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Understanding the impact of cell-to-cell variability on intracellular signaling in CAR cells through mathematical modeling
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Understanding the impact of cell-to-cell variability on intracellular signaling in CAR cells through mathematical modeling
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Content
Understanding the Impact of Cell-to-Cell Variability on Intracellular Signaling in CAR Cells
through Mathematical Modeling
by
Vardges Tserunyan
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY
(COMPUTATIONAL BIOLOGY AND BIOINFORMATICS)
May 2024
Copyright 2024 Vardges Tserunyan
ii
Acknowledgements
That I am writing this dissertation, I must first and foremost thank my academic advisor,
Dr. Stacey Finley. Ever since joining her research group, I have seen her desire to create a
welcoming and supportive environment for intellectual growth, where her dedication to
conducting expert research was always in harmony with commitment to our personal well-being.
It is a privilege to have spent the last few years under her guidance and seen her mentor us through
these challenging times. Whether it was the global pandemic, the accompanying political crises
and the succession of personal difficulties, Dr. Finley has given me all the professional and mental
support I have asked for (and certainly, more) and never left me in a position of being confused or
directionless. It is only this that allowed me to focus on my research projects, which she helped to
formulate and finish through.
Next, I would like to thank other members of Dr. Finley’s Computational and Systems
Biology Lab with whom I overlapped during my time here — Dr. Sahak Makaryan, Dr. Jess Wu,
Dr. Ding Li, Dr. Min Song, Dr. Patrick Gelbach, Dr. Colin Cess, Dr. Geena Ildefonso, Niki
Tavakoli, Holly Huber, Diamond Mangrum, Lynn Cherchia, Handan Çetin, Ariella Simoni and
Neel Tangella. While initially meeting most of them on Zoom, it was a pleasure to spend time
together in the lab. Finally, even though I never met Dr. Jennifer Rohrs in person, I would like to
extend my sincere gratitude to her, since my dissertation work was to a large extent inspired by
her own substantial progress in mathematical modeling of CAR T cell signaling.
I would also like to thank the members of my thesis committee — Dr. Nicholas Graham,
Dr. Adam MacLean and Dr. Steve Kay. The schedule of a faculty member is always full of
commitments, and I deeply appreciate that they agreed to add this to their ever-growing list.
iii
Finally, I would like to thank my parents, without whom I would have never come this far
in my academic journey. I would also like to thank the rest of my family (especially, A. and A.)
— graduate school can be a demanding task, and it is thanks to them that I never felt alone on the
way. Finally, I would like to thank friends, both near and far, for the fond memories. And although
I am grateful to all of them, it is V. I must thank the most — without his support, this whole feat
would have been a lot harder.
iv
Table of Contents
Acknowledgements .........................................................................................................................
List of Tables ..................................................................................................................................
List of Figures ...............................................................................................................................
Abstract ..........................................................................................................................................
Chapter 1. Introduction ...................................................................................................................
1.1. Chimeric antigen receptor therapy .........................................................................
1.2. Structure of the CAR .............................................................................................
1.3. Immune cell signaling ............................................................................................
1.4. Systems biology .....................................................................................................
1.5. Analyzing biological variability ............................................................................
1.6. Dissertation outline ..............................................................................................
Chapter 2. Modeling predicts differences in chimeric antigen receptor T cell
signaling due to biological variability .........................................................................
2.1. Abstract ................................................................................................................
2.2. Introduction ..........................................................................................................
2.3. Methods ................................................................................................................
2.3.1. CAR-induced ERK signaling model ..........................................................
2.3.2. Monte Carlo simulations ............................................................................
2.3.3. Gradient-boosted tree predictor ................................................................
2.3.4. Permutation importance scores .................................................................
2.3.5. Parameter selection by optimization .........................................................
2.4. Results ..................................................................................................................
2.4.1. Population response with variable antigen exposure ................................
2.4.2. Population response with variable kinetic parameters ..............................
2.4.3. Mechanism of CD28-induced changes in population behavior .................
2.4.4. Sensitivity analysis of activation time .......................................................
2.4.5. Parameter selection by constrained optimization ......................................
2.5. Discussion ............................................................................................................
Chapter 3. Computational analysis of 4-1BB-induced NFκB signaling suggests
improvements to CAR cell design ..............................................................................
3.1. Abstract ................................................................................................................
3.2. Introduction ..........................................................................................................
3.3. Methods ...............................................................................................................
3.3.1. Model structure .........................................................................................
3.3.2. Activation profiles and dose response curves ...........................................
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3.3.3. Sensitivity analysis ....................................................................................
3.3.4. Monte Carlo simulations ...........................................................................
3.3.5. Mutual information ...................................................................................
3.4. Results .................................................................................................................
3.4.1. Model structure and dose response ...........................................................
3.4.2. Sensitivity of the output to kinetic parameters
and protein concentrations ........................................................................
3.4.3. Mutual information carried by the NFκB
pathway about antigen concentration .......................................................
3.4.4. Suggested improvements to CAR design .................................................
3.5. Discussion ...........................................................................................................
Chapter 4. Information-theoretic analysis of a model of CAR-4-1BB-mediated
NFκB activation ..........................................................................................................
4.1 Abstract .................................................................................................................
4.2. Introduction .........................................................................................................
4.3. Methods ................................................................................................................
4.3.1. Network structure ......................................................................................
4.3.2. Noise in the signaling pathway .................................................................
4.3.3. Candidate antigen distributions .................................................................
4.3.4. Mutual information ....................................................................................
4.3.5. Channel capacity .......................................................................................
4.3.6. Assessing error rates .................................................................................
4.4. Results .................................................................................................................
4.4.1. Channel capacities ....................................................................................
4.4.2. Signal discernibility ..................................................................................
4.4.3. Trial distributions ......................................................................................
4.5. Discussion ............................................................................................................
Chapter 5. Conclusion ...................................................................................................................
5.1. Summary ..............................................................................................................
5.2. Future directions ..................................................................................................
5.3. Concluding outline ..............................................................................................
References ....................................................................................................................................
Appendix A .................................................................................................................................
Appendix B .................................................................................................................................
Appendix C .................................................................................................................................
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List of Tables
Table 2.1. Effects of CD28 mechanisms on predicted cell activation .........................................
Table 2.2. Performance of the gradient-boosted tree ensemble on various datasets ...................
Table 2.3. Comparison of optimized systems with antigen variability .......................................
Table 2.4. Comparison of optimized systems with kinetic variability ........................................
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vii
List of Figures
Figure 1.1. Growing complexity of CAR designs .........................................................................
Figure 1.2. Iterative experimentation and computation workflow of systems biology .................
Figure 2.1. Activation of CAR T cells exposed to varying amounts of antigen ..........................
Figure 2.2. Activation of CAR T cells with varied kinetic parameters .......................................
Figure 2.3. Activation of CAR T cells considering alternative CD28 signaling
mechanisms ...............................................................................................................
Figure 2.4. Permutation importance scores for select kinetic parameters used in
the gradient-boosted tree model to predict cell activation times ...............................
Figure 2.5. Results from constrained optimization ......................................................................
Figure 2.6. Activation of CAR T cells with optimized parameter values ....................................
Figure 2.7. Activation of CAR T cells with varying kinetic parameters and
optimized values of Kcat_ZAP and Kcat_LCKPU_CD3z .........................................
Figure 3.1. A schematic outline of events leading up to the nuclear translocation
of canonical NFκB ....................................................................................................
Figure 3.2. Activation profiles for IKKβ and NFκB in response to antigen binding
the CAR ....................................................................................................................
Figure 3.3. Dose response curves for IKKβ and NFκB in response to antigen binding
the CAR ....................................................................................................................
Figure 3.4. eFAST total sensitivity indices of model output with respect to model
parameters .................................................................................................................
Figure 3.5. Information transduction along the canonical NFκB pathway ..................................
Figure 3.6. Relative changes in the mutual information ..............................................................
Figure 3.7. Dose response curves for IKKβ and NFκB in response to antigen binding
to the CAR with modified expression levels ............................................................
Figure 4.1. A schematic outline of events leading up to the nuclear translocation of
canonical NFκB .........................................................................................................
Figure 4.2. Channel capacity of CAR-4-1-BB-mediated NFκB activation ..................................
Figure 4.3. Ability of correctly distinguishing contrasting antigen concentrations
based on NFκB activation .........................................................................................
Figure 4.4. Fidelity of information transmission for different distributions of antigen
concentration .............................................................................................................
Figure 4.5. Fidelity of information transmission for different distributions of antigen
concentration when deactivation of IKKβ is disabled ...............................................
Supplementary Figure 2.1. Schematic of the CAR T cell signaling model .............................
Supplementary Figure 2.2. Dose response curves of cell activation times ..............................
Supplementary Figure 2.3. Permutation importance scores for kinetic parameters used
for creating a gradient-boosted tree model predicting cell activation times ...........
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Supplementary Figure 2.4. Comparison of activation of CAR T cells with optimized
parameter values .....................................................................................................
Supplementary Figure 2.4. Comparison of activation of CAR T cells with optimized
parameter values ......................................................................................................
Supplementary Figure 3.1. Distribution of antigen concentrations and peak NFκB
nuclear concentrations .............................................................................................
Supplementary Figure 3.2. Dose response curves of K-63 ubiquitin-bound TAB2 and
NEMO with default initial concentration or 50% underexpression of TAB2 .........
Supplementary Figure 3.3. Activation profiles for IKKβ and NFκB in response to
antigen binding the CAR with disabled deactivation of IKKβ ................................
Supplementary Figure 3.4. The transduction of information along the canonical
NFκB pathway with disabled IKKβ deactivation ....................................................
Supplementary Figure 4.1. Time courses for NFκB nuclear abundance induced by
different antigen concentrations ..............................................................................
Supplementary Figure 4.2. SGBN schematic of the model .....................................................
Supplementary Figure 4.3. Different distributions of antigen concentration for probing
the fidelity of CAR-4-1BB-mediated NFκB activation ..........................................
Supplementary Figure 4.4. Example of computing channel capacity ......................................
Supplementary Figure 4.5. Deteriorating ability to discern contrasting signals with
increasing extrinsic noise ........................................................................................
Supplementary Figure 4.6. Mutual information between the 100% antigen-positive
distribution and various metrics of pathway activation ...........................................
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Abstract
Chimeric antigen receptor (CAR) cell therapy is a novel approach to cancer
immunotherapy, which seeks to engineer immune cells with the ability to recognize and combat
tumors. Advancing this mode of therapy hinges upon understanding signaling processes within
CAR cells initiated upon encountering a target. This dissertation examines quantitative aspects of
CAR-mediated intracellular signaling, focusing on the influence of cell-to-cell variability on
signaling processes.
In the first chapter, I utilize mathematical modeling to examine CAR-CD28-mediated
signaling in heterogeneous CAR cell populations. I find that CD28 cosignaling increases the
potency of cell activation while reducing population-wide variance. Furthermore, I find that
enhancing the catalytic activity of lymphocyte-specific protein tyrosine kinase could achieve a
similar effect without necessitating CD28. In the second chapter, I focus on developing a
computational model of CAR-4-1BB-mediated NFκB signaling. Detailing the structure and
behavior of the model, I identify potential manipulations, such as overexpressing the protein
NEMO, to fine-tune the NFκB-mediated response. In the third chapter, I leverage information
theory to evaluate the fidelity of CAR-4-1BB-mediated NFκB activation. I quantify the impact of
extrinsic noise on the ability of the pathway to accurately transmit signals, finding that noisiness
tends to result in pathway underactivation. I also find that disabling the self-deactivation
mechanism of the protein IKKβ can greatly increase the accuracy of NFκB signaling.
Ultimately, the framework presented in this dissertation underscores the importance of
integrating mathematical methods into the study of CAR therapy to both understand observed
phenomena and drive CAR cell development.
1
1. Introduction
1.1. Chimeric Antigen Receptor Therapy
Adoptive cell therapy (ACT) has emerged in the recent decades as a novel approach to
cancer treatment (Cohen et al. 2017). Premised on utilizing the native anti-tumor response of the
immune system, it seeks to use immune cells transfused into the patient’s bloodstream as vehicles
that either kill cancerous targets directly or initiate a concerted immune response from the
recipient’s immunity. The earliest approach to ACT is the transfer of autologous lymphocytes.
Autologous transfer operates by resecting the tumor, isolating tumor-infiltrating lymphocytes and
transferring them back into the patient’s body following in vitro expansion. This method can be
effective in early stages of disease, but not in advanced-stage tumors. One recurring issue is the
fact that isolating cancer-specific tumor-infiltrating cells can be challenging, while it is also
difficult to maintain and expand them ex vivo.
Later developments in ACT gave rise to chimeric antigen receptor (CAR) therapy (Met et
al. 2019; Srivastava and Riddell 2015). Where autologous transfer takes the more passive approach
of trying to find and expand an already existing antitumor lymphocyte lineage, CAR therapy takes
a more proactive engineering perspective. Specifically, CAR therapy is based on immune cells
genetically modified to express a receptor with specificity against the characteristic antigen of a
target cancer cell population. The underlying assumption is that the antigen-specific CAR would
direct engineered immune cells against the cancerous target. Following this, signaling events
initiated as the CAR binds the antigen would cause cell activation. This activation manifests in the
release of cytotoxic peptides onto the target cell, such as granzymes and perforins (Benmebarek et
al. 2019). In addition, activated cells release a range of cytokines and chemokines, attracting other
CAR cells and native immune cells to the same location and resulting in an amplified response.
2
While several CAR therapies have been approved by the US Food and Drug Administration
(FDA) as of 2023, their use in routine medical practice is limited to liquid tumors (Johnson and
Abramson 2022; Sterner and Sterner 2021). Reasons cited for their inefficacy against solid tumors
include cell exhaustion in the immunosuppressive tumor microenvironment, as well as poor
penetration of CAR cells into the depth of the tumor. Furthermore, CAR therapy is commonly
associated with several side effects, such as cytokine release syndrome, tumor lysis syndrome, and
neurotoxicity. Hence, ongoing research seeks to mitigate these side effects while expanding the
clinical usage of CAR therapy.
1.2. Structure of the CAR
The defining feature of CAR therapy is the engineered transmembrane receptor (Srivastava
and Riddell 2015). Initial designs of CAR molecules featured only two domains, the antigen
recognition domain on the extracellular side and the signaling domain on the cytoplasmic side,
joined through a short transmembrane linker (Fig. 1.1A). The antigen recognition domain is
derived from the single chain variable fragment (scFv) of monoclonal antibodies, endowing the
CAR cell with specificity against the targeted tumor cell population. The cytoplasmic signaling
domain is derived from the CD3ζ signaling domain of native T cell receptors (TCR). This initial
design, now termed "first-generation CAR", proved ineffective during in vivo experiments
(Subklewe, von Bergwelt-Baildon, and Humpe 2019). In hindsight, this is not unexpected, since
immune cell activation is mediated not solely through the antigen-recognizing TCR but the
concerted interaction of multiple stimulatory and inhibitory co-receptors. These co-receptors
modulate lymphocyte activity through interactions with ligands on the surface of antigen-
3
presenting cells (Bertram, Dawicki, and Watts 2004). One example of a stimulatory co-receptor is
CD28, which is necessary for T cell activation in addition to TCR signals (Lenschow, Walunas,
and Bluestone 1996). Another example is 4-1BB, which is recognized for mediating long-term
survival of activated lymphocytes and inhibiting apoptosis (Finney, Akbar, and Lawson 2004).
Later efforts in CAR design took advantage of this knowledge by adding signaling domains from
these and other coreceptors to the engineered receptor (Fig. 1.1B). Termed "second-generation
CARs", these feature an extracellular recognition domain, a transmembrane linker, and a costimulatory signaling domain, followed by the CD3ζ domain (Srivastava and Riddell 2015).
Second-generation CARs became the foundation of successful CAR cell therapy and have gained
Figure 1.1. Growing complexity of CAR designs.
Different approaches to designing a CAR. (A) First-generation CAR, with only a CD3ζ
signaling domain; (B) Second-generation CAR with an added cosignaling domain; (C)
Third-generation CAR with multiple cosignaling domains; (D) Fourth-generation CAR
with an NFAT-dependent expression cassette,
4
FDA approval for treatment against acute lymphoblastic leukemia (ALL) and B cell lymphoma
(BCL) (Johnson and Abramson 2022).
While these approaches utilize either CD28 or 4-1BB costimulatory domains, ongoing
efforts explore the potential of other candidates, such as ICOS and OX40 (Adami and Maher 2021;
Tan et al. 2022). A conceptually novel approach is to increase the number of co-signaling domains
in the CAR ("third-generation CARs", Fig. 1.1C), hypothesizing that two costimulatory domains
in addition to the CD3ζ will achieve a more potent response and longer survival times (Srivastava
and Riddell 2015). Another direction is to engineer activation-dependent expression cassettes
parallel to the CAR, so that CAR activation would cause production of a desired mix of stimulatory
cytokines ("fourth-generation CARs", Fig. 1.1D) (Chmielewski and Abken 2015). These
approaches highlight the continuing research in furthering CAR therapy.
1.3. Immune Cell Signaling
Signaling domains included in the structure of the CAR trigger cell activation via different
but overlapping mechanisms (Tserunyan and Finley 2023). The central enzyme in early CD3ζinduced signaling events is lymphocyte kinase (LCK) (Nika et al. 2010). While LCK activity can
be upregulated by autophosphorylation, a significant part of its cellular pool exists in a basally
active state. As in the case of native TCR receptors, antigen recognition by the CAR triggers
recruitment of LCK from the cytoplasm to the plasma membrane near the immunological synapse
(Bommhardt, Schraven, and Simeoni 2019). Here, LCK phosphorylates immunoreceptor tyrosinebased activation motifs (ITAMs) of CD3ζ. Once phosphorylated, ITAMs serve as docking stations
for a range of enzymes, which then form signalosomes and trigger subsequent cascades (Acuto,
5
Di Bartolo, and Michel 2008). One such enzyme is ZAP70, which activates ERK signaling via the
Linker of activated T cells (LAT) signalosome (Djeu, Jiang, and Wei 2002).
The co-signaling domain derived from the cytoplasmic portion of CD28 plays a similar
role of enzyme recruitment (Tian et al. 2015). LCK is one of those enzymes, binding to the prolinerich motif of CD28. Upon binding, LCK phosphorylates specific tyrosine residues on CD28,
making them accessible for other enzymes and adaptor proteins. One example of such an adaptor
is the p85 subunit of the phosphoinositide 3-kinase (PI3K) enzyme complex (Prasad et al. 1994).
In addition, the interaction between CD28 and the Growth factor receptor-bound protein 2 (Grb2)
serves as a point of convergence for the extracellularsignal-regulated kinase (ERK) pathway (Kim,
Tharayil, and Rudd 1998). Specifically, Grb2 triggers a cascade of interactions culminating in the
double phosphorylation of the ERK molecule. A combination of experimental and quantitative
analyses has shown that CD28 also increases the rate of catalytic phosphorylation of ITAMs on
CD3ζ by LCK, which plays a crucial role in CD28-mediated enhancement of ERK signaling in
CAR-CD28 cells (Rohrs et. al 2020).
The cytoplasmic domain of the 4-1BB costimulatory receptor is typically less potent in its
cytotoxic effects than CD28 (Milone et al. 2009). Nevertheless, it can induce cell proliferation and
long-term survival in CAR cells. Thanks to this effect, it can help achieve greater tumor reduction
during in vivo experiments by maintaining steadier levels of CAR cells long after the initial
transfusion. This is achieved by 4-1BB's recruitment of TNF receptor-associated factor (TRAF)
proteins, which then activate the nuclear factor κB (NFκB) pathway (Zapata et al. 2018). While
the so-called canonical NFκB pathway is a positive regulator of multiple stimulatory cytokines,
the non-canonical pathway has an anti-apoptotic effect thought to be responsible for 4-1BB's
positive impact on cell survival (Philipson et al. 2020).
