial space and
in non-signaling forms that are trapped by HSPGs or inactive due to proteolysis. It is worth noting
that the fraction of the anti-angiogenic factors that is bound to pro-angiogenic factors only
comprises a small percentage, which implies that direct binding between pro- and anti-angiogenic
factors is not a major mechanism of the extracellular inhibition of pro-angiogenic signaling.
Overall, this predicted distribution indicates a tumor state favoring pro-angiogenic signaling and
neovascularization. In addition to the prediction under baseline secretion rates, we performed
Monte Carlo simulations by sampling the secretion rates of VEGF, TSP1, PF4, FGF2, MMP3 and
proMMP9 from a range of 100-fold below and 10-fold above the baseline values. The results
(Appendix A Figure A-1) show that, even with potential uncertainty in the secretion rates, the
main conclusions of the tumor distribution remain unchanged.
34
Figure 2-4: Effects of secretion of angiogenic factors on the angiogenic state of the tumor
tissue. Column I shows the angiogenic ratio in the log10 scale. Column II to V show the signaling
complex levels (normalized to the baseline prediction) in the log10 scale. The value range is given
by the colorbar. The horizontal and vertical axes of each subplot show the fold-change of the
corresponding secretion rates, relative to their baseline values. The different rows show the effects
of varying the secretion rates of different angiogenic factors: (A) VEGF and TSP1 secretion rates
vary. (B) VEGF and PF4 secretion rates vary. (C) FGF2 and TSP1 secretion rates vary. (D) FGF2
and PF4 secretion rates vary. The predictions shown in the figures are based on the steady state of
the system.
2.4.2. Secretion of anti-angiogenic factors modulates both pro- and anti-angiogenic signaling
To characterize the angiogenic state of the tumor, we defined the angiogenic ratio: the ratio
of the concentrations of the pro-angiogenic signaling complexes to the anti-angiogenic signaling
35
complexes. This ratio captures the activation level of pro-angiogenic receptors relative to the
activation level of anti-angiogenic receptors. We examined how different angiogenic factors shift
the angiogenic ratio (Figure 2-4, column I) by varying the secretion rates of VEGF, FGF2, TSP1,
and PF4 in a range of 100-fold below and 10-fold above the baseline values. We also predict how
the concentrations of pro- and anti-angiogenic signaling complexes change in response to varying
the secretion rates of the angiogenic factors (Figure 2-4, columns I to V). Varying the secretion
rates explores how targeting angiogenic factors changes the tumor angiogenic state, assuming 100-
fold below represents strong inhibition and 10-fold above represents upregulation. We plot the
angiogenic ratio and the concentrations of the angiogenic complexes normalized to condition with
baseline secretion rates.
Higher secretion of the two pro-angiogenic factors shifts the angiogenic ratio by increasing
the level of their corresponding pro-angiogenic complexes (Figure 2-4). The gradient along the
vertical axis in Figure 2-4 A and B, column I shows the angiogenic ratio will significantly increase
with increasing VEGF secretion, which indicates that the tumor moves to a more pro-angiogenic
state. The normalized level of the VEGF signaling complexes (Figure 2-4 A and B, column II)
shows evident color changes along the vertical axis, which indicates the VEGF signaling is
strongly enhanced with higher VEGF secretion. Meanwhile, the normalized level of FGF2, TSP1,
and PF4 signaling complexes (Figure 2-4 A and B, columns III to V) shows no pronounced
gradient along the vertical axis, implying that these signaling pathways are not affected by
changing VEGF secretion.
Similarly, upregulating FGF2 secretion shifts the angiogenic ratio mainly through
enhancing the formation of FGF2 pro-angiogenic complexes. The angiogenic ratio change along
vertical axis in Figure 2-4 C, column I implies that the upregulation of FGF2 secretion increases
36
the angiogenic ratio and promotes angiogenesis. The normalized level of the FGF2 complex
(Figure 2-4 C and D, column III) significantly increase with increasing FGF2 secretion, while the
concentration of the VEGF signaling complexes (Figure 2-4 C and D, column II) is highly stable
when the FGF2 secretion is changed. The TSP1 and PF4 signaling complexes (Figure 2-4 D,
columns IV to V) slightly change in response to FGF2, where increasing FGF2 secretion to a high
level slightly promotes the formation of TSP1 bound and PF4 bound anti-angiogenic complexes.
Increasing the secretion of anti-angiogenic factors, particularly PF4, modulates the
angiogenic ratio both by upregulating the levels of anti-angiogenic complexes and downregulating
the pro-angiogenic complexes levels (Figure 2-4). The gradient along the horizontal axis in Figure
2-4 A and C, column I indicates that increasing the secretion of TSP1 can decrease the angiogenic
ratio. We also examined the change in the normalized levels of the angiogenic complexes. We
found only TSP1 signaling complexes (Figure 2-4 A and C, column IV) show an evident color
change along the horizontal axis in response to changing TSP1 secretion rates, which indicates
that TSP1 secretion decreases the angiogenic ratio mainly through promoting the formation of
TSP1-bound anti-angiogenic complexes. Model predictions show that changing PF4 secretion can
strongly shift the angiogenic ratio (Figure 2-4 B and D, column I). In addition, increasing PF4
secretion promotes the formation of both TSP1- and PF4-bound anti-angiogenic complexes
(Figure 2-4 B and D, columns IV to V). However, there also appears to be a limit to the effect of
PF4, where PF4 does not continue to significantly promote the formation of TSP1 anti-angiogenic
complexes when its secretion rate is higher than a certain level. Although varying PF4 secretion
only slightly affects the formation of VEGF signaling complexes (Figure 2-4 B, column II), the
color change along the horizontal axis in Figure 2-4 B and D, column III shows that increasing
PF4 secretion can strongly inhibit the formation of FGF2 signaling complexes. Furthermore, the
37
secretion of PF4 can nearly neutralize the effect of FGF2 secretion on the formation of FGF2
signaling complex (Figure 2-4 D, column III).
Overall, the model predicts that VEGF, FGF2 and TSP1 mainly bind to their own receptors
to form more anti-angiogenic complexes and shift the angiogenic ratio, while PF4 affects the
formation of signaling complexes of various angiogenic factors to change the angiogenic ratio.
Figure 2-5: Effects of PF4 secretion on the formation of specific angiogenic complexes.
(A) The change of species in the FGF2 axis. (B) The change of species in VEGF axis. (C) Change
of VEGF165. (D) Change of VEGF121. The predictions shown in the figures are based on the steady
state of the system.
2.4.3. Platelet factor 4 secretion can increase the levels of unbound pro-angiogenic factors
Increased secretion of PF4 is predicted to affect the formation of both anti- and pro-
angiogenic signaling complexes. To get detailed insight into how PF4 modulates the distribution
38
of other angiogenic factors, we report the change of specific signaling species upon varying the
PF4 secretion rate (Figure 2-5 and Appendix Figure A-2). For these simulations, the PF4
secretion rate is again varied in a range of 100-fold below and 10-fold above the baseline value. In
the figures, the fold-change of the species on the vertical axis is the species’ concentration
normalized to its concentration when PF4 secretion is 100-fold below the baseline value (the lower
bound of the range over which the secretion rate was varied). Since PF4 mainly influences the
other angiogenic factors by competing for the heparan sulfate binding sites, we investigated how
the cHSPG level, a tumor-specific property, also affects the outcome of changing PF4 secretion.
When we describe the cHSPG level below, we assume the baseline level as intermediate level. For
low cHSPG levels, we ran simulations when cHSPG is 2-, 10- and 100-fold lower than the baseline
level. For high cHSPG levels, we considered cHSPH levels 2- and 10-fold higher than the baseline
level.
Although anti-angiogenic factors, PF4 and TSP1, can bind to pro-angiogenic factors,
VEGF and FGF2, to sequester pro-angiogenic factors, our model predicts that the levels of
unbound pro-angiogenic factors do not necessarily decrease in the presence of more anti-
angiogenic factors (Figure 2-5). Interestingly, varying PF4 secretion can significantly elevate the
levels of unbound FGF2 and unbound VEGF in tumor tissue. For low cHSPG levels, increasing
PF4 secretion may only slightly affect the levels of unbound FGF2 (Figure 2-5 A, column I; gray
and blue lines), while unbound VEGF levels can decrease with increasing PF4 secretion (Figure
2-5 B, column I; blue lines). However, the secretion of PF4 strongly increases the level of unbound
FGF2 if the tumor has intermediate to high cHSPG level (Figure 2-5 A, column I; red, orange,
and black lines). Similarly, PF4 secretion can increase unbound VEGF when the cHSPG level is
high (Figure 2-5 B, column I; red and orange lines). Examining the levels of specific isoforms of
39
VEGF, we find that both unbound VEGF165 and unbound VEGF121 are affected. The change of
VEGF165 is more pronounced (Figure 2-5 C, column I). Since the majority of unbound VEGF is
VEGF121, the fold-change of VEGF highly resembles the change of VEGF121 (Figure 2-5 D,
column I).
The counterintuitive increase of unbound the pro-angiogenic factors with increasing PF4
secretion is caused by PF4 displacing pro-angiogenic factors from the cell surface heparan sulfate
binding sites. PF4 preferentially competes for the HSPG on the cell surface first, causing cHSPG-
bound VEGF and FGF2 to decrease with increasing PF4 secretion (Figure 2-5 A and B, column
V). The decrement of cHSPG:FGF2 leads to a reduction of the trimeric complex
FGFR1:HSPG:FGF2 (Figure 2-5 A, column IV) and the FGF2 signaling dimer (Figure 2-5 A,
column II), which are only formed using cHSPG-bound FGF2. At the same time, the binding of
PF4 to cHSPG reduces the availability of HSPG to bind to VEGF and VEGF receptors. Since the
cHSPG affects VEGF binding to VEGFR2 and NRP1, the levels of VEGF-bound VEGFR2 and
NRP1 change with increasing PF4 secretion. At high cHSPG level (Figure 2-5 B, columns III to
IV; red and orange lines), increasing PF4 secretion promotes the formation of VEGF-bound
VEGFR2 and NRP1. At low to intermediate cHSPG levels (Figure 2-5 B, columns III to IV; black,
grey, light blue and dark blue lines), increasing PF4 secretion inhibits the formation of VEGF-
bound VEGFR2 and NRP1. This switch is because of the biphasic response to cHSPG level, which
will be explored in next section. Since the two isoforms of VEGF have different binding property
to receptors, VEGF165 and VEGF121 bound to VEGFR2 show very different fold-changes in
response to increasing PF4 secretion (Figure 2-5 C and D, column III). However, for both isoforms,
varying PF4 secretion has differential effects on the levels of the pro-angiogenic ligated receptor
complexes, depending on the cHSPG level.
40
iHSPG serves as a reservoir of angiogenic factors that can store and release pro-angiogenic
factors. With increasing PF4 secretion, the pro-angiogenic factors displaced from cHSPG bind to
iHSPG and form more FGF2- and VEGF-bound iHSPG (black, orange, and red lines in Figure 2-
5 A and B, column VI). After the depletion of the available cHSPG, secreted PF4 competes for
iHSPG binding sites, and iHSPG-bound PF4 significantly increases as the PF4 secretion rate
increases. At high PF4 secretion rates, PF4 is even able to displace FGF2 and VEGF from iHSPG
and reduce the iHSPG-bound pro-angiogenic factors (Figure 2-5 A and B, column VI; black,
orange, and red lines).
In summary, the predictions show that the HSPG is an important mediator in how PF4
regulates pro-angiogenic factors. We found that, depending on the HSPG level, the secreted PF4
can displace more pro-angiogenic factors from the HS binding sites than the amount being
sequestered, which eventually increases the level of unbound pro-angiogenic factors in the tumor
interstitium.
2.4.4. VEGF signaling shows a biphasic response to the HSPG level and PF4 secretion rate
As presented above, the model predicts that the secretion of PF4 can increase the level of
pro-angiogenic complexes on the cell surface. In the case of FGF2, the pro-angiogenic signaling
complexes involving FGFR1 dimers decrease with increasing PF4 (Figure 2-5 A, column II) and
the non-signaling complexes of ligated FGFR1 monomers increase with increasing PF4 secretion
(Figure 2-5 A, column III). These signaling and non-signaling forms of cell-surface FGF2 are also
affected by cHSPG levels. Interestingly, for the VEGF axis, all three VEGF signaling complexes
increase with increasing PF4 secretion, particularly for the high cHSPG condition (Figure 2-5 B,
columns II to IV; red and orange lines). This indicates an activation of VEGF pro-angiogenic
signaling caused by the anti-angiogenic factor PF4. To explain these results, we further investigate
41
how cHSPG level and PF4 secretion modulate the signaling complexes for each of the angiogenic
factors modeled in the tumor tissue (Figure 2-6).
Figure 2-6: Impact of PF4 and cHSPG on the formation of specific angiogenic complexes.
The horizontal axis of each subplot shows the fold-change of cHSPG level, relative the baseline
value, and the vertical axes show the fold-change of PF4 secretion rate, relative to its baseline
value. The value indicated by the colorbar is in the log10 scale. (A) The change of the angiogenic
ratio and normalized levels of signaling complexes: Column I shows the change of the angiogenic
ratio and column II to V show the changes of the normalized signaling complex levels (the values
are normalized to the baseline prediction). (B) The change of the normalized levels of specific
VEGF signaling complexes. The predictions shown in the figures are based on the steady state of
the system.
As shown in Figure 2-6 A, column I, the model predicts that increasing cHSPG increases
the angiogenic ratio (the tumor tissue is shifting to a more pro-angiogenic state) and increasing
PF4 decreases the angiogenic ratio (shifting the tumor tissue to a less pro-angiogenic state).
Together, these results indicate that HSPG promotes angiogenesis in tumor tissue, and the
secretion of PF4 counteracts the pro-angiogenic effect of HSPG. Given the molecular detail of the
model, we can explain these results. HSPG traps the two anti-angiogenic factors TSP1 and PF4.
Thus, by increasing the HSPG level, the levels of TSP1 and PF4 signaling complexes are reduced
42
(Figure 2-6 A, columns II and III). However, HSPG is needed for the formation of the pro-
angiogenic FGF2 signaling dimers. Although the HSPG traps FGF2 as well, the predictions show
that increasing HSPG increases the FGF2 signaling complexes (Figure 2-6 A, column IV).
Additionally, increasing PF4 decreases FGF2 signaling complexes (Figure 2-6 A, column IV) by
displacing FGF2 from cHSPG, as explained in the previous section.
In contrast, VEGF shows biphasic response to HSPG. The gradient along the horizontal
axis in Figure 2-6 A, column V shows that the concentrations of the VEGF signaling complexes
increase and then decrease with increasing HSPG level. Since PF4 competes for HSPG, increasing
PF4 secretion decreases the HSPG availability to VEGF. Therefore, VEGF signaling also shows a
biphasic response to PF4 secretion. For instance, at a medium HSPG level (dashed white line in
Figure 2-6 A, column V), along the vertical axis, the color changes from blue to purple then back
to blue, which means the concentrations of the VEGF signaling complexes go up and then back
down with increasing PF4 secretion. The VEGF signaling complexes include of VEGFR1-,
VEGFR2-, and NRP1-bound VEGF. In addition, different types of VEGF signaling complexes,
including VEGFR1-, VEGFR2- and NRP1-bound VEGF complexes, show a biphasic response to
HSPG and PF4 secretion (Figure 2-6 B, columns III and IV).
In summary, although PF4 secretion increases the unbound FGF2 level, the PF4 secretion
strongly inhibits the formation of FGF2 signaling dimers that need HSPG to be formed. However,
the VEGF signaling complexes can be formed through HSPG-dependent and HSPG-independent
ways. Therefore, the VEGF signaling shows a biphasic response to the HSPG level. A low level
HSPG limits the formation of VEGF signaling complexes through HSPG-dependent way. At the
intermediate HSPG level, the VEGF signaling complexes reaches a peak level, while HSPG
mainly traps VEGF and decreases VEGF signaling when it is present at a high level. Given the
43
fact that PF4 secretion can efficiently limit HSPG availability, VEGF signaling shows a biphasic
response to PF4 secretion as well. Therefore, at certain HSPG levels, the secretion of PF4 can
enhance the VEGF pro-angiogenic signaling in tumor tissue.
2.4.5. HSPG level affects the response to platelets activation and exogeneous PF4 therapy
Building on the simulations in which we vary the secretion rate of PF4, we apply the model
to predict the effects of a local release of PF4 at the tumor site, mimicking PF4 release following
platelet activation (where angiogenic factors are released) or a bolus injection of exogeneous PF4
as an anti-tumor therapy. The system is first allowed to reach steady state, which occurs in the first
day. We then simulate two pulses of 5 mg PF4 per week, injected into the tumor interstitial space.
This leads to a peak PF4 concentration of approximately 800 nM. The two pulses of PF4 occur at
days 1 and 3.5. The release of PF4 follows an exponential decay with rate constant 2.8 ´10
-5
s
-1
,
assuming the PF4 are encapsulated in a biomaterial delivery vehicle
25
. We also perform the
simulation at three different cHSPG levels to represent different tumor microenvironments: low
(10-fold below the baseline value), medium (baseline value), and high (10-fold above the baseline).
In this way, we examined how the tumor-specific property affects the response. Consistent with
the results presented above, the model predictions reveal that depending on the HSPG level,
platelet activation and recombinant PF4 can impact the pro-angiogenic signaling pathways in
different ways.
The model predicts that cHSPG level significantly changes the response of VEGF signaling
to the PF4 release (Figure 2-7). In a tumor microenvironment with high HSPG, the release of PF4
in the tumor leads to an activation of VEGF signaling pathway. Specifically, the concentration of
unbound VEGF increased from 128 pM to 177 pM (a 1.9-fold increase) after the release of PF4,
44
and it goes back down due to the degradation of PF4 (Figure 2-7 A, red line). The levels of
VEGFR1-, VEGFR2-, and NRP1-bound VEGF increase by 1.1-, 1.5-, and 8.1-fold, respectively
(Figure 2-7 B-D, red line). However, in a microenvironment with medium HSPG level, the release
of PF4 inhibits VEGF signaling (Figure 2-7, black line). The concentrations of unbound VEGF
and ligated VEGFR1 and VEGFR2 slightly decrease following the release of PF4, while NRP1-
bound VEGF decreases 1.4-fold. In the tumor with low HSPG level, the release of PF4 shows a
stronger inhibition, particularly for unbound VEGF and the VEGFR2 and NRP1 complexes
(Figure 2-7, blue line). The concentrations of unbound VEGF and VEGFR2-bound VEGF each
decreased 1.2-fold, and NRP1-bound VEGF significantly decreased, by 2.3-fold.
Figure 2-7: Effect of PF4 pulse release on VEGF signaling pathway. The system is allowed to
reach a steady state, followed by two pulses of PF4. The start time of PF4 release is indicated by
the arrows: at day 1 and day 3.5. The concentrations of species in the VEGF signaling pathway
are predicted: (A) Concentration of free VEGF: Solid line, VEGF; Dashed line, V165; Dotted line,
V121). (B) VEGF:VEGFR1 complexes. (C) VEGF:VEGFR2 complexes. (D) VEGF:NRP1
complexes.
45
In addition to affecting the VEGF signaling complexes, release of PF4 influences the FGF2
signaling complexes to different extents, depending on the tumor microenvironment (Figure 2-8).
Both unbound FGF2 and FGF2-bound FGFR1 complexes increase upon release of PF4 (Figure
2-8 A-B). However, the concentration of the trimeric complex HSPG:FGFR1:FGF2 significantly
decreased following each PF4 pulse (Figure 2-8 C), which results in the reduction of FGF2-bound
dimers. In a tumor with medium HSPG expression, the concentration of FGF2-bound dimers
shows the largest decrease (6.5-fold). For low and high HSPG level, the FGF2-bound dimer
concentration exhibits a 3.1- and 1.3-fold reduction, respectively.
Figure 2-8: The effect of PF4 pulse release on FGF2 signaling pathway. The system is allowed
to reach a steady state, followed by two pulses of PF4. The start time of PF4 release is indicated
by the arrows: at day 1 and day 3.5. The concentrations of species in the FGF2 signaling pathway
are predicted: (A) Concentration of free FGF2. (B) FGF2:FGFR1 complexes. (C)
HSPG:FGFR1:FGF2 complexes. (D) HSPG:FGFR1:FGF2 dimers.
46
To summarize, we simulated relevant tumor scenarios in which the PF4 concentration
would suddenly increase, such as following platelet activation or administration of exogenous PF4
as an anti-angiogenic treatment strategy. The model predicts that PF4 has differential effects on
the concentrations of pro-angiogenic signaling complexes involving VEGF and FGF2, depending
on the cell-surface level of HSPG. Particularly, at a high cHSPG level, PF4 is shown to have a
counterintuitive effect of promoting the formation of pro-angiogenic VEGF complexes. Overall,
these simulations demonstrate the utility of the modeling framework in understanding the possible
outcomes of events that are physiologically relevant to tumor angiogenesis.
2.5. Discussion
In this chapter, we present a novel systems biology model describing the distribution of
two potent pro-angiogenic factors and two important anti-angiogenic factors in tumor tissue. This
model significantly expanded previous works to enable a study of four relevant angiogenic factors.
Our model considers their interactions with each other in the extracellular space of tumor tissue,
which was missing in previous models. In addition, the model expansion allows us to investigate
the impact of heparan sulfate proteoglycans (HSPG) on the angiogenic factors’ distribution. HSPG
is an important modulator of tumor angiogenesis that is present on the cell surface, in the
extracellular matrix, and in the cellular basement membranes. HSPG binds to and stores the
angiogenic factors, facilitates the angiogenic factors’ signaling and mediates the extracellular
interactions of pro- and anti-angiogenic factors. Thus, HSPGs are a vital part of the extracellular
network of angiogenic factors. Although the role of HSPGs in FGF2 signaling has been modeled
in several studies
28,89,112
, the impact of HSPGs on VEGF ligand binding has not been modeled
explicitly before. We addressed this gap by incorporating knowledge reported in experimental
47
studies of the synergistic binding of VEGF, its receptors and heparin
29
. With the expansions upon
previous models, our work reports a new computational framework for a comprehensive study of
the angiogenic regulation in the extracellular space of tumor tissue.
