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Mechanistic model of chimeric antigen receptor T cell activation

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Mechanistic model of chimeric antigen receptor T cell activation

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Mechanistic Model of Chimeric Antigen Receptor T cell Activation

By

Jennifer A. Rohrs

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
of
THE UNIVERSITY OF SOUTHERN CALIFORNIA

In partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in
BIOMEDICAL ENGINEERING

August 2018

Copyright 2018 Jennifer Ann Rohrs

i
Dedication

This thesis is dedicated to my family, who supported me,
and my friends, who distracted me.

ii
Acknowledgements

I’d like to start by thanking my co-advisors, Professor Pin Wang and Professor
Stacey Finley. I am eternally grateful for their support and how easy they made it to work
together on this collaborative project. From my first day of graduate school, Prof. Wang
was encouraging and open to trying every new idea we could think of. Throughout my
Ph.D., he was always excited to discuss new ideas and learn along with me, guiding me to
expand my horizons and explore new avenues of science. I will never forget how
empowering it felt to have a boss who believes in my abilities enough to entertain any new
idea that I came up with.
Professor Finley has been an advisor, confidant, and mentor to me. Together with
Professor Wang, she was open and trusting enough to branch out into a variety of
collaborations that made this body of work possible. Additionally, she helped me extend
myself in many other ways, such as applying to conferences, building connections in the
field, and allowing me to watch the process of her own career development. Without these
skills and insights, I do not believe I would have the same amount of confidence and
preparedness for my own future. More personally, Professor Finley was a shoulder to lean
on during the ups and downs of graduate school. Her ability to support me as both a teacher
and a friend is something that I aspire to embody in my own relationships.
Next, I would like to thank my committee members Professor Nicholas Graham
and Professor David D’Argenio. Prof. Graham also collaborated on this work. His
readiness to work with us on a brand-new project still surprises me to this day. He not only
helped me with the experiment, but also took the time to teach me and ensure that I came
out with important skills that I can use in the future. I appreciate his time and patience.
iii
Prof. D’Argenio was the first teacher to introduce me to biological computational
modeling as my undergraduate research mentor. I am forever thankful for the time he took
to teach me about this growing field. He started me in this area of study, helped me build
connections and get internships to expand my skills, and watched my progress throughout
my Ph.D. as a qualifying exam and defense committee member. I can honestly say, I would
not be here if it weren’t for his support and encouragement.
I would also like to thank Professor Norbert Grzywacs. He helped me see that it
doesn’t matter what you study, as long as you have the skills to learn. This was both a
driving force for me to start a Ph.D. and a saving grace during the difficult times when it
seemed like there was no end in sight.
Next, I would like to thank all of my friends and lab mates. I would particularly like
to thank Dr. Paul Bryson and Dr. Yarong Liu for their patience in answering all of my
questions, Dongqing Zheng for helping me learn new skills in mass spectrometry, Dr.
Yujeong Kim, Dr. Natnaree (Ploy) Siriwon, Elizabeth Siegler, Dr. Mahua Roy, Quanhui
(Jess) Wu, Gunce Cinay, Sahak Makaryan, Nethika Ariyasinghe, and Krisna Bahargava
for their conversations and friendships that made my time in lab feel less like work, John
Mac, Dr. Xiaoyang Zhang, Dr. Si Li, Xianhui Chen, Yun Qu, Min Song, Ding Li, Alireza
Delfarah, James Joly, Nicolas Hartel, Christopher Sulistio, and Ryland Mortlock for their
support and friendship. And all of the other lab members during my time at USC who
helped make graduate school fun and productive.
I would especially like to thank my family for their support. My father, Dr. Charlie
Rohrs, has been an amazing influence, and I don’t think I would have considered graduate
school if it weren’t for his example. My mother, Catherine Matthews, continually helps me
iv
separate my own dreams from the expectations of others. And my sisters, who understand
me in a way that no one else does: Kelly Rohrs Jankowski, who taught me that no matter
how much of a bad ass woman you are, family is always the most important, and you can
do it both, and Ali Rohrs who is the most understanding and compassionate person I can
imagine and helps pry me out of my cold analytical shell and relate to other people in better,
deeper ways. And especially the William, who constantly inspires me. I love you all.
Thank you to my fiancée Dr. Robert Craig II. We went through the worst and best
of graduate school together, and, for that, I am forever grateful. Rob pushes me to be the
best that I can be without feeling like I’m competing or trying to keep up. I didn’t know
how it felt to truly be partners with someone until I met Rob. We grew together in graduate
school, and Rob is forever the best thing I got out of my Ph.D. I love you.
Finally, my roommates: Morgan Bowser, the house dad, who always takes care of
us, plans all of our fun adventures, and keeps me grounded, Victoria Aveyard, who helps
me take a break from science and learn thousands of random facts about everything from
the ancient Rome to the latest celebrity couple, and Tori Ahl, who I have lived with (more
or less) since freshman year of college, who opens us up with her heart-to-hearts and then
clings to those hearts with her tiny little hands. I can’t imagine a better group of friends, I
would have died in graduate school without you, or at least probably quit a long time ago.
You are family and I love you. Same goes to the rest of my friends in Adventuretime.
You’re the real deal and my life would be sad and boring without you. I can’t wait until we
grow up and all live together again on a cul-de-sac.
v
Table of Contents

Dedication i

Acknowledgments ii

List of Figures viii

List of Tables x

CHAPTER 1: Introduction 1
1.1. Chimeric antigen receptor engineered T cells 2
1.2. T cell activation 4
1.2.1. Intracellular signal activation 5
1.2.2. Phosphatase activity and feedback 7
1.2.3. CD28 signaling 9
1.2.4. Comparison of TCR and CAR signaling 10
1.3. Mechanistic modeling 11
1.4 Summary of T cell Activation Models 14
1.5 Dissertation Outline 17

CHAPTER 2: Predictive Model of Lymphocyte-specific Protein Tyrosine
Kinase Autoregulation

21
2.1. Abstract 22
2.2. Introduction 23
2.3. Materials and Methods 26
2.3.1. Data extraction 26
2.3.2. Model structure 26
2.3.3. Numerical implementation of the model 27
2.3.4. Parameter estimation 28
2.3.5. Clustering 30
2.3.6. Sensitivity analysis 30
2.3.7. Statistical analysis 31
2.4. Results 33
2.4.1. Model construction 33
2.4.2. Determining the optimal parameter sets 36
2.4.3. Model fitting 42
2.4.4. Model validation 46
2.4.5. Sensitivity analysis 48
2.4.6. Predicted mechanism of LCK activation 50
2.5. Discussion and Conclusion 55
2.6. Acknowledgements 61

vi
CHAPTER 3: Computational Model of Chimeric Antigen Receptors Explains
Site-specific Phosphorylation Kinetics

63
3.1. Abstract 64
3.2. Introduction 65
3.3. Materials and Methods 67
3.3.1. Recombinant protein expression and purification 67
3.3.2. Liposome preparation 69
3.3.3. Protein phosphorylation time courses 69
3.3.4. Standard curve preparation 70
3.3.5. Phospho-proteomic sample preparation 71
3.3.6. Phospho-proteomic data collection 71
3.3.7. Mass spec data analysis and normalization 73
3.3.8. Statistical analysis 74
3.3.9. Sigmoidal parameter calculations 74
3.3.10. Mechanistic computational modeling 75
3.4. Results 78
3.4.1. Tyrosine sites on CD3ζ are phosphorylated by LCK with
different kinetics

78
3.4.2. LCK catalyzes CD3ζ tyrosine site with different substrate
specificities

81
3.4.3. The CD3ζ ITAM sites are phosphorylated independently 84
3.4.4. LCK binding and catalytic parameters are correlated 90
3.4.5. Computational model predicts the emergence of 21 kDa CD3ζ in
the presence of ZAP-70 and phosphatases

91
3.4.6. LCK binding helps protect slowly phosphorylated ITAMs from
dephosphorylation

95
3.4.7. CD28 tyrosine sites are phosphorylated more slowly than CD3ζ
tyrosine sites

97
3.4.8. CD28 increases the phosphorylation rate of CD3ζ 99
3.4.9. CD28 may decrease the threshold of CD3ζ ITAM activation 102
3.5. Discussion 104
3.6. Conclusion 108
3.7. Acknowledgements 109

CHAPTER 4: Computational Model Predicts the Mechanism of CD28 Co-
stimulation in CAR-engineered T cells

111
4.1. Abstract 112
4.2. Introduction 113
4.3. Methods 115
4.3.1. Construction of a mechanistic computational model of CAR T
cell activation

115
4.3.2. Parameter fitting 121
4.3.3. Sensitivity analysis 121
4.3.4. Cell lines and reagents 122
4.3.5. Stable transduction of CAR and CD19 expressing cell lines 123
vii
4.3.6. T cell stimulation and ppERK analysis 124
4.3.7. Experimental data curve fitting 125
4.4. Results 126
4.4.1. Model of CAR ppERK activation 126
4.4.2. Sensitivity analysis 130
4.4.3. Model fit to experimental data 132
4.4.4. Model recreates experimental results from the literature 135
4.4.5. Tuning of SHP1 negative feedback 139
4.4.6. Comparison of CD28 effects on SOS and CD3ζ 140
4.4.7. Experimental data of ERK activation in CAR T cells 145
4.5. Discussion 149
4.6. Conclusion 154
4.7. Acknowledgements 155

CHAPTER 5: Conclusion 157
5.1. Summary 158
5.2. Future Directions 160
5.3. Conclusion 162

References 163

viii
List of Figures

Figure 1-1: CAR development 3
Figure 1-2: Schematic of CAR signaling 12

Figure 2-1: Schematic of LCK interactions 35
Figure 2-2: Method for choosing the optimal parameter sets 39
Figure 2-3: Predictions for three parameter set clusters 41
Figure 2-4: LCK minimal model fit to experimental data 43
Figure 2-5: Optimal parameter set values for LCK minimal model 45
Figure 2-6: LCK minimal model validation 47
Figure 2-7: Sensitivity indices of LCK minimal model parameters 49
Figure 2-8: Schematic of predicted LCK kinase activity 51
Figure 2-9: Model predictions of intermediate LCK species 53

Figure 3-1: Standard curves for phosphorylated:unphosphorylated peptide
intensity normalization
72
Figure 3-2: Model fit of LCK initial condition 76
Figure 3-3: CD3ζ sites are phosphorylated by LCK randomly with different
kinetics
79
Figure 3-4: Sigmoidal fit to CD3ζ site-specific phosphorylation data 81
Figure 3-5: Sequential and random order model fits 83
Figure 3-6: The individual tyrosine sites do not influence the phosphorylation
kinetics of each other
87
Figure 3-7: Additional CD3ζ ITAM site phosphorylation model fits 89
Figure 3-8: CD3ζ phosphorylation is consistent across a range of LCK binding
and catalytic rates
91
Figure 3-9: A range of ZAP-70 binding parameters and phosphatase activities
lead to the formation of the 21 kDa partially phosphorylated form of CD3ζ
93
Figure 3-10: LCK binding and protection of partially phosphorylated ITAMs
allows for slowly phosphorylated ITAM sites to reach higher steady state
phosphorylation levels
96
Figure 3-11: CD28 tyrosine sites are phosphorylated more slowly than CD3ζ
tyrosine sites
98
Figure 3-12: CD28 can affect the phosphorylation of CD3ζ sites 101
Figure 3-13: CD28-CD3ζ LCK binding model analysis 103

Figure 4-1: Minimal LCK model reduction 117
Figure 4-2: Schematic of signaling model through ERK activation
incorporating models from literature
127
Figure 4-3: First order (Si) and Total (STi) sensitivity indexes of model
parameters
131
Figure 4-4: A subset of the model parameters were fit to data from Hui et al 134
Figure 4-5: The model can reproduce known effects of T cell signaling in the
literature
136
Figure 4-6: SHP1 negative feedback in CD3ζ CAR stimulated T cells 140
ix
Figure 4-7: Ensemble models of CD28 ERK activation mechanisms 142
Figure 4-8: Model predictions for ERK response due to pair-wise
combinations of CD28 signaling mechanisms
144
Figure 4-9: Experimental validation of CAR activated ERK response time 146
Figure 4-10: Quantification of CAR surface expression 147

x
List of Tables

Table 1-1: Summary of molecules included in mechanistic T cell activation
models in the literature
15
Table 2-1: LCK minimal model reacting species and parameters 32
Table 3-1: CAR phosphorylation minimal model parameter values 77

1
1.

Chapter 1:

Introduction

2
1.1. Chimeric antigen receptor engineered T cells
T cells are the members of the immune system that are responsible for identifying
and killing diseased cells in the body. They do this through binding of the T cell receptor
(TCR) to a major histocompatibility complex (MHC) displaying a foreign antigen (Figure
1-1A). Often, cancer cells are able to evade this immune response because they are derived
from normal tissues in the body, and it is difficult for the T cells to distinguish the mutated
disease-indicating antigens from self-antigens. The cancer cells also develop mechanisms
to down-regulate the immune response through modification of MHC expression or
overexpression of immune inhibitory ligands (Gilboa, 1999). Therefore, chimeric antigen
receptors (CARs) were developed to engineer T cells to attack cancer cells (Sadelain,
2017). CARs combine a tumor associated antigen binding region, typically an antibody-
derived single chain variable fragment (scFv), with a variety of intracellular signaling
domains derived from the TCR, such as the TCR activating domain CD3ζ, and T cell co-
stimulatory domains, like CD28 (Figure 1-1B).

3

Figure 1-1: CAR development.
(A) T cell activation is initiated by the TCR binding to a foreign peptide displayed on
an MHC molecule. Co-receptors, like CD4 and CD8 help stabilize these
interactions. They also bind to intracellular signaling molecules to localize them
at the site of the TCR. Additional signals from co-stimulatory domains, like CD28
and 41BB, integrate with signals downstream of the CD3 chains of the TCR to
activate transcription factors and turn on T cell activation gene transcription.
(B) CARs are engineered proteins capable of activating T cells. They combine an
antibody derived scFv, designed to bind to a tumor associated antigen (TAA),
with a variety of different T cell activating domains. Most commonly these
domains include the CD3ζ chain of the TCR and one or more co-stimulatory
domains. Signaling through the CAR activates similar transcription factors as the
TCR, leading to T cell activation.

4
CARs have proven to be extremely useful in treating B cell malignancies, with two
CAR therapies approved by the FDA for treatment of CD19 positive B cell lymphomas in
the past year (Mullard, 2017). B cell malignancies are prime targets for T cell therapies, in
part because of the ideal properties of the CD19 tumor-associated antigen target, and also
because B cells can be completely eradicated without killing the patient. This allows for
CD19-targeting CAR T cells to kill all of the CD19-bearing B cells without causing lasting
damage to the patient. However, it has been very difficult to engineer CARs that can more
selectively differentiate between cancer cells and healthy tissue to adapt these therapies to
other cancer types (D’Aloia et al., 2018; Morgan et al., 2010). Additionally, even in the
optimal CD19-targeted CAR therapies, some patients do not respond to treatment while
others have an over activation of the CAR T cells, which can be fatal (Makita et al., 2017;
Senior, 2017). Therefore, more work needs to be done to better understand how CARs are
activating the T cells so that they can be engineered to improve treatment.