6
Research into signaling properties has increased our understanding of the mechanisms by
which costimulatory molecules demonstrably enhance the potency of CAR cells. For example,
longer survival times characteristic of CAR-4-1BB cells have been tied to upregulation in NFκBregulated genes (Philipson et al. 2020). Thus, further studies exploring signaling pathways utilized
by cosignaling domains could provide mechanistic insight into observed properties of CAR cells
and point to potential avenues for further engineering.
1.4. Systems biology
Systems biology is a novel perspective on life science research that seeks to combine
experimental and mathematical approaches to gain a more holistic understanding of biological
systems (Kitano 2002). This involves parallel streams of experimentation to obtain data describing
the system, along with mathematical modeling to obtain quantifiable relations between system
components (Fig. 1.2). The notable advantage of mathematical modeling is that it enables to run
computational simulations, helping elucidate biological phenomena and generate testable
hypotheses while avoiding expensive and prolonged experimentation. Approaches to
mathematical modeling include data-driven models, which derive insight from statistical trends in
datasets, and Boolean models, which represent components of complex biological networks as
binary on/off states (Macklin 2019; R.-S. Wang, Saadatpour, and Albert 2012). Ordinary
differential equation (ODE)-based modeling of biochemical processes is another method with
distinct advantages (Raue et al. 2013). First, by clearly delineating biochemical reactions occurring
in the system and translating them into ODEs, we can quantify the mechanistic and causal
relationships between system components. This stands in contrast to data-driven modeling
7
approaches, which underline statistical trends and correlations between system components, but
do not provide causal explanations for observed patterns. Secondly, ODEs allow to capture and
analyze the dynamic behavior of systems, providing insights into how variables change and
interact through time. Boolean models are limited in this respect since they represent states of the
system in terms of binary on/off values, omitting the fact that biological variables are continuous,
and hard thresholds are rarely observed. Thus, ODE-based mechanistic modeling provides distinct
benefits for manipulating model parameters and exploring in silico the full range of behaviors
exhibited by the system in different circumstances.
Advantages of ODE modeling have been leveraged by various research groups to gain
quantitative understanding of immune cell signaling. For instance, this approach proved effective
in characterizing the activation of the MAPK/ERK signaling pathway induced by the TCR (AltanBonnet and Germain 2005). In another case, an ODE-based model was used to explore the
Figure 1.2. Iterative experimentation and computation workflow of systems biology.
8
synergistic effects for the simultaneous application of radionuclide and CAR T therapies
(Adhikarla et al. 2021). Meanwhile, prior work in our group was successful in simulating the ERK
signaling pathway in CAR-CD28 T cells upon antigen binding (Rohrs et al. 2018). By calibrating
model parameters against data from phosphoproteomic measurements, this ODE-based model
achieved a close agreement between in silico predictions and experimental observations. We used
this correspondence to conduct quantitative comparisons between first-generation CAR T cells
featuring only the CD3ζ signaling domain and second-generation CAR T cells with an additional
CD28 co-stimulatory domain. We pinpointed mechanistic reasons which make second-generation
CARs more potent than first-generation CARs. This example demonstrates the utility of ODEbased quantitative modeling as an effective methodology for explaining biological behaviors and
generating testable hypotheses. As such, it provides a strong foundation for the work presented in
this dissertation.
1.5. Analyzing Biological Variability
Biological systems are widely recognized for their variability, with individual cells
displaying properties that are significantly different from population average (Eling, Morgan, and
Marioni 2019). Even within a population of phenotypically similar cells, there is a diversity of
protein expression patterns. In fact, such variability has been observed in T cell populations (Yuan,
Cheng, and Malek 2014). Thus, it is natural to expect that different sources of variability would
result in heterogeneous behaviors of individual cells in a population of CAR-engineered cells.
Prior research has evaluated how cellular noise affects cell signaling. These studies have
underlined two sources of noise (Lei et al. 2015). One is intrinsic noise, attributed to fluctuations
9
in reaction rates due to the stochastic Brownian motion of molecules in the cytoplasm and across
cellular compartments. The other source is extrinsic noise due to cell-to-cell variability in protein
concentrations. Both of these factors confound the signaling response of a population of cells,
making the activation level of secondary messengers a blurred reflection of the received signal
(Ladbury and Arold 2012). This phenomenon can be studied by utilizing methods from
information theory (Rhee, Cheong, and Levchenko 2012; Waltermann and Klipp 2011).
Information theory is a mathematical framework that analyzes signal transmission and
communication (Cover and Thomas 2012). Mutual information serves as a central concept in this
approach. It quantifies the amount of information, in bits, that two stochastic variables contain
about each other (Shannon 1948). Mutual information offers distinct advantages as a quantifiable
measure over other methods. First, unlike correlation, it is zero if and only if the variables are
independent. Second, it makes no underlying assumptions of linearity (unlike Pearson's correlation)
or monotonicity (unlike Spearman's correlation) (Schober, Boer, and Schwarte 2018).
Mutual information has found practical use in the domain of signal communication,
assessing relationships between the input signal and the transmitted message (Cover and Thomas
2012). Interestingly, biological signaling systems behave in ways similar to signal communication
systems (Topolewski and Komorowski 2021). Specifically, they initiate changes in the cellular
abundance of a secondary messenger proportionate to the abundance of a primary signaling
molecule. By regarding the primary messenger as the signal and the secondary messenger as the
pathway's output, past analyses have applied information-theoretic methods to analyze signal
transmission. In this approach, channel capacity is seen as a key property (Uda 2020). Channel
capacity is the maximum feasible rate of information transfer through the channel. Defined for a
hypothetical information-maximizing input, it is an inherent characteristic of the channel. Previous
10
experimental and quantitative investigations suggested that most biological pathways have a
channel capacity of around 1 bit, enabling pathways to differentiate only the presence and absence
of input signals (Topolewski and Komorowski 2021). Nevertheless, certain signaling systems
exhibit greater capacity. For example, apoptosis mediated by the tumor necrosis factor-related
apoptosis-inducing ligand (TRAIL) has a channel capacity of 3.41 bits, enabling finer control of
the percentage of cells undergoing apoptosis in response to a signal (Suderman et al. 2017).
Information-theoretic analyses have underlined the necessity of examining signaling
pathways in the context of variability. Given the importance of cell signaling to CAR cell
functionality, it becomes evident that utilizing information theory to understand CAR signaling
can provide a novel perspective on CAR cells.
1.6. Dissertation Outline
This dissertation seeks to apply computational systems biology approaches to analyze
signaling processes in CAR cells in the context of cell-to-cell variability. By focusing on extrinsic
noise, I analyze population-wide differences in cell signaling as the CAR cell is exposed to target
antigen.
In the first chapter, I explore the performance of first- and second-generation engineered
CAR T cells in the context of population-wide variability of kinetic parameters. I use a mechanistic
model of CAR-CD28-induced signaling to focus on the impact of the CD28 co-signaling domain
on the properties of the ERK pathway. My findings reveal that CAR-CD28 second-generation cells
have shorter activation times and reduced population-wide variability compared to first-generation
cells. To pinpoint the mechanism responsible for these effects, I isolate various routes by which
11
CD28 could affect ERK signaling and identify the effect of CD28 on kinetic parameters of LCK
enzymatic activity as the most important mechanism. Next, I utilize a black-box model based on
gradient-boosted trees (GBT) to identify kinetic parameters that are most important in determining
the dose response of ERK activation. By training GBTs on a synthetic dataset and applying
permutation importance scores, I pinpoint five parameters with significant downstream influence.
Finally, I employ a constrained optimization method to isolate parameters whose manipulation
would result in the greatest increase in ERK activity when the CAR is exposed to antigen.
Specifically, I find that enhancing the catalytic activity of LCK when phosphorylating CD3ζ
ITAMs would provide the greatest boost to ERK signaling.
In the second chapter, I introduce a novel mathematical model for NFκB signaling
mediated by CAR-4-1BB. My model recapitulates key dynamics observed in the system.
Specifically, consistent with experimental data, it shows that IκB kinase beta (IKKβ) transient
activity peaks at 10-15 minutes post-stimulation, with transient nuclear NFκB activity peaking at
around 30 minutes. I then use this model to explore the characteristics of CAR-4-1BB-mediated
signaling. I show that the magnitudes of transient peaks in active IKKβ and NFκB are responsive
to antigen concentration, while the timing of these peaks remains relatively consistent across
physiological stimulus concentrations. I also perform a global sensitivity analysis identifying
parameters that significantly influence pathway activation. This analysis indicates that the model
is constrained with respect to most parameters, with concentrations of the IKK complex and NFκB
having the most notable impact on NFκB activation. Next, I investigate the progression of
information transfer along successive levels of the NFκB cascade. This analysis leads to actionable
suggestions for increasing the accuracy of NFκB signaling initiated by CAR-4-1BB. Specifically,
I find that overexpressing NFκB's essential modulator protein (NEMO) and disabling self-
12
deactivation of IKKβ would greatly increase the mutual information between the antigen and
nuclear levels of NFκB. I hypothesize that this would manifest in greater precision of CAR-4-1BB
cell response against cancerous targets.
In the third chapter, I further the information-theoretic approach to CAR-4–1BB-mediated
NFκB activation. I start by evaluating the channel capacity for signal transmission, considering as
encoding measures both absolute nuclear NFκB concentration and its fold change compared to
baseline levels. I find that fold change is more effective in transmitting information about the
encountered antigen, exhibiting less dependence on extrinsic noise and approaching 1 bit for most
noise levels. I also examine the pathway's ability to distinguish contrasting signals, revealing that
most errors are "false negatives". Consistent with my analysis of channel capacity, fold change in
NFκB outperforms absolute abundance in discerning inputs accurately. Finally, I further analyze
the impact of disabling IKKβ deactivation on CAR-4-1BB-mediated NFκB activation. According
to my simulations, this manipulation increases channel capacity and enhances the pathway's ability
to discern contrasting signals with a lower error rate.
13
2. Modeling predicts differences in chimeric antigen receptor T cell signaling due to
biological variability
Portions of this chapter are adapted from: Vardges Tserunyan and Stacey D. Finley. Royal
Society Open Science, 2022
2.1. Abstract
In recent decades, chimeric antigen receptors (CARs) have been successfully used to
generate engineered T cells capable of recognizing and eliminating cancer cells. The structure of
CARs typically includes costimulatory domains, which enhance the T cell response upon antigen
encounter. However, it is not fully known how those co-stimulatory domains influence cell
activation in the presence of biological variability. In this work, we used mathematical modeling
to elucidate how the inclusion of one such costimulatory molecule, CD28, impacts the response of
a population of CAR T cells under different sources of variability. Particularly, we demonstrate
that CD28-bearing CARs mediate a faster and more consistent population response under both
target antigen variability and kinetic rate variability. Next, we identify kinetic parameters that have
the most impact on cell response time. Finally, based on our findings, we propose that enhancing
the catalytic activity of lymphocyte-specific protein tyrosine kinase (LCK) can result in drastically
reduced and more consistent response times among heterogeneous CAR T cell populations.
2.2. Introduction
T cells engineered to express a chimeric antigen receptor (CAR) have emerged as a novel
tool for combatting cancer by generating an immune response against cancer cells. The key step
14
in this immunotherapeutic approach is to produce T cells expressing an artificially designed CAR,
which activates the T cell upon encountering a target cancer cell (Met et al. 2019). To achieve this
goal, CARs feature an antigen recognition domain derived from a single-chain variable fragment
of a monoclonal antibody specific to the antigen of interest, while their cytoplasmic portion
includes different combinations of intracellular signaling domains (Akhoundi et al. 2021). The first
generation of CARs had a single cytoplasmic CD3ζ signaling domain attached to the recognition
domain by a transmembrane linker. Later advances in CAR design resulted in second-generation
CARs, which have an additional cosignaling domain originating from natively occurring
costimulatory receptors (Srivastava and Riddell 2015). The cytoplasmic domain of the CD28
costimulatory receptor is a commonly used example (Albinger, Hartmann, and Ullrich 2021).
Notably, adding CD28 cosignaling enhances proliferation and target cytotoxicity among the CAR
T cells (Zhao et al. 2015). In spite of significant progress, certain gaps in CAR T cell performance
remain. Importantly, current CAR T cell therapies are sufficiently effective only against liquid
tumors, while the performance against solid tumors is still limited (Sterner and Sterner 2021). In
addition, CD28-based CAR T cell therapies suffer from some major side effects (Namuduri and
Brentjens 2016), which can be life-threatening (Tabernero and Thompson 2018). These
considerations necessitate further improvements in the CAR T cell technology, with two broad
aims: on one hand, make CAR T cells efficient against a more extensive set of targets, on the other
hand, mitigate the observed side effects.
Mathematical modeling is an integral approach in systems biology and has been applied to
explain biological phenomena and generate testable hypotheses to guide experimental research
(Kitano 2002). One successful strategy of mathematical modeling is ordinary differential equation
(ODE)-based mechanistic modeling of biochemical processes (Raue et al. 2013). With suitable
15
estimates of interaction parameters and initial concentrations, these ODEs can be integrated to
obtain time courses for each component of the system. In the past, various research groups have
used ODE-based mechanistic modeling to gain quantitative insights into immune cell signaling
dynamics. For example, this approach was successful in describing native T cell receptor (TCR)-
induced activation of mitogen-activated protein kinase/extracellular signal-regulated kinase
(MAPK/ERK) signaling (Altan-Bonnet and Germain 2005). Our group has used this approach to
simulate the dynamics of ERK signaling in CAR T cells in response to antigen binding (Rohrs et
al. 2018). Particularly, by calibrating model parameters against data obtained by
phosphoproteomic measurements, it was possible to obtain a close correspondence between model
predictions and observed experimental dynamics. This was used to make quantitative comparisons
between first-generation CAR T cells with CD3ζ as the only signaling domain and secondgeneration CAR T cells with an additional CD28 co-stimulatory domain. Thus, modeling was
successfully used to gain quantitative insights into CAR T cells and augment experimental
knowledge.
Variability has been observed for essentially all dimensions of single-cell measurements,
with the ensemble behavior of a cell population not necessarily reflecting the behavior of an
individual cell (Altschuler and Wu 2010). Examples of variability caused by differential protein
expression have been observed among endogenous T cell populations, including T regulatory cells
(Yuan, Cheng, and Malek 2014), T helper cells and T killer cells alike (Zhang et al. 2019). The
influence of variable protein levels on the accuracy of the nuclear factor κB (NFκB) signal
transduction pathway in CAR cells was subject of a detailed analysis by our research group
(Tserunyan and Finley 2022a). Although we previously used our model of CAR-mediated
signaling to investigate the effects of variability in the expression levels of signaling proteins on
16
ERK activation (Cess and Finley 2020), other manifestations of variability remain to be addressed.
First, while in prior single-cell simulations, we assumed that the cell encounters a well-defined
antigen concentration on the surface of the target, this is not true in the therapeutic setting. For
example, prior measurements on primary myeloma cells found a range of values for the cell surface
concentration of CD19 (Nerreter et al. 2019), the signature antigen targeted by many CAR T cells.
Second, the chemical reactions that mediate signal transduction are subject to fluctuations not only
owing to stochastic protein expression, but also variability in cell state, local microenvironment
and the number of molecular collisions (McAdams and Arkin 1999; Harton and Batchelor 2017).
Thus, in our current work, we set out to investigate and compare the performance of firstgeneration and CD28-bearing second-generation CAR T cells under two modes of heterogeneity:
exposure to stochastic concentrations of the target antigen and stochastic kinetic rates of signaling
processes. Then, we quantify the importance of different kinetic parameters for determining the
ERK activation time of cells. Finally, based on these findings, we propose strategies to further
enhance the efficiency of CAR T cells in a therapeutic setting.
2.3. Methods
2.3.1. CAR-induced ERK signaling model
The ODE-based model used in our work was developed in Matlab by our research group
(Rohrs et. al 2018). The model includes four signaling modules: phosphorylation of
immunoreceptor tyrosine-based activation motif (ITAM) regions of the CD3ζ domain in response
to antigen binding, inhibitory activity of CD45 and SHP1, linker for activation of T cells (LAT)
17
signalosome formation and MAPK signaling (Appendix A, S. Fig. 2.1). This model was calibrated
on experimental data and gives accurate quantitative estimates of the levels of signaling species,
indicating that it constitutes a plausible description of the underlying biological process.
Particularly, it gives a mechanistic explanation for the increased cytoplasmic concentration of
doubly phosphorylated ERK (ppERK) in response to antigen binding to the CAR. We chose to use
ppERK as the primary model output, as it mediates many cell responses accompanying activation.
Given the non-transient "all-or-nothing" response typically displayed by ppERK in response to
antigen stimulation (Altan-Bonnet and Germain 2005), we termed all cells with more than half of
their total ERK pool in the doubly phosphorylated form as "active", with the time needed to reach
this state termed "activation time".
2.3.2. Monte Carlo simulations
In simulations of variable antigen concentration encountered by CAR T cells, we assumed
the antigen distribution (in units of molecules per µm2
) to be lognormal with location parameter µ
= 1.0 and scale parameter σ = 0.5. Our choice was based on the fact that most intracellular protein
abundances closely obey a lognormal distribution (Furusawa et al. 2005). We picked the location
and scale parameters to match the observed concentration of CD19, a frequent target of CAR T
cell therapies, which was measured to be between 0.16 molecules per µm2 and 5.2 molecules per
µm2 in primary myeloma cells (Nerreter et al. 2019). Simulations for the variability of kinetic
parameters were carried out by sampling each parameter from an independent normal distribution
with the mean equal to the parameter's accepted value and a standard deviation equal to a third of
the mean. These simulations were repeated for different antigen concentrations: 4.5 molecules per
18
µm2 ("low", close to experimentally observed) and 45 molecules per µm2 ("high", near saturating).
Monte Carlo simulations were run in Matlab for 100,000 iterations, since using this number
showed a reliable convergence with multiple random seeds.
2.3.3. Gradient-boosted tree predictor
The gradient-boosted tree (GBT) ensemble is a nonlinear machine learning method used
successfully for both regression and classification tasks. It is based on a succession of individually
weak decision trees. The first tree in the sequence fits the observed outcome directly, while each
successive tree fits the residual left from the collective prediction of its predecessors. Thus,
together, these decision trees achieve a significantly enhanced performance over a single decision
tree (James et al. 2013). We used the scikit-learn implementation of GBT in Python 3.7 (Pedregosa
et al. 2011) to obtain a predictor of cell activation time based on the values of kinetic parameters.
The synthetic dataset for training and testing was generated by using the ODE-based model to
compute ERK activation while simultaneously varying values of 48 impactful kinetic parameters.
These parameters were selected based on our prior findings, which showed that among all the
kinetic parameters of the model, only this subset has a measurable impact on ERK activation time
(Rohrs et al. 2018). We chose to simulate 100,000 different values for the kinetic parameter vector
since at this value, the accuracy of the predictor converged to a consistent number for all random
seeds we tested. The accuracy of the GBT model was adjusted by tuning hyperparameters and
evaluating resultant performance by fivefold cross-validation of the coefficient of determination
(R2
) and explained variance (EV). Notably, by analyzing the formulae for these metrics, it can be
shown that if the obtained R2 and EV are equal, then the predictor is unbiased.
19
2.3.4. Permutation importance scores
The permutation importance score for features is defined to be the decrease in the R2 value
of model prediction when a single feature value is randomly shuffled across all data points
(Pedregosa et al. 2011). This shuffling procedure preserves the marginal distribution of the feature
across the population but decouples it from the output value of the data point. The underlying
assumption is that if a feature is important in determining the output value, then this populationwide random shuffling will greatly reduce the predictive power of the model and result in a
proportionate drop in predictor performance as evaluated by the R2
. Similarly, since this
decoupling procedure is highly unlikely to improve the performance of a predictor, permutation
importance scores are expected to be non-negative. We used the scikit-learn library in Python 3.7
to calculate permutation importance scores with five different shufflings for each parameter, using
these iterative calculations to evaluate the statistical significance of obtained scores according to a
one-tailed t-test.