Given the molecular detail of the model, we gain mechanistic insight into the extracellular
regulation of tumor angiogenic signaling. In the tumor extracellular space, TSP1 and PF4 are
thought to regulate the formation of pro-angiogenic signaling complexes involving VEGF and
FGF2 through two different mechanisms: sequestration – binding directly to VEGF and FGF2 to
prevent binding to their pro-angiogenic receptors, and competition – competing for cell-surface
HSPG to inhibit the formation of pro-angiogenic complexes. Our study shows that PF4
significantly inhibits pro-angiogenic signaling, mainly by competing for cell-surface HSPG
binding sites, not through direct binding. Our model predicts that the majority of TSP1 is in a
cleaved form owing to the action of proteases, and this cleaved form is inactive and unable to
compete for cell-surface HSPG. Therefore, our predictions show that TSP1 does not strongly
inhibit the formation of VEGF and FGF2 signaling complexes. Moreover, the measured binding
affinities between the anti-angiogenic factors (TSP1 and PF4) and the pro-angiogenic factors
(VEGF and FGF2) are much weaker than their affinities to the receptors, which explains that the
binding between them cannot efficiently sequester the pro-angiogenic ligands.
Our model predicts possible counterintuitive outcomes for the angiogenic state of
following the release of anti-angiogenic factors. The secretion of anti-angiogenic factors, PF4 and
TSP1, is generally assumed to reduce the concentrations of the free pro-angiogenic factors and
inhibit the formation of pro-angiogenic signaling complexes. However, our model predicts that
increasing the secretion of PF4 in tumor tissue can lead to two counterintuitive results: an increase
in interstitial FGF2 and VEGF levels (Section 2.4.3.) and greater formation of pro-angiogenic
48
signaling complexes, particularly in the VEGF signaling pathway (Section 2.4.4.). The reason for
the increased VEGF and FGF2 levels in the tumor interstitium following PF4 secretion is that PF4
competes for the HSPG binding sites in the cell surface, basement membrane and extracellular
matrix, thereby releasing the pro-angiogenic factors from those sites and increasing level of free
pro-angiogenic ligands. When this effect is stronger than the sequestration that occurs when PF4
binds directly to pro-angiogenic factors, the level of unbound VEGF and FGF2 will be higher
compared to the tumor microenvironmental condition with lower PF4 secretion (Figure 2-5
Column I). In addition, this counterintuitive outcome depends on the HSPG level. The schematic
shown in Figure 2-9 illustrates this point. In a low HSPG microenvironment, the pro-angiogenic
factors (VEGF and FGF2) primarily bind to their corresponding cell surface receptors, and the rest
are mostly in the free form (Figure 2-9 A, Column I). In a high HSPG microenvironment, the free
pro-angiogenic factors are trapped and stored as an HSPG-bound form (Figure 2-9 A, Column II).
As secretion of anti-angiogenic factors (TSP1 and PF4) increases, the secreted anti-angiogenic
factors bind directly to pro-angiogenic factors and reduce the free pro-angiogenic factors level in
a low HSPG condition (Figure 2-9 B Column I), while they mainly replace the pro-angiogenic
factors from the HSPG in a high HSPG environment due to their stronger affinity to heparan sulfate
(Figure 2-9 B Column II).
The greater formation of VEGF signaling complexes (which presumably will activate
intracellular signaling) caused by PF4 is because of the intrinsic biphasic response to HSPG level
(Figure 2-6 A Column V). At low levels, HSPG limits the formation of VEGF signaling
complexes. When HSPG is present at an intermediate level, it promotes VEGF signaling by
facilitating VEGF binding to receptors. However, when HSPG is at an even higher level, it traps
VEGF and reduces the formation of VEGF signaling complexes, which leads to a low VEGF
49
signaling again. Higher secretion of PF4 allows PF4 to more strongly compete for HSPG, which
can alleviate the HSPG sequestration of VEGF and promote VEGF signaling in certain conditions.
Unlike the VEGF signaling complexes, which can be formed through HSPG dependent and
independent ways, we assume the formation of FGF2 signaling complexes requires HSPG as a co-
receptor in the model
113
. Therefore, the biphasic response is not seen in FGF2 signaling complexes
(Figure 2-5 A Column II), in which the increasing of PF4 secretion always decreases the formation
of FGF2 signaling complexes.
Figure 2-9: The outcomes of anti-angiogenic factor secretion in different microenvironments.
Column I shows the condition of low HSPG level and Column II shows the condition of high
HSPG level. (A) Before the secretion of anti-angiogenic factors. (B) After the secretion of anti-
angiogenic factors.
50
These predicted counterintuitive results are clinically relevant for understanding the
outcome of platelet activation and anti-angiogenic therapy. In the human body, PF4 is stored in
platelet α-granules and released upon platelet activation. It is reported that the serum
concentrations of PF4 exceeds 8 μg/mL (276 nM) during platelet activation
106–109,114
. Given the
fact that platelets are attracted and accumulated at tumor sites
115
, it is possible that even higher
concentrations of PF4 may be present in the local tumor microenvironment when platelet
activation occurs. Besides the release of endogenous PF4 from platelets, recombinant PF4 (rPF4)
has been studied as an anti-tumor therapeutic to prevent angiogenesis, showing efficacy in both in
vitro and in vivo settings
41,116
. rPF4 was tested in a mouse model to inhibit tumor growth with a
dosage at 0.1 µg/µL for 5 µg in total
41
, and rPF4 has been tested in patients with advanced
colorectal carcinoma at a dosage of 3 mg/kg in 30-minute infusions
117
. Thus, the administration of
rPF4 as a therapeutic agent will greatly increase the total PF4 level in the tumor. To mimic the
local increase of PF4 concentration due to either platelet activation or a bolus injection of rPF4,
we simulated a situation of controlled release of PF4 in the tumor interstitium. The simulation
results highlight the impact of HSPGs level on the outcome of platelet activation and anti-
angiogenic therapy (Section 2.4.5.).
In addition, our model also has other practical applications, complementing pre-clinical
and clinical studies. The model can be further expanded to a whole body model to study the
clinically tested anti-angiogenic therapy and patient response, as modeling work that characterizes
VEGF distribution in human patients
70
. Therefore, our model provides a basis to study the anti-
angiogenic therapy targeting multiple angiogenic factors, including VEGF, FGF2, TSP1 and PF4.
In our study, we used the angiogenic ratio to characterize the overall angiogenic state of the tumor
tissue. This is based on the assumption that the different types of signaling complex have same
51
contribution to angiogenic signaling, which may not represent the real case. Linking the signaling
complexes with corresponding downstream signaling network can help address this issue and
enable a better understanding of tumor angiogenesis. The signaling complexes in our model are
also the species initiating downstream signaling in previous published downstream signaling
models
89,118,119
; therefore, our model can be connected with models of intracellular signaling to
characterize the downstream signaling changes.
We acknowledge that the predictions from the model are sensitive to the values of
parameters. In our study, the experimental data we are comparing to are the measured levels of
angiogenic factors in tumor tissue samples (Table 2-1). Since the predicted level of angiogenic
factors is highly sensitive to the secretion rates of angiogenic factors, we explicitly performed
simulations to vary the secretion rates of angiogenic factors in this study. In addition, we explored
the effect of the HSPG level, another influential parameter. We specifically varied the cHSPG
level in the model because cHSPG serves both as the reservoir and the co-receptor of angiogenic
factors. It is important to notice that there are other unexplored parameters that could affect the
model predictions. For example, changing the secretion rates of MMPs will affect the cleavage of
VEGF, which can subsequently change the amount of VEGF bound to the extracellular matrix and
receptors. Additionally, the affinities of angiogenic factors to HSPG could affect the regulatory
role of HSPG. We did not explore all possible parameters in this study. Instead, we focus primarily
on the effects of angiogenic factor secretion and HSPG level, parameters that account for key
aspects of tumor heterogeneity. In the future, the model can be used to investigate the effects of
many more parameters.
There are some more limitations of our model that can be addressed in future work. Given
the scarcity of the quantitative data, we used the measurements from tumor types other than breast
52
cancer to tune the baseline value of the angiogenic factors secretion rates. Since there are no
available measurements of the PF4 level directly from tumor tissue sample, we use the measured
blood PF4 level in breast cancer patients as an estimation of tumor interstitial PF4 level.
Additionally, HSPG includes various types, each with different masses and number and types of
heparan sulfate chains
30
. This great complexity is difficult to fully characterize mathematically and
warrants its own highly detailed mechanistic model. To make the model more useful, we made a
simplification to only explicitly define two generic species of HSPGs that capture the two key
HSPG classes with distinct functions, rather than a detailed description of all HSPG species. One
of the types of HSPGs in the model is on the cell surface (cHSPG) that can bind to ligand, couple
with receptors, and is subject to internalization. The other type is the interstitial HSPG (iHSPG) in
the extracellular matrix and basement membranes, which only traps free angiogenic ligands and is
not subject to degradation and internalization. We acknowledge that the soluble form of HSPG,
such as heparin, is also important to consider in the context of the tumor
120
. However, we do not
explicitly model this class of HSPGs, because its binding to ligands and receptors, as well as its
degradation, makes it very similar to the cHSPG in the model. If needed, our model can be
extended to include more types of HSPGs. Despite these limitations, our model provides relevant
mechanistic insight into interactions between angiogenic factors, their receptors, and HSPGs.
In conclusion, in this study, we present a novel model to characterize the extracellular
distribution of four important angiogenic factors: VEGF, FGF2, TSP1, and PF4. The model
provides mechanistic insights into the regulation of the angiogenic interaction network in the
extracellular space of tumor tissue. We expect that the insights generated by our model will enable
a better understanding of tumor angiogenesis interactions and aid the development of new anti-
angiogenic therapy.
53
Chapter 3. Modeling of angiogenic interaction network in cancer patient
Portions of this chapter are adapted from:
Ding Li and Stacey D. Finley. Integrative Biology, 2018 Apr 23; 10(4): 253-269
3.1. Abstract
Multiple promoters and inhibitors mediate angiogenesis, the formation of new blood
vessels, and these factors represent potential targets for impeding vessel growth in tumors.
Vascular endothelial growth factor (VEGF) is a potent angiogenic factor targeted in anti-
angiogenic cancer therapies. In addition, thrombospondin-1 (TSP1) is a major endogenous
inhibitor of angiogenesis, and TSP1 mimetics are being developed as an alternative type of anti-
angiogenic agent. The combination of bevacizumab, an anti-VEGF agent, and ABT-510, a TSP1
mimetic, has been tested in clinical trials to treat advanced solid tumors. However, the patients’
responses are highly variable and show disappointing outcomes. To obtain mechanistic insight into
the effects of this combination anti-angiogenic therapy, we have constructed a novel whole-body
systems biology model including the VEGF and TSP1 reaction networks. Using this molecular-
detailed model, we investigated how the combination anti-angiogenic therapy changes the amounts
of pro-angiogenic and anti-angiogenic complexes in cancer patients. We particularly focus on
answering the question of how the effect of the combination therapy is influenced by tumor
receptor expression, one aspect of patient-to-patient variability. Overall, this model complements
the clinical administration of combination anti-angiogenic therapy, highlights the role of tumor
receptor variability in the heterogeneous responses to anti-angiogenic therapy, and identifies the
tumor receptor profiles that correlate with a high likelihood of a positive response to the
combination therapy. Our model provides novel understanding of the VEGF-TSP1 balance in
54
cancer patients at the systems-level and could be further used to optimize combination anti-
angiogenic therapy.
3.2. Introduction
Angiogenesis is a hallmark of cancer that facilitates tumor progression in many aspects
78
.
Tumor growth relies on the formation of new blood vessels to enable waste exchange and to deliver
oxygen and nutrients to the tumor. In addition, angiogenesis increases the likelihood of metastasis
by enabling tumor cells to enter the bloodstream and disperse to other sites in the body
121
.
Considering the outstanding importance of angiogenesis for tumor development, anti-angiogenic
therapy was designed to starve the tumor of its nutrient supply and limit its growth
5
.
Tumor angiogenesis is controlled by both pro and anti-angiogenic signaling
122–124
.
Common anti-angiogenic therapy uses single agents to reduce the pro-angiogenic signals, and the
primary anti-angiogenic agent being used in the clinic inhibits signaling mediated by vascular
endothelial growth factor-A (VEGF), a potent promoter of angiogenesis. However, this approach
is not effective in all cancers. For example, bevacizumab, a monoclonal antibody that binds VEGF,
is no longer approved for the treatment of metastatic breast cancer because it was not shown to be
effective and safe for patients
125
. Sunitinib, a tyrosine kinase inhibitor that targets VEGF receptors
and other growth factor receptors, has also shown limited success
52
. These limitations of anti-
VEGF treatment prompt the need to optimize anti-angiogenic therapy. One alternate approach is
to enhance the signal of anti-angiogenic factors. Thrombospondin-1 (TSP1) is one of the most
studied endogenous inhibitors of angiogenesis and has been shown to inhibit vascular growth and
tumorigenesis in preclinical trials
10,126,127
. Inspired by the effect of TSP1, TSP1 mimetics were
developed for tumor treatment
79
. One such drug, named ABT-510, reached Phase II clinical trials.
55
However, ABT-510 failed to show clear evidence of efficacy and is no longer tested as a single-
agent drug in clinical development
53,128
.
The disappointing outcomes of clinical studies of anti-angiogenic drugs as single agents
prompt the development of combination anti-angiogenic therapy. Administering a combination of
anti-angiogenic agents that simultaneously target multiple angiogenic signals is expected to
achieve efficient and durable suppression of angiogenesis by strongly shifting the relative balance
of inducers and inhibitors of angiogenesis to oppose the “angiogenic switch”
7,44
. The combination
of agents targeting different pathways might also prevent tumors from leveraging complementary
pathways to escape anti-angiogenic treatment. With this in mind, the ABT-510 TSP1 mimetic was
clinically tested in combination with bevacizumab in patients with advanced solid tumors.
However, patients displayed a heterogeneous response to this combination therapy
55
: one patient
had a partial response and only 32% of the patients had prolonged stable disease (≥ 6 months).
Unfortunately, the mechanisms driving these disappointing results were not elucidated in the trial.
Three fundamental questions remain: do the levels of TSP1 and VEGF balance one another in
tumor tissue, how does combination therapy influence this VEGF-TSP1 balance, and does inter-
patient heterogeneity lead to significantly different responses. Answering these questions
contributes to our understanding of the action of combination therapy. In addition, considering the
angiogenic balance at the levels of tissue, organs and the whole body can help us optimize anti-
angiogenic therapy. In this study, we address these questions using a computational systems
biology model.
Mathematical modeling serves as a useful tool to study the response to anti-angiogenic
treatment, complementing experimental and clinical studies. Various modeling approaches have
been applied to study anti-angiogenesis therapies
71
. However, these existing models do not provide
56
information regarding the balance of pro- and anti-angiogenic signals and cannot be used to study
the mechanistic effects of anti-angiogenic therapy targeting both sides of the angiogenic balance.
In this study, one of our goals is to understand the anti-angiogenic therapy targeting VEGF and
TSP1 simultaneously, which has not been the focus of previous models. To achieve this goal, we
build a novel ordinary differential equation (ODE) based multi-compartment model.
The model presented here significantly builds upon previous modeling efforts, and is
mainly based on two published models. One model is the whole-body model of the VEGF-receptor
system, which was previously used to illustrate the counterintuitive increasing of VEGF after anti-
VEGF treatment
70
. Second, we build on a tumor tissue model of TSP1 and VEGF interactions in
tumor tissue, which predicts the effects of various strategies mimicking TSP1’s anti-angiogenic
properties
25
. This model of the VEGF-TSP1 balance in tumor tissue, however, omits the trafficking
of soluble species and only considers drugs delivered directly into the tumor. Here, we
significantly expand these two previous works
25,129
to generate a novel whole-body model of the
VEGF-TSP1 interaction network. The expanded model has three compartments to incorporate the
drug pharmacokinetics (PK) and species distribution in the human body. The model also
incorporates pharmacodynamics (PD). Since the binding of angiogenic factors to their receptors
triggers a cascade of intracellular reactions, including phosphorylation of the receptors, we use the
number of ligand-receptor complexes as an approximation of the receptor activation level to
capture the status of pro- and anti-angiogenic signaling in tissue. Altogether, our new model
enables a complete PK/PD study of the clinically tested combination anti-angiogenic therapy
targeting both VEGF and TSP1.
We apply the model to understand how the angiogenic balance of VEGF and TSP1 is
modulated by bevacizumab and ABT-510 combination therapy. Then we use the model to
57
investigate the impact of inter-patient heterogeneity, specifically the tumor receptor heterogeneity,
on the response to combination anti-angiogenic therapy. Compared to other inter-patient
variability, tumor receptor heterogeneity is one of the most well supported in published literature.
It has been observed experimentally that tissue samples from patients with different types of cancer
and different samples from patients with the same type of cancer have different receptor
expressions
97,130–132
. Additionally, the VEGFR2 heterogeneity was shown to affect the response to
an anti-angiogenic cyclophosphamide treatment in an in vitro experimental setting
133
. The patient-
to-patient VEGFR1 and neuropilin variability has been associated with the response to
bevacizumab treatment as intra-tumoral biomarkers
134,135
. Thus, understanding the effects of tumor
receptor variability is clinically relevant
66,133–135
. Our model predicts that the metric of angiogenic
receptor expression can serve as a predictive tissue biomarker to distinguish the patients in which
the combination anti-angiogenic therapy will elicit a strong therapeutic response. Overall, we
establish a new computational framework to predict the effects of anti-angiogenic therapies and
understand clinical observations.
3.3. Methods
3.3.1. The compartmental whole-body model
This mechanistic model characterizes the extracellular distribution of angiogenic species
in the human body. We follow the compartmental model structure used in previous works
74,129
. In
this approach, a tissue is assumed to be a collection of capillaries, surrounded by parenchymal
cells. The interstitial space lies between the parenchymal cells and the capillaries, which is
comprised of the extracellular matrix (ECM), parenchymal basement membranes (PBM) and
endothelial basement membranes (EBM). The soluble species are assumed to diffuse within the
58
available interstitial space very fast compared to the timescale of the biochemical reactions
136
, thus
all of the structures are modeled in a spatially-averaged manner as a simplification. A human
cancer patient is represented by a three-compartment model: normal tissue (“normal,” represented
by skeletal muscle), the vasculature (“blood”), and diseased tissue (“tumor”) (Figure 3-1). The
soluble species are introduced to the system by being secreted by cells and are removed from the
system through degradation and clearance from the blood. Receptors are uniformly distributed on
the cell surfaces and can be internalized by the cell and recycled back to the surface. It is largely
unknown how the expression level of angiogenic receptor changes over time during anti-
angiogenic treatment. Additionally, the timescale over which receptor levels typically vary (on the
order of minutes) is much shorter than the timescale over which we are simulating in the model
(days to weeks). Therefore, we assumed the total number for each type of receptor is conserved at
every simulated time point (the receptor recycling rate is the same as the internalization rate).
Transport of soluble species between the compartments is mediated by transcapillary permeability
and lymphatic flow.
Model construction is based on certain assumptions. Firstly, we formulate the
compartmental model assuming that the tumor volume is constant. Admittedly, there is a change
in the number of healthy or diseased cells in human patients undergoing anti-angiogenic therapy,
as a primary goal of treatment is to reduce tumor volume. However, as we have shown in our
previous work
105
, that since the tumor is nearly 2,000 times smaller than the normal compartment,
the tumor volume must change by at least two orders of magnitude (to ~3300 cm
3
) for it to
significantly influence the distributions of the soluble factors, which is a central focus of our
PK/PD compartment model. Since this size of tumor is not physiologically realistic, we assume
constant tumor volume and instead focus on the distribution of the soluble factors and the
59
formation of pro- and anti-angiogenic complexes in each of the compartments. Accordingly, we
assume that the total surface area of the microvessels is constant, as the tissue vascularity is
characterized as the ratio of the microvascular surface area to the tumor volume. Finally, we
assume that the vascular permeability between compartments is fixed. We implement this
simplification because there is a scarcity of quantitative data available to formulate a mathematical
equation to capture the relationship between the anti-angiogenic therapy and vascular permeability.
Rather than impose further uncertainty in the model, we maintain a constant value for the
permeability.
Figure 3-1: Compartmental model of VEGF-TSP1 system in human cancer patients. The
model includes three compartments: normal tissue, blood, and tumor tissue. The endothelial cells
and parenchymal cells secrete soluble species (VEGF, TSP1, MMP3, and proMMP9) into the
compartments. Receptors are localized on the luminal and abluminal surfaces of endothelial and
parenchymal cells. Free and ligand-bound receptors can be internalized. Transport between
compartments occurs by trans-endothelial permeability and lymphatic flow. Soluble species are
degraded in the tissue or cleared from the blood.
60
Figure 3-2: The molecular interactions in the network of TSP1 and VEGF. The compartment
model includes: (A) The molecular interactions of two active VEGF isoforms (VEGF121 and
VEGF165), receptors (R1 and R2), and co-receptors (N1 and N2); (B) The interactions between
TSP1, its receptors (CD36, CD47, β1, and LRP1), VEGF and VEGFR2; (C) The activation of
proMMP9 via cleavage by MMP3; cleavage of TSP1; and proteolysis of VEGF165 (free or bound
to glycosaminoglycan, GAG, chains) to form VEGF114 by active MMPs; (D) The sequestration of
VEGF165 and TSP1 by GAG chains in the extracellular matrix and the cellular basement
membranes; (E) The sequestration of VEGF by α2M in blood; (F) The binding between ABT-510
and receptors and sequestration of VEGF by bevacizumab.
3.3.2. VEGF-TSP1 reaction network
Here, we briefly summarize the molecular interactions in the VEGF-TSP1 reaction
network (Figure 3-2). Following previous works
70
, the model includes two active VEGF isoforms
(VEGF165 and VEGF121). The inactive form, VEGF114, is the product of proteolytic cleavage of
VEGF165. Two predominant VEGF receptors, VEGFR1 and VEGFR2 (R1 and R2), and neuropilin
61
co-receptors, NRP1 and NRP2 (N1 and N2), are considered (Figure 3-2 A). TSP1 binds to its
receptors, CD36, CD47, low density lipoprotein receptor-related protein 1 (LRP1) and αxβ1
intergrins (β1, a generic form representing several species) (Figure 3-2 B). We also include matrix
metalloproteinase species (MMP3, MMP9 and proMMP9), which promote VEGF cleavage. TSP1
impedes the activation of MMP9 (Figure 3-2 C) as a means of inhibiting pro-angiogenic signaling.
Glycosaminoglycan (GAG) chains reside in the interstitial space, representing the extracellular
matrix, as well as in the cellular basement membranes. GAG chains are able to bind and sequester
TSP1 and VEGF165 (Figure 3-2 D). The α-2-macroglobulin (α2M) species, a protease inhibitor, is
confined to the blood compartment, where it binds to VEGF (Figure 3-2 E).