1.2. T cell activation
The known mechanisms of endogenous T cell activation provide a good starting
point to begin studying CAR T cell activation. Typically, the endogenous TCR is composed
of a TCR alpha/beta heterodimer, connected to three CD3 dimers: one CD3e/CD3d
heterodimer, one CD3e/CD3g heterodimer, and one CD3ζ/CD3ζ homodimer (Love and
Hayes, 2010). The CD3 chains all contain pairs of tyrosine phosphorylation sites called
immunoreceptor tyrosine-based activation motifs (ITAMs). CD3e, CD3d, and CD3g each
contain one ITAM, while CD3ζ contains three, resulting in ten total ITAM motifs in the
TCR.
5

1.2.1. Intracellular signal activation
Signaling is initiated when the extracellular alpha/beta chains of the TCR bind to
an MHC molecule displaying a foreign antigen, which allows the Src family kinases to
phosphorylate the CD3 ITAM (Mustelin et al., 2002). The most important Src family
kinase in T cell signaling is LCK (Lovatt et al., 2006; Nika et al., 2010; Palacios and Weiss,
2004). LCK is regulated by two tyrosine phosphorylation sites, Y394 and Y505, which
enhance and inhibit the catalytic activity, respectively (Chakraborty and Weiss, 2014). It
is widely known that LCK can activate itself by autophosphorylating Y394 in trans, but it
has recently been shown that LCK is also able to autophosphorylate Y505 (Hui and Vale,
2014). Additionally, Y505 can be phosphorylated by the negative regulatory kinase CSK
(Bougeret et al., 1996). The constant activity of these kinases, as well as regulatory
phosphatases, discussed below, work to control the basal activity of LCK in resting T cells.
The phosphorylation state of LCK in resting T cells is not well understood, and
measurements in the literature have been conflicting (Ballek et al., 2015; Nika et al., 2010).
A stable pool of active LCK could help initiate the extremely fast response of T cell
activation toward cells bearing foreign antigens. This has been driven by the data that, on
the cellular level, the phosphorylation state of LCK does not change upon T cell activation
(Nika et al., 2010). This observation gave rise to the standby theory of LCK driven T cell
activation, in which LCK is sequestered away from the unbound TCR, but, upon TCR
binding, this active pool of LCK can immediately begin phosphorylating its substrates on
the CD3 chains (Nika et al., 2010). However, more recent studies have shown that the
phosphorylation state of LCK near the TCR does increase upon T cell activation, indicating
6
that more dynamic mechanisms are responsible for the activation of this kinase in T cells
(Philipsen et al., 2017).
Once ITAMs are doubly phosphorylated by the Src family kinases, they can
strongly bind the kinase ZAP-70 (Bu et al., 1995; Wang et al., 2010). ZAP-70 can then be
activated through phosphorylation at several tyrosine sites by LCK, and possibly additional
autophosphorylation (Shah et al., 2016). Although this is thought to be the main mechanism
of ITAM signal propagation, there is evidence that the various ITAMs differ in their
specific downstream signaling; but, the exact features of these independent pathways have
not been identified (Chae et al., 2004; Combadière et al., 1996; Johnson et al., 1995; Zenner
et al., 1996). Additionally, there is evidence that singly phosphorylated ITAMs may be
able to recruit phosphatases to turn off signaling that does not reach the threshold of full
ITAM phosphorylation (Kersh et al., 1999). This is thought to be particularly important for
the recruitment of the phosphatase SHP-1, which plays an important negative feedback
role, discussed more below (Stefanová et al., 2003).
Once ZAP-70 is able to bind and become activated, it can go on to phosphorylate
the protein, LAT (Katz et al., 2017; Shah et al., 2016). LAT acts as a docking site for a
variety of different SH2-bearing adaptor proteins, such as GADS and Grb2 (Balagopalan
et al., 2010; Wonerow and Watson, 2001). These proteins bind to subsequent signaling
proteins, like SLP76, ITK, and VAV, which can also be phosphorylated by active ZAP-70
or other proteins in the signalosome (Mustelin et al., 2002). These groups of proteins form
large complexes that can initiate a variety of downstream signaling cascades that lead to
the activation of transcription factors (i.e. NFkB, and NFAT) and transcription factor
regulators (i.e. ERK and JNK). These proteins are able to turn on the T cell effector
7
functions such as cellular proliferation and survival, cytokine production, which activates
other immune cells, and perforin and granzyme release, which kills the diseased cells.

1.2.2. Phosphatase activity and feedback
Throughout these signaling pathways, there are also phosphatases acting to shut
down the signal propagation. Up to 30 protein tyrosine phosphatases have been shown to
play a role in T cell signaling, but most of them are not well studied (Mustelin et al., 2003).
Indeed, phosphatases play an important role in dampening the basal T cell signaling
activity, as evidenced by the ability of phosphatase inhibitors to enable T cell signaling
(Secrist et al., 1993). There are, however, three main phosphatases that have been shown
to have important regulatory or feedback roles in the initiation of early T cell signaling.
CD45 is the most widely implicated phosphatase in T cell signaling, and it has been
shown to have both positive and negative feedback roles (Alexander et al., 1992; Ledbetter
et al., 1993). CD45 is able to positively promote T cell signaling by dephosphorylating the
inhibitory Y505 site of LCK. By more strongly dephosphorylating the inhibitory tyrosine
than the activating tyrosine site Y394, CD45 exerts a net positive effect on the activity of
LCK (Ledbetter et al., 1993). Conversely, CD45 has also been shown to have significant
activity against almost every tyrosine phosphorylation in the upstream T cell activation
pathway, including the CD3 chains, CD28, ZAP-70, LAT, and SLP76 (Hui et al., 2017). It
is generally believed that physical exclusion is responsible for controlling the local
concentrations, and therefore activity, of CD45 upon T cell stimulation (Leupin et al.,
2000). CD45 has a tall, stiff extracellular region that is typically larger than the distance
between a T cell and an antigen presenting cell when the TCR binds to the peptide-MHC
8
complex (Chang and Chen, 2017). Therefore, upon TCR binding to an MHC on an antigen
presenting cell, CD45 is pushed away from the narrow space between the two cells. When
the cells move apart, CD45 is able to return to the area and dephosphorylate any remaining
signal to return the T cell to a resting phase.
The other two phosphatases widely studied in relation to T cell activation are SHP-
1 and SHP-2 (Lorenz, 2008). Both of these are cytosolic proteins that can be recruited to
the T cell signaling domains upon activation of the TCR or other co-receptors. SHP-1 plays
a negative feedback role in the system, dephosphorylating LCK to reduce its phosphatase
activity (Stefanová et al., 2003). However, this negative feedback can be interrupted by
ERK phosphorylation of LCK on a protection site, which prevents SHP-1 interaction
(Altan-Bonnet and Germain, 2005).
The role of SHP-2 is more poorly defined, but recently has been implicated in the
regulation of the co-stimulatory receptor CD28, described in detail below (Hui et al., 2017).
SHP-2 is recruited to the TCR signaling area by binding to the T cell inhibitory receptor
PD-1, and possibly other receptors. Once bound at the membrane, SHP-2 is able to
dephosphorylate several proteins in the signaling pathway; however, it has significantly
higher activity against CD28 than any other proteins in the system. Conversely, SHP-2 has
also been shown to play an important role in promoting ERK activation through the MAPK
pathway (Cunnick et al., 2002). It is possible that these dual roles of SHP-2 may work
together in an incoherent feedback mechanism to both dampen and promote T cell
activation.

9
1.2.3. CD28 signaling
While T cell activation is being initiated by the TCR, other co-stimulatory
receptors, like CD28, 41-BB, OX-40, and others, can bind to their ligands on the antigen
displaying cells and help augment the intracellular signaling (Chen and Flies, 2013).
Historically, CD28 has been considered the most important co-stimulatory domain for T
cell activation. In fact, T cell activation has been labeled a “two-step” activation, requiring
binding of the TCR and CD28 for complete signaling (Bretscher, 1999). CD28 was also
the first co-stimulatory domain incorporated into the CAR, and an anti-CD19 CAR bearing
the CD28 and CD3ζ intracellular domains is currently approved by the FDA for the
treatment of B cell lymphoma (Mullard, 2017). Therefore, in this work, I specifically focus
on the effects of the CD28 co-stimulation.
There are four tyrosine phosphorylation sites on CD28 as well as two proline-rich
binding sites (Tian et al., 2015). In its resting state, CD28 is thought to be inhibited by
binding of basic residues in the intracellular region to acidic lipids on the inner leaflet of
the T cell plasma membrane (Dobbins et al., 2016). CD28 is activated by binding to its
ligands, CD80 and CD86, which are believed to pull the intracellular region away from the
membrane through either a mechanical force or structural change. Once free, the CD28
intracellular domain can recruit and be phosphorylated by LCK (Boomer and Green, 2010;
Esensten et al., 2016). This allows for the activation of the phospho-tyrosine binding sites.
It also increases the local concentration of LCK at the membrane, which could potentially
increase the phosphorylation of other LCK substrates, like the TCR. The phospho-tyrosine
and proline-rich binding sites on CD28 recruit a variety of the same adaptor proteins found
downstream of the TCR, including SLP76, Grb2, GADS, ITK, VAV, and others (Esensten
10
et al., 2016). Significantly, the N-terminal phospho-tyrosine site on CD28 intracellular
domain can bind to PI3K, which has not been found in the LAT signalosome initiated by
the TCR. This gives CD28 the ability to signal through the AKT pathway, which may
promote survival and prolong the life of stimulated T cells.

1.2.4. Comparison of TCR and CAR signaling
Despite the fact that CARs use endogenous T cell signaling domains derived from
the TCR and its co-stimulatory receptors, it is not necessarily true that CARs and TCRs
will activation T cells with the same kinetic mechanisms. Recently, work by Harris et al.
has attempted to directly compare T cell activation by TCRs and CARs through
experiments with modified TCRs that contain the same scFv binding region used on the
CARs (Harris et al., 2018). This system allowed them to directly compare T cell signaling
activation through the CAR and TCR when the two proteins have the same antigen binding
kinetics. Their experimental data showed that CARs are 10- to 100-fold less sensitive than
TCRs, even when the TCR is expressed in cells lacking the CD4 or CD8 co-receptors,
which can help recruit LCK to the signaling site. Harris et al. then used a simple model of
kinetic proofreading coupled with an incoherent feedforward loop to explore the kinetics
of both CAR and TCR activation (Lever et al., 2017). Using this model, they hypothesize
that the CAR likely has weaker receptor activation, but similar downstream signaling
following receptor phosphorylation. Therefore, we assume that the differences between
CAR and TCR signaling will primarily arise from differences in receptor activation. In this
work, I use this assumption explore the effects of structural changes to the CAR on
downstream signaling and T cell activation in order to optimize CAR activation.
11

1.3. Mechanistic modeling
Considering the complexity of the positive and negative feedback and multiprotein
interactions in the CAR signaling pathway (Figure 1-2), it is difficult to predict how
changing from TCR activation to CAR activation would affect the outputs of the system.
Computational systems biology combines quantitative experimental data with mechanistic
modeling techniques to create an in silico platform that can be used to explore the response
of a system. This type of mechanistic computational modeling provides a unique
opportunity to quantitatively explore the system and better understand how individual
components influence the output (Chakraborty and Das, 2010). It also allows us to test new
hypotheses regarding the activation of engineered T cells by a variety of engineered
receptors.

12

Figure 1-2: Schematic of CAR signaling. The main mechanisms of CAR signaling are
shown here. Solid black arrows represent phosphorylation event, blunted black lines
represent dephosphorylation events. Molecules with an inhibitory effect are shown in red,
the main activating kinases are shown in green. Red lines indicate negative feedback
induced by receptor phosphorylation, green lines indicate positive feedback induced by
downstream signaling.

13
Computational systems biology models can generally be classified into two groups:
statistical data-driven models and differential equation based mechanistic models.
Statistical models are typically derived from correlations within the experimental data
itself. These correlations are then used to predict the underlying connections in the system.
This approach can account for all of the possible interactions within a system, but it can be
difficult to pull out information about how one specific mechanistic interaction influences
the system. Therefore, it is difficult to use statistical models to predict how a structural
change, like the inclusion of a co-stimulatory domain on the CAR, will affect downstream
signaling. Nevertheless, this type of modeling can be useful to look at the dominant
properties of a system, about which little is known.
Mechanistic models start from known interactions and reactions between individual
molecules in a system. The parameters that govern these interactions are then mined from
the literature or fit to data such that the model can predict the response of the system to
various physical changes. In theory, this approach can be expanded in a step-wise manner
until a framework is developed in which the individual interactions can work together to
predict the emergent properties of the system as a whole. This type of modeling is useful
for examining how changes to a particular set of interactions influence the system output.
Therefore, to specifically study how CARs activate T cells, I have chosen to use a bottom-
up approach to build a mechanistic model of CAR signaling that is able to combine the
individual signaling pathways initiated by CD3ζ and CD28.

14
1.4. Summary of T cell Activation Models
To build this model of CAR T cell activation, I have started from previously
developed models of TCR signaling in the literature. Both statistical (Kemp et al., 2007)
and mechanistic systems biology models have been used to study endogenous TCR
activation, helping to elucidate the important roles of individual protein feedback
mechanisms and emergent properties of the system. The species included in the most
prominent mechanistic T cell signaling models are shown in Table 1-1. Significantly,
however, nearly all of these models of T cell activation assume that T cell activation is
driven solely by the CD3ζ chain of the TCR, ignoring the mechanistic contributions of the
other CD3 chains as well as any of the co-stimulatory signals (Zheng et al., 2005). This
results in the cumulative effects of all of these activating domains being lumped into the
parameters governing CD3ζ activation. Even when CD28 is included in a model, the
differences between activation with or without CD28 are not accounted for (Chylek et al.,
2014). Additionally, many of the models further simplify the CD3ζ chain to a single ITAM,
assuming that the extra ITAMs serve the sole purpose of signal amplification (Deswal et
al., 2011; Sjölin-goodfellow et al., 2015). The models that do individually address the six
ITAM tyrosine sites on CD3ζ simply explore questions of their activation, without
exploring the effects on downstream signaling pathways (Mukhopadhyay et al., 2013,
2016).

15

Table 1-1: Summary of molecules included in mechanistic T cell activation models in
the literature

16
Beyond the initial activation kinetics, several models have attempted to explain
individual effects of elements downstream of TCR phosphorylation. These models include
minimal binding events in the LAT signalosome (Mukherjee et al., 2013; Nag et al., 2009,
2012; Sukenik et al., 2017) and the activation of Ras, which leads to the MAPK pathway
(Das et al., 2009; Jun et al., 2013). While many of these models have identified important
regulatory mechanisms within these pathways, none of them have described how the
structure of the T cell activating domains influence the response. The few models that have
attempted to link TCR ligation to downstream ERK response generally simplify the
intermediate interactions to focus on individual feedback elements (Altan-Bonnet and
Germain, 2005; Chylek et al., 2014; Das et al., 2009; Feinerman et al., 2008). Despite these
limitations, the mechanistic insights from these models are useful as I construct my model
of CAR signaling.
Computational mechanistic modeling has proven to be a useful tool in
understanding the regulation of T cell activation through the TCR, but more work needs to
be done to specifically identify the individual effects of the different ITAM and co-
stimulatory domains. For example, the majority of TCR signaling models assume that the
multiple ITAMs in the TCR serve as a simple amplification mechanism, even though it is
known that the ITAMs can have different effects on downstream signal activation.
Additionally, any effects of the co-stimulatory domains in these models are largely lumped
into a single activation parameter downstream of the TCR, without any mechanistic insight
into the proportion of the signal arising from co-stimulation. In the following three
chapters, I attempt to address these issues through the development and characterization of
17
a mechanistic computational model of CAR signaling that is capable of differentiating
between CD3ζ signaling alone and in combination with the CD28 co-stimulatory domain.