2.3.5. Parameter selection by optimization
Having quantified the importance of kinetic parameters, we had the goal of isolating a
handful of kinetic parameters whose manipulation would result in the largest reduction of ERK
activation time. For this purpose, we picked as candidates five parameters with the highest
permutation importance score among first-generation cells in low-antigen conditions, excluding
the affinity constant between the CAR and the antigen (to focus on intracellular processes). Next,
we used particle swarm optimization to minimize the following objective function:
�!"# + � ∑ &��� $!
$!,#
& ,
20
where TERK is ERK activation time, pi is the parameter value to be optimized, pi,0 is the default
value of that parameter, while λ is a user-defined constraint parameter varied across a range. The
structure of the objective function, inspired by the least absolute shrinkage and selection operator
(LASSO) parameter selection technique, allows us to optimize parameters with the goal of
decreasing activation time while changing as few parameters as possible. Particularly, it is long
established that the penalization of the sum of absolute values in classic LASSO results in
parameter selection by which only a subset of parameters is assigned non-zero values, while the
rest remain at zero (Tibshirani 1996). Since, in our case, the "default" value of the parameter is
non-zero, the use of the logarithm of fold change allows us to assign zero penalty to unchanged
values, while penalizing any change in proportion to the default value. We hypothesized that this
manner of penalization would result in parameter selection such that ERK activation times would
be reduced by manipulating as few parameters as possible. We varied λ starting from a large
enough value (λ = 10) so that the constraint term is prohibitive and prevents any change in
parameter values, down to a low enough value (λ = 0.1) to identify parameters that are consistently
selected by the optimization procedure.
21
2.4. Results
2.4.1. Population response with variable antigen exposure
We simulated the response of CAR T cell populations to a distribution of antigen
concentrations. Thus, 100,000 cells expressing either the first- or second-generation CARs were
stimulated in silico by an antigen concentration coming from a lognormal distribution, and their
activation times were recorded. Particularly, we obtained the number of CAR T cells that became
active during the simulation (Fig. 2.1A) and summarized their activation times in a histogram (Fig.
2.1B). The presence of the CD28 costimulatory domain in the second-generation CAR resulted in
a higher percentage of activated cells (82.6% versus 99.9% for first- and second-generation CAR
Figure 2.1. Activation of CAR T cells exposed to varying amounts of antigen.
Predicted activation for 105 cells with first- and second-generation CAR constructs stimulated
by the same stochastic antigen concentrations in silico. (A) Number of cells becoming active
or remaining inactive in the course of the 30 min simulation (no inactive cells were detected
among second-generation cells); (B) Distribution of the activation times for cells that became
active in the course of the 30 min simulation. Active
100 000
80 000
60 000
40 000
Number of Cells
20 000
10 000
8 000
6 000
4 000
2 000
Inactive
First-generation cells (CAR-CD3ζ)
Second-generation cells (CAR-CD28-CD3ζ)
0 5 10 15 20 25 30
Activation Time, min
A B
22
T cells, respectively), with a shorter mean activation time (18.5 min versus 8.9 min for first- and
second-generation cells, respectively). Additionally, the distribution of the population response
had a smaller standard deviation among second-generation cells compared to the first-generation
cells (3.0 min versus 5.4 min, respectively). This indicates that the CD28 domain not only confers
greater activation in a shorter time, but also provides for a more consistent response. These effects
of the CD28 domain can be attributed to the shifted dose response curve (Appendix A, S. Fig. 2.2).
2.4.2. Population response with variable kinetic parameters
Another source of variability we set out to explore is the variability in effective rates of the
reactions involved in signal transduction. Various sources of biological noise can result in
heterogeneity of effective kinetic rates across a genetically uniform population. Thus, it is
important to compare the performance of first- and second-generation CAR cells with variable
kinetic parameters to account for the consequences of this mode of heterogeneity. To investigate
the effects of kinetic variability, we performed simulations for first- and second-generation cells
with randomized values of 48 influential parameters in conditions of either "low" or "high" antigen
exposure. As evidenced by the resulting population distributions, the inclusion of the CD28
domain results in shorter mean activation time and a smaller standard deviation (Fig. 2.2A, B).
Particularly, in low-antigen conditions, more cells were activated in cells expressing the CAR that
contains the CD28 domain (76.7% versus 94.2%, for first- and second-generation cells,
respectively), with a shorter activation time (14.1 min versus 8.9 min, for first- and secondgeneration cells, respectively) and reduced standard deviation (6.5 min versus 5.2 min, for firstand second-generation cells, respectively). In high-antigen conditions, the presence of CD28
23
caused a similar change in the population response, albeit less pronounced (98.4% versus 98.9%
of cells were activated, with mean activation time of 4.5 min versus 3.3 min and standard deviation
of 2.8 min versus 2.0 min, for first- and second-generation cells, respectively).
Figure 2.2. Activation of CAR T cells with varied kinetic parameters.
Simulated activation for 105 cells with first- or second-generation CAR constructs stimulated by
the same antigen concentration (high or low) with stochastic kinetic parameters. (A) Number of
cells becoming active or remaining inactive in the course of the 30 min simulation with lowantigen stimulation; (B) Distribution of the activation times for cells from (A) that became active
in the course of the 30 min simulation; (C) Number of cells becoming active or remaining inactive
in the course of the 30 min simulation with high-antigen stimulation; (D) Distribution of the
activation times for cells from (C) which became active in the course of the 30 min simulation. Active
100 000
80 000
60 000
40 000
20 000
0
Number of Cells
Inactive
Active
Inactive
100 000
80 000
60 000
40 000
20 000
0
Number of Cells
0 5 10 15 20 25 30
Activation Time, min
0 5 10 15 20 25 30
Activation Time, min
25 000
20 000
15 000
10 000
5 000
25 000
20 000
15 000
10 000
5 000
A B
C D
24
2.4.3. Mechanism of CD28-induced changes in population behavior
A natural question to pursue is to determine the mechanism by which CD28 causes this
reduction in the mean and standard deviation of response times. Specifically, we focused on three
possible mechanisms: the interaction between CD28 and the adaptor protein Grb2, the interaction
between CD28 and the adaptor protein GADS (Watanabe et al. 2006), and the enhancement of the
catalytic activity of LCK by CD28 (Rohrs et al. 2020). The baseline model includes all three of
these CD28 mechanisms (Appendix A, S. Fig. 2.1). To isolate the contribution of each interaction,
we repeated simulations with stochastic kinetic parameters but with only one CD28-mediated
mechanism available at a time. We found that in the case of the isolated CD28/Grb2 interaction,
second-generation cells perform poorly compared to first-generation cells, with increased mean
activation time and standard deviation (Fig. 2.3A and Table 2.1). Similar results were obtained for
the case of the isolated CD28/GADS interaction (Fig. 2.3B and Table 2.1). On the other hand, with
the isolated effect of CD28 on LCK catalytic activity, we saw the reduced mean and standard
deviation that are the hallmark of second-generation cells (Fig. 2.3C and Table 2.1). Thus, based
on our simulations, the kinetic effect of CD28 on LCK activity is the leading mechanism of CD28's
role in influencing ERK activation. Overall, the interaction between CD28 and Grb2 or the
interaction between CD28 and GADS proved insufficient to bring about any improvement, while
CD28's effect on LCK's catalytic activity is shown to be necessary and sufficient.
25
Condition %-age cells active
Mean activation time
(std. dev.), min
Low
Antigen
High
Antigen
Low
Antigen
High
Antigen
CD3ζ-only CAR 76.95 98.7 14.16 (6.49) 4.52 (2.83)
CD28/Grb2 interaction only 60.93 98.35 16.57 (6.55) 5.64 (3.51)
CD28/GADS only 60.93 98.35 16.58 (6.55) 5.64 (3.51)
CD28-mediated LCK effects only 94.31 99.08 9.08 (5.10) 3.38 (1.95)
Table 2.1. Effects of CD28 mechanisms on predicted cell activation.
0 5 10 15 20 25 30 Inactive Active
Figure 2.3. Activation of CAR T cells considering alternative CD28 signaling mechanisms.
Predicted activation for 105 cells with first- and second-generation constructs with one CD28
signaling mechanism implemented at a time. (A) CD28 exclusively associates with Grb2; (B)
CD28 exclusively associates with GADS; (C) CD28 exclusively affects the activity of LCK. Bar
plots show the number of cells becoming active or remaining inactive in the course of the 30 min
simulation. Histograms show the distribution of the activation times for cells that became active
in the 30 min simulation. Top, low-antigen simulation. Bottom, high-antigen simulation.
3 000
2 500
2 000
1 500
1 000
500
0
0 5 10 15 20 25 30
10 000
8 000
6 000
4 000
2 000
0
Inactive
Active
3 000
2 500
2 000
1 500
1 000
500
0
0 5 10 15 20 25 30
Activation Time, min
3 000
2 500
2 000
1 500
1 000
500
0
0 5 10 15 20 25 30
0 5 10 15 20 25 30
3 000
2 500
2 000
1 500
1 000
500
0
3 000
2 500
2 000
1 500
1 000
500
0
First-generation cells (CAR-CD3ζ)
Second-generation cells (CAR-CD28-CD3ζ)
10 000
8 000
6 000
4 000
2 000
0
10 000
8 000
6 000
4 000
2 000
0
10 000
8 000
6 000
4 000
2 000
0
Inactive
Active
Inactive
Active
Inactive
Active
Inactive
Active
10 000
8 000
6 000
4 000
2 000
Number of Cells 0
Inactive
Active
3 000
2 500
2 000
1 500
1 000
500
0
0 5 10 15 20 25 30
Number of Cells
Activation Time, min Activation Time, min
0 5 10 15 20 25 30
10 000
8 000
6 000
4 000
2 000
0
A B C
26
2.4.4. Sensitivity analysis of activation time
Next, we aimed to quantify the impact of each parameter on ERK activation time through
a data-driven procedure. In order to obtain importance scores for those 48 parameters, we first
created a synthetic dataset in which the model was simulated for 100,000 different and
independently sampled values of the 48 parameters. This created a 48-by-100,000 matrix of
parameter values with corresponding activation times. The procedure was performed for four
settings: first- and second-generation cells, each in "low" and "high" antigen conditions. Then, we
developed a GBT ensemble and trained it on each dataset. Here, each of the 48 parameters was
Figure 2.4. Permutation importance scores for select kinetic parameters used in the
gradient boosted tree model to predict cell activation times.
A gradient-boosted tree model was used to predict cell activation times based on model kinetic
parameters. We show the most important kinetic parameters that influence the predicted
activation time under different conditions: (A) CAR-CD3ζ with low-antigen concentration;
(B) CAR-CD3ζ-CD28 with low-antigen concentration; (C) CAR-CD3ζ with high-antigen
concentration; (D) CAR-CD3ζ-CD28 with high-antigen concentration. Importance Score0.6
0.5
0.4
0.3
0.2
0.1
0
Importance Score0.6
0.5
0.4
0.3
0.2
0.1
0
0.6
0.5
0.4
0.3
0.2
0.1
0
0.6
0.5
0.4
0.3
0.2
0.1
0
A B
C D
Ant_Kd
Kcat_LCKPU_CD3z
CSKon
Kcat_ZAP
Kcat_CD45_LCK505
Kcat_CD45_A1
Ant_Kd
Kcat_LCKPU_CD3z
CSKon
Kcat_ZAP
Kcat_CD45_LCK505
Kcat_CD45_A1
Ant_Kd
Kcat_LCKPU_CD3z
CSKon
Kcat_ZAP
Kcat_CD45_LCK505
Kcat_CD45_A1
Ant_Kd
Kcat_LCKPU_CD3z
CSKon
Kcat_ZAP
Kcat_CD45_LCK505
Kcat_CD45_A1
27
treated as an input feature and activation time as the output value. GBT hyperparameters were
tuned until satisfactory predictive performance by fivefold cross-validation was obtained. Two
performance metrics, R2 and EV, are given for each condition in Table 2.2. Since the obtained
values for R2 and EV are identical in each setting, this implies that the GBT is an unbiased
estimator.
With a successful predictor at hand, we set out to quantify the importance of each parameter
for the prediction made by the GBT. We did this by using permutation importance scores. The
importance of each parameter was quantified in each of the four conditions (Fig. 2.4; Appendix A,
S. Fig. 2.3). With these results, we isolated the top five kinetic parameters that have a large impact
on first-generation cells in low-antigen conditions: the catalytic activity of LCK in phosphorylating
ITAM regions of CD3ζ (Kcat_LCKPU_CD3z), association rate of CSK with LCK (CSKon),
catalytic activity of ZAP70 (Kcat_ZAP), catalytic activity of CD45 in dephosphorylating LCK
(Kcat_CD45_LCK505) and the catalytic activity of CD45 in dephosphorylating ITAM regions of
CD3ζ (Kcat_CD45_A1). Notably, the three highest-scoring parameters were identical between
first- and second-generation cells in low-antigen conditions.
Antigen concentration
Construct type
First-generation Second-generation
"Low" R2 = 0.905 ± 0.0008 R2 = 0.900 ± 0.0004
EV = 0.905 ± 0.0008 EV = 0.9001 ± 0.0004
"High" R2 = 0.816 ± 0.0024 R2 = 0.807 ± 0.0035
EV = 0.816 ± 0.0024 EV = 0.807 ± 0.0035
Table 2.2. Performance of the gradient-boosted tree ensemble on various datasets.
28
2.4.5. Parameter selection by constrained optimization
We hypothesized that owing to the large impact in determining the activation time of the
cell, each of the five influential parameters identified from the permutation importance scores
could serve as a target for engineering more efficient CAR T cell lineages. A key goal of such
engineering would be to minimize the number of interventions into the system given the
complexity of designing proteins with desired properties and then expressing them in engineered
cells. Thus, we performed parameter selection by constrained optimization to identify which one
of these parameters could serve as the most optimal target of a limited experimental intervention.
The objective function was designed to minimize activation time while modifying as few
Figure 2.5. Results from constrained optimization.
Logarithms of fold changes in each of the five parameters used in the constrained
optimization to minimize activation time are shown for given constraint strength (λ), under
different conditions: (A) First-generation cells under low antigen; (B) Second-generation
cells under low antigen; (C) First-generation cells under high antigen; (D) Secondgeneration cells under high antigen. Log10(fold change)
2.5
2.0
1.5
1.0
0.5
0
-0.5
-1 0 +1
Log10(fold change)
2.5
2.0
1.5
1.0
0.5
0
-0.5
-1 0 +1
2.5
2.0
1.5
1.0
0.5
0
-0.5
-1 0 +1
2.5
2.0
1.5
1.0
0.5
0
-0.5
-1 0 +1
Log10(λ) Log10(λ)
Kcat_LCKPU_CD3z
CSKon
Kcat_ZAP
Kcat_CD45_LCK505
Kcat_CD45_A1
A B
C D
29
parameters as possible (see 2.3. Methods section). This optimization routine was performed with
both first- and second-generation cells, each in low- and high-antigen conditions, and with
different values of the optimization constraint parameter (Fig. 2.5). When the value of the
constraint parameter is 10, kinetic parameters do not change at all in course of the optimization.
However, as we relax the constraint parameter (i.e., reduce its value to 1.0), two kinetic parameters
change within one order of magnitude to actuate a decrease in cell activation time:
Kcat_LCKPU_CD3z and Kcat_ZAP. These two kinetic parameters remain the only ones whose
values are optimized even when we further decrease the constraint parameter. Thus, we predict
that when the goal is to decrease cell activation time, a change in Kcat_LCKPU_CD3z and
Kcat_ZAP will result in the largest such decrease.
To test the consequences of targeting the parameters identified by the optimization
procedure, we repeated simulations with varying antigen concentrations, with one or both of the
selected parameters set to their optimized values and all others kept at their default values. Based
on our results, setting Kcat_ZAP to the optimized value resulted in a reduction of the activation
time (Fig. 2.6A; Appendix A, S. Fig. 2.4), with a greater fraction of second-generation cells
becoming active compared to first-generation cells (Table 2.3). However, setting
Kcat_LCKPU_CD3z to the optimized value was sufficient to not only induce a drastic reduction
in cell activation time, but also to make first-generation cells more efficient than second-generation
cells (Fig. 2.6B, C and Table 2.3). Particularly, with Kcat_LCKPU_CD3z optimized alone, both
populations showed 100% activation with mean activation times 5.2 min versus 6.3 min for firstand second-generation cells, respectively; when both Kcat_LCKPU_CD3z and Kcat_ZAP were
optimized, both populations showed 100% activation with mean activation times of 3.1 min versus
3.5 min for first- and second-generation cells, respectively (Table 2.3). When we reran simulations
30
of kinetic variability with the same optimized parameters, we obtained similar results. Specifically,
Kcat_LCKPU_CD3ζ optimization is predicted to be sufficient to make first-generation cells
respond faster to antigen presence than second-generation cells (Fig. 2.7 and Table 2.4; Appendix
A, S. Fig. 2.5).
Figure 2.6. Activation of CAR T cells
with optimized parameter values.
Simulation of cells with first- or
second-generation CAR constructs
upon implementing the optimized
values of the two most influential
parameters, Kcat_ZAP and
Kcat_LCKPU_CD3z. (A) Simulated
results with optimized Kcat_ZAP only;
(B) Simulated results with optimized
Kcat_LCKPU_CD3z only; (C)
Simulated results with both Kcat_ZAP
and Kcat_LCKPU_CD3z optimized.
Active
Inactive
100 000
80 000
60 000
40 000
20 000
0
Number of Cells
0 5 10 15 20 25 30
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
Active
Inactive
Active
Inactive
100 000
80 000
60 000
40 000
20 000
0
Number of Cells
100 000
80 000
60 000
40 000
20 000
0
Number of Cells
0 5 10 15 20 25 30
0 5 10 15 20 25 30
Activation Time, min
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
First-generation cells (CAR-CD3ζ)
Second-generation cells (CAR-CD28-CD3ζ)
A
B
C
31
CAR Parameter optimized %-age cells
active
Mean activation time
(std. dev.), min
Firstgeneration
Kcat_ZAP only 99.85 9.98 (3.64)
Kcat_LCKPU_CD3z only 100 5.20 (1.34)
Both 100 3.09 (0.56)
Secondgeneration
Kcat_ZAP only 100 4.62 (1.19)
Kcat_LCKPU_CD3z only 100 6.25 (1.78)
Both 100 3.54 (0.76)
Table 2.3. Comparison of optimized systems with antigen variability.
Figure 2.7. Activation of CAR T cells with varying kinetic parameters and optimized values
of Kcat_ZAP and Kcat_LCKPU_CD3z.