3.3.3. Rule-based model Implementation
The characterization of the species’ dynamics is based on the principles of mass action
kinetics and biological transport. BioNetGen, a rule-based modeling approach, is used to construct
the model
104
. The biological reaction rules are defined in BioNetGen, which automatically
generates the set of ordinary differential equations (ODEs) that describe how the species’
concentrations evolve over time. This approach provides great help in models that involve dynamic
assembly of multi-protein complexes. Our model is a whole-body model incorporating VEGF
transport and kinetics, as well as the transport and kinetics of TSP1. We included all the significant
species, which are shown in Figure 3-1. The seed species and reaction rules are defined in
BioNetGen, the rule-based modeling framework. These defined 86 seed species (29 in normal, 28
in blood, and 29 in tumor) participate in 452 reaction rules (129 in normal, 184 in blood, and 139
in tumor). Because of the numerous multi-species complexes, the 452 reaction rules and 86 seed
species produce a total of 561 species and 2618 reactions. It is worth noting that this large number
of species is due to the formation of complexes of species and the propagation of the reactions, of
62
which some are highly similar and do not affect the soundness of the model. In the end, the
BioNetGen will produce the MATLAB (The MathWorks, Natick, MA, USA) file needed to
simulate the reaction network, which is a model that comprised of 561 non-linear ordinary
differential equations (ODEs) predicting the species’ concentrations over time.
3.3.4. Model parameterization
There are 157 parameters presented in our model, including geometric parameters, kinetic
parameters, receptor numbers, secretion and degradation rates, transport rates, and parameters for
the drug properties. The model parameter values are reported in Appendix B Table B-1, with
literature references and described below.
Geometric Parameters (27 Parameters): The geometric parameters characterize the
fundamental structure of the model, defining the volume of compartments, the interstitial space
volume, and tissue surface areas of endothelial and parenchymal cells. These parameters are based
on experimental measurements taken directly from in vivo mouse tumor models
74
. We assume that
the geometric characteristics of xenograft tumors in mice recapitulate human tumors, rather than
relying on data from in vitro cell culture. The set of geometric parameters has been used in multiple
previous studies
70,105,129
, and we adopt the parameters without changing their values.
Kinetic Parameters (47 Parameters): The kinetic parameters specify the association and
dissociation rates for the binding of molecular species. For the VEGF axis, the kinetic parameters
are based on experimental measurements for the biochemical interactions of VEGF and its
receptors, which have been implemented in previous models
129,137
. Likewise, the kinetic
parameters for TSP1 axis are based on experimental measurements that estimate the rates of
63
interactions between TSP1 and its receptors and other binding partners, which were systematically
reported in the published model of VEGF and TSP1 in tumor tissue
25
.
Receptor Numbers (32 Parameters): The receptor numbers for the VEGF axis (VEGFR1,
VEGFR2 and neuropilin-1 and -2) are taken from quantitative measurements of receptor
expression on cells from mouse xenograft studies. The cell surface expression of these receptors
was measured via flow cytometry
130,131
. For the TSP1 receptor numbers, we referred to the
qualitative measurements reported in the Human Protein Atlas
97
, assuming “high”, “medium”, and
“low” expression levels correspond to 10,000, 5,000, and 2,500 receptors/cell, respectively.
Secretion and Clearance Rates (34 Parameters): The clearance and degradation rates are
based on the reported protein half-life values. The secretion rates of VEGF were fit based on
modeling in vivo population PK data in our previous study
129
. The secretion rates of TSP1, MMP3
and proMMP9 (10 parameters) are fitted in this study to match the experimental measurements
shown in Table 3-1.
Transport Rates (6 Parameters): We assume passive transport for all soluble species in our
model. That is, the transport of angiogenic species between compartments is only mediated by
lymphatic flow and vascular permeability. The rate of lymphatic flow is based on the reported
experimental measurements
138
. The vascular permeability of VEGF is determined in our previous
work
74
, by considering the Stokes-Einstein radius for the VEGF protein. Since other angiogenic
factors are similar in size to VEGF
139,140
, we assume that all of the newly introduced angiogenic
species have the same vascular permeability as VEGF. This assumption can be relaxed in future
work.
Properties of the Anti-angiogenic Drugs (11 Parameters): The degradation and clearance
rates of bevacizumab and ABT-510 are converted from their reported half-life values measured in
64
clinical trial. The vascular permeability of bevacizumab and its binding rates are the same as those
used in our previous modeling work
105
, which capture the clinically-measured pharmacokinetic
data
141
(Figure 3-3 A). The vascular permeability of ABT-510 was set to be the same as VEGF.
Since ABT-510 is a TSP1-derived peptidomimetic that specifically binds to the CD36 receptor,
we assume it has the same affinity to CD36 as TSP1. The bioavailability of ABT-510 is tuned to
be 30% in subcutaneous injection
142
, in order to match PK data of TSP1
143
(Figure 3-3 B).
Table 3-1: Comparison of predicted steady state and experimental concentrations of VEGF,
TSP1 and MMPs.
Species Range of Experimental
Measurements
†
Predicted
Concentration
Source and References
Tumor Tissue
VEGF 8.0-389 pM 148.6 pM Multiple cancer types
105
TSP1
‡
1.0-6.2 nM (2.0) 2.0 nM Breast cancer patients
144
MMP3 1.8-65.1 nM (5.1) 4.9 nM Oral squamous cell carcinoma
145
MMP9 total 1.0-287.8 nM (9.0) 9.3 nM Oral squamous cell carcinoma
145
MMP9 active 0-22.4 nM (0.8) 0.2 nM Oral squamous cell carcinoma
145
Plasma
VEGF 0.4-3.0 pM 1.6 pM Multiple cancer types
146
TSP1
‡
0.8-2.1 nM (1.2) 1.2 nM Breast cancer patients
144
MMP3 1.9-2.0 nM 1.9 nM Breast cancer patients
147
MMP9 total 0.6-0.7 nM 0.7 nM Breast cancer patients
147
Normal Tissue
VEGF 0.3-3.0 pM 1.0 pM Healthy subjects
105
TSP1
‡
0.2 nM 0.9 nM Healthy subjects
148
MMP3 0.9-66.4 nM (4.1) 4.2 nM Oral squamous cell carcinoma
145
MMP9 total 0.8-27.7 nM (5.0) 3.2 nM Oral squamous cell carcinoma
145
MMP9 active 0-4.1 nM (0.02) 0.05 nM Oral squamous cell carcinoma
145
†
Median value is shown in parentheses, if provided in literature. If the experimental data reflects
the total concentration in tissue, we assume 50% of the total protein amount is localized in
extracellular space.
‡
TSP1 concentration includes both the active TSP1 and the cleaved TSP1.
65
Figure 3-3: The comparison of model prediction and measured pharmacodynamics of
bevacizumab and ABT-510 in cancer patients. The dots are measured data in clinical trials using
bevacizumab
141
or ABT-510
143
as single-agent treatment. The solid lines are predictions from the
whole-body systems biology model.
In summary, parameters are either taken from our previous modeling studies or estimated
based on experimental measurements. Only 11 parameters in total are fitted in this study (the
secretion rates of TSP1, MMP3 and proMMP9 in the compartments and the ABT-510
bioavailability). Given the presence of the uncertainty of the parameters, we performed a global
sensitivity analysis to understand the robustness of the baseline model predictions.
66
3.3.5. Sensitivity Analysis
We perform the extended Fourier amplitude sensitivity test (eFAST), a global variance-
based sensitivity analysis, to understand how the uncertainty of parameters (“model inputs”) affect
the baseline model predictions (“model outputs”)
149
. We analyzed the effects of three groups of
parameters (receptor numbers, kinetic parameters, and vascular permeability) on nine different
model outputs (the concentrations of TSP1, VEGF, proMMP9, MMP9, and MMP3; the TSP1-
VEGF, proMMP9-MMP3, and MMP3-TSP1 complexes; and the angiogenic ratio) in each of the
three compartments. In each case, the parameter values were allowed to vary 10-fold above and
below the baseline values (a total range of two orders of magnitude) to account for uncertainty in
the model parameters. In the eFAST method, the inputs are varied together, at different frequencies.
The Fourier transform of the outputs is calculated to identify the influence of each parameter, based
on the amplitude of each input’s frequency. Two different sensitivity indices are generated in the
eFAST analysis: the first-order FAST indices, Si, and the total FAST indices, STi. The first-order
indices (Si) measure the local sensitivity of individual inputs, while the total indices (STi) represent
the global sensitivity by accounting for second- and higher-order interactions between multiple
inputs. The eFAST method is implemented using MATLAB code developed by Kirschner and
colleagues
149
. We have performed this analysis to characterize the robustness of our previous
models
25,129
.
3.3.6. Simulating Receptor Variability
To investigate the impact of tumor receptor heterogeneity, we perform a Monte Carlo
analysis. In this analysis, parameter values are randomly varied, by drawing from a defined
distribution for each parameter. Here, we vary the receptor expression parameter values in the
67
tumor compartment. In total, the densities of 16 receptors are varied in the simulations: four VEGF
receptors on tumor cells (R1_Tum, R2_Tum, N1_Tum, N2_Tum), four TSP1 receptors on tumor
cells (CD36_Tum, CD47_Tum, LRP1_Tum, β1_Tum), four VEGF receptors on tumor endothelial
cells (R1_disEC, R2_disEC, N1_disEC, N2_disEC), and four TSP1 receptors on tumor endothelial
cells (CD36_disEC, CD47_disEC, LRP1_disEC, β1_disEC). The densities of these receptors were
randomly chosen from a uniform distribution within a range of 10-fold above and below the
baseline value. We generated 1,000 different combinations of receptor density profiles,
representing 1,000 unique cancer patients. We ran the model for each of the receptor profiles with
anti-angiogenic treatment to examine how the response to treatment varies across the 1,000
parameter sets.
3.3.7. Simulation of therapy
Administration of Combination Therapy: The combination therapy of bevacizumab and
ABT-510 is simulated by mimicking the administration strategy used in clinical trials
55
. We first
allowed the model to reach steady state (this occurs within 24 hours) before the start of treatment.
We then simulated one cycle of the combination therapy: bevacizumab was administered once at
the beginning of the cycle; ABT-510 was administered every 12 hours for 14 days. Bevacizumab
was given at a dose of 10 mg/kg through intravenous infusion lasting 90 minutes, while ABT-510
was administered at 100 mg twice daily through subcutaneous injection. The bolus of ABT-510
was given directly to a subcutaneous compartment
150
(assumed to be a reservoir with a volume of
30 cm
3
), and it is subsequently transported into blood. The transportation between the
subcutaneous and blood compartments is unidirectional and is assumed to occur at the same rate
as the transport between the normal and blood compartments. ABT-510 binds to TSP1 receptor
CD36 to induce an anti-angiogenic signal
151
(Figure 3-2 F). Bevacizumab is a VEGF antibody
68
that sequesters VEGF to keep it from binding to its receptors, thereby inhibiting the pro-angiogenic
signal (Figure 3-2 F).
Characterization of the Response to Treatment: In our study, the response to anti-
angiogenic treatment is characterized based on the angiogenic balance in tumor tissue. We define
the angiogenic balance as the ratio of the concentrations of the pro-angiogenic complexes to the
anti-angiogenic complexes. The ratio indicates the activation level of the pro-angiogenic receptors
relative to the activation level of anti-angiogenic receptors. Specifically, the pro-angiogenic
complexes include the ligand-bound VEGF receptors that are not interacting with active TSP1
receptors. Here we assume a ligand-bound VEGF receptor coupled with active TSP1 receptor is
not a pro-angiogenic complex, since the downstream signaling of the ligand-bound VEGF receptor
could be inhibited by TSP1
87,152
. The anti-angiogenic complexes are the active TSP1 receptors,
those bound to TSP1 or the TSP1 mimetic. The fold-change of the angiogenic ratio in the tumor
compartment (F) characterizes the response to anti-angiogenic treatment:
! =
$%&'(&)%'* +,-'( (/(0- −-2),-3)%-)
$%&'(&)%'* +,-'( (/2) −-2),-3)%-)
=
[678!:+)*]
!
"#$%
[;
!
=
$
$ " *
!"#$$$
%
&'
%
&'
()
&'
. Here,
+
&'
+
&'
",
&'
is the fraction of the number of VEGF bound R2
complex on endothelial cells over the total R2 receptors on the endothelial cell surface. With this
ratio, we calculated >
!
with a sigmoid function to represent the activation level of the R2 receptors.
101
Here, > is the activation level of pro-angiogenic or pro-tumorigenic effect (ranges from 0 to 1)
and C2/(C2+R2) is the fractional occupancy of the signaling VEGF receptors. To our knowledge,
there are no robust, quantitative measurements available that can be used to specify the relationship
between the receptor occupancy and downstream signaling activation level. Therefore, we assume
the downstream signaling is highly sensitive to the expression of VEGF and the activation of
downstream signaling has switch-like nonlinear behavior, in which 1% occupancy of the VEGFR2
is able to have nearly maximum pro-angiogenic or pro-tumorigenic effect and 0.1% will have
nearly zero activation. Accordingly, the parameters of exponents (6 and 1000) are selected to allow
> =
$
$ " *
!"#$$$∗$. $#
= 0.98 (1% VEGFR2 occupancy) and > =
$
$ " *
!"#$$$∗$. $$#
= 0.006 (0.1%
VEGFR2 occupancy).
where >
#
=
$
$ " *
!"#$$$
%
,'
%
,'
()
,'
. Similarly,
+
,'
+
,'
",
,'
is the fraction of the number of VEGF bound R2
complexes on tumor cells over the number of total R2 receptors on the tumor cell surface. Here,
we assume that tumor cells have no programmed cell death and that their growth is inhibited by
hypoxia. We use a sigmoid function to model switch-like behavior: tumor growth will be strongly
inhibited when the oxygen (nutrient) level H is lower than the threshold value Hgrow. Following a
previous study
201
, we calculated the oxygen level with 8 =
$%%!
!"#
$%
&. (
, which is based on the
observation that vessels make up approximately 9.2% of a growing tumor, and such tumors have
an oxygen level of approximately 10 mmHg. For our baseline model, we use a logistic growth
model for tumor cells. The tumor carrying capacity, tcap, limits the maximum size of the tumor.
102
We also explored two alternative tumor growth models: linear growth model (Equation 3)
and Bertlanffy model (Equation 4). These two types model have same number of parameters as
the logistic model, but they have different assumptions on the tumor growth dynamics. The linear
model assumes an initial exponential growth followed by a constant growth rate over time. In
Equation 3, the initial exponential growth rate is given by
-
-./0
.
and the later constant growth rate
is tgrow. The Bertalanffy equation was created initially for describing the growth of an organism.
This model assumes that the growth rate is proportional to the surface area the tumor, and there is
a decrease in the tumor size due to cell death with rate constant b. The rationale for the selection
of the logistic model as baseline model is based on the data fitting error shown in Section 4.4.1.
4.3.2.2. Molecular Species
VEGF Ligand: Endothelial cells in the system secrete VEGF (V) with a constant rate.
Hypoxia (conditions of low oxygen level, H) promotes the secretion of VEGF from tumor cells.
VEGF can bind to the free VEGF receptors on cell surfaces and dissociate from bound receptors.
VEGF is degraded with a constant rate.
103
VEGF Receptors: The free VEGF receptors R1 and R2 are expressed on both the tumor
cell surface (RT1 and RT2) and on the endothelial cell surface (RE1 and RE2). Secreted VEGF can
bind to free receptors and form corresponding ligand-bound complexes (CT1, CT2, CE1 and CE2).
104
4.3.2.3. Therapeutic Agents
Bevacizumab: Following previous study, we use a two-compartment model to characterize
the pharmacokinetics of bevacizumab treatment
76
, which is commonly known to have a biphasic
plasma concentration-time curve. The drug is assumed to be rapidly absorbed into circulatory
system (blood compartment) after injection. The drug is subject to elimination in the blood
compartment. It can also extravasate into the tumor site (tumor compartment). In the tumor
compartment, Bevacizumab will bind to free VEGF and prevent VEGF from binding to receptors
on the cell surface. The drug can be degraded after binding to VEGF. AB represents free
bevacizumab in the blood compartment. AT is free bevacizumab in the tumor compartment and
AV is VEGF-bound bevacizumab in the tumor compartment. We simulate the drug injection by
changing the concentration of AB.
Nab-paclitaxel: We apply the model to understand the synergy between anti-VEGF and
other anticancer therapies in reducing tumor growth. We model chemotherapy by simulating
administration of Nab-paclitaxel to kill cancer cells. There are various pharmacokinetic (PK)
studies that use complex models to precisely describe Nab-paclitaxel dose-concentration curves.
Here, we use a simplified three-compartment model for ABX PK behavior. In our model, the
chemotherapy agents are assumed to be given to the blood compartment (B) and then transported
into the extracellular space of the tumor site (T). ABX in the tumor compartment can be absorbed
105
by cells and then enter the intracellular space of cancer cells (I), which affects the net growth rate
of tumor cells. For the ABX pharmacodynamic (PD) behavior, we use a four-stage model
202
for
the ABX-triggered tumor cell death. The high concentration of absorbed ABX (XI) will promote
the transition from regular tumor cells (T) to damaged tumor cells (T2). The transition rate from T
to T2 is a non-linear Hill function of the drug concentration. We assume that T2 cells do not
proliferate but can recover and transit to regular tumor cells with a slow rate. The T2 cells will also
transit to T3 and then to T4, which is the irreversible cell death process.
For all the simulation compared to experimental data, the dosing is simulated by mimicking
the administration strategy used in preclinical trials (dose and frequency).
Hypothetical anti-angiogenic treatment: To understand the cell type specific effect of anti-
VEGF treatment, we simulate three hypothetical treatment conditions, including MuteE, MuteT
106
and MuteET. These hypothetical treatments are assumed to completely block VEGF signaling in
specific cell types. MuteE represents blocking endothelial cells’ VEGF signaling. MuteT means
blocking tumor cells’ VEGF signaling. MuteET blocks the signaling of both cell types. To simulate
blocking VEGF signaling, we simply set the parameter µE, µT, or both, to 0 at the start of treatment,
which means the treatment affects the cell such that ligand-bound R2 does not contribute to cell
proliferation. Specifically, MuteE has µE to be 0; MuteT has µT to be 0; MuteET has both µE and
µT to be 0.
4.3.3. Parameterization
There are 38 parameters presented in our model, including molecular dynamics parameters,
cellular response parameters and drug PK/PD parameters. The parameter values of baseline model
are reported in following tables.
4.3.3.1. Molecular dynamics parameters
The molecular dynamics parameters include the VEGF secretion rate, receptor numbers,
ligand-receptor binding parameters, degradation and internalization rates. Parameters are derived
from previous modeling and experimental studies. We used Tvol to represent the volume of the
interstitial space of the tumor sites. To calculate Tvol, we first compute the tumor volume, TV, by
converting the predicted number of cells to tumor volume (cm
3
) with ,
/
= $ × 2.2 × 10
0&
+
,× 10
0&
. We assumed that the volume of one EC is 2.2 × 10
01
EF
203
and that of one TC is
1 × 10
01
EF
204
. Then, we compute the interstitial space volume with the ratio of interstitial space
to tumor tissue volume.
,
234
= ,
/
× ($6H_#JF_KLM_NLM +$4H_#JF_KLM_NLM + .4H _#JF_KLM_NLM)
107
Table 4-1: List of tumor geometric parameters.
Symbol Description Unit Value Ref.
ECM_Vol_tis_dis Volume of extracellular matrix available
species in a breast tumor
*3
'
*3
'
-'00>)
0.51931
70,74
EBM_Vol_tis_dis Volume of microvessel basement membrane
available to soluble species in a breast tumor
0.00027
PBM_Vol_tis_dis Volume of tumor cells basement membrane
available to soluble species in a breast tumor
0.002446
Table 4-2: List of VEGF ligand-receptor system parameters.
Symbol Description Unit Value Ref.
s E VEGF secretion rate of endothelial cells
()*+
),++,*- /0++1
234
!"
0.0046
129
s T Maximal VEGF secretion rate of tumor cells 0.0555
r E1 VEGFR1 receptor number on endothelial cells
()*+
),++,*- /0++1
0.0062
205
r E2 VEGFR2 receptor number on endothelial cells 0.0005
r T1 VEGFR1 receptor number on tumor cells 0.0018
r T2 VEGFR2 receptor number on tumor cells 0.001
k on1 Association rate of VEGF binding to VEGFR1
()*+
!"
234
!"
4.97/T vol
206
k on2 Association rate of VEGF binding to VEGFR2 1.66/T vol
207,208
k off1 Dissociation rate of VEGF-VEGFR1
234
!"
86.4
70
k off2 Dissociation rate of VEGF-VEGFR2 86.4
k deg Degradation rate of VEGF 16.68
209
k int Internalization rate of VEGF receptors 24.19
73
4.3.3.2. Cellular response parameters
The cellular response parameters, are related to cell proliferation and death. H0 is set to
16.3, assuming that mouse tumor xenografts start from a normoxic condition, in which the oxygen
level is equivalent to the condition in which vessel cells exist in the site (15%). To be consistent
with the previous study
201
, we set the tumor cell quiescence threshold, Hgrow, and the angiogenic
factor secretion switch threshold, Hangio, to 5.5 mmHg and 10 mmHg, respectively. We fixed the
108
endothelial cell apoptotic rate when we are using the cell numbers data to estimate these two
parameters, because eapo and egrow are not identifiable at the same time. For the VEGF-VEGFR2
driven tumor cell proliferation, we assume the rate of tumor cell secretion is 10 times more
sensitive to VEGFR2-bound complexes than endothelial cells. We also explored other assumptions,
as discussed in the Section 4.5.. Together, we have four cell response parameters left to be
estimated based on experimental tumor volume data. Two of them, egrow and µE, are global
parameters. The other two parameters, tgrow and tcap, are dataset-specific parameters.
Table 4-3: List of global cellular response parameters.
Symbol Description Unit Value Ref.
H 0 Initial Nutrient (oxygen) level for tumor xenograft
mm Hg
16.3 Fixed
H grow Threshold of nutrient (oxygen) level for growth
inhibition
5.5
201
H angio Threshold of nutrient (oxygen) level for VEGF
secretion
10
201
e grow Basal cell proliferation rate of endothelial cells day
-1
1.07 Estimated
e apo Apoptotic rate of endothelial cells 1 Fixed
µ E VEGF-VEGFR2 driven endothelial cells proliferation
dimensionless
0.07 Estimated
µ T VEGF-VEGFR2 driven tumor cells proliferation 0.7 Fixed
†
†
µT is assumed to be 10 times µE.
Table 4-4: List of dataset-specific tumor growth kinetic parameters.