1.5. Dissertation Outline
To better understand how CAR signaling differs from TCR signaling and how the
individual CAR signaling domains CD3ζ and CD28 influence the downstream activation,
I have used a bottom-up modeling approach to build a framework that will allow for the
exploration of the specific mechanisms of CAR T cell activation. Here, I combine
quantitative experimental data with mechanistic ordinary differential equation-based
models to investigate CAR T cell activation.
In chapter one, I develop a computational model to better understand how the main
T cell activating kinase, LCK, is autophosphoryated at its inhibitory and activating tyrosine
sites. This kinase plays an important role in CD3ζ and CD28 phosphorylation.
Additionally, CARs are not known to associate with the CD8 or CD4 co-receptors that can
bind LCK and help preserve its activity at the sites of the TCR. Therefore, the
autoregulation of LCK is particularly important for understanding the amount of active
LCK potentially available to phosphorylate the CAR. This model, trained using in vitro
experimental data of LCK autophosphorylation and phosphorylation by the kinase CSK,
identifies key mechanisms required for T cell regulation. Particularly, it indicates the role
that both LCK homodimers and LCK-CSK heterodimers play in regulating the activity of
LCK. It also predicts that different phosphorylated species of LCK have different substrate
preferences may help regulate the pool of active LCK in T cells.
18
In chapter two, I focused on the interaction between LCK and the CD3ζ and CD28
intracellular signaling domains of the CAR. I first collect quantitative phospho-proteomic
mass spectrometry measurements to measure the phosphorylation kinetics of different
CAR structures. I fit this data using a computational model of CD3ζ phosphorylation by
LCK. Testing how different model structures compare to the data, I am able to confirm that
these sites are phosphorylated randomly with different rates. The model also predicts that
the CD3ζ sites are phosphorylated independently, which I confirm experimentally. When
CD28 is added upstream of CD3ζ, the experimental data shows that the phosphorylation
rates of all CD3ζ ITAM sites are increased, and the order of the site phosphorylation is
altered. In light of this, I use this computational model to explain a mechanism for the
appearance of differentially phosphorylated forms of CD3ζ in resting T cells and determine
that protein binding to singly phosphorylated ITAM sites plays an important role in
influencing the overall phosphorylation of these sites.
Finally, in chapter three, I combine the LCK autoregulation and CD3ζ/CD28
phosphorylation models with downstream mechanisms from several other models in the
literature to predict how CARs with or without the CD28 co-stimulatory domain affect
downstream ERK activation. I use an ensemble modeling approach to explore the specific
mechanisms of CD28 that contribute to ERK activation in anti-CD19 CD28-CD3ζ CAR-
bearing Jurkat T cells. The model produces several hypotheses for how ERK response time
could be affected by various binding events and kinetic changes initiated by CD28 co-
stimulation. I then perform experiments to validate the main CD28 mechanism of
activation in CAR T cells. Thus, the model provides new mechanistic insights into the
functions of T cell co-stimulatory domains.
19
Altogether, my model provides a framework with which to study CAR engineered
T cell activation. In the future, the model can be further expanded to study other co-
stimulatory domains, like 41-BB, and inhibitory domains, like PD-1. I envision this model
as a tool to help understand and optimize CAR T cell activation to improve future CAR
therapies.
20

21

Chapter 2:

Predictive Model of Lymphocyte-specific Protein Tyrosine Kinase (LCK)
Autoregulation

Portions of this chapter are adapted from:
Jennifer A. Rohrs, Pin Wang, and Stacey D. Finley. Cellular and Molecular
Bioengineering (2016 Young Innovators Special Edition), 9(3): 351-367.

22
1.6. Abstract
Lymphocyte-specific protein tyrosine kinase (LCK) is a key activator of T cells;
however, little is known about the specific autoregulatory mechanisms that control its
activity. We have constructed a model of LCK autophosphorylation and phosphorylation
by the regulating kinase CSK. The model was fit to existing experimental data in the
literature that presents an in vitro reconstituted membrane system, which provides more
physiologically relevant kinetic measurements than traditional solution-based systems.
The model is able to predict a robust mechanism of LCK autoregulation. It provides
insights into the molecular causes of key site-specific phosphorylation differences
between distinct experimental conditions. Probing the model also provides new
hypotheses regarding the influence of individual binding and catalytic rates, which can be
tested experimentally. This minimal model is required to elucidate the mechanistic
interactions of LCK and CSK and can be further expanded to better understand T cell
activation from a systems perspective. Our computational model enables the evaluation
of LCK protein interactions that mediate T cell activation on a more quantitative level,
providing new insights and testable hypotheses.

23
1.7. Introduction
Lymphocyte-specific protein tyrosine kinase (LCK) is a key regulator of T cell
activation and differentiation (Brownlie and Zamoyska, 2013; Salmond et al., 2009). LCK
helps to activate healthy T cells against diseased cells in the body by phosphorylating
immunotyrosine activating motifs (ITAMS) on the CD3ζ chain of the T cell receptor (TCR)
(Love and Hayes, 2010). Mutations in the LCK gene can lead to autoimmune disease and
contribute to cancer (Burnett et al., 1991; Goldman et al., 1998). Recently, LCK has been
shown to play an important and complex role in the activation of chimeric antigen receptor
(CAR) engineered T cells (Kofler et al., 2011). CARs are engineered proteins that contain
a variety of T cell signaling domains linked to an extracellular antibody single chain
variable fragment (scFv). These proteins can activate T cells against a tumor-associated
antigen to eradicate cancer cells (Kofler et al., 2011; Sadelain et al., 2013). As CARs are
adapted and modified to more specifically target different types of cancer cells,
understanding the detailed mechanisms that govern their activation has become more
important. Despite its strong role in regulating T cell signaling, little is known about the
specific mechanisms that control LCK catalytic activity.
LCK is a multi-domain protein that can catalyze the phosphorylation of many
substrates in T cells, including itself. LCK has two main phosphorylation sites, the tyrosine
residues Y394 and Y505. Y394 is located close to the kinase domain, and, therefore, has
been shown to play a significant role in substrate specificity (Laham et al., 2000). Y505 is
located near the C-terminal tail of the protein. When phosphorylated, this tail is thought to
fold up and bind in cis, locking the molecule in a “closed” conformation (Chakraborty and
Weiss, 2014). Therefore, it is commonly accepted that phosphorylation at Y394 (denoted
24
as LCK species P394U505) increases the catalytic activity of LCK and phosphorylation at
Y505 (species U394P505) decreases catalytic activity (Yamaguchi and Hendrickson, 1996).
It has been shown that the unphosphorylated and doubly phosphorylated forms of LCK
(species U394U505 and P 394P 505, respectively) retain an intermediate catalytic activity when
acting on some substrates, although they may have more complex kinetics on others (Hui
and Vale, 2014). These four forms of LCK distribute and aggregate differently within cells
(Rossy et al., 2013), and, while all four forms exist in resting T cells, efforts to calculate
the exact ratios of the species have been inconclusive (Ballek et al., 2015; Nika et al., 2010).
Several proteins have been shown to control LCK phosphorylation. For example,
C-terminal Src kinse (CSK) is a regulatory kinase that phosphorylates LCK specifically at
Y505 (Sondhi et al., 1998). In addition, several phosphatases act on LCK and CSK, most
notably CD45 and PTPN22 (Zikherman et al., 2010). It is commonly accepted that LCK
can autophosphorylate at Y394 (Yamaguchi and Hendrickson, 1996), but it has only
recently been appreciated that LCK can also autophosphorylate at Y505 (Hui and Vale,
2014).
The kinetics of these LCK phosphorylation and dephosphorylation reactions
determine the pool of catalytically active LCK available to control T cell activation in vivo.
Traditionally, the kinetics of these reactions are studied experimentally with recombinant
proteins in solution (Bergman et al., 1992; Ramer et al., 1991); however, inside the cell,
LCK is largely bound to the plasma membrane, in a two-dimensional density distribution
(Ilangumaran et al., 1999; Zimmermann et al., 2010). This binding to the plasma membrane
can profoundly influence a protein’s kinetics in several ways: (i) by altering the
conformation of the protein, opening or closing available binding pockets, (ii) by changing
25
the diffusion kinetics, which can alter the rate at which the enzyme encounters its substrate,
and (iii) by altering the spatial segregation of certain groups of proteins in densely packed
membranes, which may alter the ratio of active to inactive molecules in the system (Berry,
2002). Indeed, Hui et al. showed that the kinetics of LCK phosphorylation are vastly
different when LCK is able to autophosphorylate on a membrane surface compared to in
solution (Hui and Vale, 2014). These differences are both qualitative, in the order of
phosphorylation of the two sites, and quantitative, in the rates of phosphorylation.
In order to better understand the mechanisms through which LCK is regulated on
the cell membrane, we have developed a computational model of LCK
autophosphorylation and phosphorylation by the regulating kinase CSK. The model is fit
to experimental data from the two-dimensional reconstituted membrane system developed
by Hui and Vale (Hui and Vale, 2014). This data uses two concentrations of LCK: 500
molecules/µm
2
, which corresponds to a physiological level of LCK in the cell, and 50
molecules/µm
2
. One concentration of CSK is used, 500 molecules/µm
2
, which is slightly
higher than the maximal amount of CSK present in the cells. Modeling this minimal system
will allow us to predict the fundamental mechanisms of LCK activation and improve our
understanding of the differences between two- and three-dimensional enzyme kinetics.
Several computational models have been developed to study the early phosphorylation
events in T cell activation (Altan-Bonnet and Germain, 2005; Mukhopadhyay et al., 2013;
Sjölin-goodfellow et al., 2015); however, none of them have accounted for the different
species of LCK or the effects that the various catalytic and binding activities of these
different species will have on T cell activation. The model of LCK activation that we have
developed provides a basis for understanding LCK phosphorylation and catalytic activity
26
and can be implemented in larger models of T cell signaling. Thus, our work will enable a
better understanding of how LCK autoregulation affects the control of T cell activation in
the context of TCR antigen discrimination and CAR signaling.

1.8. Materials and Methods
1.8.1. Data extraction
Experimental data was extracted from Hui and Vale (Hui and Vale, 2014) using the
MATLAB GRABIT program (The MathWorks Inc., Natick, MA). To correspond to the
data, all simulations were normalized by the simulated amount of LCK at 90 minutes.
1.8.2. Model Structure
Several different models were tested to find the simplest mechanism that is able to
reproduce the data. Each model was progressively more complex. First, a mechanism in
which the LCK phosphorylation events are directly catalyzed without a binding step to
form intermediate dimers, a model described by 18 kinetic parameters, was implemented.
Subsequently, a Michaelis-Menten mechanism in which the individual LCK enzymatic
species have the same catalytic rate regardless of the substrate, a model involving 25 kinetic
parameters, was implemented. Neither of these models was able to both reproduce training
data used for parameter estimation and predict data not used in the fitting process (results
not shown).
The third model implemented a Michaelis-Menten mechanism in which all of the
LCK species have different binding and catalytic rates. This mechanism was able to fit the
training data and predict new data. In this model, it is assumed that the phosphorylation
events are primarily governed by two main factors: the strength of the interaction between
27
the enzyme-substrate pair (i.e. the dissociation constant, kd), and the catalytic rate of the
enzyme on the substrate. The dissociation constant is the dissociation rate (Koff) divided by
the association rate (Kon). To avoid over parameterizing the model, we assume the
association rate to be the same for all of the 16 LCK pairs, reducing the number of LCK
binding parameters from 32 to 17. In Michaelis-Menten kinetics, the catalytic rate is
generally the rate limiting step, so Kon was kept constant for all LCK-LCK or LCK-CSK
binding pairs, as it is not expected to be rate limiting. The simplification of the association
rates is also supported by studies showing that Kon generally falls within a relatively small
range (about one order of magnitude) for many different protein interactions (Northrup and
Erickson, 1992; Schlosshauer and Baker, 2004). However, we still allow the kd values to
differ between the LCK dimers by implementing a different Koff for each pair. By
estimating the same association rate and different dissociation rates for the different LCK
dimers, each binding pair can remain bound for different amounts of time depending on
the strength of the individual interactions, allowing the kd to span its full physiologically
relevant range (more than 10 orders of magnitude) (Mangialavori et al., 2010; Piran and
Riordan, 1990).

1.8.3. Numerical implementation of the model
The model used to fit the training data is comprised of 23 non-linear ordinary
differential equations (ODEs), and the model used for generating predictions with the
catalytically inactive LCK is composed of 73 ODEs. The equations were written as a set
of rules in BioNetGen (Faeder et al., 2009), and implemented in MATLAB (The
MathWorks Inc., Natick, MA).
28

1.8.4. Parameter estimation
Binding, on and off, and catalytic rates were estimated in an unbiased approach to
find parameter sets that could both qualitatively differentiate between the rate of
phosphorylation of Y394 and Y505 of LCK and quantitatively provide the best fit the data.
Due to the large number of parameters to be fit, 38, and a lack of prior information
about their possible ranges, a two-step approach was used to fit the model. First, a series
of parameter sets was calculated by minimizing the weighted sum of the squared residual
(WSSRhybr) for a hybrid objective function that accounts for both the quantitative fit to the
data and the qualitative order of the phosphorylation curves of the two substrate sites (Y394
and Y505) (Kanodia et al., 2014). Without the addition of the qualitative order of the curves
in the hybrid WSSR, all of the optimal parameter sets over-fit the conditions in which Y394
is phosphorylated faster than Y505 (High LCK, High LCK + CSK, and Low LCK) without
capturing the increase in Y505 phosphorylation in the Low LCK + CSK case. Parameter
sets that did not capture that increase were penalized by having a higher WSSRhybr.
The WSSRhybr is calculated by adding the WSSR for each data point to the WSSR
for the distance between the Y394 and Y505 curves in each experimental condition:
min$%&&'
()*+
(-)/ =min123%
4
5678
$9
:;<,4
5678
−9
?4@,4
5678
(-)/A
B
C
4DE
+23%
4
5GHG
$9
:;<,4
5GHG
−9
?4@,4
5GHG
(-)/A
B
C
4DE
+23%
4
I4JJ
KL9
:;<,4
5678
−9
:;<,4
5GHG
M−$9
?4@,4
5678
(-)−9
?4@,4
5GHG
(-)/NA
B
C
4DE
O
29
where 9
:;<,4
5678
and 9
:;<,4
5GHG
are the i
th
experimentally measured LCK phosphorylation data
point for Y394 or Y505, respectively. 9
?4@,4
5678
and 9
?4@,4
5GHG
are the simulated LCK
phosphorylation at the i
th
time point. %
4
5678
, %
4
5GHG
, and %
4
I4JJ
are weighting terms, taken
as 1/9
:;<,4
5678
, 1/9
:;<,4
5GHG
, and 1/L9
:;<,4
5678
−9
:;<,4
5GHG
M, respectively. n is the total number of
experimental measurements. The minimization is subject to the upper and lower bounds of
the free parameters, q.
Particle swarm optimization (PSO) was used to find 1,000 parameter sets that
reached a minimum in the WSSR for the hybrid objective function (Iadevaia et al., 2010).
Briefly, PSO is able to efficiently search a parameter space by mimicking the ways in which
groups of animals make decisions, for example how a colony of bees finds a new nesting
site. Many particles move around the parameter space communicating their WSSR at each
position. With each iteration, the positions and velocities of the particles are updated such
that they approach a minimal WSSR. We used 31 particles searching a 38-dimensional
bounded parameter space, with the particles starting at random points in the parameter
space. Each iteration, a WSSR is calculated for every particle and the particles’ positions
and velocities are then updated based on the their current WSSR and the global minimal
WSSR. The algorithm is terminated when the global minimum WSSR remains constant
for 50 iterations.
Next, the parameter sets from the hybrid WSSR were tailored to fit a quantitative
WSSR (WSSRquant). The 1,000 hybrid parameter sets were then used in the second step as
inputs to a more local parameter estimation approach, performed by the MATLAB
lsqnonlin function. This algorithm solves the non-linear least squares problem using the
trust-region-reflective optimization algorithm, minimizing the WSSR quant:
30
min$%&&'
PQRCS
(-)/= min123%
4
5678
$9
:;<,4
5678
−9
?4@,4
5678
(-)/A
B
C
4DE
+23%
4
5GHG
$9
:;<,4
5GHG
−9
?4@,4
5GHG
(-)/A
B
C
4DE
O
where the variables are the same as those used in the WSSRhybr function.