Simulated results are presented for low-antigen concentration (top row) and high-antigen
concentration (bottom row). (A) Simulated results with optimized Kcat_ZAP only; (B)
simulated results with optimized Kcat_LCKPU_CD3z only; (C) Simulated results with both
Kcat_ZAP and Kcat_LCKPU_CD3z optimized. Active Inactive
100 000
80 000
60 000
40 000
20 000
Number of Cells 0
0 0 5 10 15
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
Active
Inactive
100 000
80 000
60 000
40 000
20 000
Number of Cells 0
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
Active
Inactive
100 000
80 000
60 000
40 000
20 000
0
0 0 5 10 15
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
100 000
80 000
60 000
40 000
20 000
0
100 000
80 000
60 000
40 000
20 000
0
100 000
80 000
60 000
40 000
20 000
0
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
0 0 5 10 15
0 0 5 10 15 0 0 5 10 15 0 0 5 10 15
Activation Time, min Activation Time, min Activation Time, min Active Inactive Active Inactive Active Inactive
First-generation cells (CAR-CD3ζ)
Second-generation cells (CAR-CD28-CD3ζ)
40 000
35 000
30 000
25 000
20 000
15 000
10 000
5 000
0
A B C
32
2.5. Discussion
In this study, we applied an existing ODE-based mechanistic model of CAR-induced ERK
signaling to compare the performance of first- and second-generation engineered CAR T cells in
context of cell-to-cell variability. By simulating variable antigen concentrations, we showed that
costimulatory signaling from CD28 causes both a reduced activation time and more consistent
population response. In addition, when considering kinetic variability caused by biochemical noise,
second-generation cells yielded similar results: reduced activation time and variability of the
population response compared to first-generation cells. In order to track the mechanism by which
CD28 induces this change, we repeated simulations of kinetic variability with only one CD28-
mediated mechanism available at a time: the association between CD28 and Grb2, the association
between CD28 and GADS, or the CD28-mediated change in the catalytic activity of LCK. We
found that the effect of CD28 on the catalytic activity of LCK is both necessary and sufficient to
produce the performance improvement in second-generation cells. Next, we set out to identify
parameters that could be modulated to further reduce response times and variability in the
population response. To this end, we trained a GBT ensemble, which could predict system
CAR
Parameter optimized
%-age cells active Mean activation time
(std. dev.), min
Low
antigen
High
antigen
Low
antigen
High
antigen
Firstgeneration
Kcat_ZAP only 92.69 97.97 9.10 (5.53) 5.19 (3.39)
Kcat_LCKPU_CD3z only 98.12 97.22 5.94 (3.38) 6.74 (4.03)
Both 98.92 98.7 3.41 (2.02) 4.01 (2.47)
Secondgeneration
Kcat_ZAP only 99.01 99.12 2.95 (1.65) 2.36 (1.22)
Kcat_LCKPU_CD3z only 98.98 99.00 2.68 (1.52) 2.89 (1.60)
Both 99.14 99.15 2.03 (1.09) 2.14 (1.09)
Table 2.4. Comparison of optimized systems with kinetic variability.
33
activation time based on values of kinetic parameters. After confirming the predictor's accuracy,
we quantified the importance of each kinetic parameter for making an accurate prediction. Using
this method, we isolated five influential kinetic parameters. Then, we performed a constrained
optimization procedure on our model by using an objective function that sought to minimize cell
activation time while manipulating as few of the five candidate parameters as possible. Based on
the results of this optimization procedure, the most optimal targets are predicted to be the catalytic
activity of LCK in phosphorylating ITAM motifs of the CD3ζ domain (Kcat_LCKPU_CD3z) and
the catalytic activity of the kinase ZAP70 (Kcat_ZAP). To elucidate how implementing these
changes would affect population performance of CAR T cells, we repeated simulations of the
system with antigen variability and kinetic variability by using the optimized parameter value.
Optimizing Kcat_ZAP resulted in an overall reduction in cell response time. Meanwhile,
manipulating Kcat_LCKPU_CD3z independently or in conjunction with Kcat_ZAP not only
drastically improved performance, but also made first-generation cells perform at least as
efficiently as, and in some cases better than, second-generation cells. The suggested manipulations
closely align with the central role both enzymes play in T cell signaling. The Src family kinase
LCK is recruited to CD3ζ after target recognition and phosphorylates ITAM motifs, making them
available for docking by downstream proteins involved in signal transduction, including ZAP70
(Courtney, Lo, and Weiss 2018). Active ZAP70 associates with phosphorylated ITAMs of CD3ζ
and phosphorylates different targets, including the adaptor protein LAT. After being
phosphorylated by ZAP70, LAT recruits signaling proteins involved multiple cascades, including
the ERK cascade (Fischer et al. 2010).
Experimental studies have shown that the second-generation CAR constructs with a CD28
costimulatory domain promote a better immune response during in vivo testing, compared to first-
34
generation constructs. While theoretical underpinnings of this phenomenon were explored in prior
research, our work provides a new context for this discrepancy. Particularly, we showed that the
incorporation of the CD28 costimulatory domain results in both shorter and more consistent
response times in the face of various sources of variability. A population of CAR T cells infused
into the patient's bloodstream would encounter highly variable external and internal conditions. As
this variability is not as strongly reflected in a controlled in vitro setting, our predictions provide
valuable insight into the features of engineered CAR T cells. In addition, we explored potential
routes for the further improvement of CAR T cell therapies. Prior work has mostly focused on
incorporating more signaling domains or activity-dependent expression cassettes into the structure
of the CAR (Akhoundi et al. 2021). We explored the alternative possibility of enhancing CAR T
cell response by manipulating the catalytic activity of enzymes involved in signal transduction.
The ability to engineer enzymes with desired properties, including improved catalytic activity, has
already found broad applications in biotechnology (Lutz and Iamurri 2018). While traditional
methods use either a targeted substitution of key amino acids or directed evolution of random
mutations, new approaches based on machine learning empower specialists to look for candidates
in silico (Yang, Wu, and Arnold 2019). Based on our model, engineering a more catalytically
active isoform of LCK would cause first-generation cells to become at least as efficient as
otherwise equivalent CD28-bearing CAR T cells. It is established that despite their greater efficacy,
second-generation cells suffer from multiple side effects, and mitigating those side effects is a
significant concern. We believe that enhancing LCK catalytic activity as an alternative to having
the CD28 domain in the CAR structure can be one such mitigating strategy, since it would
potentially exclude undesirable effects of CD28 without compromising ERK signaling.
35
Along with the significant findings produced by our work, we recognize some limitations
of our approach that can be addressed in the future. When exploring the population response of
CAR T cells to stochastic antigen concentrations, we assumed a lognormal distribution chosen to
fall within an experimentally observed range. For simulations of kinetic heterogeneity, we
assumed a normal distribution centered around the accepted default value with a standard deviation
as a third of this value. While these distributions have a clear experimental basis, they are not the
only option possible. By trying other hypothetical distributions, a more comprehensive
understanding of the CAR T cell population response may emerge. Another limitation of our study
concerns the choice of optimized values for Kcat_ZAP and Kcat_LCKPU_CD3z when considering
heterogeneity. Our objective function penalized changes in each parameter proportional to the
absolute value of the logarithm of the fold change compared to its baseline value. Since the
baseline value of Kcat_LCKPU_CD3z is different between first- and second-generation cells
owing to CD28's effects in the latter, we obtained different optimal values of Kcat_LCKPU_CD3z
for first- and second-generation cells. However, since our goal was to simulate the observed effects
of an artificially enhanced LCK, we assumed that the catalytic properties of such enhanced LCK
would be the same regardless of the CAR structure. Thus, we were compelled to use the same
optimal Kcat_LCKPU_CD3z value when performing simulations that accounted for antigen and/or
kinetic variability. Future experimental work can explore the validity of our assumption.
36
3. Computational analysis of 4-1BB-induced NFκB signaling suggests improvements to CAR
cell design
Portions of this chapter are adapted from: Vardges Tserunyan and Stacey D. Finley. Cell
Communication and Signaling, 2022
3.1. Abstract
Chimeric antigen receptor (CAR)-expressing cells are a powerful modality of adoptive cell
therapy against cancer. The potency of signaling events initiated upon antigen binding depends on
the costimulatory domain within the structure of the CAR. One such costimulatory domain is 4-
1BB, which affects cellular response via the NFκB pathway. However, the quantitative aspects of
4-1BB-induced NFκB signaling are not fully understood. We developed an ordinary differential
equation-based mathematical model representing canonical NFκB signaling activated by CAR-4-
1BB. After a global sensitivity analysis on model parameters, we ran Monte Carlo simulations of
cell population-wide variability in NFκB signaling and quantified the mutual information between
the extracellular signal and different levels of the NFκB signal transduction pathway. Based on
our results, in response to a wide range of antigen concentrations, the magnitude of the transient
peak in NFκB nuclear concentration varies significantly, while the timing of this peak is relatively
consistent. Global sensitivity analysis showed that the model is robust to variations in parameters,
and thus, its quantitative predictions would remain applicable to a broad range of parameter values.
The model predicts that overexpressing NEMO and disabling IKKβ deactivation can increase the
mutual information between antigen levels and NFκB activation. Our modeling predictions
provide actionable insights to guide CAR development. Particularly, we propose specific
37
manipulations to the NFκB signal transduction pathway that can fine-tune the response of CAR4-1BB cells to the antigen concentrations they are likely to encounter.
3.2. Introduction
In the last two decades, adoptive cell therapy has emerged as a powerful tool for combatting
cancer (Met et al. 2019). One successful approach is to confer adoptive immune cells with
specificity against antigens expressed on cancer cells by engineering them to express chimeric
antigen receptors (CAR) (Srivastava and Riddell 2015). Currently, T cells are the predominant
immune cell type used for CAR-based immunotherapy, and multiple CAR T cell therapies have
received FDA approval (Johnson and Abramson 2022). CARs feature an antigen recognition
domain derived from single-chain variable fragments (scFv) of monoclonal antibodies, while their
cytoplasmic portion includes different intracellular signaling domains. The first generation of
CARs had a single cytoplasmic CD3ζ signaling domain connected to the recognition domain by a
transmembrane linker. Later advances resulted in second-generation CARs, which have one
additional signaling domain originating from natively occurring costimulatory receptors
(Akhoundi et al. 2021). 4-1BB (also referred to as CD137) is one such costimulatory domain
frequently incorporated in the structure of the CAR (Campana, Schwarz, and Imai 2014).
The effects mediated by the 4-1BB domain in immune cells have been tracked to the
Nuclear Factor κB (NFκB) signaling pathway (Philipson et al. 2020), which is comprised of two
branches, termed canonical and non-canonical NFκB signaling (Trares, Ackermann, and Koch
2022). The canonical NFκB signaling is triggered in a matter of minutes after stimulation, while
the non-canonical system is slower and depends on protein translation to exert its effect (Zarnegar
38
et al. 2008). In addition, there is a functional difference between the two branches: the sets of genes
activated by each are not identical (Shih et al. 2011). The genes of many cytokines, such as those
of IL-1α/β (Mori and Prager 1996; Hiscott et al. 1993), IL-6 (Son et al. 2008), IL-10 (Cao et al.
2006) and IFNγ (Sica et al. 1997), as well as perforin (Zhou et al. 2002), show experimental
evidence of canonical NFκB regulation. Meanwhile, the non-canonical NFκB pathway was found
to be responsible for improved survival rates among 4-1BB-bearing second-generation CAR T
cells (Philipson et al. 2020). Thus, investigating NFκB signaling initiated by 4-1BB can help gain
a deeper understanding of the observed biological features of CAR cells.
Computational systems biology provides tools to explore signaling systems without the
need for expensive and prolonged experimentation (Kitano 2002). For example, this approach was
successful in describing T cell receptor-induced activation of MAPK/ERK signaling (AltanBonnet and Germain 2005). Recently, our research group successfully utilized an ordinary
differential equation (ODE)-based model to describe MAPK signaling in a heterogeneous CAR T
cell population (Cess and Finley 2020; Tserunyan and Finley 2022b). Several mathematical
models have been published for NFκB signaling as well. Some of these mathematical models have
mostly focused on downstream events of the pathway, replacing the dynamics of IKKβ with an
assumed activation profile (Hoffmann et al. 2002; Kearns and Hoffmann 2009; Basak, Behar, and
Hoffmann 2012), while other models have incorporated a more explicit account of upstream
processes (Sharp et al. 2013; Schliemann et al. 2011; Lipniacki et al. 2004). Mathematical
modeling was also used to analyze the NFκB pathway as an information transmission channel.
This work has shown that the pathway can encode approximately 1 bit of information at most, i.e.,
whether the extracellular stimulus is present or absent (Cheong et al. 2011; Tudelska et al. 2017).
Insights from the information-theoretic analysis of NFκB signal transmission were extended to the
39
expression patterns of genes regulated by NFκB (Maity and Wollman 2020). However, none of
these analyses address NFκB signaling in the context of CAR cells. In addition, while some
published models include aspects of NFκB activation via 4-1BB (Konstorum et al. 2019), they are
based on a Boolean modeling approach and do not capture the dynamic chemical interactions in
response to stimulation.
Hence, in our current work, we set out to develop a mechanistic ODE-based model of
canonical NFκB signaling initiated by antigen binding to a CAR-4-1BB. We applied the model to
quantitatively investigate the features of 4-1BB-mediated NFκB signaling. We found that in
response to antigen binding, 4-1BB initiates a transient increase in the nuclear concentration of
NFκB. The timing of peak NFκB concentration is relatively consistent, while its magnitude shows
a much greater dependence on the antigen level. Next, we found that very few of the model
parameters have a significant impact on the activation time and magnitude of the NFκB pathway,
indicating that the behavior of the model would be robust to large variations in kinetic parameters
and protein concentrations. Finally, by analyzing the mutual information between antigen
concentration and successive levels of the NFκB pathway in conditions of simulated variability,
we proposed potential improvements to CAR-4-1BB cells. Specifically, our results suggest that
the overexpression of NEMO or the disabling of IKKβ deactivation would make NFκB activation
level more suited to the encountered antigen concentration. Altogether, we provide a quantitative
framework that can be used to guide the development and optimization of 4-1BB-induced CAR
signaling.
40
3.3. Methods
3.3.1. Model Structure
By performing an extensive literature search, we compiled a list of key protein–protein
interactions and chemical reactions, which form the core of the activation of the canonical NFκB
pathway. In our model, in response to antigen binding, the 4-1BB domain of the CAR induces the
formation of a signalosome, in which TRAF2 trimers play a key role (Y. Li et al. 2018; Arch and
Thompson 1998; Zapata et al. 2018). Acting as a ubiquitin ligase, TRAF2 promotes the attachment
of long K63 ubiquitin chains to RIP1 (T. H. Lee et al. 2004; Alvarez et al. 2010). Once RIP1 is
ubiquitinated, its K63 ubiquitin chains enable the docking of TAB1/2/3, the adaptor subunits of
the TAK enzymatic complex (Kanayama et al. 2004). Similarly, the IKK multimeric complex is
docked with NEMO (also known as IKKγ) as an adaptor subunit to the K63 ubiquitin chains of
RIP1 (Ea et al. 2006). The protein TAK1, the enzymatic subunit of the TAK complex,
phosphorylates the β subunit of the IKK complex in a ubiquitin-dependent manner (C. Wang et al.
2001). IKKβ activation is transitory since phosphorylation of a cluster of 10 serine residues at a
regulatory domain deactivates it (Delhase et al. 1999; Karin 1999). Catalytically active IKKβ
phosphorylates the protein IκBα, targeting it for proteasomal degradation (Senftleben et al. 2001;
Zandi et al. 1997; Woronicz et al. 1997). In resting cells, IκBα tightly associates with cytoplasmic
NFκB, preventing it from shuttling to the nucleus. However, the degradation of IκBα under the
influence of catalytically active IKKβ releases cytoplasmic NFκB from this sequestration and
makes it free to translocate to the nucleus, where it can function as a transcription factor and alter
the expression profile of the cell (Ghosh, May, and Kopp 1998). In this work, we do not explicitly
consider the transmembrane domain, as we have not uncovered experimental evidence indicating
41
that the transmembrane domain has a direct effect on NFkB signaling. Rather, 4-1BB domain's
recruitment of TRAF proteins seems to be the defining event that triggers downstream signaling.
These reactions were represented as interaction rules in RuleBender (v2.3.1) (Faeder,
Blinov, and Hlavacek 2009) . Then, RuleBender was used to generate a corresponding set of
ordinary differential equations (ODEs) describing the temporal dynamics of the system. Matlab
(v2019a/b) was used to integrate the system of ODEs to obtain time courses of the species involved.
Kinetic parameters and protein concentrations were compiled from prior models of different
components of the system or direct experimental measurements.
3.3.2. Activation profiles and dose response curves
We simulate binding of CD19, a common target for CAR therapies, to the antigen
recognition domain of the CAR. Prior experimental measurements of CD19 estimated its surface
concentration to have a mean of 3.4 molecules per µm2 on NALM-6, a human acute lymphoblastic
leukemia-derived cell line, while CD19 concentration on primary myeloma cells was in the range
of 0.16–5.2 molecules per µm2 (Nerreter et al. 2019). We took these values as a basis for our
simulations of activation profiles and dose response curves but used the wider range of 100.5–102.5
molecules per µm2 to capture the behavior of the model for a broader range of antigen
concentrations.
42
3.3.3. Sensitivity analysis
We performed sensitivity analysis to determine how strongly model inputs (kinetic
parameters and initial protein concentrations) affect the quantitative predictions of the model. We
used the extended Fourier Amplitude Sensitivity Test (eFAST) method of quantifying global
sensitivity of a mathematical model to underlying parameter values (Marino et al. 2008). The
sensitivity coefficients are obtained by simultaneously varying parameters of interest at different
pre-assigned signature frequencies and evaluating a system output for each subsequent value of
the parameter vector. Then, the Fourier transform of sequential values of system output is
computed to reveal its spectral composition. The underlying assumption is that if a parameter
influences system output to a significant extent, then its periodic variation according to a certain
signature frequency would cause large variations in the model output at that frequency, as revealed
by a higher amplitude in the Fourier transform. The significance of different parameters is
evaluated in comparison with the sensitivity coefficient attained by a "dummy" parameter, a
parameter with no involvement in the system at all. Following the spectral decomposition of the
output, if the amplitude at any system parameter's characteristic frequency is lower than that for
the "dummy" parameter, the system parameter is taken to have no significant impact on system
output.
3.3.4. Monte Carlo simulations
We considered a population of CAR-expressing cells by accounting for cell-to-cell
variability in protein concentrations. Motivated by prior experimental findings (Furusawa et al.
2005), we modeled the intrinsic noise of the population response by assuming that proteins
43
involved in signal transduction in each cell have varying initial concentrations subject to a
lognormal distribution. We chose the location parameter of each distribution so that the median
concentration across the CAR cell population would equal the accepted value of the protein
concentration. The scale parameter was taken to be the same for all proteins, and different
hypothesized values of this scale parameter were investigated to gain a more complete picture
(termed "noise parameter" throughout). We included variability in target antigen concentration by
assuming a lognormal distribution and choosing the location and scale parameters such that the
distribution would mostly lie within the measured range of 0.16–5.2 molecules per µm2 for
myeloma cells and have a mean of approximately 3.4 molecules per µm2 as measured for
lymphoma cells (Nerreter et al. 2019). This random sampling with subsequent simulation was
repeated 2,000 times to yield representative distributions.
3.3.5. Mutual information
Mutual information is a quantity measuring the mutual dependence of two random
variables (Shannon 1948). As such, its value is zero if and only if two random variables are
independently distributed, and a positive number if they depend on each other. We used the
Kraskov algorithm for computing mutual information based on distribution entropies, with the
entropies estimated through a K-nearest neighbors procedure (Kraskov, Stögbauer, and
Grassberger 2004).
We computed the mutual information between antigen levels and five different stages of
signal transduction: concentration of antigen-bound CAR, amount of TRAF2 bound to the 4-1BB
domain, amount of RIP1 bound to the TRAF2 signalosome, concentration of enzymatically active
44
TAB2/TAK1, peak concentration of enzymatically active NEMO/IKKβ, and peak nuclear
concentration of NFκB. In order to quantify the amount of information reaching a certain level
along signal transduction, we randomized the concentrations of all proteins upstream of that level,
leaving the rest of the protein concentrations unchanged. Then, we stimulated the system by a
randomly sampled antigen concentration. Since only the steps leading up to the given level were
randomized, any variation at this level would reflect upstream stochasticity and not an artifact of
randomizing the protein in question. On the other hand, by randomizing all upstream proteins, we
ensured that the contribution of every upstream component to overall stochasticity is accounted
for. By performing this procedure for five different levels of the signal transduction pathway, we
were able to track how much mutual information is shared between the antigen concentration and
a given level of the signaling cascade.