Symbol Description Unit Value Dataset
t grow
Basal growth rate of tumor cells
day
-1
4.36 ELHajjar
3.78 Volk2011a
5.58 Volk2011b
9.67 Volk2008
1.92 Zibara
0.13 Roland
0.62 Tan
109
0.87 Volk2011c
14.72 Fujita
t cap
Carrying capacity of tumor cells
million cells
2806 ELHajjar
1803 Volk2011a
1849 Volk2011b
1757 Volk2008
2490 Zibara
4997 Roland
2489 Tan
1435 Volk2011c
7163 Fujita
4.3.3.3. Pharmacokinetic and Pharmacodynamic Parameters
We derived the PK/PD parameters for Bevacizumab from previous study
201
, which are
estimated with fitting to experimental data
201,210
.
Table 4-5: List of the PK/PD parameters of Bevacizumab.
Symbol Description Unit Value Ref.
k onAV Bevacizumab binding to VEGF pmol
-1
day
-1
2.98/T vol
201,211
k offAV Dissociation rate of VEGF-bevacizumab
day
-1
86.4
k A12 Bevacizumab transportation rate from blood to tumor 10.1605
201
k A21 Bevacizumab transportation rate from tumor to blood 7.3999
k Ael Elimination rate of bevacizumab 0.3654
We estimated the chemotherapy (Nab-paclitaxel) parameters by fitting to experimental
data. Three pharmacokinetic parameters (kX12, kX21 and kX23) are estimated by fitting to plasma
concentration-time data
212
, while the cell killing effect is estimated with fitting to tumor volume
data
213
.
110
Table 4-6: List of the PK/PD parameters of Nab-paclitaxel.
Symbol Description Unit Value
k X12 Transportation rate of Nab-paclitaxel from blood to tumor
day
-1
32.567
k X21 Transportation rate of Nab-paclitaxel from tumor to blood 0.9676
k X23 Tumor cells absorption rate of Nab-paclitaxel 0.0854
k Xel Elimination rate of Nab-paclitaxel 0.7702
n Pharmacodynamic Hill function parameters dimensionless 0.08
C Pharmacodynamic Hill function parameters pmol/ml 1.00
k chemo Maximum cell killing rate of Nab-paclitaxel
day
-1
49.91
k b Transition rate of reversible cell damage 1.392
k t Transition rate of irreversible cell death 0.1857
4.3.4. Sensitivity Analysis
We perform the extended Fourier amplitude sensitivity test (eFAST), a global variance-
based sensitivity analysis, to understand how uncertainty in the parameter values affects the model
predictions. Specifically, we examined how the cellular response parameters affect the tumor
growth dynamics. We defined the area under the curve (AUC) as the response output. In the eFAST
analysis, the parameter values were varied within physiological range if available or two orders of
magnitude change (10-fold above and below the estimated baseline values) to account for
uncertainty. The selected parameters were varied together at different frequencies. The eFAST
analysis generates total sensitivity indices (STi) to identify the influence of each parameter.
The STi values can range from 0 to 1, where a higher Sti index indicates the input is more
influential to the output. The eFAST method is implemented using MATLAB code developed by
Kirschner and colleagues
214
.
111
4.3.5. Model calibration and validation
There are 38 parameters presented in our model, including molecular dynamic parameters,
cellular response parameters and drug pharmacokinetic/pharmacodynamic (PK/PD) parameters.
Most of the parameters are derived from previous studies. In our work, we focus on estimating
four parameters, including two global parameters for VEGF-mediated angiogenesis (egrow and µE)
and two dataset-specific parameters for tumor growth kinetics (tgrow and tcap). The four parameters
are estimated by fitting the model to tumor volume data. Experimental data from various mouse
xenograft studies were extracted using the WebPlotDigitizer program
215
. The data extracted from
published studies indicates that tumor growth is variable in each dataset, even though they were
generated using the same breast cancer cell line and similar experimental protocols. Several
reasons can contribute to the discrepancies, including the mouse strain, intrinsic properties of the
cancer cells, number of the tumor cells injected, the location of the injection site, and the method
used to quantify tumor volume. To account for these dataset-specific variations, the tumor cell
growth rate (tgrow) and carrying capacity (tcap) are selected as dataset-specific parameters, meaning
they have different values for different datasets to capture the variation in tumor growth dynamics
across studies. We must estimate the dataset-specific parameters individually for each dataset first,
and then use the estimated parameters to predict the response to anti-VEGF. Parameters were
estimated with the Particle Swarm Optimization (PSO) algorithm, which minimizes the sum of
squared residuals (SSR)
216
. We experimented with different numbers of dataset-specific
parameters and performed sensitivity analysis. We settled upon fitting tgrow and tcap, as other
combinations led to overfitting or underfitting the data.
112
Figure 4-2: Schematic illustrating the process of parameter estimation and model validation.
We collected seven published datasets of breast cancer that used the MDA-MB-231 cell
line to form xenografts in nude mice
193–198
. These data are used to establish the baseline model.
The process of parameter estimation and model validation is illustrated in Figure 4-2. To estimate
the parameters and validate the model, we separate the seven datasets into training data (six
datasets) and test data (one dataset, e.g. ELHajjar et al.). Firstly, in step 1, we use the six training
datasets to estimate the values of global parameters and the values of dataset-specific parameters
for the training datasets. In step 2, we use the control data from the test dataset to estimate the
values of dataset-specific parameters for that dataset. To do so, we use the global parameters
113
estimated from the first step. In step 3, we validate the estimated model parameters by predicting
the anti-VEGF response with the parameter values from the first and second steps and comparing
to the treatment group data in the test dataset. In this way, we are able to confirm the global
parameters and dataset-specific parameters for test dataset.
To examine the bias introduced from the selection of training data, we applied leave-one-
out cross validation to investigate the predictive capability of the model. Specifically, we trained
and validated the model seven times. Each time, a different dataset from these seven datasets was
selected as the test dataset with the other six datasets used for training. After the cross-validation,
we further validate the model on one dataset of breast cancer for the MDA-MB-435 cell line
197
and one dataset of head and neck squamous cell carcinomas with the UM-SCC-17B cell line
191
to
investigate the generalizability of the model. For this validation, the global parameters are set to
the values estimated with MDA-MB-231 datasets. The dataset-specific parameters are estimated
with the control group data. The treatment group data is used in validation.
In addition to the anti-VEGF therapy, our model includes chemotherapy to simulate the
administration of Nab-paclitaxel (ABX). For the chemotherapy module, we use a dataset of the
ABX plasma concentration-time profile
212
in a mouse xenograft model to estimate the PK
parameters. The parameters for the cell killing effect were estimated by fitting the model to tumor
volume datasets in which ABX was administered in mouse xenografts formed using the MDA-
MB-231 cell line
197
. Then we compare the model prediction for various combination therapies
with experimental data from breast cancer xenografts formed using the MDA-MD-435 cell line
197
to validate the prediction of the combination therapy.
114
4.3.6. Quantification of treatment response
To predict the tumor volume change, the predicted numbers of tumor cells (TCs) and
endothelial cells (ECs) are converted to tumor volume following the approach used in previous
study
76
: tumor volume in μl is V = (volume of 1 million ECs)×E + (volume of 1 million TCs)×T,
where E and T are the predicted number of ECs and TCs, respectively. The volume of 1 EC is
reported to be 2.2×10
−6
μl
203
and that of 1 TC is 1×10
−6
μl
204
. With the developed model, we can
generate the tumor volume dynamics for the control and treatment groups.
We used the simulated tumor volume dynamics to quantify two different indicators of
response to anti-VEGF therapy. Firstly, we computed the area under the curve (AUC) of simulated
tumor volume and use the AUC to calculate tumor volume response (RAUC). Specifically, for
different combinations of growth rate and carrying capacity, we simulated the control and
treatment condition for 90 days (assuming a three-month observation window similar to
experimental studies. For the treatment condition, we simulated administering 4 mg/kg
bevacizumab twice a week for two weeks, once the tumor volume reached 0.5 ml. To quantify the
effect of treatment, we compare the AUC of the simulated tumor volume for the control case
compared to treatment. We calculated the response as (
56+
=
56+
12.3
0 56+
2.4526472
56+
12.3
. In addition
to RAUC, we defined the half-time response, RHalf-time. To calculate RHalf-time, we simulate the control
and treatment conditions until steady state is reached and record the time required for the tumor
volume to reach 50% of the final tumor volume. The difference in the half-time is defined as half
time response: RHalf-time = Half-timetreatment – Half-timectrl, which indicates the effect of treatment
in delaying the time to reach half of the final tumor volume.
For the survival estimates, we simulate a heterogeneous in silico mouse population, by
generating 100 sets of values randomly selected from a uniform distribution within the range of
115
the parameter estimations for the two tumor-specific parameters (tgrow and tcap). We predicted the
tumor volume dynamics for each virtual mouse (a unique combination of tgrow and tcap) and applied
time-to-event analysis to determine the survival of the whole mouse population. Following the
approach used in previous study
192
, 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 predicted tumor volume remains below 2 cm
3
but ends at a time t that
is before the end of the pre-defined simulation time. All other mice are retained in the study and
recorded as ‘alive’. Survival curves were estimated by the Kaplan–Meier method in GraphPad
Prism (GraphPad Software, San Diego, CA, USA).
4.4. Results
4.4.1. The selection of tumor growth model
We experimented with these three tumor growth models (Equation 2, 3, 4) to determine
the best model to proceed with and present the results in Table 4-7. We compared the ability of
the three tumor growth models to simulate tumor volume measurements for seven datasets from
published experimental studies
193–198
that quantified tumor volume in mice bearing MDA-MD-231
xenograft tumors with and without anti-VEGF treatments. Six datasets are used as training for the
estimation of global parameters and the values of dataset-specific parameters for the training
datasets (Figure 4-2). The second column of Table 4-7 shows the sum of squared residuals (SSR)
in the model fitting. Akaike information criterion (AICC) score is calculated with the SSR and the
number of fitted parameters
217
. Then, with the estimated global parameters, we use control data
from an independent dataset (ELHajjar et al.
198
, “test” dataset) to estimate the two corresponding
dataset-specific parameters for test dataset. Lastly, we simulate bevacizumab treatment using the
116
estimated global parameters and the dataset-specific parameters for test dataset. The SSR is
calculated by comparing the model predictions and the treatment group data from the test dataset,
which are reported in the fourth column as the test error. The results in Table 4-7 show that the
logistic model has the lowest training error (1.440), lowest AICC score (-519) and lowest test error
(0.7533). Therefore, we use the logistic growth for tumor cell growth in our baseline model.
Table 4-7: Comparison of tumor growth models
Model Equation Fitting SSR
†
AICc Test SSR
‡
Dataset Specific Parameters
Logistic (2) 1.440 -529 0.7533 t grow t cap
Linear (3) 2.957 -437 6.353 t grow b
Bertalanffy (4) 5.261 -363 5.971 t grow b
†
Six Training datasets, including Volk2011a, Volk2011b, Volk2008, Zibara, Roland, and Tan.
‡
EL-Hajjar dataset is used as test dataset.
4.4.2. Parameters Analysis
The estimated parameter values provide insights into different characteristics of tumor
growth. Figure 4-3 presents the estimated parameter values from the leave-one-out cross
validation. For each dataset held out (e.g., ELHajjar et al.), we use the other six datasets to estimate
the parameter values, including two global parameters (egrow and µE) and dataset-specific
parameters (tgrow and tcap) for six training datasets. We report the ten best fits with the lowest errors
for each condition (e.g., ten black dots for “ELHajjar Out”). The estimated values for the two
global parameters (egrow and µE) are within a very tight range, which implies that these two
parameters can be determined with high confidence and the choice of training datasets does not
introduce much bias into the estimation of these two parameters. Intuitively, the dataset-specific
parameters (tgrow and tcap) show different values for different datasets. For example, all of the
datasets from Volk et al.
196,197
have estimated tumor cell growth rates higher than 2 day
-1
, while
the dataset from Roland et al.
193
has estimated tumor cell growth rates lower than 0.5 day
-1
. The
117
value of the carrying capacity is relatively consistent across the datasets, ranging from 1.6 × 10
0&
to 3 × 10
0&
cells. For the datasets from Roland et al.
193
and Tan et al.
195
, some estimated carrying
capacity values are extremely higher than other values, even reaching the upper bound. The reason
is that the experimental data for these two datasets do not show a clear logistic growth dynamic,
and instead have a nearly exponential growth trend at the last few time points. Thus, these outliers
can be ignored. We used the red solid lines in Figure 4-3 to indicate the median value for the
estimated parameter values in different conditions, which are selected as the baseline values for
our model and are used in the subsequent predictions and analyses.
Figure 4-3: Distribution of estimated parameters values. Leave-one-out cross validation was
applied with seven datasets to establish the baseline value of model parameters. The estimated
values of the global parameters (egrow and µE) and dataset-specific parameters (tgrow and tcap) are
presented. The color of the dots indicates the dataset held out for testing. With one dataset held
out, the other six datasets are used to estimate parameters and the ten bests fits are reported for
each holdout (ten dots for a single color indicating the dataset held out). Therefore, each global
parameter shows 70 fits in total. The dataset-specific parameter only shows 60 fits in total for each
dataset (x-axis label), because the parameter is not estimated when the dataset is being hold out
(e.g., tgrow ELHajjar column does not have black dots). The dashed red lines mark the predefined
upper and lower bounds for the parameter estimation process performed with particle swarm
optimization (PSO). The solid red lines indicate the median values for the baseline model.
118
We performed sensitivity analysis to understand the impact of parameters on the model
prediction (Figure 4-4). We found that the response of anti-VEGF treatment is significantly
affected by two tumor specific parameters (tumor growth rate tgrow and carrying capacity tcap). The
two global parameters (egrow and µE) are also very influential on outputs. Specifically, the µE is
found to be influential on the response, which is the parameter of VEGF-VEGFR2 driven
endothelial cells proliferation. Intuitively, the value of µE directly affects VEGF-driven cell
proliferation and thus influences the predicted response. Although egrow is found to be influential
on the predicted AUC, it is shown to be not influential on the response. In addition, Hgrow is found
to influence the prediction of the area under curve (AUC) for the control condition (no treatment).
Overall, the eFAST results indicate the key parameters affecting the results. The impact of two
tumor specific parameters (tgrow and tcap) on the response of anti-VEGF treatment has been
specifically investigated in the following work in this chapter. The baseline values of other
influential parameters are either derived from previous work (Hgrow) or fitted with experimental
data (egrow and µE).
Figure 4-4: The total sensitivity index STi values. Eight cellular response parameters (x-axis) are
selected as the inputs for the eFAST sensitivity analysis. The tumor volume AUC for control and
treatment and tumor volume AUC response were selected as outputs (y-axis). The calculation
method of tumor volume AUC and response is documented in the Section 4.3.6.
A B C D E F G H
1
2
3
0
0.2
0.4
0.6
0.8
1.0
AUCctrl
AUCtreatment
Response:
AUCctrl — AUCtreatment
AUCctrl
H0 Hgrow Hangio egrow E μ T μ tgrow tcap
Fig. S7
119
4.4.3. Model validation
The cross-validation is used to examine the prediction capacity of the model calibrated
with different splits of training and validation data. We applied leave-one-out cross validation with
the seven collected datasets. Each time, we held out one dataset as a test dataset and use the other
six datasets as training datasets. The training datasets are used to estimate the two global
parameters (egrow and µE) and dataset-specific parameters for training datasets. With the estimated
values for global parameters, we use the control group data from the test dataset to estimate the
dataset-specific parameters (tumor cell growth rate tgrow and carrying capacity tcap) for the test
dataset. We also use the predicted tumor volume dynamic under anti-VEGF treatment compared
to experimental data from the test dataset for model calibration. Figure 4-5 shows the results of
cross-validation. We also confirm that the predictions generated using these baseline values closely
match the experimental data (Appendix C Figure C-1). The model simulations for the control
tumor volumes (solid blue line) have a good match with experimental data (blue triangles), which
indicates that the model can capture the control group tumor dynamics in various settings by fitting
two tumor-specific parameters. The model predictions for the volumes with anti-VEGF treatment
(solid red line) are also very consistent with the corresponding data (red squares). It implies that
the model can accurately predict the response to anti-VEGF. Although our model is calibrated to
data for breast cancer xenografts formed from the MDA-MB-231 cell line, the model can also be
applied to other cancer cell lines and other types of cancer. We further validated the model on one
dataset of breast cancer from the MDA-MB-435 cell line
197
and one dataset of head and neck
squamous cell carcinomas from the UM-SCC-17B cell line
191
. As described above, the control
data is used to estimate dataset-specific parameters, while the treatment group data is used to
validate the model. Figure 4-6 shows that the model prediction also quantitatively matches the
120
experimental data for these tumor xenografts. With a carefully constructed model validated with
experimental data, we can apply the model to investigate the effects of anti-VEGF strategies.
Figure 4-5: Cross-validation comparing the model predictions with experimental data. Seven
datasets of breast cancer MDA-MB-231 xenograft tumors are used for cross-validation. Control
group data (blue triangles) is used to estimate the dataset-specific parameters. The predicted
response to anti-VEGF treatment (red line) is compared with the experimental data (red squares)
for validation. The shaded area shows the confidence interval for the predictions. Grey shading
area indicates the time period for anti-VEGF treatment.
121
Figure 4-6: Model validation with additional experimental datasets. One dataset of breast
cancer (MDA-MB-435 cell line, Volk2011c) and one dataset of head and neck squamous cell
carcinomas (UM-SCC-17B cell line, Fujita) are used to validate the model. Control group data
(blue triangles) is used to estimate the tumor-specific parameters. The predicted response to anti-
VEGF (red line) is compared with the experimental data (red squares) for validation. The shaded
area shows the confidence interval for the predictions. Grey shading area indicates the time period
for anti-VEGF treatment.
4.4.4. Anti-VEGF inhibits tumor growth primarily by blocking VEGF pro-angiogenic effect
With the constructed model, we simulate in vivo tumor growth under different hypothetical
therapeutic conditions to help us better understand the mechanism of action of anti-VEGF
treatment on tumor and endothelial cells
174
. VEGF binds to its receptors on both tumor cells and
endothelial cells to promote cell proliferation. To understand the cell type specific effect, we
simulated five different conditions, given in Figure 4-7: no treatment control (dashed blue line),
bevacizumab treatment (anti-VEGF, dashed red line), blocking endothelial cells’ VEGF signaling
(MuteE, solid brown line), blocking tumor cells’ VEGF signaling (MuteT, solid magenta line) and
blocking the signaling of both cell types (MuteET, solid black line). For the anti-VEGF treatment,
we follow the protocol used in each referenced experimental studies. To simulate blocking VEGF
122
signaling, we simply set the parameter µE, µT, or both, to 0 at the start of treatment, which means
the treatment condition affects the cell such that ligand-bound R2 does not contribute to cell
proliferation. Overall, MuteE is fully blocking the VEGF pro-angiogenic effect and MuteT is fully
blocking the VEGF pro-tumorigenic effect. The MuteET is fully blocking both the pro-angiogenic
and pro-tumorigenic effects, which sets the maximum efficacy bound for the anti-VEGF. We
reported the predicted tumor volume changes (Figure 4-7 A) and the percentage change of
endothelial cells to reflect the dynamic of the degree of vasculature (Figure 4-7 B).
Figure 4-7: Predicted outcome of anti-VEGF treatment and hypothetical treatments
targeting tumor and endothelial cells. A, Predicted tumor volume. B, Number of endothelial
cells relative to the total number of cells. I, Simulation with the estimated dataset specific
parameters and anti-VEGF treatment protocol for Volk2011a
197
. II., Simulation with the estimated
dataset specific parameters and anti-VEGF treatment protocol for Tan
195
. III., Simulation with the
estimated dataset specific parameters and anti-VEGF treatment protocol for Zibara
194
. Grey
shading area indicates the time period for anti-VEGF treatment.
123
The results show that anti-VEGF treatments reduce the degree of vasculature to inhibit the
tumor growth. We present three cases with representative anti-VEGF regimens in Figure 4-7, and
Appendix C Figure C-2 includes the simulation results for other dataset conditions. The results
show that the curves of anti-VEGF are below the control group, which indicates the anti-VEGF
inhibits tumor growth (Figure 4-7, Row A), corresponding to the reduced degree of vasculature
(Figure 4-7, Row B). Continuous bevacizumab treatment can delay the tumor growth dynamics
and reduce the final tumor volume at steady state (Figure 4-7, column I). In comparison, a short
period of bevacizumab treatment cannot reduce the final tumor volume (Figure 4-7, columns II
and III). This is because the drug is degraded and cannot promote a significant effect if given over
a short period of time. The overlapping of the MuteT (magenta) and Control (blue) curves implies
that MuteT has a similar effect as no treatment at all, which indicates that blocking the pro-
tumorigenic effect of VEGF does not significantly contribute to inhibiting tumor growth. The
MuteE curve (brown) is significantly lower than Control (blue) in all figures and very close to the
MuteET (black), which proves that blocking VEGF-driven endothelial cell proliferation can
strongly reduce tumor angiogenesis and inhibit the tumor growth. MuteET is the lowest tumor
volume curve in all figures, which means completely blocking both tumor cells and endothelial
cells has the strongest therapeutic response. The curves of anti-VEGF group (red) are above the
MuteET (black), which indicates the anti-VEGF only partially blocks VEGF signaling in these
conditions. Together, the results suggest that anti-VEGF inhibits the tumor growth primarily
through targeting ECs, blocking the pro-angiogenic effect of the VEGF.
4.4.5. The tumor cells’ growth rate affects the response to anti-VEGF treatment
We quantified the impact of two tumor specific parameters, tumor cells growth rate tgrow
and carrying capacity tcap, on the response of anti-VEGF treatment. This is related to our previous
124
works
189,192
, where we identified tumor growth kinetics as biomarkers for the outcomes of anti-
VEGF treatments. The estimated tumor-specific parameters could take on a range of values,
depending on the dataset being fit: the tumor cell growth rates ranged from 0.1 to 10 s
-1
, and
carrying capacities ranged from 1´10
9
to 2´10
10
cells. Thus, we predicted the tumor volume and
vasculature degree changes for various combinations of the tumor-specific parameters with and
without anti-VEGF treatment (Figure 4-8). For the anti-VEGF treatment, we simulated two weeks
of treatment in which bevacizumab was administered twice per week (two bolus injections at Day
1 and Day 4) at a dose of 4 mg/kg (a dosage commonly used in experimental studies)
197
. The
treatment starts when the tumor volume reaches 0.5 cm
3
.
Figure 4-8: Predicted dynamics of tumor volume and vasculature degree with representative
combinations of dataset-specific parameter values.