1.8.5. Clustering
Parameter set clustering was done using the MATLAB kmeans function. The
optimal number of clusters was determined using the silhouette method (Rousseeuw,
1987). The silhouette plots measure the confidence that a given point lies in the cluster to
which it is assigned, with each point getting a score from -1 to 1. We used the sum of the
silhouette plot to calculate the optimal number of clusters, which was found to be three.

1.8.6. Sensitivity analysis
The extended Fourier amplitude sensitivity test (eFAST), a global variance-based
sensitivity analysis, was used to understand how different parameters (“model inputs”)
affect model predictions (“model outputs”). This method has been used previously to
analyze computational biological models (Finley et al., 2013; Linderman et al., 2015). In
this method, the values of all of the inputs are varied together at different frequencies within
a specified range and the model outputs are recorded. We varied the parameters 100-fold
up and down from their median values, shown in Table 2-1. The Fourier transform of the
output indicates which parameter frequencies contribute most, thus, which parameters are
most sensitive. Varying all of the parameters together allows us to calculate two different
indices of sensitivity: the first-order FAST indices, Si, a measurement of the local
31
sensitivity of individual inputs, and the total FAST indices, STi, a measurement of the
global sensitivity which accounts for second and higher-order interactions between
multiple inputs. A greater total index than first-order index indicates that an input is more
important in combination with other parameters than alone. We implemented the eFAST
method using MATLAB code developed by Kirschner and colleagues (Marino et al.,
2008).

1.8.7. Statistical analysis
All statistical analyses were determined with a one-way analysis of variance
(ANOVA) using Graphpad Prism version 6 for Mac (GraphPad Software, San Diego, CA).

32
Table 2-1: LCK minimal model reacting species and parameters

33
1.9. Results
1.9.1. Model construction
We have constructed a model of LCK autophosphorylation and phosphorylation by
the kinase CSK. Below, we describe the salient features of the model, and full details are
provided in the Methods section. Hui et al. experimentally proved that LCK, starting from
a pool of unphosphorylated LCK, is able to phosphorylate itself in trans, and that this is
the predominant form of phosphorylation (Hui and Vale, 2014). Accordingly, our model
assumes that each LCK substrate site, Y394 and Y505, must be phosphorylated by a
catalytic site on a different LCK molecule. This is done by implementing a Michaelis-
Menten mechanism in which each pair of enzyme and substrate LCK species has different
binding and catalytic rates. This model is characterized by 38 kinetic parameters and is
described in detail in the Methods section.
In the model, each of the four LCK species, referred to by their phosphorylation
status as U394U505, P 394U505, U 394P505, and P394P505, are able to bind and phosphorylate the
four substrate sites, Y394 of U 394U 505 and U394P505 and Y505 of U394U505 and P394U505, with
different kinetics. To simulate this, the catalytic domain of one LCK species in the model
can interact with the Y394 or Y505 residue from another LCK species. This results in
several possible dimer conformations between an LCK pair that each has the same
association rate (Kon), but have different dissociation rates (Koff). The phosphorylation
reactions can also be catalyzed at different rates depending on both the enzyme and
substrate; subsequently, each of the 16 LCK dimer intermediates has a different catalytic
rate (Kcat). As an illustrative example, the interactions for a representative pair of LCK
species, U394U505 and P394U505, are shown in Figure 2-1a. These two species have 3
34
different phosphorylation sites, Y394 on U394U505 and Y505 on U 394U 505 and P 394U 505,
resulting in three different intermediate dimers. After binding with the same rate of
association (Kon), each of these species can unbind (Koff,1, Koff,2, Koff,3) or catalyze a
phosphorylation reaction (K cat,1, K cat,2, K cat,3) with different rates.
Like the LCK homodimers, CSK is able to associate with all of its substrates with
the same association rate and has different dissociation and catalytic rates, depending on
the substrate (Figure 2-1b). It has been widely established in the literature that CSK is only
able to phosphorylate LCK at Y505 (Sondhi et al., 1998). Therefore, there are only two
substrates available to CSK in the model (U 394U505 and P394U 505), resulting in two
intermediate CSK-LCK dimers.
The complete list of interacting pairs in the model and their respective dissociation
and catalytic rates is shown in Table 2-1. In total, the model includes in 23 unique species,
the concentrations of which are described by 23 ordinary differential equations (ODEs).
The association rate for all LCK pairs (Kon) has a median value of 8.9×10
-4

TU
B
UVWXYZWX[∙[XY ⁄ and a 90% confidence interval of 6.8×10
-4
-1.9×10
-3

TU
B
UVWXYZWX[∙[XY ⁄ . The association rate for all CSK-LCK pairs (K on,CSK) has a median
value of 5.9×10
-4
TU
B
UVWXYZWX[∙[XY ⁄ and a 90% confidence interval of
4.4×10
-4
-1.2×10
-3
TU
B
UVWXYZWX[∙[XY ⁄ . The procedure used to estimate these rates is
described in detail below.

35

Figure 2-1: Schematic of LCK interactions.
(a) The possible interactions between a representative pair of LCK species, U394U 505
and P394U505, are illustrated. LCK can phosphorylate itself in trans when the
catalytic domain of one molecule binds to a tyrosine phosphorylation site on
another molecule. Phosphorylated tyrosine residues are red and have a filled red
circle labeled with “P”, unphosphorylated sites are green and have an empty red
circle. Each LCK species (U394U505, P394U505, U394P505, and P 394P 505) is
represented by a different color molecule. All of the species can bind to a
substrate site (Y394 or Y505) with a single rate of association (Kon) and different
dissociation rates (Koff,1, Koff,2, Koff,3). The catalytic rates are also different
depending on the enzyme and substrate pairs (denoted as (Kcat,1, Kcat,2, Kcat,3).
(b) Diagram of all possible interactions of the enzyme CSK with LCK. CSK can
phosphorylate LCK U394U505 or P394U505 on Y505. The pairs can bind with the
same association rate (Kon,CSK), but CSK-LCK pairs will dissociate (Koff,CSK-UU,
Koff,CSK-PU) and phosphorylate (Kcat,CSK-UU, Kcat,CSK-PU) with different rates.

36
1.9.2. Determining the optimal parameter sets
The model was fit to quantitative western blot data of LCK phosphorylation at
Y394 and Y505 in a two-dimensional membrane reconstituted system obtained by Hui and
Vale (Hui and Vale, 2014). We used four sets of Y394 and Y505 site-specific
phosphorylation data to train the model: 500 molecules LCK/µm
2
, 500 molecules
LCK/µm
2
+ 500 molecules CSK/µm
2
, 50 molecules LCK/µm
2
, and 50 molecules LCK/µm
2

+ 500 molecules CSK/µm
2
. A fifth set of site-specific data in which 50% of the LCK in the
system is catalytically inactive was used as model validation, to test that the model
parameters are able to predict data not used in the fitting process.
As most kinase kinetic studies are performed in solution, we could not directly
apply any previous assumptions for the range of parameter values in this two-dimensional
system. While there are numerical techniques that enable conversion of three-dimensional
kinetic parameters to a two-dimensional system, there is no kinetic binding data of LCK-
LCK dimers in either a two-dimensional or three-dimensional system to start from, apart
from the autophosphorylation described in the paper by Hui and Vale. Additionally, Hui
and Vale compared the autophosphorylation of LCK in solution to their two-dimensional
membrane system and found that the phosphorylation kinetics for Y394 and Y505 do not
change proportionately when transitioning between the two systems. In the membrane
system, Y394 is phosphorylated much faster than Y505, while in solution it appears that
Y505 is phosphorylated faster. In the solution data there is an initial rapid jump in Y505
phosphorylation above that of Y394, followed by a plateau and then a second phase in
which both sites are rapidly phosphorylated, while in the membrane data the
phosphorylation of Y505 is much steadier. These different dynamics imply that it would
37
not be straightforward to inter-convert two-dimensional and three-dimensional kinetics.
Therefore, we used an unsupervised fitting procedure in which the parameters are allowed
to vary within very wide bounds (10
-20
to 10
10
TU
B
UVWXYZWX[∙[XY ⁄ for Kon, and 10
-20
to
10
10
1 [XY ⁄ for Koff and Kcat).
We used a two-step fitting procedure to search the large parameter space and find
parameter sets that can both qualitatively and quantitatively describe the training data. In
the first step, we used particle swarm optimization (PSO) to minimize a hybrid weighted
sum of the squared residuals (WSSR) objective function (Kanodia et al., 2014). This hybrid
WSSR was used to optimize both the quantitative fit to the data points as well as a
qualitative readout of the difference between the curves of phospho-Y394 and phospho-
Y505 in each experimental setting (see methods for more detail). We used PSO to obtain
1,000 parameter sets that could describe the differences in the rates of phosphorylation of
the two sites for the different experimental conditions. PSO is a global optimization
technique that enables efficient exploration of the parameter space (Iadevaia et al., 2010).
The hybrid WSSR values ranged from 3.3×10
1
-3.8×10
9
, with a median value of 4.1×10
2
.
However, in the second step, all of the parameter sets obtained using PSO, regardless of
their hybrid WSSR value, were tailored to better quantitatively fit the data using the
MATLAB lsqnonlin function (MathWorks Inc., Natick, MA). Specifically, the parameter
sets from PSO were used as starting points to minimize an objective function that calculates
the WSSR between the experimental data and the model predictions. Each of the 1,000
PSO parameter sets was tailored twice, resulting in 2,000 parameter sets. The frequency
distributions of the quantitative WSSR values are shown in Figure 2-2a, ranging from
6.3×10
0
-1.1×10
3
.
38
We used three criteria to determine the optimal parameter sets used for model
simulations. Due to the large bounds, the majority of the 2,000 parameter sets represented
local minima that did not properly capture the data. Therefore, we first considered the
parameter sets that were close to a global minimum, with respect to the training data, using
the cumulative density function (CDF) of the WSSR. Secondly, we wanted to ensure that
the parameter sets chosen were able to predict data not used in the fitting, termed validation
data. Therefore, we used the CDF of the WSSR with respect to the validation data to find
parameter sets that were able to predict the validation data well. Thirdly, we selected
parameter sets that matched a molecularly detailed aspect of the Hui et al. data: in the high
LCK experimental conditions, nearly 100% of the LCK is doubly phosphorylated by 90
minutes. To do this, we removed the parameter sets in which less than 90% of the LCK, in
the high LCK condition, was doubly phosphorylated by 90 minutes.
Figure 2-2a, b shows CDF plots for the distributions of the quantitative WSSR
values, which are used to find the parameter sets with good fits and predictions,
respectively. The general trend is a sigmoidal function, with a tail at the beginning
containing the parameter sets that all have low WSSR values. We started with the CDF
plot for the training data set, and chose the end of the first step in the function as the cutoff
for good fitting parameter sets (Figure 2-2a, purple region, WSSR<7.1). Then, taking
only those parameter sets in the purple region, we calculated the WSSR values for the
predicted data, which had a WSSR ranging from 2.3-8.9. Figure 2-2b shows the CDF
function of these values. A similar cutoff point was chosen for parameter sets that had a
good fit to the validation data (WSSR<3.3), indicated by the yellow region.

39

Figure 2-2: Method for choosing the optimal parameter sets.
(a) The cumulative density function of the weighted sum of the squared residuals
(WSSR) for training data sets that were used to fit the model. The tail of low
WSSR parameter sets was selected (purple region).
(b) The parameter sets from the purple region in panel (a) were sorted into a
cumulative density function based on the WSSR for the validation data set.
Parameter sets with low WSSR were selected (yellow region) and further filtered
based on their ability to reach steady state by the end of the 90 minute simulation
time.
(c) The resulting 33 parameter sets were sorted into clusters and compared for trends
in their parameter values as well as their ability to fit the training data. The red
cluster showed the best fit to the predictive data set, as well as strong statistical
differences between many of the parameter values, indicating a clear mechanism
of LCK autoregulation.

40
The model fitting and parameter selection procedures described above resulted in
33 optimal parameter sets. However, these parameter sets showed high variability, and the
median parameter values were not able to reproduce the data. Therefore, we clustered these
parameter sets into three groups using the MATLAB kmeans function (Figure 2-2c). The
three clusters’ predictions of the validation data are shown in Figure 2-3, with median
quantitative WSSR values of 6.8, 7.0, and 6.9 for the green, blue, and red clusters,
respectively. These three groups provided different hypotheses for the kinetics of LCK
phosphorylation. Although the green cluster had the lowest WSSR, it contained highly
variable parameter sets without a significant difference between any of the catalytic rates
(data not shown). Without statistical significance, no clear parameter values or mechanistic
trends can be observed. The blue and red clusters did show significant differences between
the parameters for different LCK species, indicating that specific LCK species interact with
different kinetics (Figure 2-3). The primary difference between the blue and red clusters
was the kinetics for the interactions of enzyme P 394U505 with Y505 on U394U 505 and enzyme
P394P505 with Y505 on P394U505. These differences effectively switched the contribution of
these two reactions to the phosphorylation of Y505 in the training data simulations.
Significantly, the red cluster had a lower WSSR value, indicating that it was able to match
the training data and predict the validation data better than the blue cluster; therefore, the
20 parameter sets within the red cluster were determined to be optimal and were used in
subsequent simulations.

41

Figure 2-3: Predictions for three parameter set clusters. Results of model validation
of the three different parameter clusters, green (a), blue (b), and red (c), from Figure 2-
2c. This validation data, taken from Hui and Vale, 2014, uses a reconstituted in vitro
membrane system of LCK phosphorylation in which 50% of the LCK is catalytically
inactive due to a point mutation at the ATP binding site and 50% is normally active. The
model fits (lines) to the data (dots) are shown with 50% and 95% confidence intervals
(dark and light shaded areas, respectively), for phospho-Y394 (green) and phospho-Y505
(purple). The experimental data is normalized by the western blot band intensity at 90
minutes, and the simulations are normalized by the concentration of LCK at the end of
the 90 minutes simulation.

42
1.9.3. Model fitting
Using the 20 optimal parameter sets, the model is able to accurately match the
experimental data from Hui and Vale (Figure 2-4). In Figure 2-4a-c, LCK Y394 is
phosphorylated faster than Y505, and there is more phospho-Y394 in the system than
phospho-Y505 at each time point. Conversely, in Figure 2-4d, these rates are reversed,
and there is more Y505 in the system. The model is able to capture this switch in the rates
of Y505 and Y394 phosphorylation. In the high LCK data without or with CSK (Figure 2-
4a, b, respectively), there is a very sharp increase in Y394 phosphorylation within the first
15 seconds, followed by a much slower increase in phosphorylation. The model is able to
capture this biphasic nature as well. Additionally, the model can refine the sharp response
in the low LCK + CSK condition, compared to the high LCK conditions (Figure 2-4d,
blue line).

43

Figure 2-4: LCK minimal model fit to experimental data. The model is able to fit
experimental data from Hui and Vale, 2014. To mimic the experimental conditions, the
model included initial conditions of (a) 500 molecules of LCK/µm
2
, (b) 500 molecules of
LCK/µm
2
+ 500 molecules of CSK/µm
2
, (c) 50 molecules of LCK/µm
2
, or (d) 50
molecules of LCK/µm
2
+ 500 molecules of CSK/µm
2
. Each graph shows the
experimental data (dots) and median model fit (dark lines) with the 50% and 95%
confidence intervals (dark and light shaded regions, respectively). The data shows the
total amount of phospho-Y394 (blue) and phospho-Y505 (red) over time based on
quantitative western blots. The experimental data is normalized by the western blot band
intensity at 90 minutes, and the simulations are normalized by the concentration of LCK
at the end of the 90 minutes simulation.