3.4. Results
3.4.1. Model structure and dose response
To understand the signaling dynamics predicted by our model (Fig. 3.1), we generated time
courses for enzymatically active IKKβ, which is a key convergence point for NFκB-activating
signals (Odegaard and Chawla 2012; Mieczkowski et al. 2015; Veerappan et al. 2017), and nuclear
NFκB for a range of physiologically relevant antigen concentration values (Fig. 3.2). The model
predicts that in response to persistent antigen binding, there is only transient activation of IKKβ.
The IKKβ concentration is predicted to exhibit a rapid-onset, short-term peak typically occurring
10-15 min after stimulation (Fig. 3.2A). We observed a similar transient peak for the nuclear
45
concentration of NFκB. Here, the peak was broader, with the maximum concentration occurring
after approximately 20–40 min of stimulation with physiologically relevant antigen concentrations
(Fig. 3.2B).
Next, we obtained dose response curves for the activation of IKKβ and NFκB (Fig. 3.3).
Notably, only a small fraction of the total IKKβ pool (< 15%) was activated even at its maximal
level and with saturating antigen levels (Fig. 3.3A). Peak concentration achieved by active IKKβ
had a sigmoidal dependence on antigen concentration and was sensitive to antigen levels. A 1,000-
fold change in antigen concentration results in a 193-fold change in active IKKβ peak
concentration. In contrast, the timing of the IKKβ peak was relatively robust to the antigen
concentration. Specifically, a 1,000-fold range of antigen concentrations produces only a 3-fold
change in the time at which IKKβ peaked (Fig. 3.3B). The nuclear concentration achieved by
NFκB increased with increasing antigen concentration (21-fold change in the response range) and
showed a sigmoidal dependence on antigen concentration (Fig. 3.3C). In addition, the timing of
peak nuclear NFκB concentration was relatively consistent for different antigen concentrations
(2.9-fold change in the response range, Fig. 3.3D).
46
Figure 3.2. Activation profiles for IKKβ and NFκB in response to antigen binding the CAR.
The pathway was stimulated with 10 different antigen concentrations in silico and activation
profiles for IKKβ and NFκB were recorded for each antigen concentration. (A) Enzymatically
active IKKβ; (B) Nuclear concentration of NFκB.
IKK
βact. conc., molec. per μm2
15
10
5
0
10 20 30 40 50 60 70 80 90 100
Time, minutes
10 20 30 40 50 60 70 80 90 100
70
60
50
40
30
20
10
0
102.5
10-0.5 Antigen conc., molec. per μm2
NFκB
βn conc., molec. per μm2
102.5
10-0.5 Antigen conc., molec. per μm2
Time, minutes
A B
Figure 3.1. Key steps resulting in CAR-4-1BB-mediated NFκB activation, which manifests in
the translocation of NFκB from the cytoplasm to the nucleus.
47
Figure 3.3. Dose response curves for IKKβ and NFκB in response to antigen binding the
CAR.
Relative magnitude and timing of the peak concentration of active IKKβ and nuclear NFκB
were recorded for a range of antigen concentrations. (A) Relative magnitude of the peak
concentration of enzymatically active IKKβ; (B) Relative magnitude of the peak
concentration of nuclear NFκB; (C) timing of the peak concentration of enzymatically active
IKKβ; (D) timing of the peak concentration of nuclear NFκB IKK
βact. peak timing, min NFκB
βn peak timing, min
Maximum IKK
βact. (% of total)
100 101 102 100 101 102
100 101 102 100 101 102
Antigen conc., molec. per µm2
Antigen conc., molec. per µm2
Antigen conc., molec. per µm2
Antigen conc., molec. per µm2
Maximum NFκB
βn. (% of total) 100
80
60
40
20
0
25
20
15
10
5
0
60
50
40
30
20
10
0
12
10
8
6
4
2
0
A B
C D
48
3.4.2. Sensitivity of the output to kinetic parameters and protein concentrations
Once we established basic features of pathway activation predicted by our model, we
proceeded to evaluate how the output is impacted by the model parameters. This would allow us
to see how sensitive the quantitative predictions from our model are with respect to choices of
specific values for kinetic constants and protein initial concentrations. To this end, we used the
Extended Fourier Amplitude Sensitivity Test (eFAST), a method of global sensitivity analysis, on
the kinetic constants for regimes of low, medium and high antigen stimulation (Fig. 3.4A). We
evaluated the impact of the kinetic constants on four measures of the system output: (1) the timing
of peak active IKKβ concentration, (2) the magnitude of peak active IKKβ concentration, (3) the
timing of peak nuclear NFκB concentration and (4) the magnitude of peak nuclear NFκB
concentration.
Figure 3.4. eFAST total sensitivity indices of model output with respect to model parameters.
(A) Sensitivity indices for kinetic parameters; (B) Sensitivity indices for protein initial
concentrations. From top to bottom: low (0.10 mol. per µm2
), medium (1.0 mol. per µm2
) and
high (10 mol. per µm2
) antigen concentration.
k_ant f
k_ant d
k_car_cd137_traftri_f
k_car_cd137_traftri_d
k_traftri_rip1_f
k_traftri_rip1_d
k_rip1_ubq_f
k_rip1_tab2_f
k_rip1_tab2_d
k_rip1_nemo_f
k_rip1_nemo_d
k_tab2_tak1_f
k_tab2_tak1_d
k_tak1_act_f
k_nemo_ikkb_f
k_nemo_ikkb_d
k_ikkb_tak1
k_ikkb_inh
kcat_ikkb_ikba
km_ikkb
k_ikba_nfkb_f
k_ikba_nfkb_d
k_nfkb_exp
k_nfkb_eq
k_ikba_exp
k_ikba_eq
k_ikba_deg
k_ikba_nfkb_exp
k_transcript
k_translate
NFκBtime
NFκBmax
IKKtime
IKKmax
NFκBtime
NFκBmax
IKKtime
IKKmax
NFκBtime
NFκBmax
IKKtime
IKKmax
A
B
NFκBtime
NFκBmax
IKKtime
IKKmax
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TRAF2
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49
Based on our results, the responses of both IKKβ and NFκB appear to be relatively robust
with respect to variations in the kinetic parameters. In fact, only very few parameters are shown to
significantly impact the timing and magnitude of their peak concentrations. For example, at most
eight of the 30 kinetic constants influence the magnitude or timing of nuclear NFκB across the
conditions we considered. Particularly, at low antigen concentrations, nuclear import/export rates
of NFκB and IkBα strongly influence peak nuclear NFκB concentration. At higher antigen
concentrations, parameters related to the enzymatic activity of IKKβ exert more influence.
Next, we performed eFAST on the initial concentrations of the proteins involved in signal
transduction (Fig. 3.4B). We observed a very strong dependence of the timing and magnitude of
peak nuclear NFκB concentration on the total cellular amount of NFκB. In addition, with nonsaturating antigen concentrations, the NFκB response is predicted to depend on the amount of IkBα,
the protein that sequesters NFκB in the cytoplasm. Interestingly, while the activation of the
upstream protein IKKβ depends on the amounts of many of the upstream proteins, those upstream
species do not significantly affect NFκB.
The robustness of model output to kinetic parameters and initial concentrations of pathway
proteins demonstrates that the dynamics of the NFκB pathway predicted by the model would
remain essentially similar across a wide range of parameter values. This indicates that the
quantitative insights derived from the model would be applicable to a broad range of systems,
including engineered CAR-4-1BB cells, even though the model is chiefly based on studies
performed on fibroblasts. This provides confidence that we can gain biological insights form the
model predictions.
50
3.4.3. Mutual information carried by the NFκB pathway about antigen concentration
Signal transduction pathways are subject to biochemical noise, which can prevent
downstream messengers from serving as an exact reflection of the extracellular signal (Tostevin
and ten Wolde 2010). In the case of CAR-4-1BB signaling, this means that the activation of the
NFκB pathway and subsequent changes in gene expression patterns mediated by the nuclear
localization of NFκB may not necessarily match the amount of antigen to which the cell is exposed.
In order to make assessments about the accuracy of signal transduction of canonical NFκB
signaling in CAR-4-1BB cells, we simulated a population of CAR-4-1BB cells in which the
accurate population-level response to target antigen was precluded by stochastic variations in the
intracellular concentrations of proteins involved in signaling. We were particularly interested in
how accurately each successive level of the transduction pathway reflects the amount of antigen
Figure 3.5. Information transduction along the canonical NFκB pathway.
Calculated mutual information in bits between antigen concentration and concentration of
clustered TRAF2, clustered RIP1, enzymatically active TAK1, enzymatically active IKKβ and
nuclear NFκB Mutual Information, bits
0.10 0.25 0.50 0.75 1.0 2.0
Noise Level
8
6
4
2
0
Clustered TRAF2
Clustered RIP1
Active TAK1
Active IKKβ
Nuclear NFκB
51
stimulation. To this end, we performed simulations by stochastically varying all protein
concentrations upstream from a given level of the pathway. We also varied the antigen
concentration level. Then, we computed the mutual information between the distribution of
responses at this level and the distribution of antigen concentrations (Fig. 3.5). This allowed us to
track how the amount of information carried by the pathway changes at each level of signal
transduction. Since experimental measurements on the cell-to-cell variability of CAR-4-1BB cells
were not available, we performed our simulations for multiple values of the noise parameter. In
this way, we were able to identify common observable trends that characterize the system,
regardless of a specific variability level considered.
We can visually observe differences between the distribution of peak NFκB nuclear
concentrations and the antigen distribution (Appendix B, S. Fig. 3.1). Interestingly, we observed
that for the same underlying distribution of antigen concentrations, higher levels of noise diminish
the strength of NFκB signaling (Appendix B, S. Fig. 3.1). Our analysis of the mutual information
provides a quantitative measure of differences between the antigen distribution and the distribution
of activation for successive steps in the signaling pathway (Fig. 3.5). We predict that the proteins
recruited early in signal transmission exhibit a relatively small loss of information following
antigen stimulation. By definition, the mutual information between two distributions cannot
exceed the marginal entropies of each of those distributions (Shannon 1948). The marginal entropy
for the distribution of antigen concentrations we used was 8.79, while the mutual information at
the level of TARF2 clustering was close to this upper limit, between 7.36 and 8.50 bits, depending
on the noise level. Most information loss consistently occurred between the enzymatic activation
of the TAB2/TAK1 complex and enzymatic activation of the NEMO/IKKβ complex. In some
conditions, there was up to a tenfold reduction in the mutual information at this stage. Meanwhile,
52
signal transduction between enzymatically active IKKβ and the nuclear translocation of NFκB
seemed relatively accurate with only a small reduction in mutual information. In summary, we
find that for all noise levels, mutual information is predicted to decrease as the signal is transduced
through the pathway, with the steps directly leading up to the activation of IKKβ as the least
accurate in signal transduction.
3.4.4. Suggested improvements to CAR design
A primary goal of CAR therapy is to enhance the on-target cytolytic activity of CAR cells
while avoiding side effects. Some of these side effects include cytokine release syndrome, ontarget-off-tumor effects, and graft-versus-host disease (Mansouri, Yazdanpanah, and Rezaei 2022) .
We hypothesized that if secondary messengers more accurately reflect the amount of antigen
encountered by the engineered CAR cell, CAR cells would show a more specific response to
antigen binding. Particularly, we suggest that increasing the mutual information between the
antigen levels and the nuclear concentration of NFκB would affect the therapeutic performance of
cells in a manner such that the cells do not become unnecessarily active when encountering only
trace amounts of the target, while showing enhanced activity levels when encountering higher
amounts of antigen.
Thus, we applied the model to investigate how changing the initial concentration of each
protein involved in signal transduction affects the mutual information between antigen
concentration and nuclear NFκB concentration (Fig. 3.6). We repeated our Monte Carlo
simulations, this time increasing or decreasing by 50% the initial concentrations for individual
proteins. We also considered modulating pairs of proteins that together form multimeric enzymes,
53
such as TAB2/TAK1 and NEMO/IKKβ, to check for possible synergistic effects. The analysis
showed that it is possible to increase mutual information by 23% by overexpressing NEMO (Fig.
3.6A). The overexpression of NEMO yielded the same increase as its joint overexpression with
IKKβ, indicating a lack of synergistic effects. Mutual information decreased by 20% when TAB2
was overexpressed separately or in conjunction with TAK1. We believe that these results indicate
that overexpressing NEMO experimentally would make the nuclear NFκB concentration in
response to activation more reflective of the extracellular antigen concentration. Thus, the potency
of the cellular response triggered by NFκB would have a closer correspondence to the targets
encountered. When repeating the same procedure for decreased protein concentrations (Fig. 3.6B),
the estimated mutual information between antigen levels and nuclear NFκB is predicted to increase
by 43% with TAB2 underexpressed but is reduced by 33% when underexpressing NEMO.
Figure 3.6. Relative changes in the mutual information.
The mutual information between antigen concentration and peak nuclear NFκB is calculated
for a noise parameter value of 0.75. (A) Relative change in mutual information due to 50%
simulated protein overexpression; (B) Relative change in mutual information due to 50%
simulated protein underexpression.
MI change relative to default, %
50
40
30
20
10
0
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TRAF2
RIP1
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TAK1
NEMO
IKKβ
IkBα
NFκB
TAB/TAK1
NEMO/ IKKβ
A B
54
In order to elucidate the mechanism by which the overexpression of NEMO and
underexpression of TAB2 cause an increase in mutual information between antigen exposure and
NFκB activation, we obtained dose response curves for peak concentrations of active IKKβ (Fig.
3.7A) and nuclear NFκB (Fig. 3.7C), and their timings (Fig. 3.7B, D) in each of those cases. We
can see that in cases of intermediate and high antigen concentrations but not low concentrations,
the overexpression of NEMO causes an increase in peak concentration attained by active IKKβ,
compared to the default concentration levels (Fig. 3.7A). The enhancing effect of NEMO
Figure 3.7. Dose response curves for IKKβ and NFκB in response to antigen binding to the
CAR with modified expression levels.
Peak concentration times and relative magnitudes were recorded for active IKKβ and nuclear
NFκB for a range of antigen concentrations and with different proteins under- or
overexpressed. (A) Relative magnitude of the peak concentration of active IKKβ; (B) Relative
magnitude of the peak concentration of nuclear NFκB; (C) Timing of the peak concentration
of active IKKβ; (D) Timing of the peak concentration of nuclear NFκB. N.B. Peak timings for
the case of disabled IKKβ deactivation are not shown in (C) and (D) since neither IKKβ nor
NFκB show substantial local maxima.
Antigen conc., molec. per µm2 Antigen conc., molec. per µm2
100 101 102
Maximum IKK
βact. (% of total) Maximum NFκB
βn (% of total) 100
80
60
40
20
0
40
30
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βact. peak timing, min
100 101 102
30
25
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10
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0
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0
NFκB
βn peak timing, min
Antigen conc., molec. per µm2
100 101 102
Antigen conc., molec. per µm2
100 101 102
A B
C D
Default Parameters
Overexpressed NEMO
Underexpressed TAB2
IKKβ deactivation off
55
overexpression on nuclear NFκB peak concentration (Fig. 3.7C) is limited to intermediate antigen
concentrations. Thus, NEMO overexpression alters the response of the canonical NFκB pathway
in a way, such that the pathway is slightly more active in case of moderate antigen concentrations
without showing such an enhancement at lower antigen concentrations.
By plotting similar dose response curves for the case of TAB2 underexpression (Fig. 3.7),
we saw an effect by which the decreased amount of TAB2 caused more IKKβ activation. This was
highly surprising, since the TAB2/TAK1 complex is known to phosphorylate and activate the
NEMO/IKKβ complex, where TAB2 and NEMO are the docking subunits of each multimeric
enzyme (Kanayama et al. 2004; Ea et al. 2006). We hypothesized that since both TAB2 and NEMO
dock at K63 ubiquitin tails attached to RIP1, the underexpression of TAB2 would make more
docking sites available to NEMO and, thus, increase the amount of IKKβ available for activation.
Indeed, when we ran simulations to compare concentrations of ubiquitin-bound TAB2 and NEMO,
we saw that with underexpressed TAB2, there is a greater abundance of ubiquitin-bound NEMO
accompanying the decrease in ubiquitin-bound TAB2 (Appendix B, S. Fig. 3.2). This can also
explain the greatly reduced mutual information when TAB2 is overexpressed (Fig. 3.6A), since in
this case, TAB2 would outcompete NEMO for access to docking sites. Thus, both over- and
underexpression studies underline the centrality of NEMO abundance for enhancing the response
of the canonical NFκB pathway.
Finally, given the importance of IKKβ activity for nuclear translocation of canonical NFκB,
we investigated how altering the IKKβ activation profile may affect signal transduction.
Specifically, we tested whether more persistent IKKβ activity resulting from disabled deactivation
would enhance canonical NFκB signaling for low and intermediate antigen concentrations. We
were motivated by the fact that such manipulations were shown to be feasible experimentally
56
(Delhase et al. 1999). As expected, the model predicted that lasting IKKβ activation (Appendix B,
S. Fig. 3.3A) results in more persistent nuclear concentration of NFκB upon antigen stimulation
(Appendix B, S. Fig. 3.3B).
In order to test the consequences of this hypothetical manipulation on accuracy of signal
transduction, we repeated our simulations to compute the mutual information carried by the
pathway when IKKβ deactivation is disabled. Notably, the mutual information between antigen
concentration and nuclear NFκB concentration showed a dramatic increase for all values of the
noise parameter (Appendix B, S. Fig. 3.4). In order to find out the reasons for this increase, we
plotted dose response curves for the system under disabled IKKβ deactivation (Fig. 3.7).
Deactivation of IKKβ increases the peak level of IKKβ for intermediate to high antigen
concentrations (Fig. 3.7A). On the other hand, there was a substantial amplification of the NFκB
response in low and intermediate antigen concentration conditions, with the amplification
observed for the intermediate range being much more dramatic (Fig. 3.7C). This suggests that if
IKKβ deactivation is absent, the canonical NFκB pathway would be highly sensitive to antigen
concentrations of the order of 1 molecule per µm2
, without demonstrating as high activation levels
for much lower antigen concentrations. Interestingly, the timing of the peak IKKβ and NFκB were
not significantly affected by IKKβ deactivation (Fig. 3.7B, D).
3.5. Discussion
We present a novel mathematical model of NFκB signaling mediated by 4-1BB.
Importantly, the model predicts signaling features that agree with what is already known about
NFκB signaling. Particularly, prior measurements have shown that IKKβ activity peaks 10–15 min
57
after stimulation, and nuclear NFκB peaks approximately 30 min after stimulation in the dynamic
range of the pathway (Cheong et al. 2006). Thus, the model generates dynamics that have been
observed experimentally, and it can be used to investigate the effects of 4-1BB stimulation.
We applied this model to investigate various characteristics of 4-1BB-mediated signaling.
By examining the dose response of active IKKβ and NFκB, we found that the magnitudes of their
transient peaks are sensitive to antigen concentration, while the timing of their peaks changes very
little within the range of physiologically relevant stimulus concentrations. Next, we used a global
sensitivity analysis to identify parameters that have a significant influence on the magnitude of
pathway activation. Particularly, our results highlight the influence of NFκB nuclear import/export
parameters in determining the peak nuclear concentration of NFκB for most levels of antigen
concentrations. Finally, our analysis of mutual information between antigen concentration and
successive levels of the NFκB pathway enabled us to suggest specific strategies for enhancing the
accuracy of NFκB signaling initiated by 4-1BB. Particularly, overexpressing NEMO and disabling
of IKKβ deactivation can greatly increase the information transmission capabilities of the NFκB
pathway. Thus, we provide quantitative insights to motivate bioengineering efforts for CAR cells,
which are feasible with modern experimental techniques (Delhase et al. 1999; Sakuma, Barry, and
Ikeda 2012; Ramos et al. 2018). Prior experimental studies have shown that such targeted
manipulations can greatly increase the therapeutic potential of CAR cells. Specifically, partially
impeding the phosphorylation of the CD3ζ ITAM sequences was found to increase CAR cell
persistence and confer superior antitumor ability (Feucht et al. 2019), while directing the CAR
gene insert to specific loci can result in steadier expression levels and diminished tonic signaling
(Eyquem et al. 2017). Thus, our modeling analysis provides biologically relevant insight that can
be similarly applied to engineered immune cells. CAR-4-1BB Natural Killer (NK) cells are a
58
particularly promising platform for future work. It has been shown that NK-based adoptive cell
therapies tend not to suffer from graft-versus-host disease (Sakuma, Barry, and Ikeda 2012; Ramos
et al. 2018; Feucht et al. 2019) and cytokine release syndrome (Eyquem et al. 2017; Iliopoulou et
al. 2010; Fang, Xiao, and Tian 2017), disadvantages that frequently accompany CAR T cell-based
therapy (Mansouri, Yazdanpanah, and Rezaei 2022). Thus, modeling-driven design improvements
to CAR-4-1BB NK cells motivated by a greater understanding of cell signaling would contribute
to further progress in CAR development.