With the simulated dynamics, we quantified two responses of the anti-VEGF (RAUC and
RHalf-time), as mentioned in Section 4.3.6. We note that in the model, tgrow and tcap are assumed to
be constant tumor-specific properties and are not affected by treatment. Specifically, the tumor
tcap = 2000 tcap = 10000
Fig. S5
0 10 20 30 40 50 60 70 80 90 100
0
1
2
3
Time (Days)
Tumor Volume (ml)
0.1
1
10
10-ctrl
0.1-ctrl
1-ctrl
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
Time (Days)
ECs / (ECs + TCs) (%)
0.1
1
10
10-ctrl
0.1-ctrl
1-ctrl
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
Time (Days)
Tumor Volume (ml)
0.1
1
10
10-ctrl
0.1-ctrl
1-ctrl
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
Time (Days)
ECs / (ECs + TCs) (%)
0.1
1
10
10-ctrl
0.1-ctrl
1-ctrl
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
Time (Days)
ECs / (ECs + TCs) (%)
0.1
1
10
10-ctrl
0.1-ctrl
1-ctrl
tgrow 0.1
tgrow 1
tgrow 10
Control
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
Time (Days)
ECs / (ECs + TCs) (%)
0.1
1
10
10-ctrl
0.1-ctrl
1-ctrl
tgrow 0.1
tgrow 1
tgrow 10
Anti-VEGF
125
cell growth rate (tgrow) discussed here is a model parameter representing the basal tumor cell growth
rate. The model predicts that the tumor cell growth rate (tgrow) and carrying capacity (tcap)
significantly affect the outcome of anti-VEGF treatment (Figure 4-9). The color change from red
to blue along the diagonal direction (from upper left to lower right) in Figure 4-9 A shows that the
tumor volume response (RAUC) is stronger in tumors with lower tumor cell growth rate and higher
carrying capacity. Additionally, the color gradient is more pronounced along the vertical direction
(color changing from red to blue in Figure 4-9 A), which implies the variation in tumor cell growth
rate can significantly influence the response in conditions with different carrying capacities. This
is more evident in Figure 4-9 B (the half time response, RHalf-time), which shows the color mainly
changes along the vertical axis. Therefore, the variations of tumor cells’ growth rate might be an
important contributor to the heterogeneous response of anti-VEGF observed in pre-clinical and
clinical studies.
Figure 4-9: Impact of dataset-specific parameters on the response to anti-VEGF treatment.
We vary the dataset-specific parameters and calculate the response to anti-VEGF treatment (RAUC
and RHalf-time ) as mentioned in section 4.3.6. The circles in different colors represent the estimated
parameter combinations for different datasets used in previous sections.
126
4.4.6. Chemotherapy can synergize with anti-VEGF through reducing tumor cell growth rate
Since we observed that the lower tumor cell growth rate generates a stronger response to
anti-VEGF, we hypothesized that anticancer therapy that reduces tumor cell growth rate can
synergize with anti-VEGF treatment. We included a simplified chemotherapy submodule into the
model to simulate the treatment of nab-paclitaxel (ABX). ABX is a cell-cycle-phase specific drug,
which targets cells in the G2/M phase of the cell cycle, while having a limited effect on cells in
G1/G0 phase
218
. Therefore, it has higher killing effect on highly proliferating cells. Here, we
assume that ABX only affects the tumor cells. This assumption can be relaxed, and we consider
the implications of this assumption in Discussion section. In our model, ABX will trigger a
transition of regular tumor cells to damaged cells. The damaged tumor cells do not proliferate and
will either recover to regular tumor cells or go through an irreversible cell death process. This cell
damage and death model is adapted from previous work
202
and is detailed in Section 4.3.2.3.
Overall, the administered ABX modulates the net growth rate of tumor cells.
The pharmacokinetic parameters of ABX (three parameters) are estimated by fitting the
chemotherapy submodule to experimentally measured paclitaxel plasma concentrations
212
. The
fitting result is shown in Figure 4-10 A. Then the parameters that characterize ABX’s cell killing
effects (six parameters) are estimated with by fitting the tumor growth model combined with the
chemotherapy module to tumor volume data for treatments involving ABX (Figure 4-10 B, blue
and brown curves)
197
. The model simulations precisely capture the observed synergy of
bevacizumab and ABX in the experimental data (Figure 4-10 B). The combination treatment
group (Figure 4-10 B, brown) shows a significant regression of tumor volume, while the ABX
group alone (blue) leads to much less tumor volume regression and bevacizumab alone (red) only
delays the increase of tumor volume.
127
Figure 4-10: Predicted synergy of anti-VEGF and chemotherapy. A, Results from estimating
the ABX pharmacokinetic parameters (kX12, kX21, and kX23) by fitting the model into experimental
data. B, Comparing the simulated tumor volume dynamics with the experimental data. The cell
killing parameters of ABX are estimated by fitting the model to experimental data (Group ABX
and Group Bevacizumab + ABX).
Given this result for the effects of ABX and anti-VEGF combination therapy, we applied
the fitted model to predict the response to different ABX/bevacizumab combination treatment
regimens. The combination treatment results shown in Figure 4-10 are for two cycles of ABX and
bevacizumab given together throughout the treatment period. Here, we sought to investigate the
effects of alternative combination treatment protocols. The three selected combination treatment
protocols (Figure 4-11) were previously tested in an in vivo mouse study with mouse bearing
breast cancer MDA-MB-435 xenografts
197
. The model predicts the combination of intermittent
ABX with continuous bevacizumab that extends beyond the final dose of ABX (Group 3) has the
best overall therapeutic outcome. We also simulated intermittent ABX followed by a period of
continuous bevacizumab treatment (Group 1) and a protocol in which bevacizumab is given
continuous along with intermittent ABX where both treatments end at the same time (Group 2).
Compared to Group 1, Group 2 leads to a lower tumor burden for approximately 80 days, but the
tumor growth rebounds and has an accelerated growth after bevacizumab treatment is discontinued
at day 100. These predictions (Figure 4-11 A) qualitatively match the trend shown in the
experimental data of breast cancer MDA-MB-435 mouse xenografts (Appendix C Figure C-3).
The model also predicts the increase of the degree of vasculature (Figure 4-11 B) in Group 2 after
128
day 100, which potentially explains the rapid rebound of the tumor volume observed in
experimental data. Specifically, the treatment protocols that reduce both tumor growth and control
the size of the endothelial cell population (Groups 1 and 3) have slower tumor regrowth after
treatment. Group 3 in particular exhibits strong control of overall tumor growth, as the number of
endothelial and tumor cells is significantly reduced with treatment.
Figure 4-11: Predicted outcome of the combination of anti-VEGF and chemotherapy. A, The
predicted tumor volume dynamics. B, The predicted dynamics of the degree of vasculature. C, The
predicted dynamics for the number of tumor cells. D, The predicted dynamics for the number of
endothelial cells.
129
In summary, bevacizumab alone strongly reduces the number of endothelial cells, while
ABX reduces the number of tumor cells. Since they target two distinct cell populations, the
combination of ABX and bevacizumab has the strongest effect, and the two drugs are even able to
synergize. Altogether, these simulation results show that an anticancer treatment that robustly
inhibits growth of both the tumor and endothelial cell populations can lead to tumor regression.
4.4.7. Combination therapy can extend survival time in a virtual mouse population
We next investigated the effects of different combinations of bevacizumab and ABX in
terms of survival time. We generated a population of 100 virtual mice by uniformly sampling the
tumor-specific parameters within the range of the estimated values. With the virtual mouse
population, we simulate various treatment strategies and apply time-to-event analysis to produce
the survival data. As shown with the Kaplan–Meier survival estimates (Figure 4-12), the model
predicts that bevacizumab treatment alone only slightly improves the median survival, while
chemotherapy alone and other combination therapies can significantly improve the median
survival, even increasing survival time by more than two months compared to control. Adding
bevacizumab after ABX treatment has ended (Group 1) is less effective compared to Groups 2 and
3 where ABX and bevacizumab are given simultaneously. This suggests that the concurrent
combination therapy is important for extending the overall survival time of the population. Among
the three combination therapies, the combination of intermittent ABX with simultaneous and
continuous bevacizumab extending beyond the end of ABX treatment (Group 3) shows the best
therapeutic outcome. Interestingly, the model predicts that ABX and bevacizumab have a
synergistic effect on the median survival days. Treatment Group 3 extends the median survival
days to 109 days, which improves the survival days by 40 days compared to ABX alone (Group
130
1). This improvement is significantly larger than the 6-day increase in survival time between the
bevacizumab and the control groups.
Figure 4-12: Kaplan-Meier survival estimates for the heterogeneous virtual mouse
population. We generated a heterogeneous population of 100 mice by varying the dataset-specific
parameters. The mice were subjected to different treatments: bevacizumab alone, ABX alone, and
three combinations of bevacizumab and ABX. The survival for each group is compared to no
treatment.
4.5. Discussion
In this work, we constructed a computational model to understand the experimentally
observed heterogeneous response of anti-VEGF treatment and its synergy with other anticancer
strategies. There are several novel aspects of our modeling approach that help achieve this goal.
Our previous works identify that tumor growth kinetics has a great potential to serve as biomarkers
of the outcome of anti-VEGF treatment. The model used in previous work includes 258
species, 129 global parameters and 3 tumor-specific parameters estimated with control group
data
189,192
. Here, we greatly simplified the model structure and reduced the number of parameters,
131
increasing its utility and ease of understanding. In this work, we build on the structure from Jain
et al.
76
, removing the intracellular signaling details while retaining the VEGF ligand-receptor
interaction network and cellular cross-talk. Our model consists of 20 species and 38 parameters.
Importantly, the model is able to explain the same sets of experimental data explored in previous
works
189,192
and link the heterogeneous response to easily interpretable growth kinetic parameters.
Specifically, we reduced the number of tumor-specific parameters to two, both of which have clear
biological meaning. This enables us to investigate the impact of tumor-specific growth properties
on the response to anti-VEGF treatment and directly illustrate the connection between tumor
growth kinetics and the response to anti-VEGF. Additionally, this model is sufficiently detailed at
the cellular level to investigate the effects of interventions that target a specific cell type. Lastly,
we included a simple module modeling the administration of nab-paclitaxel to investigate the
synergy of a chemotherapeutic agent with anti-VEGF treatment, which is also a significant
extension of previous models. Achieving these features in one model is a significant advantage
over previous modeling works.
The model provides unique insights into the anti-VEGF therapeutic outcome. With the
developed model, we generated a novel understanding of the two-pronged effect of the anti-VEGF
on both endothelial cells and tumor cells, which is hard to fully evaluate in the experimental setting.
It is reported that VEGF not only promotes the endothelial cells’ growth but also increases tumor
cell proliferation
130,176
. Therefore, the anti-VEGF can block both the pro-angiogenic and pro-
tumorigenic effects of VEGF by influencing endothelial and tumor cells, respectively.
Interestingly, our model predictions show that the therapeutic outcome of anti-VEGF is mainly
from blocking the pro-angiogenic effect of VEGF, while blocking VEGF-mediated cancer cell
proliferation only slightly contributes to inhibiting the tumor volume increase. The parameters
132
value in our model show that the basal growth rate of tumor cells (0.1-14.7 s
-1
) is much higher than
the basal growth rate of endothelial cells (0.07 s
-1
considering the basal cell proliferation and
apoptosis rates together). Activation of the VEGF receptors significantly changes the endothelial
cells’ growth rate but only slightly contributes to the tumor cells’ net growth rate. This explains
the prediction of the model that VEGF has a strong impact on inhibiting endothelial cells. It is
important to note that this prediction is not influenced by the assumption that tumor cells are more
sensitive to VEGF than endothelial cells. In this work, we assumed that the VEGF receptors on
tumor cells has the same affinity to VEGF as the receptors expressed on endothelial cells.
Therefore, the VEGFR2 fractional occupancy for both cell types is the same value. However, for
these two cell types, the same fractional occupancy can have distinct effects on proliferation
depending on the values of µT and µE. In the baseline model, we set the parameter µT to be ten
times larger than µE. We explored other assumptions, setting µT to be 10 times smaller than µE or
even equal to µE. The model prediction that VEGF more strongly affects endothelial cells rather
than tumor cells holds true independently of the relative values of µT and µE. In addition, the value
of µT is shown to not strongly influence the model predictions, based on our sensitivity analysis
results. This prediction is useful for understanding the role of VEGF receptors on the tumor cell
surface. A direct implication is that therapeutic agents competing for VEGF binding sites on the
tumor cell surface might have unintended effects. As we found in previous modeling works
186,187
,
anti-angiogenic agents binding to non-signaling binding sites of VEGF might release the VEGF
ligand and force it to bind to signaling sites, leading to counter-therapeutic outcomes. Therefore,
this model prediction can provide guidance to the pre-clinical and clinical development of
anticancer agents blocking VEGF receptors
16
.
133
The clinically observed heterogeneous tumor response of anti-VEGF treatments is a major
drawback to their use. The wide range of responses has prompted the investigation of biomarkers
to identify patients for which anti-angiogenic therapy will be effective. Our work greatly
supplements studies exploring the use of tumor growth kinetics as biomarkers of anti-VEGF
response
192,219–221
. Various experimental studies investigated using tumor growth kinetics as a
prognostic biomarker, in which the tumor volume dynamics are correlated with survival rate and
used to determine the efficacy of anti-angiogenic treatment
189,192,219,220,222,223
. In this work, we
quantitatively profiled the impact of two tumor-specific properties of growth kinetics, the tumor
cell growth rate and carrying capacity, on the response to anti-VEGF treatment. The model
predicted that individual mice with lower tumor cell growth rate and higher carrying capacity have
a stronger response to anti-VEGF treatment, which indicates that VEGF treatment might be more
beneficial for patients with tumors that have a slow progression but the ability to reach a larger
tumor burden. Indeed, the variations of tumor growth rate and carrying capacity are observed in
various pre-clinical and clinical trials
224
, which can be a contributor to the observed heterogeneous
response of anti-VEGF. Furthermore, these two growth kinetic parameters can be estimated with
early scans of the patients’ tumor in clinical practice
225
. Therefore, the model could be used to
predict the prognosis and select the patients that will be benefit from the treatment.
Additionally, this work proposes a new potential mechanism for the synergy between
chemotherapy and anti-VEGF treatment. The combination therapy of anti-VEGF with other drugs
has been intensively studied in recent years
226,227
. Various anticancer therapies, including
chemotherapy, immunotherapy and radiation therapy, show a synergistic effect with anti-VEGF
treatment in different settings. In this work, we explored the hypothesis that chemotherapy is able
to synergize with anti-VEGF simply through reducing the tumor cells’ growth rate. To investigate
134
this hypothesis, we simulated administering nab-paclitaxel to modulate the net growth rate of
tumor cells combined with simulating anti-VEGF treatment, and we successfully reproduced the
synergy observed in experimental data. Commonly, the synergy between chemotherapy therapy
and anti-VEGF is explained by the chemotherapeutic agent normalizing the tumor vasculature and
modulating the vessel permeability to improve delivery of the anti-VEGF to the tumor
228,229
. Our
work provides a new angle to examine the observed synergy with anti-VEGF. Although we are
specifically simulating the administration of nab-paclitaxel, this mechanism can be applied to other
anticancer therapies that modulate the tumor cell growth rate. Therefore, the insight generated by
the model can guide future experimental or clinical studies of an anti-VEGF in combination with
various anticancer therapies.
The model developed in this work can help explore different regimens for combination
therapy including anti-VEGF treatment and other agents. For a combination of the same drug
agents, different dosing schedules can lead to highly different outcomes
197
. Therefore, arranging
dosing sequences in a proper way to maximize the synergy effect has been an active research area
of combination therapy. Such studies can lead to important discoveries for the administration
protocol and ultimately, greater biological understanding of the effects of the treatment
protocols
229,230
. In this work, we compared three combination therapies with different dosing
schedules. The model predicts that concurrent therapy of chemotherapy and continuous anti-VEGF
treatment (Group 3 in Section 4.4.6.) leads to the best treatment outcomes. Importantly, our model
not only generates the tumor volume dynamics that match the data, but also provides details on
how the degree of vasculature varies, along with the Kaplan-Meier survival estimates. Measuring
the dynamics of tumor vasculature and survival estimates is a time- and resource-intensive
endeavor. However, these details are necessary for understanding the mechanism behind the tumor
135
volume change. Therefore, our model has great practical interest for pre-clinical studies, providing
a time- and cost-effective way to explore different combination strategies to establish proof of
concept before moving to in vivo studies.
We acknowledge some limitations of the model that can be addressed in future studies. In
our model, we assumed the oxygen level has a linear relationship with the percentage of endothelial
cells. However, this assumption could be oversimplified and not physiologically realistic. For
example, oxygen diffusion and the physical properties of tumor tissues strongly influence the
development of oxygen gradients. Given this complexity, in our studies, we do not directly
compare the model prediction to the oxygen measurements reported in experimental studies. There
are existing models that can characterize the in vivo oxygen level change in tumor
xenografts
229,231,232
. It is possible to combine these models with our model to address this limitation.
In addition, endothelial cell maturation and vascular normalization are important processes that
have been shown to influence tumor progression and were reported to be affected by the anti-
angiogenic treatment; however, they are not included in our model. These aspects have been
investigated in previous computational works
77,233
, but the models are not rigorously calibrated
due to the scarcity of experimental data. This limitation can be addressed as more quantitative data
become available, enabling us to account for vessel maturation. Lastly, to constrain the scope of
our work, the influence of tumor angiogenesis on the drug transport between the blood and the
tumor is not considered in our model. We assumed a constant transportation rate of the therapeutic
agents during tumor progression. Published PK/PD models with more details
234,235
can be
incorporated into our model to further improve the accuracy of the drug dose-response
prediction. Finally, in the chemotherapy module, we assumed that normal cells (Endothelial cells)
136
are not affected by chemotherapy drugs, which might not be true in real condition. We can relax
this assumption and easily adapted the model for broader research purpose.
Overall, our model provides quantitative mechanistic insight into the effects of VEGF-
targeted treatment on tumor cells and endothelial cells. Importantly, the model explains the
heterogeneous response of tumor xenografts to anti-VEGF treatment, generates novel
understanding of the synergy of combination therapy and provides a framework for testing various
treatment regimens.
137
Chapter 5. Modeling in vivo tumor growth mediated by VEGF and FGF
5.1. Abstract
Tumors induce the sprouting of new blood vessels from surrounding vasculature to obtain
nutrients and exchange waste. Anti-angiogenic therapy is proposed to suppress tumor growth
through inhibiting angiogenesis. Various studies established the importance of VEGF in tumor
angiogenesis and developed cancer therapies that target angiogenesis by blocking VEGF signaling.
However, the anti-VEGF therapy only achieved limited success in clinic. The tumor can make use
of alternative pro-angiogenic signaling pathways and promote vasculature even when the VEGF
pathway is blocked. Furthermore, upregulation of alternative pro-angiogenic signaling pathways
can lead to resistance to anti-VEGF treatment in the long term, which is considered as a major
influencing factor for the variable response that is observed in pre-clinical and clinical studies.
FGF2 is another important pro-angiogenic factor that has been investigated as cancer therapy target.
Specifically, co-targeting of FGF2 and VEGF has been studied as a promising approach to achieve
efficient and durable suppression of angiogenesis and tumor growth.
In the previous chapter, we constructed a predictive model for in vivo tumor growth in
response to anti-VEGF. To investigate therapy targeting VEGF and FGF simultaneously, we
extend that previous model to include an additional component describing FGF-mediated tumor
growth and build a novel computational model of in vivo tumor growth mediated by VEGF and
FGF. Here, we present the results of model construction and the predictions of the response to
VEGF-trap and FGF-trap. This model can be further developed and used to inform the
development of effective anti-angiogenic strategies targeting multiple angiogenic factors.
138
5.2. Introduction
Tumor angiogenesis is regulated by the signaling of multiple angiogenic factors. The most
studied regulatory factor is vascular endothelial growth factor (VEGF)
12,17,174
, a family of signaling
species that induces pro-angiogenic signals through binding to their corresponding tyrosine kinase
receptors (RTKs). Basic fibroblast growth factor (bFGF or FGF2) is another potent pro-angiogenic
factor
9,28
, which binds to its cognate receptors, in particular FGFR1, to induce pro-angiogenic
signaling that enhances proliferation, migration, and survival of endothelial cells. VEGF and FGF2
are reported to functionally interact with each other. VEGF expression is able to induce FGF2
expression or vice versa
236
. In addition, VEGF and FGF2 can synergistically promote angiogenesis
through the enhancement of downstream signaling
33,89,119
. The synergistic effect of VEGF and
FGF2 on angiogenesis also has been identified in studies using a quantitative three-dimensional
fibrin angiogenesis system and mouse xenograft models
237,238
. It is reported that both VEGF and
FGF play a role in tumor angiogenesis, with VEGF signaling predominating in initiation, while
FGF signaling supports the maintenance in a cooperative fashion
56,239
.
Since VEGF and FGF2 promote the formation of new blood vessels in tumor progression,
therapies blocking their signaling have been developed for cancer treatment. The importance of
VEGF in tumor angiogenesis has been well confirmed in various studies, which have led to the
approval of multiple agents targeting VEGF signaling for treatment of specific human cancers
4,181
.
While the impact of FGF ligands on angiogenesis has been long recognized, the general
importance of FGF for tumor angiogenesis and growth has remained unclear, and cancer therapy
targeting FGF signaling is less developed than anti-angiogenic therapy targeting VEGF. To date,
several VEGF inhibitors have been used in the clinic to treat cancer patients, including a
neutralizing antibody that sequesters the VEGF ligand and small molecule agents that block the
139
signaling of tyrosine kinase receptors
4,44,240
. However, sole anti-VEGF therapy showed limited
clinical benefits, due to low efficacy and the development of resistance
4,42,44,64
. The upregulation
of FGF signaling has been considered as an important mechanism for the development of tumor
resistance to anti-VEGF therapy. Specifically, FGF2 expression was shown to significantly
increase in a xenograft model of acquired anti-VEGF resistance in head and neck squamous cell
carcinoma
241
. The compensatory induction of FGF2 resulted by anti-VEGF therapy has also been
discovered in a study using a mouse model of oxygen-induced retinopathy (OIR)
242
. Another study
of the response to VEGF receptor inhibition revealed that the upregulation of FGF ligands is
associated with VEGF-independent revascularization in tumors
243
. In addition, an increase of
FGF2 serum levels after anti-VEGF treatment is observed in patients with metastatic colorectal
cancer
244
. Altogether, findings from multiple pre-clinical and clinical studies implicate FGF2 in
the development of resistance to anti-VEGF therapy.
Simultaneous blockade of both VEGF and FGF2 has been considered as a potential way to
strongly inhibit the tumor angiogenesis, and potentially overcome the limitations of targeting a
single angiogenic signaling pathway. Previous studies indicated that inhibiting both VEGF and
FGF2 signaling can completely abrogate tumor growth in animal models with anti-VEGF resistant
xenografts
241
. Compared to anti-VEGF therapy alone, administering FGF-trap, a soluble decoy
receptor that binds to FGF ligands, in combination with an antibody targeting the VEGFR2
receptors, is shown to attenuate revascularization and tumor growth at the time of relapse
243
.