44
There are clear statistical differences between many of the estimated kinetic rates,
despite high variability in their fitted values (Figure 2-5). The majority of the estimated
parameter values vary over a wide range, sometimes over 10 orders or magnitude or more.
However, all of the sets are able to reproduce the data used in parameter fitting. Comparing
the rates of different enzymes catalyzing the phosphorylation of a single substrate is of
particular interest (Figure 2-5a, c), as these comparisons enable a better understanding of
the catalytic activity of individual LCK species. In general, the catalytic rates between
enzyme species on a single substrate vary more than the dissociation rates for that substrate.
Most of the dissociation rates are relatively high compared to the rate of association, with
the exception of the dissociation rate of P394P505 enzyme with P 394U505 substrate, which is
consistently lower than the rate of association. This indicates that the P394P 505-P394U505
dimer can remain bound for a longer period than most others. The catalytic rate of U 394P 505
is always statistically lower than the catalytic rate of all other species. Interestingly, both
the LCK and CSK association rates, which are shared between the dimer pairs, are highly
conserved, with only one parameter set falling outside of a tight range of less than two-fold
(Figure 2-5b).

45

Figure 2-5: Optimal parameter set values for LCK minimal model. The distributions
for the estimated parameter values are shown for the (a) dissociation rates, (b) association
rates, and (c) catalytic rates. The values of the 20 best parameter sets, along with the
median and range, are shown. Statistically significant differences between different LCK
enzymes acting on the same substrate are denoted by bars above the points, with different
thickness representing different levels of statistical significance as calculated by a one-
way ANOVA.

46
1.9.4. Model validation
In addition to fitting the training data and estimating the optimal parameter values,
the model with the optimal parameter sets is able to match validation data not used in the
fitting. Hui and Vale quantified the amount of phospho-Y394 and -Y505 when 50% of the
LCK in the system (250 molecules LCK/µm
2
) was made catalytically inactive by a point
mutation in the ATP binding site. To simulate this condition, we included a separate LCK
species that can be phosphorylated at Y394 and Y505, but cannot act as an enzyme to
catalyze the phosphorylation of other molecules. This model assumes that the catalytically
inactive LCK interacts with the same kinetic parameters as active LCK. Figure 2-6 shows
that the optimal parameter sets from the model fitting also provide a good match to the
experimental validation data not used in the fitting, capturing the sharp early increase in
phospho-Y394, the variable slope of phospho-Y505 levels, and the finding that the rate of
Y394 is higher than that of Y505. This lends confidence to the predictive ability of the
optimized model.

47

Figure 2-6: LCK minimal model validation. The model is able to reproduce data not
used in the parameter fitting. This data, taken from Hui and Vale, 2014, uses a
reconstituted in vitro membrane system of LCK phosphorylation with a high LCK
concentration in which 50% of the LCK (250 molecules LCK/ µm
2
) is catalytically
inactive due to a point mutation at the ATP binding site and 50% is normally active. The
model fit (lines) compared to the data (dots) are shown with 50% and 95% confidence
intervals (dark and light shaded areas, respectively), for phospho-Y394 (blue) and
phospho-Y505 (red). The experimental data is normalized by the western blot band
intensity at 90 minutes, and the simulations are normalized by the concentration of LCK
at the end of the 90 minutes simulation.

48
1.9.5. Sensitivity analysis
Despite the large variation in many of the parameters, the model is robust and can
withstand a high level of biological variability. This is evident in the tight range of model
fits and predictions shown in Figures 2-4 and 2-6, respectively (i.e., the small band
illustrating the 90% confidence intervals). Additionally, even using the median parameter
values from all 20 optimal parameter sets, the model is still able to recreate the data within
the 50% confidence interval. This indicates significant model robustness, even considering
a high level of biological variability.
To further quantify how sensitive the model is to the parameters, we performed a
parameter sensitivity analysis using the extended Fourier amplitude sensitivity test
(eFAST) (Marino et al., 2008). The eFAST analysis is a global variance-based method in
which all of the parameters are varied together at different frequencies. The Fourier
transform of the output can then be analyzed to determine which frequencies, and thus
which parameters, have the most influence on the model outputs. This method calculates
the first order eFAST indices (Si), a measurement of the local sensitivity of each parameter,
as well as the total eFAST indices (STi), which takes into account the effects of higher
order interactions between parameters.
Results from the global sensitivity analysis further quantify the robustness of the
model. We performed the eFAST analysis to determine the sensitivity of the total phospho-
Y394 and total phospho-Y505 in the system, at specific time points, with respect to all 38
kinetic parameters. There were no significant differences between the eFAST results for
the high and low concentrations of LCK. Additionally, the qualitative results for the LCK
specific parameters did not change with the addition of CSK; therefore, we only show the
49
indices for the condition of high LCK+CSK (Figure 2-7). The first order indices were
slightly lower than the total indices, but qualitatively the same. The values of the sensitivity
indices show that the levels of phosphorylated Y394 and Y505 are most sensitive to the
association rates of the LCK species with each other and with CSK, the dissociation rate
of CSK and U394U505, and the catalytic activity of CSK for U394U505. These are the same
parameters for which the estimated values obtained from the model fitting have a narrow
distribution. However, the levels of phospho-Y394 and -Y505 are insensitive to most of
the parameters, justifying the large deviation in the distributions of the parameters’
estimated values (Figure 2-5).

Figure 2-7: Sensitivity indices of LCK minimal model parameters. The eFAST
analysis was used to calculate the first order (Si) and total (STi) parameter sensitivity
indices for two model outputs: total phospho-Y394 (Y394) and total phospho-Y505
(Y505). Red indicates the parameters to which Y394 and Y505 are very sensitive, and
white represents parameters that do not significantly influence Y394 and Y505. The
dissociation and catalytic rate parameters are labeled by the enzyme-substrate pair
involved in the reaction.

50
1.9.6. Predicted mechanism of LCK activation
The molecular detail of our model allows us to make predictions regarding the
mechanisms of LCK autophosphorylation and phosphorylation by CSK. Specifically, we
can compare the median value of the estimated catalytic rates for each of the LCK enzyme
species, P394U505, U394P505, U394U505, and P 394P505, as shown in Figure 2-8a, b, c, d,
respectively, with a summary of the pairwise interactions shown in Figure 2-8e. The
parameter estimation reveals that P394U 505 has the highest overall catalytic activity (i.e.,
this enzyme species only has red or purple arrows pointing to the phosphorylation
reactions, Figure 2-8a). Conversely, U394P 505 has the lowest activity (Figure 2-8b). These
results are in agreement with what has been shown in the literature for the catalytic rates
of these enzymes on other substrates, such as the CD3z chain ITAMs (Chakraborty and
Weiss, 2014; Hui and Vale, 2014). The catalytic activity of the U394U505 and P394P505
species varies depending on the substrate. U394U505 preferentially phosphorylates itself and
catalyzes phosphorylation at Y394 and Y505 with approximately the same rate. In
comparison, P394P505 shows a strong preference for site Y394 of U394U 505. CSK is estimated
to have higher catalytic activity against P394U 505 than U394U505, predicting that CSK will
phosphorylate P394U505 more readily than U394U 505, which has been validated
experimentally (Bougeret et al., 1996; Sondhi et al., 1998).

51

Figure 2-8: Schematic of predicted LCK kinase activity. The schematics show the
catalytic rates for LCK enzymes (a) P 394U 505, (b) U394P 505, (c) U 394U 505, and (d) P 394P 505
catalyzing each of the four possible LCK phosphorylation reactions. In each panel, dotted
arrows represent a phosphorylation reaction that can be catalyzed (clockwise from top
left, U394U505àP394U505, P394U505àP394P 505, U394P505àP394P505, U394U505àU394P505). The
enzyme catalyzing the reactions in each panel is shown in green with phosphorylated
sites shown in red circles. The color of the solid arrows denotes the median value of the
catalytic rate for the indicated reaction for the 20 best parameter sets. The reactions
catalyzed by CSK are also shown in each panel, with the color of CSK denoting the
median value of the CSK catalytic rate. (e) Pairwise heatmap of the LCK enzyme
catalytic reactions.

52
The estimated catalytic activities identify specific molecular interactions that
produce a negative feedback loop in LCK activation. The P394U505 species, the most
catalytically active form of the LCK, preferentially phosphorylates Y505, compared to
Y394, with a difference of over three orders of magnitude (Figure 2-8a, red arrows). This
is significant because Y505 is thought to be the inhibitory site, generally, and its
phosphorylation reduces the catalytic activity of LCK, thus providing a possible form of
negative feedback. Doubly phosphorylated LCK, P394P505, on the other hand, preferentially
phosphorylates U394U505 to P394U 505, increasing the overall catalytic activity of the pool of
LCK. It has been shown that other intermolecular feedback mechanisms do play an
important role in controlling and tailoring the T cell response (Stefanová et al., 2003);
however, these specific autoregulatory feedback mechanisms have not been identified
before. Thus the model predicts, for the first time, that competing intramolecular feedback
loops could help stabilize and control the overall activity of LCK. It will be important to
see if these effects are still significant when more complex interactions between
phosphatases and other substrates are taken into account.
The model also predicts the relative amounts of each LCK species in the system
over time. In general, LCK starts in a completely unphosphorylated form and transitions
through a singly phosphorylated intermediate to end with all of the LCK doubly
phosphorylated (Figure 2-9). The results are shown for both high and low LCK
concentrations with and without CSK.

53

Figure 2-9: Model predictions of intermediate LCK species. The graphs represent the
model simulations for total (a-d), free (e-h), and bound (i-l) LCK species over time.
From left to right, the columns represent data from conditions of 500 molecules of
LCK/µm
2
, 500 molecules of LCK/µm
2
+ 500 molecules of CSK/µm
2
, 50 molecules of
LCK/µm
2
, and 50 molecules of LCK/µm
2
+ 500 molecules of CSK/µm
2
. The results are
shown as a percentage of the total LCK in the system, with the 50% and 95% confidence
intervals (dark and light shaded regions, respectively).

54
The predicted levels of the LCK species are directly influenced by the binding
kinetics. The model predicts that a significant amount of P394U505 and P 394P 505 can remain
bound together when they are both present in the system (Figure 2-9i, k). This is due to
the low dissociation rate for enzyme P394P505 bound to substrate P394U505 (Figure 2-5a).
U394P 505 and U 394U 505 are also able to bind together, but this association is not as strong as
that of P394P505 and P 394U 505 and seems to be primarily a result of the low catalytic activity
for all binding conformations of these pairs. A similar, but even smaller, binding interaction
is present between U394P505 and P394U505. When CSK is added to the system, it serves as a
sink for LCK, binding to it and keeping it in the system for longer. Significantly, much
more UU is bound to CSK than PU, as shown by the sharp increase in bound UU when
CSK is present (comparing Figure 2-9l to k, blue lines), compared to the more modest
increase in PU (comparing Figure 2-9l to k, green lines).
The model allows us to explore the detailed mechanisms that govern previously
unexplained features of the data. The presence of CSK significantly influences the levels
of the LCK species. Adding CSK to the system greatly reduces the total amount of P394U505,
leaving almost none of this highly active form free to interact with other species
(comparing Figure 2-9h to g, red lines). In the low LCK conditions, CSK also increases
the amount of U 394P505, greatly reducing the overall catalytic activity of the total pool of
LCK in this experimental condition (comparing Figure 2-9d to c, green lines). In
comparison, in the high LCK + CSK experimental simulation, the total amount of U394P505
does not significantly change compared to the high LCK condition (comparing Figure 2-
9b to a, green lines), while the amount of P394U 505 is still greatly reduced (Figure 2-9b to
a, red lines). The model predicts that this difference in the change of intermediate U394P 505
55
is responsible for the shift in the curves of phospho-Y394 and phospho-Y505 in Figure 2-
4d of the model training data sets.