Prior experimental measurements of signal transduction by the canonical NFκB pathway
have shown that the channel capacity (i.e., the maximum possible mutual information) of this
pathway is approximately equal to 0.92 bits, which implies that it can resolve only 20.92 ≈ 2 levels
of extracellular signal (Cheong et al. 2011). This was interpreted to mean that the pathway is able
to only distinguish the presence of the stimulus from its absence. An information theoretic analysis
of signaling pathways has shown that even small variations in the number of bits carried by
pathways (0.6 bits vs. 0.85 bits) can result in a two-fold difference in the number of cells that
exhibit an erroneous response to the extracellular signal (Shin et al. 2020). Based on this, we
suggest that increasing the mutual information carried by the canonical NFκB pathway in response
to antigen binding the CAR can result in a closer alignment between CAR-4-1BB cell activity and
the antigen concentration it encounters. Thus, our findings can guide further attempts to improve
the performance of CAR cells. For example, the predicted improvements can allow the cell to not
only to distinguish more accurately whether there is a target or not, but also to discriminate
between various concentrations of the target.
Along with the significant findings produced by our work, we recognize some aspects that
can be addressed in the future. One limitation is that since direct measurements or assessments
59
were not available for some parameter values, we had to make order-of-magnitude estimates by
knowing the timescale at which underlying biological phenomena are observed. Values for other
kinetic parameters and protein concentrations were taken from multiple sources, all measured or
indirectly estimated in fibroblasts with tumor necrosis factor receptors (TNFR) triggering the
activation of NFκB. Our motivation for directly applying these data on CAR-4-1BB is the fact that
4-1BB itself is a member of the TNFR superfamily, and like many other members of the same
superfamily, transmits signals by means of TRAF proteins (Zapata et al. 2018; Feucht et al. 2019;
Fang, Xiao, and Tian 2017). However, more exact numerical results can be obtained if the model
is specifically calibrated for the context of CAR-4-1BB-engineered immune cells. We note that
quantitative assays via mass-spectrometry (Shiio and Aebersold 2006) have been used to quantify
the levels of proteins in NFkB signaling (Meier-Soelch et al. 2021), along with multiple other
signaling networks. More recent iterations of this experimental technique can directly provide
absolute concentrations, in contrast to relative concentrations that are then calibrated to a protein
of known abundance (M. Li et al. 2014). Secondly, even though our model accounts for
competition between TAB2 and NEMO for docking sites along K-63 ubiquitin tails, this rests on
the assumption that each ubiquitin tail has only two docking sites and that the sites do not
discriminate between different docking proteins. While the lack of such competition would likely
mitigate the negative effect of TAB2 abundance on NEMO/IKKβ activity, the strong enhancement
of NFκB signaling in case of persistent NEMO/IKKβ activation emphasizes NEMO/IKKβ
complex's centrality for potentiating the response of the pathway. Finally, another limitation is the
assumed distribution of antigen concentrations that will be encountered by the CAR-4-1BB cells.
Since it is known that at least 95% of B-cell acute lymphoblastic leukemia (ALL) cells are CD19-
positive (Anderson et al. 1984; Nadler et al. 1984) and that protein concentrations typically follow
60
a lognormal distribution (Furusawa et al. 2005), we assumed a lognormal distribution and
approximated it to match CD19 antigen levels measured on CD19-positive ALL cells (Nerreter et
al. 2019). However, specific choices of the antigen distribution could impact our calculation of
mutual information. Thus, exploring a broader range of possible distributions would help to form
a more complete picture. For instance, the same experimental study had shown that some myeloma
cells (termed "CD19-negative") show vanishingly small CD19 expression levels (around 0.001
molecules per µm2
) compared to the rest of the population (around 1 molecule per µm2
). Thus, in
the case of myeloma cells, the distribution of CD19 concentrations among the population could be
approximated by a bimodal distribution. The percentage of these CD19-negative myeloma cells
varied significantly from patient to patient in a range of 10–80% (Nerreter et al. 2019). A future
study could investigate information transmission capabilities of the NFκB pathway in the context
of a bimodal antigen distribution with different percent contributions from each unimodal
component.
61
4. Information-theoretic analysis of a model of CAR-4-1BB-mediated NFκB activation
Portions of this chapter are adapted from: Vardges Tserunyan and Stacey D. Finley. Bulletin of
Mathematical Biology, 2023
4.1 Abstract
Systems biology utilizes computational approaches to examine an array of biological
processes, such as cell signaling, metabolomics and pharmacology. This includes mathematical
modeling of CAR T cells, a modality of cancer therapy by which genetically engineered immune
cells recognize and combat a cancerous target. While successful against hematologic malignancies,
CAR T cells have shown limited success against other cancer types. Thus, more research is needed
to understand their mechanisms of action and leverage their full potential. In our work, we set out
to apply information theory on a mathematical model of NFκB signaling initiated by the CAR
following antigen encounter. First, we estimated channel capacity for CAR-4-1BB-mediated
NFκB signal transduction. Next, we evaluated the pathway's ability to distinguish contrasting
"low" and "high" antigen concentration levels, depending on the amount of variability in protein
concentrations. Finally, we assessed the fidelity by which NFκB activation reflects the encountered
antigen concentration, depending on the prevalence of antigen-positive targets in tumor population.
We found that in most scenarios, fold change in the nuclear concentration of NFκB carries a higher
channel capacity for the pathway than NFκB's absolute response. Additionally, we found that most
errors in transducing the antigen signal through the pathway skew towards underestimating the
concentration of encountered antigen. Finally, we found that disabling IKKβ deactivation could
increase signaling fidelity against targets with antigen-negative cells. Our information-theoretic
62
analysis of signal transduction can provide novel perspectives on biological signaling, as well as
enable a more informed path to cell engineering.
4.2. Introduction
Systems biology is an interdisciplinary field that combines experimental and computational
approaches to study complex biological systems (Kitano 2002). It has contributed to the
development of mechanistic models to explain biological phenomena and interpret them from
novel perspectives. One such perspective has been the application of information theory to
biological systems (Uda 2020). Information theory is the mathematical study of signal
transmission and communication (Cover and Thomas 2012). A central concept of information
theory is mutual information. As a measure of dependence between random variables, mutual
information carries several advantages. First, unlike correlation, mutual information can be zero if
and only if the variables are independent (Shannon 1948). Second, mutual information makes no
assumptions regarding the relationship between two variables. This stands in contrast to various
definitions of correlation, which quantify either linear (Pearson's r) or monotonic (Spearman's r)
relationships and fail to capture more complex patterns (Schober, Boer, and Schwarte 2018).
One application of mutual information is in signal communication systems, where it is used
to analyze relationships between the input signal and the transmitted message. Notably, biological
signaling pathways possess properties similar to those of communication systems (Topolewski and
Komorowski 2021). Specifically, a common feature of signaling pathways is to initiate
proportionate changes in the concentration of a secondary messenger based on some primary
signaling molecule. Viewing extracellular ligands as an input signal and secondary messengers as
63
the pathway's output, past analyses have treated signal transduction pathways as communication
channels and analyzed them from an information-theoretic perspective (Rhee, Cheong, and
Levchenko 2012; Waltermann and Klipp 2011). Such communication channels are commonly
described by an inherent property, channel capacity (Uda 2020). Channel capacity is the highest
rate at which information can pass through the channel (Cover and Thomas 2012). It is achieved
by the input distribution that maximizes the mutual information between itself and the
corresponding output. Previous work on multiple pathways suggests that this upper limit is
typically on the order of 1 bit (Topolewski and Komorowski 2021), meaning that the pathway's
response can reliably distinguish only 21 = 2 distinct levels of the input signal, i.e., the input's
presence or absence. However, some signaling systems have a better resolving ability. For instance,
TRAIL-mediated apoptosis has a population-wide channel capacity of 3.41 bits, meaning that in a
given population, TRAIL can accurately specify up to 23.41 ≈ 11 distinct percentages of cells
undergoing apoptosis (Suderman et al. 2017). Additionally, studies of channel capacity of the ERK
and NFκB pathways have revealed that ligand information can be more efficiently encoded when
instead of a single measurement, a whole ensemble of response metrics is used, such as the
combined vector of amplitude, timing and duration (Selimkhanov et al. 2014). Similarly,
branching or parallel signaling channels can increase the channel capacity of cell signaling,
demonstrating the impact of network architecture on signaling fidelity (Cheong et al. 2011). Thus,
channel capacity is a useful metric for quantifying the precision by which extracellular ligands can
control cellular response via cell signaling.
In recent decades, chimeric antigen receptor (CAR)-engineered cells have emerged as an
innovative modality of cancer therapy (Hiltensperger and Krackhardt 2023). CAR T cells are a
type of immune cell genetically engineered to express a receptor comprised of an extracellular
64
recognition domain (specific to the cancer-associated antigen), along with an intracellular
signaling domain that actuates cell response after target encounter (Akhoundi et al. 2021).
Following infusion into a patient's bloodstream, CAR T cells can locate and kill cancer cells that
express the targeted antigen. Initial designs of the CAR (now termed "first-generation CAR")
involved only one signaling domain derived from native T cell receptor and showed little efficacy.
However, later work incorporated additional signaling domains originating from immune
coreceptors, such as CD28, ICOS and 4-1BB (Srivastava and Riddell 2015). Termed "secondgeneration CARs", these constructs have already shown promising results against certain types of
cancer. Excitingly, four of the second-generation CAR T therapies have been approved by the US
Food and Drug Administration by 2021 (Sengsayadeth et al. 2021), with the fifth therapy approved
in 2022 (Martin et al. 2022). Despite this progress, many limitations remain. For example, existing
CAR T therapies are ineffective against solid tumors due to the immunosuppressive tumor
microenvironment and low rate of tumor infiltration (Feigl et al. 2023; Guzman et al. 2023).
Additionally, CAR T therapy can cause severe side effects, such as cytokine release syndrome and
on-target, off-tumor toxicity (Chen, Abila, and Mostafa Kamel 2023). Thus, further research into
existing CAR T therapies remains necessary to harness their full potential.
Applying principles of systems biology has yielded success in increasing our quantitative
understanding of CAR-based therapies. For instance, one experimentally validated mathematical
model has focused on analyzing the pharmacokinetics of CAR T therapy by describing CAR Tmediated cancer cell depletion (Singh et al. 2020). Another study examined signaling processes in
CAR T cells by modeling the CAR-CD28 construct's activation of the ERK pathway (Rohrs et al.
2020). By considering the impact of added CD28 signaling, this study underscored the advantages
of second-generation CARs over the first-generation design. The same model was later used to
65
compare the impact of population-wide cell heterogeneity on the activation of CAR T cells (Cess
and Finley 2020; Tserunyan and Finley 2022c). By applying insights from information theory on
CAR-4-1BB constructs, our research group was able to assess the fidelity of CAR-4-1BBmediated activation of the NFκB pathway by a candidate distribution of the targeted CD19 antigen
(Tserunyan and Finley 2022a). Moreover, it was also possible to evaluate the impact of various
perturbations on signaling fidelity. We produced actionable strategies that can enhance the
pathway's response to encountered targets. However, this study focused only on variability caused
by the upstream steps in the pathway, without considering variability in the IκBα/NFκB complex
the dissociation of which directly leads to nuclear translocation of NFκB (Shih et al. 2011).
Furthermore, we examined a specific example of target antigen distribution without evaluating
other biologically motivated candidate distributions. Hence, further analysis of cell signaling based
on insights from information theory can provide a more complete view of CAR-4-1BB-mediated
NFκB activation.
In this current work, we set out to develop a deeper information-theoretic perspective of
CAR-4-1BB-mediated NFκB activation. By considering cell-to-cell variability in protein
concentrations as the source of noise, we have estimated channel capacity of the NFκB pathway
in context of the population response. Then, we analyzed the pathway's diminishing ability to
discern contrasting signals with increasing noise levels. Finally, we evaluated the fidelity of NFκB
activation when the CAR-4-1BB construct is stimulated with different candidate distributions of
targeted antigen. Our work demonstrates that a thorough analysis of signaling systems from an
information-theoretic perspective can provide a better understanding of their capabilities.
Excitingly, this work can supply quantitative insights for engineering principles that enable more
efficient design in various synthetic biology applications.
66
4.3. Methods
4.3.1. Network structure
We used our previously published model to analyze CAR-4-1BB-mediated NFκB
activation (Fig. 4.1) (Tserunyan and Finley 2022a). This deterministic ordinary differential
equation (ODE)-based mechanistic model represents key processes as chemical reactions between
various protein species. The model is written in MATLAB and comprises 10 proteins (9 proteins
of the pathway and the extracellular antigen), along with 30 kinetic parameters. At the beginning
of each ODE-based simulation, the system is initialized with all components present in the
cytoplasm in an unbound state. Then, we allow the system to evolve based on the governing ODEs
with absent extracellular antigen until reaching a steady state corresponding to the pre-stimulation
state of the cell. Only after this steady state is reached, we introduce the extracellular antigen and
observe resulting NFκB activity (Appendix C, S. Fig. 4.1A).
Model equations represent the following dynamic process of signal transduction (Appendix
C, S. Fig. 4.2). First, once the extracellular domain of the CAR binds an antigen molecule, the 4-
1BB domain of the CAR forms a signalosome, with TRAF2 proteins playing a key role (Zapata et
al. 2018). TRAF2 promotes the attachment of K63-ubiquitin chains to RIP1, enabling docking of
the TAK and IKK enzymatic complexes (Ea et al., 2006; Kanayama et al., 2004; Lee et al., 2004).
After docking, the enzymatic subunit of TAK phosphorylates the β subunit of the IKK complex
(C. Wang et al. 2001). The activation of IKKβ is transitory and typically lasts approximately five
minutes due to an auto-dephosphorylating motif near the C-terminus (Delhase et al. 1999).
Enzymatically active IKKβ phosphorylates the protein IκBα and initiates its degradation (Zandi et
al. 1997). In the resting state, IκBα binds NFκB and sequesters it in the cytoplasm. However,
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IKKβ-mediated degradation of IκBα releases NFκB from sequestration, allowing it to translocate
to the nucleus, where it functions as a transcriptional activator (Ghosh, May, and Kopp 1998). A
negative feedback mechanism ensures that the nuclear concentration of NFκB peaks
approximately 30 minutes after activation and then returns to its initial value (Shih et al. 2011).
We have chosen the maximum nuclear abundance attained by NFκB during this transient spike as
measure of pathway activation, based on its extensive use in past studies. For example, early
experimental assays have used it as a reliable way to quantify NFκB translocation in response to
Figure 4.1. A schematic outline of events leading up to the nuclear translocation of
canonical NFκB
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various stimuli (Trask 2004). Later studies confirmed peak nuclear abundance of NFκB as an
informative metric of pathway activation (Adelaja et al. 2021).
4.3.2. Noise in the signaling pathway
We assume that the source of noise confounding signal transduction across a population of
cells is the cell-to-cell variability in concentrations of proteins comprising the pathway. Motivated
by the finding that population-wide protein concentrations obey a lognormal distribution
(Furusawa et al. 2005), we performed simulations where initial protein concentrations for each
CAR cell were independently sampled from a lognormal distribution. We chose the location
parameter for the distribution of each protein such that the median concentration across the
population would equal the accepted value for that protein. We chose the scale parameter to be the
same for all proteins (termed "noise level"), and repeated simulations for multiple candidate noise
levels in order to capture general trends in signaling properties. Each simulation regime was
performed 2,000 times to ensure a converging sample.
4.3.3. Candidate antigen distributions
We model variability in antigen concentrations encountered by a CAR cell population
based on previously published measurements of CD19 antigen (Nerreter et al. 2019). Specifically,
fluorescence microscopy showed that the CD19 surface concentration on myeloma cells is in the
range of 0.16-5.2 molecules/µm2
, with antigen-positive cells comprising 10-80% of the myeloma
population. Many other cells show CD19 concentration on the order of 0.001 molecules/µm2
,
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described as "ultra-low". Meanwhile, the mean CD19 concentration on leukemia cells from the
NALM-6 cell line is approximately 3.4 molecules/µm2
, with at least 95% of acute lymphoblastic
leukemia cells being antigen-positive. Based on this information, we inferred that the surface
antigen concentration can be modeled by a bimodal distribution with one component tightly
centered around 0.001 molecules/µm2 (corresponding to antigen-negative cells) and the other
component centered on 3.0 molecules/µm2 (corresponding to antigen-positive cells) with a scale
parameter of 0.5 to approximate the observed range of measurements. We analyzed four different
distributions based on the weight of the positive component: 20%, 50%, 80% and 100% (Appendix
C, S. Fig. 4.3). The first three distributions are bimodal, and the system would have to distinguish
antigen-negative cells from antigen-positive cells before establishing finer gradations of
concentration. In case of the fully antigen-positive distribution, the sole task is to establish the
concentration of extracellular antigen on the antigen-positive target. Thus, each of these four
candidates served as a possible distribution for the input signal (i.e., antigen concentration), and
we evaluated the mutual information between a given antigen distribution and the NFκB response
it elicited.
4.3.4. Mutual information
Mutual information for continuous variables has been defined via the following equation
(Shannon 1948):
�(�; �) = 1 �(�; �) log �(�; �)
�(�)�(�)
����
ℝ$
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One approach for computing the mutual information of two continuous variables based on a
statistical sample is to discretize them (Ross 2014). However, this can cause large discrepancies
in the calculated number based on the choice of discretization scheme. As an alternative, we have
used the Kraskov algorithm to compute mutual information, which avoids explicit discretization
(Kraskov, Stögbauer, and Grassberger 2004). Instead, it relies on a K-nearest neighbors procedure
and tends to deliver more consistent results.
4.3.5. Channel capacity
The long-standing Blahut-Arimoto algorithm and its variations have been used for
computing channel capacity for discrete variables (Cover and Thomas 2012). Unfortunately, an
exact algorithm for transmission systems where both the input (e.g., encountered antigen
concentration) and the output (e.g., nuclear concentration of NFκB) are continuous, has not been
published to our knowledge. While efforts have been made to overcome this limitation, those
attempts incorporated additional assumptions regarding the structure of probability distributions
and the relationship between input and output, and the calculated channel capacity can fluctuate if
those assumptions are not satisfied (Jetka et al. 2019).
To approach this problem, we have devised an iterative heuristic procedure to estimate the
channel capacity for CAR-4-1BB-induced NFκB activation for a single activation event. To start,
we recalled the equivalence, which expresses mutual information as the difference between
entropies of a variable's prior and posterior distributions (conditioned on the second variable)
(Cover and Thomas 2012; Rhee, Cheong, and Levchenko 2012):
�(�; �) = �(�) − �(�|�),
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where I(S; R) is the mutual information between random variables S and R (denoting the input
signal and output response, respectively), H(S) is the entropy of S's prior distribution and H(S|R)
is the conditional entropy of S's distribution provided R, with all three quantities lower bounded
by zero (Uda 2020). Since channel capacity is the maximum mutual information that can pass
through the channel, we looked for an input signal distribution that has a large prior entropy, but a
near-zero conditional entropy.