Brivanib, a selective RTK inhibitor targeting VEGFR2, VEGFR3 and FGFR1, 2, and 3, was
developed and evaluated in pre-clinical and clinical studies
56
. It has demonstrated acceptable
toxicity and efficacy in multiple solid tumors. Another study developed a fusion protein binding
140
to both VEGF and FGF2 ligands, which demonstrated potent anti-angiogenic effects in vitro and
in animal models
57
.
Overall, targeting FGF signaling together with VEGF signaling is considered a promising
way to inhibit the development of adaptive resistance that allows tumor to evade anti-VEGF
therapy. With such combination anti-angiogenic therapy, it may be possible to provide widespread
and enduring effects. However, the dual blockade of VEGF and FGF has not been used in clinic
yet. The development of Brivanib terminated at Phase II/III clinical trials, which failed to
significantly improve the overall survival of patients
245,246
. Thus, there is a need to better
understand the conditions under which targeting FGF and VEGF together is most beneficial.
To facilitate the development of anti-angiogenic therapy targeting both VEGF and FGF
signaling, I present a computational model extended from the work included in Chapter 4. A novel
aspect of the work in this chapter is linking the ligand receptor systems of both VEGF and FGF2
to the in vivo tumor growth dynamic observed in mouse xenograft model. We apply the model to
predict the observed dose-response for anti-VEGF or anti-FGF agents individually and the
response to combination therapy of anti-VEGF and anti-FGF agents. Specifically, the constructed
model is simultaneously fitted to multiple datasets collected in pre-clinical mouse xenograft
studies of anti-VEGF and anti-FGF therapy in order to identify the effects of VEGF and FGF on
in vivo tumor growth. This work provides a foundation for developing the computational tool to
predict the response to anti-angiogenic therapy targeting both VEGF and FGF signaling.
141
5.3. Methods
5.3.1. Modeling VEGF and FGF2 mediated angiogenesis and tumor growth
We construct a mathematical model to describe mouse xenograft tumor growth mediated
by VEGF and FGF2. Figure 5-1 presents a schematic of the model. The model represents a
simplified homogeneous tumor site consisting of two cellular species: tumor cells (T) and
endothelial cells (E). Following the approach used in the previous studies
76,247
, we consider a
scenario in which proliferation of the injected tumor cells in the mice will drive the formation of
hypoxia. The hypoxic condition will inhibit tumor growth and promote tumor cells to secrete the
angiogenic factors. A scaled ratio of endothelial cell number (E) over tumor cell number (T) is
used as the indicator of the degree of hypoxia in the tumor site. As an experimental study indicated
that a growing tumor is comprised of 9.2% vessel cells and has an oxygen level of 10 mm Hg
oxygen
199,200
, we assumed a linear relationship between oxygen level (H) and the percentage of
endothelial cells
76
and calculated the oxygen level with 8 = 9
!
!"#
$%
&. (
:∙100% . In the model,
tumor cell proliferation lowers the oxygen level, which drives the secretion of VEGF (V) and
FGF2 (F) from tumor cells and inhibits the further growth of tumor cells. The endothelial cells are
assumed to undergo cell death, and are removed from the system with a constant rate. The
proliferation of endothelial cells is enhanced by the binding of VEGF and FGF2 to their respective
receptors, which then increases the oxygen level, promoting tumor cell proliferation and inhibiting
the secretion of angiogenic factors. VEGF and FGF2 are secreted from both endothelial cells and
tumor cells, where the secretion from tumor cells is dependent on the oxygen level (H), while the
secretion from endothelial cells occurs at a constant rate. Angiogenic receptors are expressed on
both the tumor cell surface and on the endothelial cell surface, including two VEGF receptors
(VEGFR1 and VEGFR2) and two FGF2 receptors (FGFR1 and cHSPG). Secreted VEGF and
142
FGF2 can bind to their respective receptors to form ligand-receptor complexes. Compared to the
work in Chapter 2 and Chapter 3, we made assumptions to simplify the ligand binding network.
We assumed that VEGFR2 is the primary signaling receptor for VEGF, and VEGFR1 only serves
as non-signaling binding sites. Similarly, FGFR1 is assumed to be the primary signaling receptor
for FGF2 and cell-surface heparan sulfate proteoglycans (cHSPG) traps the FGF2 as non-signaling
receptors. Additionally, we assumed the tumor cell growth and endothelial cell growth are subject
to different physical constraints: the tumor cells’ growth is limited by the carrying capacity, while
the endothelial cells’ growth is limited by the number of tumor cells (T) to reflect that endothelial
cells are growing together with tumor cells within the tumor site.
Figure 5-1: Computational model of VEGF-FGF mediated angiogenesis and tumor growth.
Tumor and endothelial cells express VEGF receptors (VEGFR1 and VEGFR2) and FGF2
receptors (FGFR1 and HSPG). VEGF bound VEGFR2 and FGF bound FGFR1 will promote cell
proliferation. Tumor cells secrete angiogenic factors and promote hypoxia that further enhances
angiogenic factors secretion from tumor cells. Endothelial cells inhibit hypoxia, and hypoxia
inhibits tumor cell proliferation. The two anti-angiogenic agents (VEGF-trap and FGF-trap) reach
the tumor through transportation from the blood compartment.
143
5.3.2 Mathematical equations of the model
The model is represented by a set of coupled non-linear ordinary differential equations
(ODEs). We implemented the model with MATLAB (The MathWorks, Natick, MA, USA). The
ODEs were solved using the ode15s solver in MATLAB to predict the species’ quantities over
time. Here, we present the formation of the mathematical equations.
5.3.2.1. Cellular species
Two cellular species, tumor cells (T) and endothelial cells (E), are present in the model.
The number of endothelial cells depends on VEGF and FGF stimulation, spatial limitations, and
apoptosis.
where >
!
/
=
$
$ " *
!"#$$$
%
&
8)'
%
&
8)'
( )
&
8)'
and >
!
7
=
$
$ " *
!"#$$$
%
&
:)#
%
&
:)#
( )
&
:)#
. Here,
+
&
8)'
+
&
8)'
" ,
&
8)'
is the fraction
of the number of VEGF-bound VEGFR2 complexes on endothelial cells relative to the total
number of VEGFR2 receptors on the endothelial cell surface, with 6
!
/,(
represents the VEGF
ligated VEGFR2 complex on the surface of endothelial cells and (
!
/,(
represents the free
VEGFR2 receptors on the surface of endothelial cells. With this ratio, we calculated >
!
/
with a
sigmoid function to represent the activation level of the downstream signaling. In other words, >
indicates the level of pro-angiogenic or pro-tumorigenic effect (ranges from 0 to 1) and
+
&
8)'
+
&
8)'
" ,
&
8)'
is the fractional occupancy of the signaling VEGF receptors. To our knowledge, there
are no robust, quantitative measurements available that can be used to specify the relationship
between the receptor occupancy and downstream signaling level. Therefore, we assume the
144
downstream signaling is highly sensitive to the expression of VEGF and the activation of
downstream signaling has switch-like nonlinear behavior, in which 1% occupancy of the signaling
receptor is able to have nearly maximum pro-angiogenic or pro-tumorigenic effect and 0.1% will
have nearly zero activation. Accordingly, the parameters of exponents (6 and 1000) are selected
to allow > =
$
$ " *
!"#$$$∗$. $#
= 0.98 (1% receptor occupancy) and > =
$
$ " *
!"#$$$∗$. $$#
= 0.006
(0.1% receptor occupancy). Similarly, the
+
&
:)#
+
&
:)#
" ,
&
:)#
is the fraction of the number of FGF2 bound
FGFR1 complexes on endothelial cells over the total FGFR1 receptors on the endothelial cell
surface, with 6
!
7,$
represents the FGF2 ligated FGFR1 complexes on the surface of endothelial
cells and (
!
7,$
represents the free FGFR1 receptors on the surface of endothelial cells. The >
!
7
is
the activation level of FGF2 signaling receptors and is calculated in the same way as >
!
/
. Similarly,
we model the change in the number of tumor cells over time, which is influenced by VEGF and
FGF2, as well as spatial limitations and hypoxia.
where >
#
/
=
$
$ " *
!"#$$$
%
,
8)'
%
,
8)'
( )
,
8)'
and >
#
7
=
$
$ " *
!"#$$$
%
,
:)#
%
,
:)#
( )
,
:)#
.
+
,
8)'
+
,
8)'
" ,
,
8)'
is the fraction of the
number of VEGF bound VEGFR2 complexes on tumor cells over the number of total VEGFR2
receptors on the tumor cell surface and
+
,
:)#
+
,
:)#
" ,
,
:)#
is the fraction of the number of FGF2 bound
FGFR1 complex on tumor cells over the total FGFR1 receptors on the surface of tumor cells. Here,
we assume that tumor cells have no programmed cell death and that their growth is inhibited by
hypoxia. We use a sigmoid function to model switch-like behavior: tumor growth will be strongly
inhibited when the oxygen (nutrient) level H is lower than the threshold value Hgrow.
145
5.3.2.2. Molecular Species
The VEGF ligand-receptor system is derived from the model in Chapter 4. Hypoxia
(conditions of low oxygen level, denoted as “H”) promotes the secretion of VEGF from tumor
cells. VEGF secretion will be strongly activated when the oxygen level H is lower than the
threshold value Hangio. VEGF can bind to the free VEGF receptors (VEGFR1 and VEGFR2) on
the surfaces of tumor cells and endothelial cells ((
!
/,$
, (
#
/,$
, (
!
/,(
and (
#
/,(
) and dissociate from
bound receptors (6
!
/,$
, 6
#
/,$
, 6
!
/,(
and 6
#
/,(
). VEGF is degraded with a constant rate.
146
The FGF2 ligand-receptor system is incorporated into the model in the same way as VEGF.
Endothelial cells in the system secrete FGF2 (F) with a constant rate. The secretion of FGF2 from
tumor cells is dependent on the oxygen level (H). FGF2 secretion will be strongly activated when
the oxygen level H is lower than the threshold value Hangio. FGF2 can bind to the free FGFR1 and
cHSPG on the surfaces of tumor cells and endothelial cells ((
!
7,$
, (
#
7,$
, (
!
89
and (
#
89
) and
dissociate from bound receptors (6
!
7,$
, 6
#
7,$
, 6
!
89
and 6
#
89
). FGF2 is degraded with a constant
rate.
147
5.3.2.3. Therapeutic Agents
VEGF-trap. In mouse studies, VEGF-trap (T
V
) is commonly administered through
intraperitoneal injections. We use a three-compartment model to characterize the pharmacokinetics
of VEGF-trap treatment. The drug is assumed to be given into a peritoneum compartment. Then
the drug will be absorbed into the circulatory system (blood compartment). The drug is subject to
elimination in the blood compartment. It can also extravasate into the tumor site (tumor
compartment). In the tumor compartment, VEGF-trap will bind to free VEGF and prevent VEGF
from binding to receptors on the cell surface. The drug can be degraded after binding to VEGF. ,
:
/
represents the VEGF-trap injected into the peritoneum compartment. ,
;
/
represents free VEGF-
trap in the blood compartment. ,
#
/
is free VEGF-trap in the tumor compartment and ,
+
/
is VEGF-
148
bound VEGF-trap in the tumor compartment. We simulate the drug injection by changing the
concentration of ,
:
/
.
FGF-trap. The same approach is applied to model the pharmacokinetics of FGF-trap. ,
:
7
represents FGF-trap injected into the peritoneum compartment. ,
;
7
represents free FGF-trap in the
blood compartment. ,
#
7
is free VEGF-trap in the tumor compartment, which can bind to free FGF2
and form the FGF-bound FGF-trap complex in the tumor compartment ,
+
7
. We simulate the drug
injection of FGF-trap by changing the concentration of ,
:
7
.
The drug is simulated by mimicking the administration strategy used in preclinical trials
(dose and frequency).
149
5.3.3. Parameterization
There are 50 parameters presented in this model, including molecular dynamics parameters,
cellular response parameters and drug PK/PD parameters. The model parameter values are
reported in the following tables.
5.3.3.1. Molecular dynamics parameters
The molecular dynamics parameters include the angiogenic factors’ secretion rates,
receptor numbers, ligand-receptor binding parameters, degradation and internalization rates.
Parameters are derived from previous modeling and experimental studies. We used Tvol to
represent the volume of the interstitial space of the tumor sites. To calculate Tvol, we first compute
the volume of tumor cells, Tcells, by converting the predicted number of cells to tumor volume (cm
3
)
with ,
<*44=
= $ × 2.2 × 10
0&
+,× 10
0&
. We assumed that the volume of one EC is
2.2 × 10
01
EF
203
and that of one TC is 1 × 10
01
EF
204
. Then, we compute the interstitial space
volume with the ratio of interstitial space to tumor tissue volume.
,
234
= ,
<*44=
×
(!+?_/34_-A=_BA= "!;?_/34_-A=_BA= " :;?_/34_-A=_BA=)
$0(!+?_/34_-A=_BA= "!;?_/34_-A=_BA= " :;?_/34_-A=_BA=)
Table 5-1: List of tumor geometric parameters.
Symbol Description Unit Value Ref.
ECM_Vol_tis_dis Volume of extracellular matrix available
species in a breast tumor
*3
'
*3
'
-'00>)
0.51931
70,74
EBM_Vol_tis_dis Volume of microvessel basement membrane
available to soluble species in a breast tumor
0.00027
PBM_Vol_tis_dis Volume of tumor cells basement membrane
available to soluble species in a breast tumor
0.002446
150
Table 5-2: List of VEGF and FGF2 ligand-receptor system parameters.
Symbol Description Unit Value Ref.
<
5
6
VEGF secretion rate of endothelial cells
()*+
),++,*- /0++1
234
!"
0.0394
†
<
!
6
Maximal VEGF secretion rate of tumor cells 55.4757
<
5
7
FGF2 secretion rate of endothelial cells 0.0926
<
!
7
Maximal FGF2 secretion rate of tumor cells 0.1517
2
5
68$
VEGFR1 receptor number on endothelial cells
()*+
),++,*- /0++1
0.0062
205
2
5
689
VEGFR2 receptor number on endothelial cells 0.0005
2
!
68$
VEGFR1 receptor number on tumor cells 0.0018
2
!
689
VEGFR2 receptor number on tumor cells 0.001
2
5
78$
FGFR1 receptor number on endothelial cells 0.0083
89,186
2
5
:;
HSPG binding sites number on endothelial cells 0.083
2
!
78$
FGFR1 receptor number on tumor cells 0.0166
2
!
:;
HSPG binding sites number on tumor cells 0.166
k on1 Association rate of VEGF binding to VEGFR1
()*+
!"
234
!"
4.97/T vol
206
k on2 Association rate of VEGF binding to VEGFR2 1.66/T vol
207,208
k on3 Association rate of FGF2 binding to FGFR1 0.883/T vol
89,186
k on4 Association rate of FGF2 binding to HSPG 0.331/T vol
k off1 Dissociation rate of VEGF-VEGFR1
234
!"
86.4
70
k off2 Dissociation rate of VEGF-VEGFR2 86.4
k off3 Dissociation rate of FGF2-VEGFR1 403.2
89,186
k off4 Dissociation rate of FGF2-HSPG 806.4
k deg Degradation rate of angiogenic factors 16.68
209
k int Internalization rate of cell surface receptors 24.19
73
†
Estimated in the fitting to tumor volume data.
5.3.3.2. Cellular response parameters
The cellular response parameters are related to cell proliferation and death. We fixed the
endothelial cell apoptotic rate , because eapo and egrow are not identifiable at the same time. Similar
to the work in Chapter 4, we have four cell response parameters left to be estimated based on
151
experimental tumor volume data. Two of them, egrow and µE, are global parameters. The other two
parameters, tgrow and tcap, are dataset-specific parameters.
Table 5-3: List of global cellular response parameters.
Symbol Description Unit Value Ref.
H 0 Initial Nutrient (oxygen) level for tumor xenograft
mm Hg
1 Estimated
H grow Threshold of nutrient (oxygen) level for growth inhibition 5.5
201
H angio Threshold of nutrient (oxygen) level for VEGF secretion 10
201
e grow Basal cell proliferation rate of endothelial cells day
-1
1.01 Estimated
e apo Apoptotic rate of endothelial cells 1 Fixed
µ
5
6
VEGF-VEGFR2 driven endothelial cells proliferation
dimensionless
0.512 Estimated
µ
!
6
VEGF-VEGFR2 driven tumor cells proliferation 0.512 Fixed
†
µ
5
7
FGF2-FGFR1 driven endothelial cells proliferation 0.511 Estimated
µ
!
7
FGF2-FGFR1 driven tumor cells proliferation 0.511 Fixed
†
†
µT is assumed to be the same as µE. It can be changed to have more tunable parameters.
Table 5-4: List of dataset-specific tumor growth kinetic parameters.
Symbol Description Unit Value Dataset
t grow
Basal growth rate of tumor cells
day
-1
0.044 Li2014A
0.039 Li2016A
0.041 Li2016B
t cap
Carrying capacity of tumor cells
million cells
485 Li2014A
1244 Li2016A
533 Li2016B
5.3.3.3. Pharmacokinetic and Pharmacodynamic Parameters
We estimated the values of unknown pharmacokinetic (PK) parameters for FGF-trap by
fitting to the experimental measurements of the drug’s plasma concentration
248
. We assume
VEGF-trap has the same PK properties as FGF-trap. The elimination rate of VEGF-trap and FGF-
trap are set according to their reported half-life values. Their binding properties are set according
152
to the reported Kd values: 0.49 pM for VEGF-trap binding to VEGF and 5.36 pM for FGF-trap
binding to FGF2.
Table 5-5: List of the PK/PD parameters of VEGF-trap and FGF-trap.
Symbol Description Unit Value Ref.
k onVT VEGF-trap binding to VEGF pmol
-1
day
-1
3.54/T vol
57
k onFT FGF-trap binding to FGF 3.54/T vol
k offVT Dissociation rate of VEGF bound VEGF-trap
day
-1
1.7366
k offFT Dissociation rate of FGF2 bound FGF-trap 18.9963
?
$9
6!
VEGF-trap transportation rate from peritoneum to blood 1.7774 Fixed
‡
?
9'
6!
VEGF-trap transportation rate from blood to tumor 0.1631 Fixed
‡
?
'9
6!
VEGF-trap transportation rate from tumor to blood 0.7467 Fixed
‡
?
<=
6!
Elimination rate of VEGF-trap in blood 0.3654 Fixed
†
?
>3.0.CO;2-D
265. Gustafsson T, Ameln H, Fischer H, Sundberg CJ, Timmons J a, Jansson E. VEGF-A
splice variants and related receptor expression in human skeletal muscle following
submaximal exercise. J Appl Physiol. 2005;98(6):2137-2146.
doi:10.1152/japplphysiol.01402.2004
266. Gluzman-Poltorak Z, Cohen T, Herzog Y, Neufeld G. Neuropilin-2 and neuropilin-1 are
receptors for the 165-amino acid form of vascular endothelial growth factor (VEGF) and
of placenta growth factor-2, but only neuropilin-2 functions as a receptor for the 145-
amino acid form of VEGF. J Biol Chem. 2000;275(24):18040-18045.
doi:10.1074/jbc.M909259199
267. Herzog B, Pellet-Many C, Britton G, Hartzoulakis B, Zachary IC. VEGF binding to NRP1
is essential for VEGF stimulation of endothelial cell migration, complex formation
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268. Parker MW, Xu P, Li X, Vander Kooi CW. Structural basis for selective vascular
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198
Appendices
Appendix A. Supplementary Information of Tumor Tissue Model
Figure A-1: The variations of predicted tumor tissue distribution of VEGF, FGF2, TSP1 and
PF4. The secretion rates of VEGF, FGF2, TSP1, PF4 and MMPs are sampled within a range of
100-fold below and 10-fold above the baseline values. The mean value and the standard deviations
of the predictions of 5000 Monte Carlo simulations are shown in plots.
199
Figure A-2: Effects of PF4 secretion on the angiogenic distribution. The predicted change of
(A) TSP1 and (B) PF4 species with increasing PF4 secretion.