1.10. Discussion and Conclusion
We have constructed a model of LCK activation via autophosphorylation and
phosphorylation by the kinase CSK based on data from an in vitro two-dimensional
membrane system (Hui and Vale, 2014). LCK is an important regulator of T cell activation
and quantifying the kinetics that govern its activity will allow us to better understand and
engineer T cells for therapeutic purposes. The kinetics of LCK phosphorylation in this in
vitro membrane system are very different from those that occur in more commonly used
solution systems. It is believed that this two-dimensional system more accurately reflects
what occurs in vivo, as much of the LCK in T cells is bound to the inside of the membrane
(Zimmermann et al., 2010). Most prior biological computational signaling models have
relied on enzyme solution kinetic parameters for initial estimates. However, we believe
that by focusing on two-dimensional kinetics that are more representative of what occurs
in vivo, we can create models that are more predictive.
Our model is able to fit the data of membrane bound LCK phosphorylation well,
both quantitatively and qualitatively. Additionally, we are able to identify the specific
kinetic parameters that most significantly control LCK phosphorylation. One limitation of
the model is its inability to match early time point experimental measurements of the
phospho-Y505 curve in the low LCK+CSK experimental condition (Figure 2-4d).
However, there are no error bars for the experimental data, and it is possible that these data
may have some experimental error. The recombinant LCK protein used in this system is
56
autophosphorylated as it is expressed, so it must first be dephosphorylated before the start
of the experiment. Hui et al. used mass spectrometry to measure the efficiency of this
dephosphorylation and found that a small amount of Y505 is still phosphorylated at the
start of the experiment (~1.5%); however, many graphs show that the initial
phosphorylation of Y505 is much higher than that, up to ~20%. This large variability in the
starting concentration of phospho-Y505 could lead to an overestimation of the initial rate
of Y505 phosphorylation in the low LCK+CSK condition. Additionally, the data are
derived from quantitative western blotting, and there may be error in the band intensity
readings, particularly for early time points where the band intensity is very close to
background. For these reasons, it is possible that the initial increase in phospho-Y505 in
the low LCK + CSK condition does not truly reflect LCK kinetics.
We applied an unbiased approach to fit the parameters, generating a set of optimal
parameter values that are able to reproduce the data. Despite high variability in the fitted
parameters, there are statistically significant differences between the estimated dissociation
rates of the LCK dimers and catalytic activities of the LCK enzymes. The statistical
analysis along with the global sensitivity analysis indicates that the proposed mechanism
of LCK activation implemented in the model is robust and predictive. The model
predictions reveal that the levels of individual LCK species can remain within a tight range,
even with high variability in the parameter rates. This model robustness is biologically
relevant, since it has been shown that the local microenvironment around a pool of LCK in
the cell changes dramatically depending on the state of the cell and the proximity of other
molecules (Filipp et al., 2004; Huppa and Davis, 2003; Kabouridis, 2006; Rossy et al.,
2013).
57
The model brings many new insights into the autoregulatory mechanisms of LCK
with respect to the binding of LCK dimers. For example, the model predicts that P394U505
and P 394P 505 are able to form a relatively strong dimer compared to P394U 505-U394P505 or
U394U505-U394P505. Additionally, there are pairs that do not significantly dimerize at all. A
crystal structure of the LCK SH2 and SH3 domains show that these domains can
homodimerize, and that this binding may be stabilized by the addition of the
phosphorylated Y505 tail (Eck et al., 1994). However, it does not provide any information
about how interactions from other domains, particularly the domain containing Y394,
control the extent of this dimerization. The model parameters specify which dimers are
able to bind more strongly, and from that, we can infer the role that these other domains
play in LCK binding. Since the P 394U 505-P394P505 dimer is stronger than P394U505-U394P505,
we can hypothesize that the phospho-Y505 tail of P394P505 may be more amenable to
stabilizing the P394U 505-P394P505 dimer interaction than that of U394P 505. This may be
because the phospho-Y394 in P394P505 keeps the molecule in a partially open conformation
while the tail of U394P505 is held in a closed conformation through cis binding (Chakraborty
and Weiss, 2014). Also, since U394U505 and P394U505 do not dimerize with themselves or
each other, we can conclude that the stabilization from the phospho-Y505 tail is important
in the LCK intermolecular interactions.
The model also predicts that CSK plays a very strong role in controlling the
distribution of LCK species in the model, which could be important for controlling LCK
activity in vivo. Figure 2-9 shows that CSK is able to bind to LCK and increase the amount
of U394U 505 and U 394P 505 in the system while reducing the amount of P394U505 and P394P505.
It is known that clusters of T cell signaling molecules reside close to each other on lipid
58
rafts inside the T cell membrane (Filipp et al., 2004; Kabouridis, 2006). The composition
of these clusters changes as the T cell becomes activated and the immunological synapse
begins to form (Huppa and Davis, 2003). Keeping LCK clustered with CSK before synapse
formation could act as a control mechanism to reduce aberrant LCK signaling in
unstimulated cells. Once the synapse forms and CSK is sequestered outside of the synapse
region, enough LCK can accumulate to lead to high levels of active P394U505. More studies
need to be done to better understand how the possible LCK autoregulatory feedback
mechanisms and CSK function in vivo when there are more substrates and phosphatases in
the system.
The model also predicts new binding relationships between CSK and LCK that
have not been identified experimentally. The model indicates that CSK is able to bind more
strongly to U394U 505 than to P394U505 (Figure 2-9l). Conversely, studies of LCK binding to
CSK in solution have shown that CSK is able to bind to P394U505, but not U394U505
(Bougeret et al., 1996). Combined, these results suggests that CSK binding to U394U505
could be an effect of the two-dimensional membrane system, indicating a significant
difference between the mechanisms that occur in solution and those that are able to take
place in a more physiologically relevant membrane bound arrangement.
Comparing the model simulations to data from LCK phosphorylation in solution
continues to shed light on the differences between studying molecular kinetics in solution
and in the native two-dimensional distribution. Hui et al. compared their experimental
membrane system to a traditional solution system. The authors found that the rates at which
the two LCK sites were phosphorylated were significantly different, and that the measured
kinetics for levels of phospho-Y394 and -Y505 did not change proportionately. In the
59
membrane system, for high LCK, Y394 is rapidly phosphorylated while Y505 slowly
increases in a more steady manner (Figure 2-4a). In solution, however, Y394 and Y505
phosphorylation both remain at their starting levels for about 10 minutes and then both
increase very rapidly.
The model indicates that distinct mechanistic interactions can potentially contribute
to differences in the LCK phosphorylation kinetics that occur in two-dimensions compared
to solution. Our model and estimated parameter sets were obtained by fitting LCK
phosphorylation data from the in vitro reconstituted membrane system developed by Hui
and Vale (Hui and Vale, 2014). We also attempted to fit data for LCK phosphorylation
measure in solution. Since a key distinction between the two-dimensional and solution-
based systems is that the species’ amounts are given in units of density rather than
concentration, we attempted to fit the in solution data by only adjusting the association
rates. The association rates are the only parameters that depend on the amount of a species
(i.e., Kon has units of TU
B
UVWXYZWX[∙[XY ⁄ ), whereas the dissociation and catalytic rates
do not depend on concentration. We followed the same parameter fitting procedure
described above using each of the membrane bound optimal parameter sets described in
the paper as starting values to minimize the quantitative WSSR equation with the MatLab
lsqnonlin function; however, we were unable to fit the solution data. We then expanded
our fitting of the solution data to include the association and dissociation rates, or the
association, dissociation, and catalytic rates. The data still could not be fit with the
mechanism used in the model. Although more experiments need to be done to properly
compare the differences between LCK in solution and on the two-dimensional membrane
60
surface, we believe this could point to a difference not only in the parameter values but
also in the mechanism of LCK phosphorylation between the two settings.
Excitingly, the fitted model generates testable hypotheses, and the experimental in
vitro two-dimensional membrane system can be used to explore some of these model
predictions. The estimated parameter values and model predictions support the presence of
both negative and positive autoregulated feedback on the catalytic activity of LCK, which
have not been described previously. The negative feedback comes from catalytically active
P394U 505 preferentially phosphorylating other LCK molecules at the Y505 inhibitory site.
The positive feedback comes from the moderately active P 394P505 species preferentially
pushing doubly unphosphorylated LCK to the active P394U505 form (Figure 2-8a, d). These
new feedback mechanisms, hypothesized by the model predictions, can be tested with
targeted experiments that focus specifically on the catalytic activities of individual
phospho-LCK species. We can do this by mixing LCK that is either doubly phosphorylated
or specifically phosphorylated only at Y394 with other, catalytically inactive, LCK species.
It is also possible to test model hypotheses about the significance of bound dimers, like
CSK and U394U505, by inserting domain deficient mutants, such as LCK lacking the SH2
or SH3 domains, into the two-dimensional membrane system. Thus, a systems biology
approach of using an optimized and validated computational model in combination with
quantitative experimental approaches can provide new and relevant biological insight into
LCK activation.
It is possible to improve and strengthen the model by adding new proteins into this
same in vitro membrane reconstituted system and performing model parameter estimation,
as we have done here. This will allow us to better understand how individual proteins
61
combine to produce the functions of the system as a whole. For example to better
understand the mechanisms of LCK activation, we can incorporate dephosphorylating
events, through proteins like CD45 and PTPN22, into the model to see how that action
impacts the overall levels of individual LCK species (McNeill et al., 2007). Having more
data to fit the model will also help to more specifically identify the LCK kinetic parameters,
many of which are still highly variable in the current model. We can also study more
specific mechanisms of LCK by adding its substrates, CD3ζ, ZAP-70, and SHP-1 into the
system. The model also serves as a starting point for studying the order and kinetics of
LCK-mediated phosphorylation of the six CD3ζ ITAM tyrosine phosphorylation sites
(Chae et al., 2004; Kersh, 1998; van Oers et al., 2000). We believe that the model provides
a quantitative framework for studying many different protein interactions relevant to T cell
signaling, particularly those involving LCK.
In summary, the model is a predictive tool that can be used to examine the dynamics
of LCK autoregulation. As we continue to expand the model, we can use it to make new
predictions about the larger systems that govern T cell activation and explore key biological
hypotheses, like those described above. Many of the mechanistic questions described in
this paper have proven difficult to investigate experimentally; however, using the
computational framework described here, we will be able to explore these issues on a more
quantitative level, providing insights and new testable hypotheses.

1.11. Acknowledgements
The authors would like to acknowledge Dr. Ronald Vale and Dr. Enfu Hui for their
help in clarifying the experimental data. This work was supported by the National Cancer
62
Institute of the National Institutes of Health under Award Number F31CA200242 (to
J.A.R.).

63
2.

Chapter 3

Computational Model of Chimeric Antigen Receptors Explains Site-specific
Phosphorylation Kinetics

Portions of this chapter are adapted from a manuscript by:
Jennifer A. Rohrs, Dongqing Zheng, Nicholas A. Graham, Pin Wang, Stacey D. Finley.
Under review.

64
2.1. Abstract
Chimeric antigen receptors (CARs) have recently been approved for the treatment
of hematological malignancies, but our lack of understanding of the basic mechanisms that
activate these proteins has made it difficult to optimize and control CAR-based therapies.
In this study, we use phospho-proteomic mass spectrometry and mechanistic
computational modeling to quantify the in vitro kinetics of individual tyrosine
phosphorylation on a variety of CARs. We show that the ten tyrosine sites on the CD28-
CD3ζ CAR are phosphorylated by LCK independently and with different kinetics. The
addition of CD28 at the N-terminal of CD3ζ increases the overall rate of CD3ζ
phosphorylation. Our computational model explains experimental observations of CD3ζ
immunoreceptor tyrosine-based activation motif (ITAM) phosphorylation and provides
new mechanistic hypotheses for how these activating domains can be more optimally
phosphorylated. Specifically, the model highlights the importance of protein binding to
single ITAM tyrosine sites to enhance the amount of doubly phosphorylated ITAMs. This
quantitative modeling framework can be used to better understand CAR signaling and T
cell activation.

65
2.2. Introduction
One of most widely used methods for engineering a patient’s T cells to fight cancer
is through the expression of chimeric antigen receptors (CARs). CARs are proteins that
combine an extracellular antibody-derived targeting domain with intracellular T cell
activating domains derived from the endogenous T cell receptor (Fesnak et al., 2016).
These engineered T cells have emerged as promising treatments for hematopoietic cancers
(Firor et al., 2015; Mullard, 2017); however, not all patients respond to treatment and it
has been difficult to expand these therapies to solid tumors (Kingwell, 2017; Lee et al.,
2015; Moon et al., 2014; Morgan et al., 2010). Significantly, it has recently been shown
that CARs are less effective in activating T cells than engineered T cell receptors (TCRs)
(Harris et al., 2018). More work needs to be done to better understand the mechanisms
through which CAR-engineered T cells become activated so that they can be more
optimally designed and expanded to a wider patient population. In this study, we use
quantitative phospho-proteomic mass spectrometry and computational modeling to explore
the mechanisms that lead to the phosphorylation of CAR proteins. Computational models,
like the one developed here, provide a unique method to use basic engineering principles
to better understand and optimize the signaling pathways that activate CAR-engineered T
cells.
The CAR-T cell therapy Yescarta was approved by the FDA in October 2017 and
contains signaling domains derived from the CD3ζ domain of the T cell receptor (TCR)
and the CD28 co-stimulatory domain (Mullard, 2017). These T cell signaling domains are
phosphorylated by the Src family kinases, the most important of which in endogenous T
cells is lymphocyte-specific protein tyrosine kinase (LCK) (Lovatt et al., 2006; Nika et al.,
66
2010; Palacios and Weiss, 2004). CD3ζ contains six tyrosine phosphorylation sites,
arranged in pairs on three immunoreceptor tyrosine-based activation motifs (ITAMs)
(Figure 3-3A) (Chakraborty and Weiss, 2014). When doubly phosphorylated, these
ITAMs can bind to the adaptor protein ZAP-70, allowing LCK to phosphorylate ZAP-70
and also protecting the CD3ζ ITAMs from dephosphorylation (Au-Yeung et al., 2009;
Sjölin-goodfellow et al., 2015). Interestingly, in unstimulated lymphocytes and peripheral
T cells, CD3ζ is constitutively phosphorylated at the two C-terminal ITAMs (ITAMs B
and C), resulting in a 21 kDa protein (van Oers et al., 2000; Pitcher et al., 2003). Upon full
activation, all three ITAMs become phosphorylated to produce the 23 kDa form. Although
the key phosphorylation sites are readily known, the order and kinetics of their
phosphorylation have not been quantitatively studied. Thus, the mechanism through which
the 21- and 23 kDa phosphorylated species form is not known, making it difficult to control
the activation of CARs.
Combining the CD3ζ activating domain and a co-stimulatory domain on the same
protein adds additional complexity to the CAR. The CD28 co-stimulatory domain has four
tyrosine sites, which can be phosphorylated by LCK (Boomer and Green, 2010), and may
also influence the catalytic activity of LCK (Carey et al., 2000; Holdorf et al., 2002). Once
phosphorylated, CD28 tyrosine sites bind to various adaptor proteins that are also
phosphorylated downstream of CD3ζ (Tian et al., 2015). Thus, CD28 can tune the response
to CD3ζ activation. Additionally, the recruitment and competition by CD28 for LCK may
alter the phosphorylation of CD3ζ.
All ten of the tyrsoine sites on CD3ζ and CD28 work together, in different ways, to
affect the downstream signaling that controls T cell activation responses such as
67
cytotoxicity, cytokine production, proliferation, and survival (Chae et al., 2004; Kersh et
al., 1999; Lu et al., 1994; Michel et al., 2001; Teng et al., 1996). By better understanding
how these chimeric proteins are phosphorylated, we can identify ways to tune them to
create more optimal CAR therapies. In this study, we have explored the kinetics of CD3ζ
and CD28 phosphorylation in detail. We paired a recombinant protein system with
phospho-proteomic mass spectrometry to measure the site-specific phosphorylation of
CAR proteins by LCK over time. To our knowledge, this is the first study to quantify
phosphorylation at individual sites on the intact CAR protein. We then fit this data using a
computational model to robustly quantify the differences between the phosphorylation
kinetics of the ten tyrosine sites. We used the computational model to generate new
predictions regarding the mechanisms that allow for the emergence of the 21 kDa partially
phosphorylated form of CD3ζ. We can use the novel insights from this study to continue
expanding our understanding of CAR-mediated T cell activation and better engineer future
CAR therapies.

2.3. Materials and Methods
2.3.1. Recombinant protein expression and purification
His10-KKCK-CD3ζ in the pET28a vector and HIS10-LCK-G2A in the
pFastBacHTA vector were a kind gift from Dr. Ronald Vale (Hui and Vale, 2014). To
make the HIS 10-CD28-CD3ζ recombinant protein, the DNA sequence for the intracellular
domain of CD28 (aa 180-220) was codon optimized and constructed by Integrated DNA
Technologies (IDT-DNA). This sequence was then cloned directly upstream of CD3ζ in
68
the pET28a vector using Gibson assembly. All individual point mutations in the CAR
vectors were introduced by the QuikChange XL site-directed mutagenesis kit (Agilent).
The sequence for HIS10-LCK-G2A was amplified out of the pFastBacHTA vector
by PCR and cloned into the FUW vector through Gibson assembly. LCK is able to undergo
autophosphorylation at both activating and inhibitory tyrosine sites (Y394 and Y505,
respectively). We previously showed that when LCK is phosphorylated at these tyrosine
residues, it has differential catalytic activity (Rohrs et al., 2016a). Therefore, to exclude
any confounding effects due to changes in enzymatic efficiency, we used a constitutively
active form of LCK containing a tyrosine to phenylalanine mutation at the inhibitory site
(Y505F). This point mutation was introduced by the QuikChange XL site-directed
mutagenesis kit (Agilent).
All CAR proteins were expressed in the BL28(DE3) strain of E. coli cells. E. coli
cells were lysed as described in (Li et al., 2010). His10-LCK-G2A-Y505F was transiently
expressed in HEK293T cells through a standard calcium phosphate precipitation protocol
(Pear et al., 1993). 48 hours after transfection, HEK293T cells were lysed in buffer
containing 20 mM Tris·HCl, pH 7.5, 600 mM NaCl, 2 mM MgCl2, 5 mM immidazole,
10% glycerol, 1% NP-40, 1 mM Na3VO4, 10 mM NaF, and 1× complete protease
inhibitor (Roche)). All HIS10 proteins were purified using FPLC, first on a Ni-NTA
agarose column followed by gel purification using the HiPrep 16/60 Sephacryl S-200 HR
column (GE Life Sciences) in HEPES-buffered saline (HBS) solution containing 50 mM
HEPES-NaOH (pH 7.5), 150 mM NaCl, and 10% glycerol, as described in (Hui and
Vale, 2014). Protein monomer fractions were concentrated, snap frozen in liquid
69
nitrogen, and stored at −80°C. All purified recombinant proteins were quantified by SDS-
PAGE and Coomassie staining using BSA as a standard.
Mass spectrometry confirmed that nearly 100% of the purified LCK-Y505 is
phosphorylated at the activating Y394 site, while 100% of the CAR proteins were
unphosphorylated after purification.

2.3.2. Liposome preparation
Synthetic 1,2-dioleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-
oleoyl-sn-glycero-3-phospho-l-serine (POPS), and 1,2-dioleoyl-sn-glycero-3-[(N-(5-
amino-1-carboxypentyl)iminodiacetic acid)succinyl] (nickel salt, DGS-NTA-Ni) were
purchased from Avanti Polar Lipids and resuspended in chloroform. Liposomes were
prepared as described in (Hui and Vale, 2014). Briefly, phospholipids (80% POPC, 10%
POPS, 10% DGS-NTA-Ni) were dried as thin films under Ar gas and desiccated overnight.
The lipids were then resuspended in 1x kinase buffer (50 mM HEPES-NaOH (pH 7.5), 150
mM NaCl, 10 mM MgCl2, 1 mM TCEP), and subjected to 5x freeze thaw cycles. The lipid
mixture was then extruded through 200 nm pore-size polycarbonate filters to produce large
unilamellar liposomes. For liposomes with varying POPS concentration, the amount was
compensated for by adjusting the POPC concentration.