Next, we recalled that channel capacity is interpreted as the logarithm of the largest number
of distinct input levels resolvable by the channel (Topolewski and Komorowski 2021). For
example, if channel capacity is n bits, then the system can resolve up to 2n distinct input
concentrations. It follows that this capacity could be achieved by an antigen distribution if it meets
two conditions. First, in the antigen's prior distribution, these n distinct levels should be equally
probable (to maximize H(S)). Second, by knowing the secondary messenger's concentration R, we
should be able to infer with negligible error which of the n concentration levels was used for
antigen (to minimize H(S|R)). In the context of NFκB signaling, which shows a sigmoidal dose
response, we can choose specific antigen levels that would be as easy to resolve as possible. For
example, if we are trying to distinguish between two antigen concentrations, then the most
resolvable pair would be the near-absent and saturating values, since activation caused by nearabsent antigen would be indistinguishable from basal levels, while activation caused by the
saturating concentration would be higher than for any intermediate value. Similarly, the set of three
antigen concentrations where the respective outputs are easiest to distinguish would be those,
which cause 0%, 50% and 100% activation in the system, since the response distribution
corresponding to the added "middle" value would be equidistant from the other two and show least
overlap with them (assuming response distributions are symmetrical). To generalize, if we have n
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distinct antigen concentrations, they would be most resolvable if the activation levels they elicit
are evenly spaced 100%/(n-1) apart. Such concentration values can be found with the dose
response curve.
Given this assessment, we proceeded as follows. First, we assumed that the pathway
encodes only two distinct antigen concentrations, "low" at 0.7 molecules/µm2 and "high" at 70
molecules/µm2
. This was motivated by the fact that at 0.7 molecules/µm2
, the pathway shows only
5.5% activation, i.e., nuclear NFκB remains at the basal level (Tserunyan and Finley 2022a).
Meanwhile, at 70 molecules/µm2
, the pathway shows 96% saturation, and further increases in the
antigen level show no appreciable increase in the concentration of nuclear NFκB. We obtained the
response distribution for this setup and computed the mutual information between concentrations
of antigen and nuclear NFκB. If this value was close to the entropy of the input distribution
(implying H(S|R) = 0, i.e., absolute certainty of antigen concentration provided the NFκB
response), we concluded that the pathway could resolve additional input levels. Hence, we
increased the number of distinct antigen concentrations by one and continued this process until the
mutual information between antigen concentration and NFκB response stops increasing.
Following this procedure, we took the maximum mutual information observed for each noise level
as corresponding channel capacity (Appendix C, S. Fig. 4.4). When disabling IKKβ deactivation,
the dose response curve shifts (Appendix C, S. Fig. 4.1B), necessitating a different choice of
candidate antigen concentrations, but the procedure is otherwise the same (Tserunyan and Finley
2022a). In this case, we used 0.1 molecules/µm2 and 20 molecules/µm2 as the starting "low" and
"high" antigen concentrations which produce 5.5% and 96% activation levels, respectively,
matching the similar setup of the unperturbed model.
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The fidelity of NFκB activation can be confounded by two sources that diminish the mutual
information between antigen concentration and nuclear NFκB. One is the stochasticity in the
cellular abundance of NFκB and IκBα, the dissociation of which directly leads to NFκB's nuclear
translocation. Another source is the variability in upstream proteins that lead to IκBα's
phosphorylation and degradation. To discern how each of these sources affects channel capacity
of the NFκB pathway, we performed Monte Carlo simulations for two scenarios: first, where
upstream proteins are variable, but the concentrations of NFκB and IκBα are fixed to the same
value for each simulation; and second, where NFκB and IκBα are variable along with all the other
proteins. For the rest of the simulations, we focused solely on the more biologically realistic
scenario with all proteins being variable (including NFκB and IκBα). Finally, since past
experimental research has shown that the fold increase in NFκB nuclear concentration at its peak
can be more informative than the absolute value (Lee et al. 2014), we repeated our calculations of
channel capacity by taking fold increase in nuclear NFκB following stimulation, relative to
baseline, as the output variable.
4.3.6. Assessing error rates
To demonstrate that decreasing channel capacity hinders the pathway's ability to discern
antigen concentrations, we examined how its response can distinguish between "low" (0.7
molecules/µm2
) and "high" (70 molecules/µm2
) levels of antigen (Appendix C, S. Fig. 4.5). First,
we obtained distributions of peak nuclear concentration of NFκB for each of those antigen levels.
Then, we devised a backwards procedure by noting whether the likelihood of each obtained
absolute response value was higher under the assumption of coming from the "low"- or "high"-
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stimulated response distribution. When a specific value of NFκB concentration came from
simulations with a "high" antigen concentration but its likelihood is greater under stimulation with
"low" antigen concentration, we considered this an instance of a "false negative". We defined the
converse case as "false positive". We represented these data as percent of false positive and false
negative estimates for each noise level. Finally, we repeated this procedure by using fold change
in nuclear NFκB as response variable.
Given the difference between dose response curves for the unperturbed system and with
disabled deactivation of IKKβ, we performed the analysis for the second case by accepting 0.1
molecules/µm2 and 20 molecules/µm2 as the "low" and "high" concentrations.
4.4. Results
4.4.1. Channel capacities
First, we computed channel capacity implied by our model for CAR-4-1BB-mediated
NFκB signaling. We evaluated channel capacity for two simulation conditions: (1) varying
concentrations only for proteins upstream of the NFκB/IκBα complex (IκBα and NFκB initial
concentrations are fixed); and (2) varying concentrations for all proteins, including IκBα and NFκB.
For each condition, we focused on two response measures that characterize the amount of
information carried about antigen concentration by NFκB: peak value of NFκB concentration in
the nucleus following stimulation, and the peak fold change in nuclear NFκB relative to baseline.
We observed that with all other factors fixed, channel capacity decreases with increasing
noise levels (Fig. 4.2A). However, results from various simulation conditions differed in the extent
75
of this decrease. When the concentrations of NFκB and IκBα were fixed across the population,
channel capacity of the signaling system was the same whether we considered the absolute
response of nuclear NFκB or the fold change (Fig. 4.2A, blue and yellow). This is anticipated since
a fixed pre-activation concentration of NFκB and IκBα means that fold change is identical to the
absolute concentration up to a constant multiplier. However, with variable concentrations of NFκB
and IκBα, channel capacity entailed by the absolute response decreased by approximately 1 bit for
all tested noise levels (Fig. 4.2A, green). This decrease in channel capacity corresponds to a 50%
reduction in the number of distinct antigen concentrations the pathway can resolve due to
variability in NFκB and IκBα levels alone.
When the abundances of NFκB and IκBα vary, channel capacity entailed by fold change
of nuclear NFκB proved to be comparatively consistent across noise levels (in the range of 0.82-
1.4 bits) (Fig. 4.2A, magenta) and higher than channel capacity of the absolute response (Fig. 4.2A,
Figure 4.2. Channel capacity of CAR-4-1-BB-mediated NFκB activation.
Results presented for different simulation conditions for either (A) the default parameters or
(B) disabled IKKβ deactivation. In each case, channel capacity was computed for the nuclear
concentration of NFκB in a population of cells with fixed (blue) or variable (green) pools of
IκBα and NFkB, in addition to the channel capacity entailed by the fold change with fixed
(yellow) or variable (magenta) pools of IκBα and NFkB.
A B
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green). This difference grew from 0.12 bits for noise level 0.25 to 0.70 bits for noise level 2.0.
This suggests that when overall noise level was relatively low, most variability in activation levels
was attributable to stochasticity in upstream signaling species, so that measuring fold change did
not result in a significant information gain. In contrast, at higher noise levels, response variability
can be mostly attributed to the stochasticity in cellular levels of NFκB since the fold change of
nuclear NFκB showed significant information gain over the absolute response.
In our previous work, we found that disabling the deactivation mechanism of IKKβ could
increase the mutual information between the distribution of antigen concentration and NFκB
activation (Tserunyan and Finley 2022a). Now, we aim to verify whether this observation is
limited to a specific input distribution or reflects a change in transmission abilities of signaling
system. Thus, we carried out similar calculations of channel capacity with disabled deactivation
of IKKβ (Fig. 4.2B). With fixed IκBα and NFκB concentrations, we observed a consistent increase
in channel capacity by approximately 1 bit in the perturbed model for all noise levels. This was
true for both absolute response and fold change (yellow and blue in Fig. 4.2B compared to Fig.
4.2A).
When IκBα and NFκB vary, disabling IKKβ deactivation resulted in an increase in channel
capacity of the absolute response by up to 0.7 bits (green in Fig. 4.2B compared to Fig. 4.2A).
Interestingly, channel capacity of the fold change is predicted to be almost independent of the noise
parameter and confined to 1.06-1.13 bits (Fig. 4.2B, magenta). Notably, for low noise levels, fold
change had a smaller channel capacity than absolute response. However, this trend did not hold at
noise levels greater than 0.5, when the capacity of the absolute response decreased with added
noise, while the capacity of fold change stayed the same.
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In summary, we found that when IκBα and NFκB concentrations were fixed, the NFκB
pathway's capacity to transmit information about the input signal was independent of the measure
of signal transduction (absolute response vs. fold change of NFκB). This remained true when IKKβ
deactivation was disabled. If IκBα and NFκB concentrations were varied, the unperturbed pathway
had a higher capacity to transmit information via the fold change of NFκB. If IKKβ deactivation
was disabled, the pathway could better relay information via the fold change of NFκB only at
higher noise levels.
4.4.2 Signal discernibility
To further understand how variability in protein levels affects signal transmission for CAR4-1BB-mediated NFκB activation, we decided to investigate the nature of the "errors" made by the
pathway in conveying information about extracellular antigen abundance. One possible way to do
this is to see whether pathway over- or underestimates the amount antigen present due to noise.
Thus, we stimulated the pathway in silico with two contrasting antigen levels while varying all
protein concentrations. Then, we evaluated how effectively NFκB activation can distinguish those
signals. We did this by observing whether a given value of NFκB response obtained from "high"
stimulation is more characteristic of the "low"-stimulated regime ("false negative") and vice versa
("false positive"). Following this approach, we saw that for all noise levels, the false positive rate
remains near 0% for both the absolute response and the fold change (Fig. 4.3A, blue and yellow).
In contrast, the false negative rate rose to 80% for absolute response depending on the noise level
(Fig. 4.3A, teal and purple). Notably, the false negative rate was 20-25% lower if the fold change
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of NFκB is considered instead. This means that the cells are predicted to transmit information more
accurately via the fold change of NFκB when contrasting stimuli are provided.
We performed the same analysis of the error rates while disabling IKKβ deactivation. Here,
we observed that while the false positive rate remains at zero, the false negative rate is up to 35%
lower compared to the unperturbed system (Fig. 4.3B). Notably, as with the unperturbed model,
cells were better able to transmit information about the input signal via the fold change in NFκB
than the absolute response (Fig. 4.3B, purple is lower than teal).
These findings demonstrate an interesting agreement with our estimate of the channel
capacity. Errors in transmitting two contrasting inputs would imply a channel capacity less than
log2(2) or 1 bit. Consistent with this, the error rates become greater than zero at noise levels where
Figure 4.3. Ability of correctly distinguishing contrasting antigen concentrations based on
NFκB activation.
Results presented for either (A) the unperturbed model or (B) disabled IKKβ deactivation.
Error rates were computed in a population of cells based on absolute response (blue, false
positives; teal, false negatives) or fold change (orange, false positives; purple, false
negatives).
A
B
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our estimate of channel capacity is close to 1 bit or lower. For the unperturbed model, this occurred
at noise levels of 0.5 and higher, when considering the channel capacity of the absolute response
and at the noise levels of 1.0 and higher when using channel capacity of the fold change (Fig.
4.2A). Altogether, we predict that a population of cells can more accurately distinguish contrasting
signals when relaying information via the fold change in NFκB, compared to the absolute response.
This is also the case when IKKβ deactivation is disabled. Finally, this demonstrates the link
between the pathway's ability to discern different input signals is tightly related to its channel
capacity.
4.4.3. Trial distributions
While the upregulation of certain surface antigens is a common feature of cancer cells, the
extent of this upregulation can vary greatly across a population of cells. For example, CD19, a
common marker of B cells, is present among 95% of acute lymphoblastic leukemia cells, but its
abundance among myeloma cells varies between 10% and 80% depending on the patient (Nerreter
et al. 2019). In order to examine how accurately CAR-4-1BB-mediated NFκB activation can relay
information about encountered antigen concentration depending on the proportion of CD19-
positive cells, we set out to compare the information content of the pathway when stimulated by
four different antigen distributions. These four distributions considered is bimodal and comprised
of the same antigen-negative and antigen-positive components, but the distributions differ by the
proportion of the antigen-positive component (20%, 50%, 80%, 100%) (Appendix C, S. Fig. 4.3).
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We calculated mutual information between each antigen distribution and the NFκB
activation it actuated (while all proteins of the signaling pathway were varied). Information
transmitted about those four antigen distributions among a population of CAR-4-1BB cells was
nearly identical for the absolute response at all noise levels (Fig. 4.4A). Considering the fold
change in NFκB levels showed higher mutual information between NFκB activation and the
distributions with an antigen-negative component, particularly at low noise levels (Fig. 4.4B). In
this case, information transmitted about the fully positive distribution diminished faster with
increasing noise (Fig. 4.4B, blue), relative to distributions with an antigen-negative component.
Hence, fold change in nuclear NFκB is more reflective of the encountered antigen concentrations,
especially when some of the encountered targets show near-absence of antigen.
Next, we examined same antigen distributions in the context of disabled IKKβ deactivation.
Our previous work focusing on the noise upstream of NFκB/IκBα dissociation had shown that this
Figure 4.4. Fidelity of information transmission for different distributions of antigen
concentration.
Results presented for (A) Mutual information between the absolute response of NFκB and the
antigen; (B) Mutual information between fold increase of nuclear NFκB and the
concentration of antigen (dark green, 100% antigen-positive; dark-medium, 80%; lightmedium, 50%; light green, 20%).
A B
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perturbation can increase the fidelity of upstream signaling. In line with this, mutual information
between the distribution of target antigen and the distribution of absolute NFκB response it
actuated increased by up to 0.5 bits when the target had an antigen-negative component (Fig. 4.5A
compared to Fig. 4.4A). This improvement in information transmission was present for fully
antigen-positive targets as well, albeit to a much smaller extent of up to 0.1 bits.
When disabling IKKβ deactivation, mutual information between antigen and NFκB fold
change decreased for most cases (Fig. 4.5B). A notable exception was the distribution with 20%
antigen positivity, which showed an increase of up 0.22 bits (Fig. 4.5B, light magenta). IKKβ
deactivation is a mechanism to dampen the pathway response, and it is unsurprising that disabling
it makes the response more accurate for an antigen distribution where the antigen-positive
component has low abundance. Conversely, the fully antigen-positive distribution showed a
Figure 4.5. Fidelity of information transmission for different distributions of antigen
concentration when deactivation of IKKβ is disabled.
Results presented for (A) Mutual information between the absolute response of NFκB and the
antigen; (B) Mutual information between fold increase of nuclear NFκB and the
concentration of antigen (dark magenta, 100% antigen-positive; dark-medium, 80%; lightmedium, 50%; light magenta, 20%).
A B
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significant deterioration of information transmission (dark magenta in Fig. 4.4B compared to Fig.
4.5B). This was in stark contrast with the case when NFκB and IκBα concentrations are fixed,
where a significant increase in mutual information is observed with this perturbation. To confirm
that the discrepancy is attributable to the added variability in NFκB and IκBα, we plotted the
mutual information between antigen concentration and different metrics of pathway activation
(Appendix C, S. Fig. S6). We observed that compared to the unperturbed system, NFκB indeed
receives more information from the upstream processes. This is noted by the fact that when NFκB
and IκBα were fixed, the mutual information for the perturbed system between antigen and NFκB
absolute response was higher by up to 0.77 bits compared to the baseline model. However, added
variability of NFκB and IκBα changed this pattern. Specifically, the mutual information between
antigen and NFκB absolute response remained largely the same for the perturbed system, while
the information between antigen and fold change decreased by up to 1 bit. Hence, deactivating
IKKβ can have different effects on signaling accuracy depending on the prevalence of antigen in
the targeted population and the response measure used to estimate information content.
In summary, we find that when all components of the signaling pathway were variable,
fold change in nuclear NFκB was a more accurate measure of encountered antigen concentrations,
especially if the distribution of targeted antigen contained an antigen-negative component. This
finding is consistent with the greater channel capacity attributable to fold change. Perturbing the
signaling pathway by disabling IKKβ deactivation resulted in an increase of mutual information
between antigen concentration and the absolute response of NFκB. However, the information
content of fold change mostly showed either a small decrease (for distributions with an antigennegative component) or a drastic reduction (for distributions with only an antigen-positive
component).
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4.5. Discussion
In our work, we sought to develop an information-theoretic perspective of CAR-4-1BBmediated NFκB activation based on a mathematical model of cell signaling. First, we estimated
channel capacity of signal transmission by considering as an encoding measure either the absolute
nuclear concentration of NFκB or its fold change compared to baseline levels. We found that fold
change of NFκB tends to have a higher capacity for transmitting information about the encountered
antigen. Furthermore, channel capacity expressed by fold change showed a weaker dependence on
noisiness and is close to 1 bit for the noise levels we tested. By comparing signal transmission with
and without variability of IκBα and NFκB, we noted that this factor alone could diminish channel
capacity by up to 1 bit, corresponding to a two-fold decrease in the number of distinct inputs the
pathway accurately resolves. Next, we evaluated the NFκB pathway's declining ability to discern
contrasting signals with increasing noise levels. We found that most errors in signal transduction
are attributable to a "false negative" error, whereby the pathway shows weak activation in response
to a high antigen concentration. In contrast, "false positive" errors remained near zero for all noise
levels tested. Similar to the case with channel capacity, cells demonstrated a better ability to
discern contrasting inputs via NFκB fold change compared to the absolute response. Finally, we
evaluated the ability of CAR-4-1BB-mediated NFκB signaling to accurately reflect antigen
concentration for targets with different proportions of antigen-positive cells. We found that the
fidelity of signal transmission for 100%, 80%, 50% and 20% antigen-positive targets is roughly
identical when considering signal transmission via the absolute response of NFκB. However, when
considering transmission via NFκB fold change, the fully positive distribution showed a much
faster decline in transmission fidelity with increasing noise compared to distributions with antigennegative cells.
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In our previous work, we found that disabling IKKβ deactivation can greatly increase the
fidelity of CAR-4-1BB-mediated NFκB activation (Tserunyan and Finley 2022a). Here, we
performed a more in-depth analysis of this perturbation. Specifically, we found that with fixed
IκBα and NFκB concentrations, this manipulation could increase channel capacity by
approximately 1 bit compared to the default model. This increase held in case of varying IκBα and
NFκB concentrations and considering channel capacity entailed by absolute response. However,
the increase in capacity entailed by fold change was modest when varying IκBα and NFκB
concentrations. Additionally, we found that the perturbation improved the pathway's ability to
discern contrasting signals with a 20-25% lower error rate. Finally, we observed that disabling
IKKβ deactivation could improve the fidelity of signal transmission for input distributions with an
antigen-negative component if we consider encoding via absolute response. Interestingly, in the
case of signal encoding via fold change, the perturbation drastically reduced signaling fidelity for
the fully antigen-positive distribution.
Previous studies of a signaling pathways have demonstrated that channel capacities of most
pathways are within 0.5-1.75 bits (Topolewski and Komorowski 2021). An experimental estimate
of the channel capacity of NFκB signaling in TNF-stimulated fibroblasts suggested the value of
0.92 bits, implying that the pathway can resolve only 20.92 ≈ 2 input concentrations (Tudelska et
al. 2017). However, pathways can increase their information content by encoding stimulus strength
not in the absolute concentration of the secondary messenger, but in the ensemble of multiple
cross-wired effectors or in the fold change of the messenger's concentration (Suderman et al. 2017;
Topolewski and Komorowski 2021). For example, some experimental findings suggest that NFκB
fold change is more informative than its absolute abundance (Lee et al. 2014). This is consistent
with our finding that under most simulation scenarios, fold change shows a higher channel capacity.