200
Table A-1: List of reactions in tumor tissue model
No. Reactions Forward/Backward reaction rates
VEGF Receptor System
Ligand Binding to Cell Surface
1 R2 + V121 <-> V121:R2 Kon_V121_R2 Koff_V121_R2
2 R2+V165 <-> V165:R2 Kon_V165_R2 Koff_V165_R2
3 N+V165 <-> V165:N Kon_V165_N Koff_V165_N
4 H+V165 <-> V165:H Kon_V165_HSPG Koff_V165_HSPG
5 N:H+V165 <-> V165:N:H Kon_V165_NH Koff_V165_NH
6 R1+V121 <-> V121:R1 Kon_V121_R1 Koff_V121_R1
7 R1:N + V121 <-> V121:R1:N Kon_V121_R1 Koff_V121_R1
8 R1:H + V121 <-> V121:R1:H Kon_V121_R1 Koff_V121_R1
9 R1:N:H + V121 <-> V121:R1:N:H Kon_V121_R1 Koff_V121_R1
10 R1+V165 <-> R1:V165 Kon_V165_R1 Koff_V165_R1
11 R1:H + V165 <-> V165:R1:H Kon_V165_R1 Koff_V165_R1
Coupling of Receptors
12 N+H <-> N:H Kc_N_H Kdiss_N_H
13 V165:N+H <-> V165:N:H Kc_V165N_H Kdiss_V165N_H
14 V165:H+N <-> V165:N:H Kc_V165H_N Kdiss_V165H_N
15 V165:R2+N:H <-> R2:V165:N:H Kc_V165R2_NH Kdiss_R2_N
16 R2+V165:N:H <-> R2:V165:N:H Kc_R2_V165NH Kdiss_R2_N
17 R1+N <-> R1:N Kc_R1_N Kdiss_R1_N
18 R1+H <-> R1:H Kc_R1_H Kdiss_R1_H
19 R1+N:H <-> R1:N:H Kc_R1_N Kdiss_R1_N
R1+N:H <-> R1:N:H Kc_R1_H Kdiss_R1_H
20 R1:N+H <-> R1:N:H Kc_R1_H Kdiss_R1_H
R1:N+H <-> R1:N:H Kc_N_H Kdiss_N_H
21 R1:H+N <-> R1:N:H Kc_R1_N Kdiss_R1_N
R1:H+N <-> R1:N:H Kc_N_H Kdiss_N_H
22 V121:R1+N <-> V121:R1:N Kc_R1_N Kdiss_R1_N
23 V121:R1+H <-> V121:R1:H Kc_R1_H Kdiss_R1_H
24 V121:R1+N:H <-> V121:R1:N:H Kc_R1_N Kdiss_R1_N
V121:R1+N:H <-> V121:R1:N:H Kc_R1_H Kdiss_R1_H
25 V121:R1:N+H <-> V121:R1:N:H Kc_R1_H Kdiss_R1_H
V121:R1:N+H <-> V121:R1:N:H Kc_N_H Kdiss_N_H
26 V121:R1:H+N <-> V121:R1:N:H Kc_R1_N Kdiss_R1_N
V121:R1:H+N <-> V121:R1:N:H Kc_N_H Kdiss_N_H
27 V165:R1+H <-> V165:R1:H Kc_R1_H Kdiss_R1_H
TSP1 Receptor System
Ligand Binding to Cell Surface
28 T+CD47 <-> T:CD47 Kon_TSP1_CD47 Koff_TSP1_CD47
29 T+LRP1 <-> T:LRP1 Kon_TSP1_LRP1 Koff_TSP1_LRP1
30 V:T+LRP1 <-> V:T:LRP1 Kon_TSP1_LRP1 Koff_TSP1_LRP1
31 T+H <-> T:H Kon_TSP1_HSPG Koff_TSP1_HSPG
201
32 T+CD36 <-> T:CD36 Kon_TSP1_CD36 Koff_TSP1_CD36
33 T+B1 <-> T:B1 Kon_TSP1_B1 Koff_TSP1_B1
34 T+CD36:B1 <-> T:CD36:B1 Kon_TSP1_CD36 Koff_TSP1_CD36
T+CD36:B1 <-> T:CD36:B1 Kon_TSP1_B1 Koff_TSP1_B1
Coupling of Receptors
35 CD36+B1 <-> CD36:B1 Kc_CD36_B1 Kdiss_CD36_B1
36 T:CD36+B1 <-> T:CD36:B1 Kc_CD36_B1 Kdiss_CD36_B1
37 T:B1+CD36 <-> T:CD36:B1 Kc_CD36_B1 Kdiss_CD36_B1
VEGF-TSP1 Receptor System
Ligand Binding to Cell Surface
38 V121+R2:CD47 <-> V121:R2:CD47 Kon_V121_R2 Koff_V121_R2
V165+R2:CD47 <-> V165:R2:CD47 Kon_V165_R2 Koff_V165_R2
39 V121+R2:CD36:B1 <-> V121:R2:CD36:B1 Kon_V121_R2 Koff_V121_R2
V165+R2:CD36:B1 <-> V165:R2:CD36:B1 Kon_V165_R2 Koff_V165_R2
40 V121+R2:CD36:B1:T<->V121:R2:CD36:B1:T Kon_V121_R2 Koff_V121_R2
V165+R2:CD36:B1:T<->V165:R2:CD36:B1:T Kon_V165_R2 Koff_V165_R2
41 T+R2:CD36:B1 <-> R2:CD36:B1:T Kon_TSP1_CD36 Koff_TSP1_CD36
T+R2:CD36:B1 <-> R2:CD36:B1:T Kon_TSP1_B1 Koff_TSP1_B1
42 T+V121:R2:CD36:B1<->V121:R2:CD36:B1:T Kon_TSP1_CD36 Koff_TSP1_CD36
T+V121:R2:CD36:B1<->V121:R2:CD36:B1:T Kon_TSP1_B1 Koff_TSP1_B1
T+V165:R2:CD36:B1<->V165:R2:CD36:B1:T Kon_TSP1_CD36 Koff_TSP1_CD36
T+V165:R2:CD36:B1<->V165:R2:CD36:B1:T Kon_TSP1_B1 Koff_TSP1_B1
Coupling of Receptors
43 R2+CD47 <-> R2:CD47 Kc_CD47_R2 Kdiss_CD47_R2
44 R2+CD36:B1 <-> R2:CD36:B1 Kc_CD36_R2 Kdiss_CD36_R2
45 R2+T:CD36:B1 <-> R2:CD36:B1:T Kc_CD36_R2 Kdiss_CD36_R2
46 V121:R2+CD36:B1 <-> V121:R2:CD36:B1 Kc_CD36_R2 Kdiss_CD36_R2
V165:R2+CD36:B1 <-> V165:R2:CD36:B1 Kc_CD36_R2 Kdiss_CD36_R2
47 V121:R2+CD36:B1:T<->V121:R2:CD36:B1:T Kc_CD36_R2 Kdiss_CD36_R2
V165:R2+CD36:B1:T<->V165:R2:CD36:B1:T Kc_CD36_R2 Kdiss_CD36_R2
FGF2 Receptor System
Ligand Binding to Cell Surface
48 F+FR <-> F:FR Kon_FGF2_FGFR1 Koff_FGF2_FGFR1
49 F+H <-> F:H Kon_FGF2_HSPG Koff_FGF2_HSPG
Coupling of Receptors
50 F:H+F:R <-> F:FR:H Kc_HSPG_FGFR1 Kdiss_HSPG_FGFR1
51 F:FR:H+F:FR:H <-> (F:FR:H)2 Kc_FGFR1_FGFR1 Kdiss_FGFR1_FGFR1
PF4 Receptor System
Ligand Binding to Cell Surface
52 PF4+H <-> PF4:H Kon_PF4_HSPG Koff_PF4_HSPG
53 PF4+CXCR3 <-> PF4:CXCR3 Kon_PF4_CXCR3 Koff_PF4_CXCR3
54 PF4+LRP1 <-> PF4:LRP1 Kon_PF4_LRP1 Koff_PF4_LRP1
55 MMP9+LRP1 <-> MMP9:LRP1 Kon_MMP9_LRP1 Koff_MMP9_LRP1
Reactions in the Interstitial Space
202
56 V165+GAG<->V165:GAG Kon_V165_GAG Koff_V165_GAG
57 T+GAG<->T:GAG Kon_VTSP1_GAG Koff_TSP1_GAG
58 PF4+GAG <-> PF4:GAG Kon_PF4_GAG Koff_PF4_GAG
59 F+GAG <-> F:GAG Kon_FGF2_GAG Koff_FGF2_GAG
60 PF4+V165 <-> PF4:V165 Kon_PF4_V165 Koff_PF4_V165
61 PF4+F <-> PF4:F Kon_PF4_FGF2 Koff_PF4_FGF2
62 TSP1+F <-> TSP1:F Kon_TSP1_FGF2 Koff_TSP1_FGF2
63
TSP1+V165 <-> TSP1:V165 Kon_TSP1_VEGF Koff_TSP1_VEGF
TSP1+V121 <-> TSP1:V121 Kon_TSP1_VEGF Koff_TSP1_VEGF
TSP1+V114 <-> TSP1:V114 Kon_TSP1_VEGF Koff_TSP1_VEGF
64 V165:GAG+MMP3<->V114+GAG+MMP3 Kp_mmp
V165:GAG+MMP9<->V114+GAG+MMP9 Kp_mmp
65
proMMP9+MMP3 <-> proMMP9:MMP3 Kon_M3_proM9 Koff_M3_proM9
proMMP9:MMP3 -> MMP9+MMP3 Kcat_M3_proM9
MMP3+TSP1 <-> MMP3:TSP1 Kon_M3_TSP1 Koff_M3_TSP1
66 MMP3+V165 -> MMP3+V114 Kp_mmp
MMP9+V165 -> MMP9+V114 Kp_mmp
67 T -> T_cleaved K_TSP1cleave
203
Table A-2: List of parameters in tumor tissue model
Parameter Description Unit Model Value Reference and Notes
Geometric Parameters
Mac Gabhann et al. constructed the tissue-based model of the VEGF system and described the derivations of following geometric parameters
in their work
137
. Here we report the value and the sources of parameters used in the model file provided by us.
ECM_conc Binding site density of extracellular
matrix
M 7.5e-7
249
* The Heparan Sulfate (HS) binding site
densities are measured with FGF binding.
VEGF, TSP1 and PF4 each bind to heparan
sulfate, and we assume they bind to the HS
binding sites with different affinities.
EBM_conc Binding site density of the basement
membrane surrounding the endothelial
cells
1.3e-5
250
PBM_conc Binding site density of the basement
membrane surrounding the
parenchymall cells
1.3e-5
ECM_Vol_tis_dis Volume of extracellular matrix of which
available to soluble species in breast
tumor
cm
3
/cm
3
tissue
0.51931
EBM_Vol_tis_dis Volume of microvessel basement
membrane of which available to soluble
species in breast tumor
0.00027
PBM_Vol_tis_dis Volume of tumor cells basement
membrane of which available to soluble
species in breast tumor
0.002446
vol_Tumor Total volume of tumor tissue cm
3
33.51032
105
204
tumorSA_Vol_tis_
dis
Total tumor cells surface area in tumor
tissue
cm
2
/cm
3
tissue
1534
73
VesselSA_Vol_tis
_dis
Total microvessels surface area in
tumor tissue
105
251
tumorCellSurfAre
a_tis_dis
Surface area of one cancer cell cm
2
9.97e-6
73
VesselCellSurfAre
a_tis_dis
Surface are of the abluminal side of an
endotheali cell in tumor tissue
1.00e-5
Baseline Secretion Rates
The secretion rates of VEGF, TSP1 and MMP are consistent with previous modeling works
25,137
. Two new newly introduced parameters,
including the production rates of FGF2 and PF4, are estimated with experimental data (See Method section) in this work.
qTSP1disEC TSP1 secretion rate of endothelial cell
in tumor tissue (abluminal side)
molecul
es/cell/s
6
25
* These secretion rates are estimated in our
previous modeling work. The ratio of
tumor cell secreted TSP1 to endothelial cell
secreted TSP1 is set to be 1:10.
qTSP1tum TSP1 secretion rate of tumor cell 0.6
qMMP3_disEC MMP3 secretion rate of endothelial cell
in tumor tissue
180
qproMMP9_disEC proMMP9 secretion rate of endothelial
cell in tumor tissue
330
qV165_tumor VEGF165 secretion rate of tumor cell 0.387
129
* The tumor secretion rates were estimated
205
with experimental measurements
252–255
.
The ratio of tumor secreted VEGF165 to
VEGF121 is set to be 1:1.
qV121_tumor VEGF121 secretion rate of tumor cell 0.387
qV165_disEC VEGF165 secretion rate of endothelial
cell in tumor compartment
0.0324
205
qV121_disEC VEGF121 secretion rate of endothelial
cell in tumor compartment
0.0324*10/90
* The ratio of tumor endothelial cell
secreated VEGF165 to VEGF121 is set to
9:1
256
.
qFGF2 FGF2 production rate in tumor (mol/cm
3
tissue)
-
1
s
-1
3e-16
*The production rates of these two
angiogenic factors are tuned to match the
experimental data in this work.
qPF4 PF4 production rate in tumor 1e-14
Recycling of the receptors
The recycling rates of receptors are originally from the first tumor tissue model of VEGF-Receptor System by Gabhann et al
73
.
sR_receptors Recycling rate of unbound receptors s-1 0.00028
73
*We assume all receptors have same
internalization and recycling rates.
k_int_receptors Internalization rate of all ligated and
unbound receptors
0.00028
Kinetic Parameters
Mac Gabhann et al applied following kinetic rates of VEGF system in their work of tumor tissue model
73
and illustrated the conversion from in
vitro parameters to tissue parameters basing on geometric parameters. Following reported values are in vitro parameters, which are converted
to tissue parameters used by model with the same strategy.
kon_FGF2_GAG FGF2 binding to interstitial HSPG M
-1
s
-1
8600 *Assumed to have same association rate as
VEGF-Heparin binding.
kon_FGF2_HSGA
G
FGF2 binding to cell surface HSPG 3.66e+6
113
kon_FGF2_FGFR
1
FGF2 binding to FGFR1 monomer 4.91e+5
kon_FGF2_TSP1 FGF2 binding to TSP1 1.89e+4
93
206
kon_PF4_GAG PF4 binding to interstitial HSPG 8600 *Assumed to have same association rate as
VEGF-Heparin binding.
kon_PF4_HSGAG PF4 binding to cell surface HSPG 3.66e+6 * Assumed to have same association rate as
FGF2-cHSPG binding.
kon_PF4_CXCR3 PF4 binding to CXCR3 5.00e+5
90
* Association rates are set to fixed constant
(See method section).
kon_PF4_LRP1 PF4 binding to LRP1 5.00e+5
98
kon_PF4_V165 PF4 binding to VEGF 165 5.00e+5
116
kon_PF4_FGF2 PF4 binding to FGF2 5.00e+5
32
kon_TSP1_GAG TSP1 binding to interstitial HSPG 8600 *Assumed to have same association rate as
VEGF-Heparin binding.
kon_TSP1_HSGA
G
TSP1 binding to cell surface HSPG 3.66e+6 * Assumed to have same association rate as
FGF2-cHSPG binding.
kon_TSP1_CD36 TSP1 binding to CD36 5.00e+5
25
*The kinetic paramters of TSP1-receptor
system are estimated in our previous tumor
tissue model of VEGF and TSP1, which
included detailed derivations.
kon_TSP1_CD47 TSP1 binding to CD47 5.00e+5
kon_TSP1_LRP1 TSP1 binding to LRP1 2.10e+5
kon_TSP1_B1 TSP1 binding to β1 integrin 5.00e+5
kon_TSP1_VEGF TSP1 binding to VEGF 5.00e+5
kon_TSP1_MMP3 TSP1 binding to MMP3 1.00e+5
kon_V165_GAG VEGF 165 binding to interstitial HSPG 8600
101,2
57,25
8
207
Kon_V165_HSGA
G
VEGF 165 binding to cell surface HSPG 3.66e+6 * Assumed to have same association rate as
FGF2-cHSPG binding.
kon_V165_N1 VEGF 165 binding to Neuropilin-1 3.20e+6
259,2
60
kon_V165_N1H VEGF 165 binding to Neuropilin-1
coupled with HSPG
3.20e+6
kon_V165_R1 VEGF 165 binding to VEGFR1 3.00e+7
206
kon_V165_R2 VEGF 165 binding to VEGFR2 1.00e+7
207,2
08
kon_V121_R1 VEGF 121 binding to VEGFR1 3.00e+7
129
*Set to the same as V165- VEGR receptor
kon_V121_R2 VEGF 121 binding to VEGFR2 1.00e+7
kon_MMP9_LRP1 MMP9 binding to LRP1 9245
25
kon_MMP3_proM
MP9
MMP3 binding to proMMP9 10000
koff_FGF2_GAG FGF2 binding to interstitial HSPG s
-1
6.9e-4/80*39 *Scaled according to VEGF-Heparin
binding dissociation rate.
koff_FGF2_HSG
AG
FGF2 binding to cell surface HSPG 1.11e-3
113
koff_FGF2_FGFR
1
FGF2 binding to FGFR1 monomer 2.36e-4
koff_FGF2_TSP1 FGF2 binding to TSP1 2.05e-4
93
koff_PF4_GAG PF4 binding to interstitial HSPG 6.9e-4/80*20 *Scaled according to VEGF-Heparin
binding dissociation rate.
208
koff_PF4_HSPG PF4 binding to cell surface HSPG 1.11e-3/39*20 *Scaled according to FGF2-cHSPG
binding dissociation rate.
koff_PF4_CXCR3 PF4 binding to CXCR3 9.25e-4
90
* Measured Kd values are used to set
dissociation rates accordingly (See method
section).
koff_PF4_LRP1 PF4 binding to LRP1 0.119
98
koff_PF4_V165 PF4 binding to VEGF 165 2.5e-3
116
koff_PF4_FGF2 PF4 binding to FGF2 0.016
32
koff_TSP1_GAG TSP1 binding to interstitial HSPG 6.9e-4/80*41 *Scaled according to VEGF-Heparin
binding dissociation rate.
koff_TSP1_HSGA
G
TSP1 binding to cell surface HSPG 1.11e-3/39*41 *Scaled according to FGF2-cHSPG
binding dissociation rate.
koff_TSP1_CD36 TSP1 binding to CD36 0.115
25,26
,261
koff_TSP1_CD47 TSP1 binding to CD47 0.005
koff_TSP1_LRP1 TSP1 binding to LRP1 0.0025
koff_TSP1_B1 TSP1 binding to β1 integrin 0.05
koff_TSP1_VEGF TSP1 binding to VEGF 0.005
koff_TSP1_MMP
3
TSP1 binding to MMP3 0.0022303
koff_V165_GAG VEGF 165 binding to interstitial HSPG 6.9e-4
101,2
57,25
8
209
koff_V165_HSGA
G
VEGF 165 binding to cell surface HSPG 1.11e-3/39*80 *Scaled according to FGF2-cHSPG
binding dissociation rate.
koff_V165_N1 VEGF165 binding to Neuropilin-1 0.020
86
*Set to be 20-fold weaker than VEGF 165
binding to HSPG coupled NRP1
koff_V165_N1H VEGF165 binding to Neuropilin-1
coupled with HSPG
0.001
259,2
60
koff_V165_R1 VEGF165 binding to VEGFR1 0.001
206
koff_V165_R2 VEGF165 binding to VEGFR2 0.001
207,2
08
koff_V121_R1 VEGF121 binding to VEGFR1 0.001
129
koff_V121_R2 VEGF121 binding to VEGFR2 0.001
koff_MMP9_LRP
1
MMP9 binding to LRP1 0.00049
25
koff_MMP3_pro
MMP9
MMP3 binding to proMMP9 0.001
kc_N_H Coupling of Neuropilin and HSPG
(mol/cm
2
)
-1
s
-1
3.10e+13 *Assumed to be same as V165R2-NH
coupling.
kc_V165N_H Coupling of VEGF 165 bound Neuropilin
and HSPG
3.10e+13
kc_V165H_N Coupling of Neuropilin and VEGF 165
bound HSPG
3.10e+13
kc_V165NH_R2 Coupling of VEGFR2 and Neuropilin 1.00e+14
83,84
*Estimated in
83
using data from
84
.
kc_V165R2_NH Coupling of VEGFR2 and Neuropilin 3.10e+13
210
kc_R1_N Coupling of VEGFR1 and Neuropilin 1.00e+14
129
*Set to the same as R2-N receptor
kc_R1_H Coupling of VEGFR1 and HSPG 3.10e+13 *Set to the same as V165R2-NH coupling.
kc_CD36_R2 Coupling of CD36 and VEGFR2 3.10e+11
25
kc_CD36_B1 Coupling of CD36 and β1 integrin 3.10e+13
kc_CD47_R2 Coupling of CD47 and VEGFR2 3.10e+11
kc_H_FGFR1 Coupling of HSPG and FGFR1
monomer
3.96e+11
113
kc_FGFR1_FGFR
1
Dimerization of HSPG bound FGFR1 3.17e+17
kdissoc_N_H Coupling of Neuropilin and HSPG s
-1
0.001
kdissoc_V165N_H Coupling of VEGF 165 bound Neuropilin
and HSPG
1e-4 *Assumed to be an order tighter than the
coupling without the presence of
VEGF 165
29
.
kdissoc_V165H_N Coupling of Neuropilin and VEGF 165
bound HSPG
1e-4
kdissoc_R2_NH Coupling of VEGFR2 and Neuropilin 0.001
83,84
kdissoc_R1_N Coupling of VEGFR1 and Neuropilin 0.01
129
*Assumed to be slower dissociation than
R2-N.
kdissoc_R1_H Coupling of VEGFR1 and HSPG 0.001/5 *Set to be 5 folder stronger than HSPG-
Neuropilin binding
29
.
kdissoc_CD36_B1 Coupling of CD36 and β1 integrin 0.001
25
kdissoc_CD36_R2 Coupling of CD36 and VEGFR2 0.001
211
kdissoc_CD47_R2 Coupling of CD47 and VEGFR2 0.001
kdissoc_H_FGFR
1
Coupling of HSPG and FGFR1
monomer
3.24e-7
113
kdissoc_FGFR1_F
GFR1
Dimerization of HSPG bound FGFR1 5.83e-4
Degradation and Clearance Rates
The degradation rates and clearance rates are estimated by conversion from reported half-life time in literatures. The cleavage rate of TSP1 are
fitted to match experimental data in our previous work
25
. The catalytic rate of the activation of proMMP9 by MMP3 and the cleavage of
VEGF165 by MMP were previously reported in modeling works by Vempati
26,261
.
kdeg_VEGF Degradation rate of VEGF
s
-1
1.93e-4
209
kdeg_FGF2 Degradation rate of FGF2 1.93e-4 *Set to be same as VEGF.
kdeg_PF4 Degradation rate of PF4 0.0023 *The clearance of PF4 was reported to be
so rapid that no valid estimation of half-life
can be made
96
. Here, we use 5 mins as the
estimation
262
.
kdeg_TSP1 Degradation rate of TSP1 3.3e-4
25
kdeg_MMP Degradation rate of MMP 0.0012
k_TSP1cleave The cleavage rate of TSP1 through
proteolysis
0.00386
25,26
,261
k_act_MMP3_pro
MMP9
A Michaelis-Menten Activation
constant of the activation of MMP9 by
MMP3
0.0019
kp_mmp The proteolysis rate of VEGF by MMPs (mol/l)
-
1
s
-1
631
212
Receptor Numbers
The density of VEGF receptors and co-receptors on endothelial and tumor cells are systematically reported in our previous work
205
, which are
taken from in vitro and in vivo measurements using quantitative flow cytometry
131
. We used the reported qualitative data in Human Protein
Atlas to estimate the values for TSP1 and PF4 receptors as mentioned in Method Section. The numbers of receptors on the endothelial cell are
set to be half of that for tumor cells, assuming equal distribution on the luminal and abluminal surfaces.
CD36_number_tu
m
CD36 receptor number on tumor cell receptor
s/cell
2500
25
CD47_number_tu
m
CD47 receptor number on tumor cell 10000
LRP1_number_tu
m
LRP1 receptor number on tumor cell 5000
B1_number_tum β1 integrin number on tumor cell 10000
CD36_number_dis
EC
CD36 receptor number on tumor
endothelial cell
1250
CD47_number_dis
EC
CD47 receptor number on tumor
endothelial cell
5000
LRP1_number_dis
EC
LRP1 receptor number on tumor
endothelial cell
2500
B1_number_disEC β1 integrin receptor number on tumor
endothelial cell
5000
R1_number_tum VEGFR1 receptor number on tumor cell 1100
205
*VEGF receptor density followed our
previous studies which uses the in vivo and
in vitro measurements using quantitative
flow cytometry.