2.3.3. Protein phosphorylation time courses
HIS-tagged LCK and CAR proteins were mixed with Ni-bearing liposomes for 1
hour to allow for the proteins to attach to nickel bearing lipids on the surface of the
liposome, as calculated and described in (Hui and Vale, 2014). We used 20,000
70
molecules/µm
2
CAR proteins and titrated down LCK to a very low concentration to allow
us to distinguish the differences between the CD3ζ site phosphorylation kinetics.
Estimation of the final LCK concentration is described in the Mechanistic computational
modeling section. Once the proteins attached to the liposomes, 10x ATP in kinase buffer
was added to a final concentration of 1M. Samples were taken at various times and the
reaction was stopped by adding urea to 8M and boiling for 5 minutes. Time samples were
then frozen at -20°C until they were prepared for phospho-proteomic mass spectrometry.

2.3.4. Standard curve preparation
As different peptides will travel through the mass spectrometer with different
efficiencies resulting in different MS intensities for the same amount of peptide, a standard
curve is necessary to compare between peptide MS intestines in a sample. We constructed
our standard curves based on a known ratio of phosphorylated:unphosphorylated peptide.
For each CAR protein, we quantified the amount of protein and aliquoted the same volume
from a given sample into two vials. To one vial we added LCK and ATP and let LCK
phosphorylate the CAR overnight. To the other vial, we added equal volumes of HBS
buffer, so that the phosphorylated and unphosphorylated CAR proteins would remain at
the same concentration. The next morning, urea was added to both vials to a final
concentration of 8M. We then combined various volume ratios of the two solutions to
create a standard curve with known ratios of phosphorylated:unphosphorylated peptides.
The standard curve samples were then stored at -20°C until they were ready to be prepared
for analysis by mass spec.

71
2.3.5. Phospho-proteomic sample preparation
The time course samples were thawed to room temperature and reduced by the
addition of DTT to a final concentration of 5 mM for 1 hr at 37°C. Samples were next
alkylated with iodoacetamide at a final concentration of 25 mM for 1 hr at room
temperature in the dark. This reaction was quenched by the addition of DTT to a final
concentration of 10 mM for 30 min. Samples were then diluted to a final urea concentration
of 2 M with 100 mM Tris, pH 8, and trypsin digested overnight at 37°C. The next morning,
samples were acidified to a pH<4 with 5% TFA, purified by C18 zip-tip (Millipore)
according to the manufacturer’s instructions, and eluted into 50% acetonitrile solution.
Purified samples were then dried and stored at -80°C until they were ready to be analyzed.

2.3.6. Phospho-proteomic data collection
All data samples were run in technical duplicates. Data was run in three sets, each
with their own standard curve, shown in Figure 3-1: (1) first biological replicate of the
wild type ITAM phosphorylation on 10% POPS liposomes, the wild type ITAM
phosphorylation on 0% and 45% POPS liposomes, and a CD3ζ standard curve, (2) the
second biological replicate of the wild type ITAM phosphorylation on 10% POPS
liposomes, the individual tyrosine to phenylalanine CD3ζ ITAM point mutants, and a CD3ζ
standard curve, (3) all 28ζ proteins, including the Y206F and Y209F mutants, and a
standard curve for 28ζ, CD28-Y206F-CD3ζ, and CD28-Y209F-CD3ζ. Desalted samples
were reconstituted in buffer A (0.1% formic acid). The samples were injected into an Easy
1200 nanoLC untra-high pressure liquid chromatography coupled to a Q-Exactive Plus
mass spectrometer (Thermo Fisher Scientific). Peptides were separated by reversed-phase
72
chromatography (PepMap RSLC C18, 2µm, 100Å, 75 µm X 15 cm). The flow rate was set
to 300 nl/min at a gradient starting with 6% buffer B (0.1% FA, 80% acetonitrile) to 55%
B in 25 minutes, followed by an 8 minutes washing step to 100% B. The maximum pressure
was set to 1180 bar and column temperature was constant at 50 ˚C.

Figure 3-1: Standard curves for phosphorylated:unphosphorylated peptide intensity
normalization. Data was run on the mass spectrometer in three sets, and each set was
normalized by a standard curve run at the same time. All of the standard curves used are
shown here, with each row being used to analyze a separate set of data. Row 1 was used
to analyze the first biological replicate of the wild type ITAM phosphorylation on 10%
POPS liposomes and the wild type ITAM phosphorylation on 0% and 45% POPS
liposomes. Row 2 was used to analyze the second biological replicate of the wild type
ITAM phosphorylation on 10% POPS liposomes as well as the individual tyrosine to
phenylalanine CD3ζ ITAM point mutants. The third and fourth rows were used to
analyze all 28ζ proteins, including the Y206F and Y209F mutants.
73
Peptides separated by the column were ionized at 2.0 kV in the positive ion mode.
MS1 survey scans were acquired at resolution of 70k from 275 to 1500 m/z, with maximum
injection time of 80 ms and AGC target of 1e6. MS/MS fragmentation of the 10 most
abundant ions were analyzed at a resolution of 35k, AGC target 1e5, maximum injection
time 100 ms, and normalized collision energy 25. Dynamic exclusion was set to 10 s and
ions with charge 1, 7, and >7 were excluded.

2.3.7. Mass spec data analysis and normalization
MS/MS fragmentation spectra were searched with Proteome Discoverer SEQUEST
(version 1.4, Thermo Scientific) against the in-silico tryptic digested recombinant protein
sequences (17 entries) used in this study. The maximum missed cleavages was set to 2.
Dynamic modifications were set to oxidation on methionine, phosphorylation on serine,
threonine, and tyrosine, and acetylation on protein N-terminus. Fixed modification was set
to carbamidomethylation on cysteine residues. The maximum parental mass error was set
to 10 ppm and the MSMS mass tolerance was set to 0.02 Da. False Discovery threshold
was set to 0.01 using Percolator node validated by q-value. Phosphosite localization
probability was calculated using PhosphoRS node.
MS1 peak quantification was performed manually in Skyline (version 3.7) for each
phosphorylated/unphosphorylated peptide pair. We analyzed only peptides with no missed
cleavages and no modifications besides tyrosine phosphorylation, which were consistently
the largest peaks. One exception was made for the CD28 peptide containing tyrosine site
Y218. The unphosphorylated form of this peptide was smaller than the cutoff mass to
74
charge ratio used in our data collection. Therefore, we analyzed this site using the peptide
with one N-terminal missed cleavage.
To create our peptide standard curves, we calculated the ratio of each
phosphorylated/unphosphorylated peptide, plotted them against the known ratios and fit
the resulting linear plots (Figure 3-1). Technical replicates of each peptide were combined
together to fit the standard curves so that one standard curve was used to normalize the
phosphorylated/unphosphorylated peptide intensity ratios for each set of peptide time
course technical replicates. We then used the normalized ratios to calculate the percent
phosphorylation over time for each time course technical replicate and used the two sets to
calculate the mean and standard deviation of the data. Time courses were only normalized
to the standard curve data collected at the same time.

2.3.8. Statistical analysis
All statistical analyses were done using a one-way ANOVA followed by multiple
pair-wise comparisons using the Tukey t-test in Prism (version 7, GraphPad)

2.3.9. Sigmoidal parameter calculations
Data was fit in Prism (version 7, GraphPad) to a standard sigmoidal curve with
plateaus at 0 and 100%.

` =
EHH
EaEH
(bcd$e
fghi
/jk)∗mnhh
(Eq. 1)

75
Where x is the time on a log scale, y is the output, thalf is the half maximal time, and Hill is
the Hill coefficient. For the comparison of thalf and Hill for the random and sequential
models, the models were first fit to data using MATLAB, as described in the “Mechanistic
computational modeling” section below. The model responses were then entered into Prism
as data sets and fit to Eq. 1.

2.3.10. Mechanistic computational modeling
Our mechanistic computational model was written as a set of rules in BioNetGen
(Faeder et al., 2009) and implemented in MATLAB. We used mass action kinetics to
describe the association, dissociation, and catalytic activity of LCK for each of the six
ITAM sites. The parameters were fit to the data using particle swarm optimization (PSO)
(Iadevaia et al., 2010). Each data set was fit 50 times to get a range of parameter values.
From these parameter values, the substrate specificity (SS) of LCK for each of the six sites
was calculated as described in Eq. 2:

&& =
o
pge
q
r
=
o
pge
∙o
st
o
sii
ao
pge
(Eq. 2)

Where SS is substrate specificity, k cat is the catalytic rate, KM is the Michaelis-Menten
constant, kon is the association rate, and koff is the dissociation rate.
The initial conditions for the CAR proteins were based on the measured protein
densities used in the experiments, 20,000 molecules/µm
2
. In order to be able to distinguish
between the phosphorylation kinetics of CAR tyrosine sites, very low concentrations of
LCK were used in the experiments. This experimental condition also agrees with the
76
assumption of Michaelis-Menten kinetics that the enzyme concentration is much less than
the substrate concentration, allowing us to use the KM value in our calculation of substrate
specificity. However, this low level of LCK made it very difficult to measure the exact
concentration relative to the experimental errors. Therefore, we used the calculated
Michaelis-Menten parameters for LCK phosphorylation of CD3ζ from (Hui and Vale,
2014) to estimate a more exact initial concentration of LCK. We first took our site-specific
data and calculated the average total CD3ζ phosphorylation over time. We then made a
CD3ζ phosphorylation model using Michaelis-Menten kinetics and the parameters from
(Hui and Vale, 2014), and fit the concentration of LCK to the data. An average of
approximately 1 molecule/µm
2
fit the data best and was, therefore, used to fit our site-
specific parameters (Figure 3-2).

Figure 3-2: Model fit of LCK initial condition. The figure on the left shows the model
based on parameter from (Hui and Vale, 2014) with the LCK initial condition as
calculated by LCK recombinant protein concentration estimated against an albumin
standard. The figure on the right shows the initial LCK condition estimated by the model
to best fit our average CD3ζ phosphorylation time course.

77
To explore the emergence of the 21 kDa form of CD3ζ, we extended the model to
account for doubly phosphorylated ITAMs. We combined the ITAM tyrosine site pairs
onto the same molecule (ITAM A: A1+A2, ITAM B: B1+B2, ITAM C: C1+C2), keeping
the LCK phosphorylation kinetic parameters consistent along the contour lines shown in
Figure 3-8A based on the initial fits listed in Table 3-1. A generic first order
dephosphorylation mechanism was employed to account for a variety of different
phosphatases present in the T cells. As LCK and most phosphatases (specifically CD45)
are large molecules compared to the CD3ζ ITAMs, in the model, the phosphatase can only
act on ITAMs without LCK bound at either tyrosine site. ZAP-70 contained two binding
sites that could bind only to doubly phosphorylated ITAMs. We used this model to explore
a wide range of parameter values.

Table 3-1: CAR phosphorylation minimal model parameter values

78
2.4. Results
2.4.1. Tyrosine sites on CD3ζ are phosphorylated by LCK with different
kinetics
We first sought to explore how LCK phosphorylates the six tyrosine sites on CD3ζ.
To do this, we utilized a liposome-based recombinant protein system, developed by Hui
and Vale (Hui and Vale, 2014). In this system, his-tagged proteins are bound to nickel
chelating lipids on the surface of large unilamellar liposomes, as shown in Figure 3-3A.
Since the CAR and LCK proteins are largely membrane bound in T cells, this system allows
us to mimic the two-dimensional protein arrangement and more accurately capture the true
kinetics of the interactions between these proteins.

79

Figure 3-3: CD3ζ sites are phosphorylated by LCK randomly with different kinetics.
(A) Schematic of the experimental liposomal system. CD3ζ and LCK his-tagged proteins
were purified and allowed to bind to large unilamellar liposomes bearing nickel-
chelated lipids. Once proteins were bound, ATP was added, and the proteins were
allowed to interact for various times before being subjected to phospho-proteomic mass
spectrometry for quantification.
(B) Sequence of CD3ζ intracellular domain with trypsin cut sites denoted. Individual
ITAM tyrosine sites are labeled in different colors. Y64F indicates a tyrosine to
phenylalanine mutation to ensure that each peptide only has one tyrosine
phosphorylation site.
(C) Experimental data (dots) and model fit (lines) for CD3ζ ITAM phosphorylation on
liposomes containing 10% acidic POPS lipids. Error bars represent the standard
deviation of two technical replicates normalized by site-specific standard curves.
(D) Substrate specificity of individual CD3ζ ITAM sites, as calculated from the model fit
parameters. 50 rounds of model fitting gave nearly identical calculations of substrate
specificities.

80
The liposome-bound proteins were allowed to react in the presence of ATP, and we
performed phospho-proteomic mass spectrometry to specifically measure the
phosphorylation at each ITAM site over time. To quantify the site-specific
phosphorylation, we needed to directly compare the mass spectrometry intensity of
phosphorylated and unphosphorylated peptide pairs. To do this, we used a standard curve
with a known ratio of phosphorylated:unphosphorylated peptide (Figure 3-1) (Lee et al.,
2002). Additionally, we needed to ensure that there is only one tyrosine site on each tryptic
peptide. This is true for all CD3ζ ITAM tyrosine sites except A1 (Figure 3-3B). The
peptide containing site A1 also contains a tyrosine at position 64, which is not part of an
ITAM and has not been shown to play a significant role in T cell activation. Therefore, we
added a Y64F mutation in the CD3ζ recombinant protein. In this way, we were able to
normalize the phosphorylated:unphosphorylated intensity ratios for each ITAM site in our
time courses by the standard curves, thus calculating the percent phosphorylation over time
for each of tyrosine sites of interest.
Figure 3-3C (dots) shows the percent phosphorylation of each of the six ITAM
sites over time on liposomes that contain 10% acidic phosphatidylserine (POPS) lipids,
which is similar to the concentration of phosphatidylserine on the inner leaflet of the T cell
plasma membrane (Hui and Vale, 2014). Our measurements show that not all of the sites
are phosphorylated at the same rate. To quantify the differences, we fit these data to a four-
parameter sigmoidal curve, estimating the half maximal time and the Hill coefficient for
each site (Figure 3-4). The half maximal times show that the six sites are phosphorylated
with different kinetics (A1>B2>B1≥A2≥C2>C1). In comparison, the Hill coefficient for
all tyrosine phosphorylation sites is close to one.
81

Figure 3-4: Sigmoidal fit to CD3ζ site-specific phosphorylation data.
(A) Sigmoidal fits to experimental data.
(B) Half maximal time for each CD3ζ ITAM site. Data represents mean and standard
error of the mean of the fit to a 4-parameter sigmoidal curve.
(C) Hill coefficient for each CD3ζ ITAM site. Data represents mean and standard error of
the mean of the fit to a 4-parameter sigmoidal curve.

2.4.2. LCK catalyzes CD3ζ tyrosine site with different substrate specificities
To better understand the underlying mechanism of phosphorylation of the specific
tyrosine sites on CD3ζ, we used mass action kinetics to construct a computational model
of CD3ζ phosphorylation by LCK. Fitting a sigmoidal curve to the experimental data and
determining the half maximal time and Hill coefficient are a standard means of
characterizing the relative phosphorylation rates; however, we aim to provide a
mechanistic examination CD3ζ phosphorylation kinetics. Therefore, we used a molecular-
detailed kinetic model of LCK-CD3ζ interactions.
We tested two different model structures to see which best fit the CD3ζ site-specific
phosphorylation data: a sequential order and a random order. In the sequential order model,
LCK can phosphorylate the six sites at different rates, but in a specified order defined by
the order of the half maximal time from the sigmoidal fit (Figure 3-4B). This model leads
to a consistent increase in the Hill coefficient as it progresses through the sequence of
82
ITAM phosphorylation sites (A1, B2, B1, A2, C2, and C1) (Figure 3-5A-C). On the other
hand, in the random order model, each of the six ITAM sites interact with LCK
independently. With this model structure, each of the sites have the same Hill coefficient,
which is consistent with the experimental data (Figure 3-5D-F). Additionally, the random
order model fits the data better, with a lower residual error, than the sequential model.
Upon visual inspection, we can see that the random order model better captures the overall
trends of the data, specifically for the graduate approach to saturation. Therefore, we
proceeded with the model mechanism that uses a random order of phosphorylation to fit
our data.