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Prior modeling studies have found that a relatively small change in channel capacity from 0.85
bits to 0.6 bits can increase the number of incorrectly responding cells by twofold (Tabbaa and
Jayaprakash 2014). Thus, enhancing the fidelity of signaling pathways that actuate the therapeutic
function of CAR T cells could result in a better alignment between the response of the CAR cell
and the target it encounters. Given our finding that the same perturbation to the signaling pathway
affects information transmission differently depending on the presence of antigen-negative targets,
a successful engineering approach would consider features of likely targets for the more precise
design of CAR T cells.
Along with the novel findings in our work, we acknowledge certain areas that could be
improved upon in the future. One such area is the correspondence between our model and the
experimental system. Due to the scarcity of available measurements, we had to make order-ofmagnitude estimates for some parameters by knowing the timescale at which the underlying
process proceeds. Additionally, other parameter values were based on studies of NFκB activation
in fibroblasts via the TNF receptor (TNFR). The basis for applying these data on CAR-4-1BBmediated NFκB activation is that 4-1BB and TNFR belong to the same superfamily of receptors
and trigger cell signaling via a similar mechanism of recruiting TRAF proteins (Zapata et al.
2018). It is possible that more numerically accurate findings may be produced if our model is
calibrated against measurements performed in CAR-4-1BB cells. Similarly, our model accounts
for the fast-acting self-deactivation mechanism of IKKβ which is responsible for the transient
nature of its activity, but it excludes the action of phosphatases which restore IKKβ to the original
state enabling the system to respond to future stimuli. The model could be extended by adding
this feature and exploring the implications of processing multiple targets by the same cell.
Another limitation that we recognize is the assumption that all proteins in a heterogeneous
86
population are distributed according to a lognormal distribution with the same scale parameter.
Lognormality of protein concentrations has been widely recognized for steadily growing cells,
while experimental measurements have found that the ratio of standard deviation to the mean is
constant (Furusawa et al. 2005). By our calculations, this ratio implies an identical scale parameter
for protein distributions, roughly equal to 0.5 for E. coli cells. Studies in human B cells suggest a
smaller value of approximately 0.35 (Mitchell et al. 2018), in line with the 15-30% coefficient of
variation observed for human endogenous proteins (Sigal et al. 2006). Notably, around those noise
levels, our simulations predict a channel capacity of 0.85-1.3 bits, while the experimentally
measured value is 0.92 bits. Nevertheless, both lognormality and identical scale parameters for
protein distribution depend on the steady growth of cells. In cases when this assumption does not
hold, different proteins could have different variability levels potentially causing unexpected
behaviors of the system. This is underscored by the fact that disabling IKKβ deactivation had
diametrically opposing consequences on the accuracy of signal transmission depending on the
variability of IκBα and NFκB. We can update the model as more information becomes available
regarding the distributions of the concentration of signaling species. Finally, we have focused our
studies of the pathway on one metric of activation, the maximum NFκB concentration observed
during its transient spike. Considering other metrics of activation, such as the duration of the spike
or its average magnitude could provide further insight on information transmission by the
pathway.
In conclusion, we aimed to use mathematical modeling and information theory to grasp
CAR-4-1BB-mediated NFκB activation. We first estimated the channel capacity of this
transduction pathway under different conditions. Then, we examined the pathway's ability to
distinguish low and high signals in the presence of variability. Finally, we evaluated how
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accurately NFκB activation reflects encountered antigen concentration in a tumor population. Our
findings suggest that fold change in the nuclear concentration of NFκB has a higher channel
capacity than the absolute response. We also found that due to variability, the response of the
pathway tends to underestimate the concentration of target antigen. Finally, we discovered that
disabling IKKβ deactivation could improve signaling fidelity when encountering targets that have
antigen-negative cells. Thus, our analysis offers new insights into biological signaling and can
inform cell engineering practices.
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5. Conclusion
5.1. Summary
In this dissertation, I quantitatively analyzed signaling events in CAR cells, using
mechanistic mathematical modeling to investigate the consequences of cell-to-cell variability on
population-wide signaling. Through this analysis, I provided valuable insights into existing CAR
designs, while underlining implications for further engineering.
In the first chapter, I focused on dissecting performance disparities between first- and
second-generation CAR-CD28 cells when subjected to variations in kinetic parameters at the
population level. Leveraging a mechanistic model of CAR-CD28-induced ERK signaling, I
demonstrated that second-generation CARs equipped with a CD28 co-signaling domain have
shorter activation times and reduced population-wide variability compared to first-generation
counterparts. A black-box model powered by gradient-boosted trees (GBT) helped identify kinetic
parameters significantly influencing ERK activation. Lastly, the constrained optimization
approach pinpointed parameters to manipulate that would result in the greatest reduction in ERK
activation time. I hypothesized that engineering to enhance LCK's catalytic activity in
phosphorylating CD3ζ ITAM motifs would result in more potent ERK response.
In the second chapter, I introduced a novel mathematical model replicating the dynamics
of NFκB signaling mediated by CAR-4-1BB. This model successfully mirrored experimentally
observed dynamics, with IKKβ transient activity reaching its peak at 10-15 minutes poststimulation, followed by nuclear NFκB peaking at 30 minutes. Global sensitivity analysis
suggested that the model is relatively constrained with respect to kinetic parameters and initial
concentrations. Next, I proceeded to explore information transmission across successive levels of
the NFκB pathway, showing that most information loss occurs when activated Tat-associated
89
kinase 1 (TAK1) phosphorylates IKKβ. Finally, I used this quantitative insight to give practical
suggestions for enhancing the precision of CAR-4-1BB signaling in response to cancerous targets.
I found that overexpressing NEMO and inhibiting IKKβ self-deactivation are promising strategies
to boost the mutual information between antigen concentration and nuclear abundance of NFκB.
In the third chapter, I extended the information-theoretic exploration of CAR-4-1BBmediated NFκB activation. First, I used the model to estimate channel capacity for CAR-4-1BBinduced NFκB activation. This analysis underscored the superior accuracy of fold change in
nuclear levels of NFκB over its absolute abundance as an encoding measure. I also probed the
pathway's ability to distinguish contrasting signals in different noise levels, revealing that most
errors are "false negatives". Consistent with the analysis of channel capacity, fold change in NFκB
discerns inputs more accurately than absolute abundance. Lastly, I revisited the impact of disabling
IKKβ deactivation on CAR-4-1BB-mediated NFκB activation. Based on my simulations, this
manipulation amplifies channel capacity and improves the pathway's ability to distinguish
physiologically relevant signals.
5.2. Future directions
While presenting a novel mathematical perspective on CAR cell signaling, I also recognize
that the methods and conclusions presented here can be extended and elaborated on in future
research. One direction is to consider the impact of intrinsic noise inherent in intracellular reactions.
Throughout this work, cell-to-cell variability (also known as extrinsic noise) was taken as the only
source of noise. However, a more complete picture would emerge once we account for the dynamic
stochasticity in biochemical reaction rates. I could achieve this by replacing deterministic ODEs
90
with stochastic ODEs and integrating them via the Gillespie algorithm. This approach would
provide a more complete picture of how diverse sources of noise confound signal transmission.
Another direction to advance this work is to calibrate the models against relevant
experimental data. While the model of CAR-CD28-mediated ERK activation has been calibrated
against phosphoproteomic measurements in Jurkat T cells, the model of CAR-4-1BB-mediated
NFκB activation has been compiled from fibroblast data. The sensitivity analysis of this model
demonstrates that outcomes predicted by the model are robust to significant changes in parameter
values. Nevertheless, calibrating it to experimental data collected either from CAR T or CAR NK
cells would provide a more definitive understanding of how this signaling mechanism operates in
the relevant context. Furthermore, experimentally quantifying the amount of noise in CAR cells
would clarify the extent of variability and provide a realistic gauge of noise levels to use in
simulations. This has been achieved in other cell lines by adding a fluorescent tag to proteins and
measuring the fluorescence of individual cells via flow cytometry, thereby estimating the protein's
population-wide distribution (Furusawa et al. 2005). This approach can be applied to CAR cells
similarly quantifying the variability in protein expression.
Finally, my framework could be expanded by including further signaling modules to gain
a more holistic understanding of signaling processes. While I represented signaling processes in
my models as converging upon one secondary messenger, in reality, multiple pathways get
activated in parallel, and the balance between them can be as important in determining cellular
response as individual activities of separate pathways. Thus, performing simulations with
stochastic ODEs, calibrating model parameters against experiential observations, and adding
further biological detail are potential directions which can build upon the findings in this work and
further advance systems biology applications to CAR cell research.
91
5.3. Concluding outline
This work highlights the use of mathematical modeling in studying the impact of cell-tocell variability on CAR cell signaling. By using a combination of mechanistic and data-driven
modeling, statistics, and information theory, I gain a systems-level perspective on the functionality
of CAR cells and provide suggestions for enhancing their potency. Ultimately, this work
demonstrates how quantitative approaches can greatly benefit the understanding of biological
systems and aid in engineering applications.
92
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Appendix A
Supplementary Figure 2.1. Schematic of CAR T cell signaling model. We consider four
modules.
Module I (blue): CAR activation by LCK (whose catalytic activity is regulated by
autophosphorylation and the inhibitory kinase, CSK). Module II (red): inhibition of CAR
activation by phosphatases CD45 and SHP1/2. Module III (yellow): formation of the LAT
signalosome, a multi-protein complex. Module IV (green): downstream signaling in the MAPK
pathway, leading to ERK activation. Lines with bar indicate inhibition; lines with arrowheads
indicate activation steps.
104
Supplementary Figure 2.2. Dose response curves of cell activation times.
We varied the level of antigen exposure and simulated the activation time for different
conditions. (A) Default parameters; (B) Optimized value for Kcat_ZAP, (C) Optimized value
for Kcat_LCKPU_CD3z, (D) Optimized values for both Kcat_ZAP and Kcat_LCKPU_CD3z.
A B
C D Activation time, min
30
20
10
0
10-2 10-1 100 101
Activation time, min
30
20
10
0
10-2 10-1 100 101
Activation time, min
30
20
10
0
10-2 10-1 100 101
Activation time, min
30
20
10
0
10-2 10-1 100 101
Antigen concentration, molec. per µm2
Antigen concentration, molec. per µm2 Antigen concentration, molec. per µm2
Antigen concentration, molec. per µm2
First-generation cells (CAR-CD3ζ)
Second-generation cells (CAR-CD28-CD3ζ)
105
Supplementary Figure 2.3. Permutation importance scores for 48 kinetic parameters used for
creating a gradient-boosted tree model to predict cell activation times.
A gradient boosted tree was used to predict the cell activation times based on model kinetic
parameters. We show the permutation importance scores for all kinetic parameters under
different conditions: (A) CAR-CD3ζ with low antigen concentration, (B) CAR-CD3ζ-CD28 with
low antigen concentration, (C) CAR-CD3ζ with high antigen concentration, (D) CAR-CD3ζCD28 with high antigen concentration.
A B
C D
106
Supplementary Figure 2.4. Comparison of activation of CAR T cells with optimized parameter
values.
We show the number of cells activated and their activation times, showing shifts in the response
of CAR T cells with optimized kinetic parameters under antigen variation. Note, this is the same
simulation data as shown in Fig. 1 and Fig. 6. (A) Comparison of the number of activated cells
and their activation times for default and optimized parameter values among cells with firstgeneration CAR constructs (CAR-CD3ζ); (B) Comparison of the number of activated cells and
their activation times for default and optimized parameter values among cells with secondgeneration CAR constructs (CAR-CD3ζ-CD28).
A
B
107
Supplementary Figure 2.
5.
Comparison of activation of CAR T
cells with optimized parameter
values.
We show the number of cells
activated and their activation times,
showing shifts in the response of
CAR T cells with optimized kinetic
parameters under kinetic parameter
variation. Note, this is the same
simulation data as shown in Fig. 2
and Fig. 7. (A) Comparison of the
number of activated cells and their
activation times for default and
optimized parameter values among
cells with first
-generation CAR
constructs (CAR
-CD3
ζ), top row:
low antigen stimulation, bottom
row: high antigen stimulation; (B)
Comparison of the number of
activated cells and their activation
times for default and optimized
parameter values among cells with
second-generation CAR constructs
(CAR
-CD3
ζ-CD28). Top: low
antigen stimulation, bottom: high
antigen stimulation.
AB
108
Appendix B
300
250
200
150
100
50
0
Number of cells
400
300
200
100
0
0 5 10 15 20
0 10 20 30 40 50 60
NFκBβn conc., molec. per μm2
Number of cells
Antigen conc., molec. per μm2
A
B
Supplementary Figure 3.1. Distribution of antigen concentrations and peak NFκB
nuclear concentrations.
Histograms show: (A) Sampled antigen concentration used throughout Monte Carlo
simulations; (B) Peak NFκB nuclear concentrations observed in response to antigen
stimulations from (A) at different intrinsic noise levels.
Noise level 0.01
Noise level 0.75
Noise level 2.0
109
Supplementary Figure 3.2. Dose response curves of K63 ubiquitin-bound TAB2 and NEMO
with default initial concentration or 50% underexpression of TAB2.
Results given for (A) Concentration of bound TAB2 as a function of antigen concentration; (B)
Concentration of bound NEMO as a function of antigen concentration.
Conc. of bound TAB2, molec. per μm2
30
25
20
15
10
5
0
100 101 102
Antigen conc., molec. per µm2
100 101 102
Antigen conc., molec. per µm2
70
60
50
40
30
20
10
0
Conc. of bound NEMO, molec. per μm2
A B
Default TAB2
Underexpressed TAB2
110
Supplementary Figure 3.3. Activation profiles for IKKβ and NFκB in response to antigen
binding the CAR with disabled deactivation of IKKβ.
The pathway was stimulated with 10 different antigen concentrations in silico and activation
profiles for IKKβ and NFκB were recorded for each antigen concentration. (A) Concentration
of enzymatically active IKKβ; (B) Nuclear concentration of NFκB. IKK
βact. conc., molec. per μm2
70
60
50
40
30
20
10
0 20 40 60 80 100
Time, minutes
70
60
50
40
30
20
10
NF
κ
B
βn conc., molec. per μm2 0 20 40 60 80 100
Time, minutes
102.5
10-0.5Antigen concentration, molec. per μm2
102.5
10-0.5Antigen concentration, molec. per μm2
A
B
111
Supplementary Figure 3.4. The transduction of information along the canonical NFκB
pathway with disabled IKKβ deactivation.
Percentages show relative decrease of mutual information at the level of nuclear NFκB
concentration compared to the default model at different values of the noise parameter. MI change relative to default, %
100
80
60
40
20
0 0.1 0.25 0.50 0.75 1.0 2.0
Noise Level
112
Appendix C
Supplementary Figure 4.1. Time courses for NFκB nuclear abundance induced by different
antigen concentrations.
Presented for the (A) Unperturbed model; (B) With disabled IKKβ deactivation.
A B
113
Supplementary Figure 4.2. SGBN schematic of the model.
Membrane/Cytoplasm
Nucleus
114
Supplementary Figure 4.3. Different distributions of antigen concentration for probing the
fidelity of CAR-4-1BB-mediated NFκB activation.
Identical positive and negative components are present in varying proportions. Results
presented for (A) 100% cells antigen-positive; (B) 80%; (C) 50%; (D) 20%.
A B
C D
115
Supplementary Figure 4.4. Example of computing channel capacity.
Results for (A) mutual information between different candidates of a capacity-maximizing
antigen distribution and the pathway response (blue, two-component distribution of antigen
concentrations; orange, three; yellow, four; purple, five; green, six; cyan, seven; (B) Channel
capacity estimated as the maximum mutual information achievable at each noise level, based on
A (blue curve identical to that in Fig.4.2A)
A B
116
Supplementary Figure 4.5. Deteriorating ability to discern contrasting signals with increasing
intrinsic noise.
Noise level set at (A) 0.5, (B) 1.0, (C) 1.5, (D) 2.0. Blue shows the unperturbed pathway
stimulated with antigen concentration of 0.7 molecules/µm2
, orange shows results from
stimulation with antigen concentration of 70 molecules/µm2
. Note that with increasing noise
levels, the response distribution of "high" stimulation becomes closer to that of the "low"
stimulation. For this reason, most of the response values of "high" stimulation become more
characteristic of and indistinguishable from "low"-stimulated cells.
A B
C D
117
Supplementary Figure 4.6. Mutual information between the 100% antigen-positive
distribution and various metrics of pathway activation.
Results shown for (A) the unperturbed system and (B) with disabled deactivation of IKKβ.
Mutual information between antigen concentration and enzymatically active IKKβ in blue,
absolute response of NFκB in orange (if IκBα and NFκB are fixed), absolute response of NFκB
in yellow (if IκBα and NFκB are variable), fold change in nuclear NFκB in purple (if IκBα and
NFκB are variable).
A B
Abstract (if available)
Abstract
Chimeric antigen receptor (CAR) cell therapy is a novel approach to cancer immunotherapy, which seeks to engineer immune cells with the ability to recognize and combat tumors. Advancing this mode of therapy hinges upon understanding signaling processes within CAR cells initiated upon encountering a target. This dissertation examines quantitative aspects of CAR-mediated intracellular signaling, focusing on the influence of cell-to-cell variability on signaling processes.
In the first chapter, I utilize mathematical modeling to examine CAR-CD28-mediated signaling in heterogeneous CAR cell populations. I find that CD28 cosignaling increases the potency of cell activation while reducing population-wide variance. Furthermore, I find that enhancing the catalytic activity of lymphocyte-specific protein tyrosine kinase could achieve a similar effect without necessitating CD28. In the second chapter, I focus on developing a computational model of CAR-4-1BB-mediated NFκB signaling. Detailing the structure and behavior of the model, I identify potential manipulations, such as overexpressing the protein NEMO, to fine-tune the NFκB-mediated response. In the third chapter, I leverage information theory to evaluate the fidelity of CAR-4-1BB-mediated NFκB activation. I quantify the impact of extrinsic noise on the ability of the pathway to accurately transmit signals, finding that noisiness tends to result in pathway underactivation. I also find that disabling the self-deactivation mechanism of the protein IKKβ can greatly increase the accuracy of NFκB signaling.
Ultimately, the framework presented in this dissertation underscores the importance of integrating mathematical methods into the study of CAR therapy to both understand observed phenomena and drive CAR cell development.
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Asset Metadata
Creator
Tserunyan, Vardges
(author)
Core Title
Understanding the impact of cell-to-cell variability on intracellular signaling in CAR cells through mathematical modeling
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Computational Biology and Bioinformatics
Degree Conferral Date
2024-05
Publication Date
02/02/2024
Defense Date
01/31/2024
Publisher
Los Angeles, California
(original),
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
cancer therapy,cell signaling,computational biology,information theory,mathematical modeling,OAI-PMH Harvest
Format
theses
(aat)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Finley, Stacey D. (
committee chair
), Graham, Nicholas (
committee member
), Kay, Steve (
committee member
), MacLean, Adam (
committee member
)
Creator Email
vardgestserunyan@gmail.com,vtseruny@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC113825942
Unique identifier
UC113825942
Identifier
etd-TserunyanV-12653.pdf (filename)
Legacy Identifier
etd-TserunyanV-12653
Document Type
Dissertation
Format
theses (aat)
Rights
Tserunyan, Vardges
Internet Media Type
application/pdf
Type
texts
Source
20240208-usctheses-batch-1125
(batch),
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
cancer therapy
cell signaling
computational biology
information theory
mathematical modeling