R2_number_tum VEGFR2 receptor number on tumor cell 550
N1_number_tum Neuropilin-1 receptor number on tumor
cell
39500
213
R1_number_disEC VEGFR1 receptor number on tumor
endothelial cell
3750
R2_number_disEC VEGFR2 receptor number on tumor
endothelial cell
300
N1_number_disE
C
Neuropilin-1 receptor number on tumor
endothelial cell
20000
FGFR1_number_t
um
FGFR1 receptor number on tumor cell 20000
89
HSGAG_number_
tum
HSPG number on tumor cell surface 100000
FGFR1_number_d
isEC
FGFR1 receptor number on tumor
endothelial cell
10000
HSGAG_number_
disEC
HSPG number on tumor endothelial cell
surface
50000
CXCR3_number_t
um
CXCR3 receptor number on tumor cell 2500
*Estimated according the qualitative data
shown in Human Protein Atlas.
CXCR3_number_
disEC
CXCR3 receptor number on tumor
endothelial cell
1250
†
Here, M = moles/liter of interstitial fluid available to soluble species.
214
Appendix B. Supplementary Information of the Whole-body Model of VEGF-TSP1
Table B-1: List of parameters in whole-body model of VEGF-TSP1
Parameter Description Unit Model Value Reference and Notes
Geometric Parameters
Stefanini et al. constructed the first whole body compartmental body of the VEGF system and described the derivations of following geometric
parameters in their work
74
. They later published another modeling work
70
, which provides a more detailed supplementary table describing the
model geometric parameters with experimental measurements. Here we report the value and the sources of parameters used in the model file
provided by us.
BW Patient Body weight kg 70
Avogadro Avogadro constant mol
-1
6.02e+23
ECM_conc Binding site density of extracellular
matrix
M 7.5e-7
249
* The binding site density of VEGF and
TSP1 are assumed to be the same as FGF.
EBM_conc Binding site density of the basement
membrane surrounding the
endothelial cells
1.3e-5
250
PBM_conc Binding site density of the basement
membrane surrounding the
parenchymall cells
1.3e-5
ECM_Vol_tis_norm Volume of extracellular matrix of
which available to soluble species in
normal tissue
cm
3
/cm
3
tissue
0.061987
70,74
* The present work models a breast
cancer patient of same characteristics as
in previous works, which provide the
derivation of these geometric parameters
and sources of experimental
measurements.
EBM_Vol_tis_norm Volume of microvessel basement
membrane of which available to
soluble species in normal tissue
8.7e-5
215
PBM_Vol_tis_norm Volume of tissue cells basement
membrane of which available to
soluble species in normal tissue
3.07e-4
ECM_Vol_tis_blood Volume of fluid space in blood of
which available to soluble species
cm
3
/cm
3
tissue
0.51931
EBM_Vol_tis_blood Volume of luminal tumor endothelial
cells basement membrane of which
available to soluble species
4.3e-4
PBM_Vol_tis_blood Volume of luminal healthy
endothelial cells basement membrane
of which available to soluble species
0.00421
ECM_Vol_tis_dis Volume of extracellular matrix of
which available to soluble species in
breast tumor
cm
3
/cm
3
tissue
0.51931
EBM_Vol_tis_dis Volume of microvessel basement
membrane of which available to
soluble species in breast tumor
0.00027
PBM_Vol_tis_dis Volume of tumor cells basement
membrane of which available to
soluble species in breast tumor
0.002446
vol_Norm Total volume of normal tissue cm
3
61321
105
vol_Blood Total volume of blood tissue 5000
vol_Tumor Total volume of tumor tissue 33.51032
vol_Subc Total volume of subcutaneous
compartment
30
216
tumorSA_Vol_tis_di
s
Total tumor cells surface area in
tumor tissue
cm
2
/cm
3
tissue
1534
73
VesselSA_Vol_tis_d
is
Total microvessels surface area in
tumor tissue
105
251
VesselSA_Vol_tis_n
orm
Total microvessels surface area in
normal tissue
108
251
fiberSA_Vol_tis_nor
m
Total tissue cells surface in normal
tissue
664
tumorCellSurfArea_t
is_dis
Surface area of one cancer cell cm
2
9.97e-6
73
VesselCellSurfArea_
blood
Surface are of the luminal side of an
endotheali cell (blood)
1.00e-5
VesselCellSurfArea_
tis_dis
Surface are of the abluminal side of
an endotheali cell in tumor tissue
1.00e-5
VesselCellSurfArea_
tis_norm
Surface are of an abluminal side of an
endotheali cell in normal tissue
1.00e-5
fiberCellSurfArea_ti
s_norm
Surface area of skeletal muscle
nuclear domain
1.85e-5
251
Secretion Rates
The secretion rates of TSP1, MMP3, and proMMP9 are fitted in our study to match the experimental measurements
22,111,147,148
as mentioned in
Method section. The secretion rates of VEGF were fitted to in vivo population PK data in our previous modeling work
129
. The synthesis rates of
a2M were introduced to whole body model in another previous modeling work of us
263
.
qTSP1EC TSP1 secretion rate of endothelial cell
in normal tissue (luminal side)
1 * The secretion rates of TSP1, MMP3 and
proMMP9 for tumor cell and endothelial
217
qTSP1disEC TSP1 secretion rate of endothelial cell
in tumor tissue (abluminal side)
molecules/
cell/s
1 cells in tumor are based on previous
TSP1-VEGF breast tumor tissue model
and are further tuned to match the
experimental data as mentioned in
Methods part.
*Due to the scarcity of data, we assume
the endothelial cells in tumor tissue and in
normal tissue have same secretion
property.
qTSP1tum TSP1 secretion rate of tumor cell 1
qTSP1myo TSP1 secretion rate of a tissue cell in
normal tissue
0
qMMP3_disEC MMP3 secretion rate of endothelial
cell in tumor tissue
5
qproMMP9_disEC proMMP9 secretion rate of
endothelial cell in tumor tissue
1.2
qMMP3_EC MMP3 secretion rate of endothelial
cell in normal tissue
5
qproMMP9_EC proMMP9 secretion rate of
endothelial cell in normal tissue
1.2
qMMP3_tum MMP3 secretion rate of tumor cell 12
qproMMP9_tum proMMP9 secretion rate of tumor cell 24
qMMP3_myo MMP3 secretion rate of a tissue cell
in normal tissue
4
qproMMP9_myo proMMP9 secretion rate of a tissue
cell in normal tissue
4
qV165_tumor VEGF165 secretion rate of tumor cell 0.387
129
* The tumor secretion rates were
estimated
205
with experimental
measurements
252–255
. The ratio of tumor
secreted VEGF165 to VEGF121 is set to
be 1:1.
qV121_tumor VEGF121 secretion rate of tumor cell 0.387
qV165_disEC VEGF165 secretion rate of
endothelial cell in tumor compartment
0.0324
218
qV121_disEC VEGF121 secretion rate of
endothelial cell in tumor compartment
0.0324*10/90
* The ratio of tumor endothelial cell
secreated VEGF165 to VEGF121 is set to
9:1
256
. The normal endothelial cell is
assumed to have same secretion rate as
tumor endothelial cell. The ratio of
normal cell secreted VEGF165 to
VEGF121 is set to 92:8
264,265
.
qV165_myo VEGF165 secretion rate of tissue cell
in normal tissue
5.01e-9
qV121_myo VEGF121 secretion rate of tissue cell
in normal tissue
5.01e-9*8/92
ksyn_a2M a2M secretion rate in blood (mol/cm
3
tissue)
-1
s
-1
6.27e-14
105
ksyn_a2M_fast a2M_ fast secretion rate in blood 3.14e-14
Recycling of the receptors
The recycling rates of receptors are originally from the first tumor tissue model of VEGF-Receptor System by Gabhann et al
73
.
sR_receptors Recycling rate of unbound receptors s-1 0.00028
73
*We assume all receptors have same
internalization and recycling rates.
k_int_receptors Internalization rate of all ligated and
unbound receptors
0.00028
Kinetic Parameters
Gabhann et al applied following kinetic rates of VEGF system in their work of tumor tissue model
73
and illustrated the conversion from in vitro
parameters to tissue parameters basing on geometric parameters. Following reported values are in vitro parameters, which are converted to
tissue parameters used by model during the generation of the MATLAB model file. The kinetic parameters are from our previous tumor tissue
model of VEGF and TSP1
25
.
kon_TSP1_GAG TSP1 binding to glycosaminoglycan M
-1
s
-1
5.00e+5
25
*The kinetic paramters of TSP1-receptor
system are estimated in our previous
tumor tissue model of VEGF and TSP1,
which included detailed derivations.
kon_TSP1_CD36 TSP1 binding to CD36 5.00e+5
kon_TSP1_CD47 TSP1 binding to CD47 5.00e+5
219
kon_TSP1_LRP1 TSP1 binding to LRP1 2.10e+5
kon_TSP1_B1 TSP1 binding to β1 integrin 5.00e+5
kon_TSP1_VEGF TSP1 binding to VEGF 5.00e+5
kon_TSP1_MMP3 TSP1 binding to MMP3 1.00e+5
kon_V165_N1 VEGF165 binding to Neuropilin-1 3.20e+6
259,2
60
kon_V165_N2 VEGF165 binding to Neuropilin-2 1.00e+6
266–
268
*~3-50 fold less tight than VEGF165-
NRP1
kon_V165_R1 VEGF165 binding to VEGFR1 3.00e+7
206
kon_V165_R2 VEGF165 binding to VEGFR2 1.00e+7
207,2
08
kon_V165_GAG VEGF165 binding to
glycosaminoglycan
8600
101,2
57,25
8
kon_V121_R1 VEGF121 binding to VEGFR1 3.00e+7
129
*Set to the same as V165- VEGR receptor
kon_V121_R2 VEGF121 binding to VEGFR2 1.00e+7
kon_MMP9_LRP1 MMP9 binding to LRP1 9245
25
kon_MMP3_proMM
P9
MMP3 binding to proMMP9 10000
kon_VEGF_a2M VEGF binding to alpha-2-
macroglobulin
25
256,2
69
220
kon_VEGF_a2M_fas
t
VEGF fast binding to alpha-2-
macroglobulin
250
koff_TSP1_GAG TSP1 binding to glycosaminoglycan s
-1
0.1
25,26
,261
koff_TSP1_CD36 TSP1 binding to CD36 0.115
koff_TSP1_CD47 TSP1 binding to CD47 0.005
koff_TSP1_LRP1 TSP1 binding to LRP1 0.0025
koff_TSP1_B1 TSP1 binding to β1 integrin 0.05
koff_TSP1_VEGF TSP1 binding to VEGF 0.005
koff_TSP1_MMP3 TSP1 binding to MMP3 0.0022303
koff_V165_N1 VEGF165 binding to Neuropilin-1 0.001
259,2
60
koff_V165_N2 VEGF165 binding to Neuropilin-2 0.001
266–
268
koff_V165_R1 VEGF165 binding to VEGFR1 0.001
206
koff_V165_R2 VEGF165 binding to VEGFR2 0.001
207,2
08
koff_V165_GAG VEGF165 binding to
glycosaminoglycan
0.00069
101,2
57,25
8
koff_V121_R1 VEGF121 binding to VEGFR1 0.001
129
koff_V121_R2 VEGF121 binding to VEGFR2 0.001
221
koff_MMP9_LRP1 MMP9 binding to LRP1 0.00049
25
koff_MMP3_proMM
P9
MMP3 binding to proMMP9 0.001
koff_VEGF_a2M VEGF binding to alpha-2-
macroglobulin
1.0e-4
256,2
69
koff_VEGF_a2M_fa
st
VEGF fast binding to alpha-2-
macroglobulin
1.0e-4
kc_V165N_R2 Coupling of VEGFR2 and Neuropilin
(mol/cm
2
)
-
1
s
-1
1.00e+14
83,84
*Estimated in
83
using data from
84
.
kc_V165R2_N Coupling of VEGFR2 and Neuropilin 3.10e+13
kc_R1_N Coupling of VEGFR1 and Neuropilin 1.00e+14
129
*Set to the same as R2-N receptor
kc_CD36_R2 Coupling of CD36 and VEGFR2 3.10e+11
25
kc_CD36_B1 Coupling of CD36 and β1 integrin 3.10e+13
kc_CD47_R2 Coupling of CD47 and VEGFR2 3.10e+11
kdissoc_R2_N Coupling of VEGFR2 and Neuropilin s
-1
0.001
83,84
kdissoc_R1_N Coupling of VEGFR2 and Neuropilin 0.01
129
*Assumed to be slower dissociation than
R2-N.
kdissoc_CD36_B1 Coupling of VEGFR1 and Neuropilin 0.001
25
kdissoc_CD36_R2 Coupling of CD36 and VEGFR2 0.001
kdissoc_CD47_R2 Coupling of CD36 and β1 integrin 0.001
222
Degradation and Clearance Rates
The degradation rates and clearance rates are estimated by conversion from reported half-life time in literatures. The cleavage rate of TSP1 are
fitted to match experimental data in our previous work
25
. The catalytic rate of the activation of proMMP9 by MMP3 and the cleavage of
VEGF165 by MMP were previously reported in modeling works by Vempati
26,261
.
kdeg_aV Degradation rate of bevacizumab s
-1
4.415e-8
kdeg_VEGF Degradation rate of VEGF 1.93e-4
209
kdeg_TSP1 Degradation rate of TSP1 3.3e-4
25
kdeg_MMP Degradation rate of MMP 0.0012
kdeg_TSP1mim Degradation rate of ABT-510 1.60e-4
143
*Assumed to be same as clearance rate.
c_aV Clearance rate of bevacizumab in
blood
3.82e-7
270
*According to FDA label, Bevacizumab
has a 21 days half-life.
c_aV_VEGF Clearance rate of VEGF-bound
bevacizumab in blood
3.82e-7
270
*Assumed to be same as free
Bevacizumab.
c_VEGF Clearance rate of bevacizumab in
blood
0.0010797
138
c_TSP1 Clearance rate of TSP1 in blood 0.00033
25
* Assumed to be same as degradation
rates.
c_MMP Clearance rate of MMP in blood 0.0012
c_TSP1mim Clearance rate of ABT-510 in blood 1.60e-4
143
*According to the reported 1.2 hours half-
life in circulation of human body.
c_a2M Clearance rate of alpha-2-
macroglobulin in blood
3.85e-5
105
223
c_a2M_fast Clearance rate of alpha-2-
macroglobulin fast-binding in blood
3.85e-3
k_TSP1cleave The cleavage rate of TSP1 through
proteolysis
s
-1
0.00386
25,26
,261
k_act_MMP3_proM
MP9
A Michaelis-Menten Activation
constant of the activation of MMP9
by MMP3
s
-1
0.0019
kp_mmp The proteolysis rate of VEGF by
MMPs
(mol/l)
-1
s
-1
631
Receptor Numbers
The density of VEGF receptors and co-receptors on endothelial and tumor cells are systematically reported in our previous work
205
, which are
taken from in vitro and in vivo measurements using quantitative flow cytometry
131
. Currently, there is a paucity of quantitative data for the
number of TSP1 receptors on endothelial and tumor cells. Thus, we used the reported qualitative data in Human Protein Atlas to estimate the
values as mentioned in Method Section. The numbers of receptors on the endothelial cell are set to be half of that for parenchymal cells (tumor
cells or muscle fibre cells), assuming equal distribution on the luminal and abluminal surfaces.
CD36_number_tum CD36 receptor number on tumor cell receptors/c
ell
2500
*Estimated according the qualitative data
shown in Human Protein Atlas.
CD47_number_tum CD47 receptor number on tumor cell 10000
LRP1_number_tum LRP1 receptor number on tumor cell 5000
B1_number_tum β1 integrin number on tumor cell 10000
CD36_number_disE
C
CD36 receptor number on tumor
endothelial cell
1250
CD47_number_disE
C
CD47 receptor number on tumor
endothelial cell
5000
224
LRP1_number_disE
C
LRP1 receptor number on tumor
endothelial cell
2500
B1_number_disEC β1 integrin receptor number on tumor
endothelial cell
5000
CD36_number_norm
EC
CD36 receptor number on normal
endothelial cell
1250
CD47_number_norm
EC
CD47 receptor number on normal
endothelial cell
1250
LRP1_number_norm
EC
LRP1 receptor number on normal
endothelial cell
625
B1_number_normEC β1 integrin receptor number on
normal endothelial cell
2500
CD36_number_myo CD36 receptor number on skeletal
muscle fiber cell
2500
CD47_number_myo CD47 receptor number on skeletal
muscle fiber cell
2500
LRP1_number_myo LRP1 receptor number on skeletal
muscle fiber cell
1250
B1_number_myo β1 integrin receptor number on
skeletal muscle fiber cell
5000
R1_number_tum VEGFR1 receptor number on tumor
cell
1100
205
*VEGF receptor density followed our
previous studies which uses the in vivo
and in vitro measurements using
quantitative flow cytometry.
R2_number_tum VEGFR2 receptor number on tumor
cell
550
225
N1_number_tum Neuropilin-1 receptor number on
tumor cell
39500
N2_number_tum Neuropilin-2 receptor number on
tumor cell
39500
R1_number_disEC VEGFR1 receptor number on tumor
endothelial cell
3750
R2_number_disEC VEGFR2 receptor number on tumor
endothelial cell
300
N1_number_disEC Neuropilin-1 receptor number on
tumor endothelial cell
20000
N2_number_disEC Neuropilin-2 receptor number on
tumor endothelial cell
20000
R1_number_normEC VEGFR1 receptor number on normal
endothelial cell
550
R2_number_normEC VEGFR2 receptor number on normal
endothelial cell
350
N1_number_normE
C
Neuropilin-1 receptor number on
tumor endothelial cell
17000
N2_number_normE
C
Neuropilin-2 receptor number on
tumor endothelial cell
0
R1_number_myo VEGFR1 receptor number on skeletal
muscle fiber cell
0
R2_number_myo VEGFR2 receptor number on skeletal
muscle fiber cell
0
226
N1_number_myo Neuropilin-1 receptor number on
skeletal muscle fiber cell
34500
N2_number_myo Neuropilin-2 receptor number on
skeletal muscle fiber cell
0
Transportation Rates
The vascular permeability of VEGF uses the rates estimated in the first whole body model of VEGF basing on the size of molecule
74
. The
lymphatic flow was introduced into the model in another work later
138
.
k_lymph_dis The transport rate through lymphatic
flow from tumor to blood
cm
3
/s 0
138
*Assumed to be negligible.
k_lymph The transport rate through lymphatic
flow from normal tissue to blood
0.0333333
kperm_B_T_VEGF Microvascular permeability to VEGF
in the tumor
cm/s 4.0e-7
74
kperm_B_N_VEGF Microvascular permeability to VEGF
in the normal tissue
4.0e-8
kperm_B_T_aV Microvascular permeability to
Bevacizumab in the tumor
3.0e-7 *Assumed to be smaller than VEGF
kperm_B_N_aV Microvascular permeability to
Bevacizumab in the tumor
3.0e-8
Properties of the Anti-angiogenic Drugs
The binding properties of VEGF are directly measured in an experimental study
211
.
antiVEGF_dosage Administration dosage of
Bevacizumab
mg/kg 10
227
antiVEGF_MW Molecular weight of Bevacizumab Da 150000
infTime_antiVEGF Infusion time of Bevacizumab s 5400
* infusion in 1.5 hours.
Kd_V165_antiVEGF The dissociation constant of
Bevacizumab and VEGF165
M 2.2e-9
211
Kd_V121_antiVEGF The dissociation constant of
Bevacizumab and VEGF121
2.2e-9
koff_V165_antiVEG
F
The binding of Bevacizumab and
VEGF165 (koff)
s
-1
2.0e-4
koff_V121_antiVEG
F
The binding of Bevacizumab and
VEGF165 (koff)
2.0e-4
†
Here, M = moles/liter of interstitial fluid available to soluble species.
228
Appendix C. Supplementary Information of Xenograft Tumor Growth Model
Figure C-1: Comparison of experimental data with the baseline model predictions using
median values for the fitted parameters (Baseline values). Grey shading area indicates the time
period for anti-VEGF treatment. Blue color represents the control group. Red color represents
Bevacizumab treatment group. For the Fujita dataset, the Red represents 4mg/kg dosage
Bevacizumab treatment and the Green means 2mg/kg Bevacizumab treatment. The solid line is
the model prediction with dots indicating experimental measurements.
229
Figure C-2: Predicted outcome of anti-VEGF treatment ad hypothetical treatments targeting
tumor and endothelial cells VEGF signaling. Grey shading area indicates the time period for
treatments.
230
Figure C-3: Experimental data for combination therapies in an MDA-MB-435 mouse
xenograft model.
Abstract (if available)
Abstract
Angiogenesis is the formation of new blood vessels from pre-existing vessels and is an important hallmark of cancer. This process promotes tumor growth and progression by providing oxygen, nutrients, and waste exchange and allowing tumor cells to establish subsequent metastasis. Several angiogenic factors that affect the extent of tumor vascularization have been actively studied and are commonly categorized as pro- and anti-angiogenic factors. Pro-angiogenic factors such as vascular endothelial growth factor (VEGF) and fibroblast growth factor 2 (FGF2), bind to specific receptors to initiate pro-angiogenic signaling promoting cell proliferation, migration, and blood vessel formation. On the other side, anti-angiogenic factors, like thrombospondin-1 (TSP1) and platelet factor 4 (PF4), impede pro-angiogenic signaling and induce anti-angiogenic signaling to oppose angiogenesis. Considering the importance of angiogenesis in tumor development, anti-angiogenic therapeutics were designed to inhibit vascularization and tumor growth. However, anti-angiogenic therapeutics to date showed limited success on the clinic side due to low efficacy, the development of resistance, or toxicity. These drawbacks inspired the efforts to better understand tumor angiogenesis and optimize anti-angiogenic cancer therapy. In this work, I present multiple developed systems biology models that incorporate the interaction networks of potent angiogenic factors (VEGF, FGF2, TSP1, and PF4) to investigate various anti-angiogenic therapies. The models provide novel insights into the regulation of tumor angiogenesis and the observed response to anti-angiogenic therapies tested in preclinical and clinical studies. Meanwhile, several potential prognosis biomarkers are identified for precision medicine. Ultimately, such models can serve as simulation tools to inform the development of effective anti-angiogenic cancer therapy.
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Asset Metadata
Creator
Li, Ding
(author)
Core Title
Mechanistic modeling of angiogenic factors network and cancer therapy
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Degree Conferral Date
2021-08
Publication Date
07/27/2021
Defense Date
04/27/2021
Publisher
University of Southern California
(original),
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(digital)
Tag
angiogenesis,cancer therapy,mechanistic modeling,OAI-PMH Harvest
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English
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(provenance)
Advisor
Finley, Stacey (
committee chair
), D'Argenio, David (
committee member
), MacLean, Adam (
committee member
), Mumenthaler, Shannon (
committee member
)
Creator Email
dli588@usc.edu,glenndingli@gmail.com
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Tags
angiogenesis
cancer therapy
mechanistic modeling