83

Figure 3-5: Sequential and random order model fits.
(A) Sequential order model fit to experimental data.
(B) Half maximal time for sequential order model fit.
(C) Hill coefficient for sequential order model fit.
(D) Random order model fit to experimental data.
(E) Half maximal time for random order model fit.
(F) Hill coefficient for random order model fit.

84
We fit the experimentally determined phosphorylation levels using this random
order model structure in which all of the ITAMs interact with LCK independently (Figure
3-3C, lines), and estimated the site-specific kinetic phosphorylation parameters. For each
tyrosine site time course and lipid formulation, 50 rounds of model parameter fitting gave
nearly identical fits to the data. The substrate specificities (see methods), calculated from
the model parameters fit to the data, were also consistent across the different parameter fits
for a single biological replicate. Figure 3-3D shows the substrate specificity of LCK at
each CD3ζ ITAM site.
The values of the estimated substrate specificities follow the same overall order as
the half maximal times derived from the simple sigmoidal fit (Figure 3-4B). However, the
substrate specificity gives us additional information about the relative preference that LCK
has for each of the sites. While the difference between the half maximal time of ITAM
pairs (A1-A2, B1-B2, and C1-C2) are very similar, the same cannot be said for the substrate
specificity. There is a much larger difference between the substrate specificity of sites A1
and A2 than there is between B1 and B2. This difference is even smaller between C1 and
C2. That is, even though the two sites on ITAM C have a relatively large difference in their
half maximal phosphorylation times, LCK’s preference for these two sites is nearly
identical. In comparison, for ITAM A, LCK has a much higher preference for site A1 than
it does for site A2.

2.4.3. The CD3ζ ITAM sites are phosphorylated independently
We wanted to confirm the model prediction that the sites are phosphorylated
independently by testing for interactions between the CD3ζ ITAM sites. Specifically, we
85
wanted to identify if there are any binding or competitive effects that influence the kinetics
at distant sites. Therefore, we individually mutated each tyrosine site to a phenylalanine
and measured the percent phosphorylation over time of the other sites.
We also investigated the effect of the liposome membrane acidity. Several T cell
receptor proteins, including the closely related CD3ε and CD28 proteins, have been shown
to have basic residues in their intracellular domains that can interact with acidic lipids on
the inner leaflet of the T cell membrane (Aivazian and Stern, 2000; Dobbins et al., 2016;
Gagnon et al., 2012). These interactions are thought to help limit tyrosine accessibility,
thus controlling aberrant phosphorylation in unstimulated cells. Therefore, we also tested
if CD3ζ interactions with the acidic POPS lipids in the liposome membrane were
contributing to the different rates of phosphorylation seen in the site-specific data.
Figure 3-6A shows the overlay of all of the phosphorylation time course
experiments (six individual CD3ζ Y to F point mutations, wild type CD3ζ stimulated on
0% and 45% POPS liposomes, and two biological replicates of wild type CD3ζ stimulated
on 10% POPS liposomes) for each site. The trends for all of the site-specific time courses
are very similar, indicating that neither individual site mutations or changes to the acidic
lipid microenvironment significantly affect the phosphorylation kinetics of CD3ζ tyrosine
sites. To compare between the sites, we grouped the time course responses together for all
of the experimental conditions and used the pair-wise Tukey t-test to identify which ITAM
site phosphorylation levels were significantly different from the others (Figure 3-6B). We
compared the data sets at two different time points 10 minutes (blue), which is close to the
half maximal time of the quickly phosphorylated ITAM sites A1 and B2, and 60 minutes
(orange), which is close to the half maximal time of the majority of the other sites. The 10-
86
minute comparison shows that A2, C1, and C2 are not significantly different from each
other, while site B1 is significantly different from A2 and C1 but not C2. From both the
10-minute and 60-minute comparisons, we see that sites A1 and B2 are both significantly
different from all other sites.

87

Figure 3-6: The individual tyrosine sites do not influence the phosphorylation kinetics
of each other.
(A) Experimental data for each CD3ζ ITAM site for different experimental conditions:
WT 1 and 2 - biological replicates of CD3ζ with unmutated ITAMs on liposomes
containing 10% POPS, XX mut (where XX represents the tyrosine to phenylalanine
ITAM mutation site for CD3ζ stimulated on 10% POPS liposomes), and X% PS
(where X represents the POPS concentration for liposomes bearing CD3ζ with wild
type ITAMs). Error bars represent the standard deviation of two technical replicates
normalized by site-specific standard curves.
(B) Statistical comparison of CD3ζ ITAM site phosphorylation levels at 10 (blue) and 60
(orange) minutes as measured by pairwise Tukey t-tests (**** p<0.0001, ***
p<0.001, ** p<0.01, * p<0.05, n.s. not significant).
(C) Substrate specificity of individual CD3ζ ITAM sites. Bars represent the mean and
standard deviation as calculated from the model fits in Figure 3-3A and Figure 3-7.
Stars indicate sites that are statistically different from all other sites (* p<0.05).

88
We next fit our mechanistic kinetic model to each of these data sets. Each
experimental time course was fit to the data independently 50 times (Figure 3-7). We again
found that the model consistently fit the data well, giving nearly identical calculations of
substrate specificity for each data set. Figure 3-6C shows the mean and standard deviation
of the LCK substrate specificity between all of the experimental conditions. Although only
site A1 is significantly different from all other sites, the trends between the sites for a given
experiment are highly consistent. This analysis confirms that the CD3ζ ITAM tyrosine sites
are phosphorylated independently and without a dependence on the acidic lipid
microenvironment, as mutating individual sites or lipid concentrations does not
significantly affect the site-specific phosphorylation dynamics of CD3ζ.

89

Figure 3-7: Additional CD3ζ ITAM site phosphorylation model fits.
(A) the second biological replicate of wild type CD3ζ ITAM protein stimulated on
liposomes containing 10% POPS lipids, (B) wild type CD3ζ ITAM protein stimulated on
liposomes containing 0% POPS lipids, (C) wild type CD3ζ ITAM protein stimulated on
liposomes containing 45% POPS lipids. (D-J) CD3ζ proteins bearing individual tyrosine
to phenylalanine ITAM point mutations stimulated on liposomes containing 10% POPS
lipids.

90
2.4.4. LCK binding and catalytic parameters are correlated
The molecular-detailed nature of the model allows us to investigate how particular
molecular interactions and catalytic events influence CD3ζ phosphorylation. In model
fitting, we noticed that while the individual parameters could vary widely, the predicted
phosphorylation levels and estimated substrate specificities given by the model fits were
nearly identical. To further explore how LCK binding and catalytic activities relate, we
held the association rate constant, which has been shown to be better constrained than the
dissociation rate (Schlosshauer and Baker, 2004), and allowed the dissociation and
catalytic rates to vary. Figure 3-8A shows how the resulting half maximal time of the
phosphorylation curve shifts with different parameter combinations. In general, we found
that the dissociation and catalytic rate parameters are directly correlated, with
approximately linear contour lines on the resulting heat maps. However, as the dissociation
rate decreases, the contour lines begin to plateau. In this region of low dissociation and
catalytic rates, the majority of the LCK remains bound to the site without dissociating or
phosphorylating (Figure 3-8B). For all ITAM sites, greatly reducing the dissociation rate
can lead to this sink-like effect for LCK. In general, the dissociation rate and catalytic rate
are directly related, and changing them together will change the binding of LCK without
influencing CD3ζ phosphorylation, or the model fit to the data.

91

Figure 3-8: CD3ζ phosphorylation is consistent across a range of LCK binding and
catalytic rates.
(A) Heat map of the half maximal time estimated from the predicted phosphorylation time
course as a function of varying LCK dissociation rate (x-axis) and catalytic rate (y-
axis). The chosen baseline model fit parameters for each ITAM site are indicated by
the dots.
(B) Heat map of maximal LCK binding as a function of dissociation rate (x-axis) and
catalytic rate (y-axis). The chosen model fit parameters for each ITAM site are
indicated by the dots.

2.4.5. Computational model predicts the emergence of 21 kDa CD3ζ in the
presence of ZAP-70 and phosphatases
We next wanted to better understand how the 21 kDa form of CD3ζ could be
preferentially phosphorylated on ITAMs B and C, despite the fact that these sites are
phosphorylated more slowly than those on ITAM A. ZAP-70 is able to bind to doubly
phosphorylated ITAMs and protect them from dephosphorylation, and these two
mechanisms together are sufficient for the production the 21 kDa form of CD3ζ when
reconstituted in COS 7 cells (van Oers et al., 2000). Therefore, we extended our
computational model to explore the occurrence of the 21 and 23 kDa forms of CD3ζ in the
presence of ZAP-70 binding and phosphatase activity. To specifically explore the effects
92
of these new parameters, we first refit the data set from Figure 3-3C using the parameter
constrains described above in which the association rate is the same for all sites. Although
multiple sets of parameters (along a particular contour line in Figure 3-8A) gave similar
fits to the data, we chose one set to begin our analysis (Dots in Figure 3-8, parameters
listed in Table 3-1).
We tested a range of ZAP-70 binding and phosphatase parameters using initial
conditions with a 1:1:1 ratio of LCK:CD3ζ:ZAP-70, and recorded the steady state
phosphorylation levels of each ITAM (Figure 3-9A). All of the ITAMs were either
unphosphorylated or doubly phosphorylated, with negligible amounts of singly
phosphorylated ITAMs. These graphs show that there is a range of phosphatase activity
and ZAP-70 binding parameters that will allow for ITAM B and C to be phosphorylated at
similar levels and for ITAM A to be significantly less phosphorylated (Figure 3-9A red
dashed region), indicating that this is a robust response of the system. The time course
response of ITAM phosphorylation in the presence of phosphatase activity and ZAP-70
binding is shown in Figure 3-9B. Solid lines represent the time course for the phosphatase
and ZAP-70 parameters at the point of the red dot in Figure 3-9A. The shaded regions are
the 95% confidence interval for the range of parameters shown within the red dashed areas
on Figure 3-9A. For all parameters within the red dashed area, at steady state, ITAMs B
and C are significantly more phosphorylated than ITAM A. In general, the parameter range
in the red dashed area is characterized by high phosphatase activity and strong ZAP-70
binding. Given the observations that phosphatases, like CD45, are highly expressed and in
close proximity to the TCR and/or CARs in resting T cells, the model captures how this
93
high phosphatase activity can result in the 21 kDa form of CD3ζ cells (Bu et al., 1995;
Stanford et al., 2012).

Figure 3-9: A range of ZAP-70 binding parameters and phosphatase activities lead to
the formation of the 21 kDa partially phosphorylated form of CD3ζ.
(A) Heat maps showing the percent of doubly phosphorylated CD3ζ ITAMs at steady state
as a function of the dephosphorylation activity (x-axis) and ZAP-70 dissociation rate
(y-axis) for initial conditions of 10,000 LCK/µm
2
, 10,000 CD3ζ/µm
2
, 10,000 ZAP-
70/µm
2
. The red dashed area indicates the parameter region in which ITAM A is
significantly less phosphorylated than ITAMs B and C, representing the 21 kDa form
of CD3ζ.
(B) Time course of ITAM phosphorylation. Lines are the model response for the
parameters indicated by the red dot in (A), shaded regions are the 95% confidence
interval of the model response for the parameters within the red dashed area of (A).
(C) Heat maps showing the percent of doubly phosphorylated CD3ζ ITAMs at steady state
as a function of the dephosphorylation activity (x-axis) and ZAP-70 dissociation rate
(y-axis) for initial conditions of 10,000 LCK/µm
2
, 10,000 CD3ζ/µm
2
, 30,000 ZAP-
70/µm
2
. The red dashed area indicates the parameter region in which ITAM A is
significantly less phosphorylated than ITAMs B and C, representing the 21 kDa form
of CD3ζ. The black dashed area indicates the parameter region in which all ITAMs are
strongly phosphorylated at the same amount, representing the 23 kDa form of CD3ζ.
(D) Time course of ITAM phosphorylation. Lines are the model response for the
parameters indicated by the black dot in (C), shaded regions are the 95% confidence
interval of the model response for the parameters within the black dashed area of (C).

94
It is also known that when the immunological synapse forms upon both TCR and
CAR T cell activation, phosphatases with large extracellular regions are excluded, reducing
the local phosphatase activity (Leupin et al., 2000); however, in Figure 3-9A, low levels
of phosphatase activity result in activation of only ITAM A and B, but not ITAM C,
meaning that this cannot recreate the 23 kDa form of fully phosphorylated CD3ζ.
Therefore, we continued to explore the model to better understand how CD3ζ could
become fully phosphorylated. It has also been shown that upon initiation of the
immunological synapse, downstream signaling molecules, like ZAP-70, are recruited to
the area (Ilani et al., 2007; Jenkins et al., 2014). We therefore wanted to see how increasing
the amount of ZAP-70 would affect CD3ζ phosphorylation in the model. Figure 3-9C
shows the steady state levels of doubly phosphorylated ITAMs for an initial condition ratio
of 1:1:3 for LCK:CD3ζ:ZAP-70. In the black dashed region of Figure 3-9C, we see that
reducing the phosphatase activity in the presence of this higher level of ZAP-70 can lead
to the emergence of the fully phosphorylated form of CD3ζ. The time course of activation
is shown in Figure 3-9D. Importantly, even with the high ZAP-70 concentration,
increasing the phosphatase activity will still result in a 21 kDa form of CD3ζ in which
ITAMs B and C are more phosphorylated than ITAM A (Figure 3-9C, red dashed region).
The model can mimic the environment of resting and activated T cells, allowing us to
identify the parameter region that can govern the emergence of two biologically relevant
forms of phosphorylated CD3ζ.

95

2.4.6. LCK binding helps protect slowly phosphorylated ITAMs from
dephosphorylation
To explore the mechanism through which more slowly phosphorylated ITAMs
reach higher steady state levels of phosphorylation than the quickly phosphorylated ITAMs
in the 21 kDa form of CD3ζ, we investigated how LCK binding influences the system. To
do this, we altered the catalytic and dissociation rates of LCK together for each ITAM site
along the contour lines shown in Figure 3-8. As the substrate specificity depends on only
the parameter values (see methods), maintaining the same fold change between the
dissociation and catalytic rates will keep the same substrate specificity. In this way, the
binding activity of LCK changes, but the fit to our experimental data remains the same.
The ZAP-70 binding and phosphatase activity parameters were held constant at the values
indicated by the red dot in Figure 3-9A, in the region that allows for the emergence of this
21 kDa form.
We applied this model to predict how varying the dissociation and catalytic rates at
one ITAM affects phosphorylation of other ITAMs on CD3ζ. We allowed the dissociation
rates to vary within the linear region of Figure 3-8 (10
3
-10
9
min
-1
), and we matched the
catalytic rates to agree with the average site-specific substrate specificities across all
experiments (shown in Figure 3-6C). Figure 3-10A shows how changing the LCK binding
kinetics of ITAM A tyrosine sites affects the steady state phosphorylation percent of each
ITAM. The dissociation rates for ITAM A1 and A2 are shown on the x- and y- axes,
respectively. Changing the catalytic and dissociation rates of these sites influences the
overall phosphorylation of the system. When the rates of are reduced, LCK is slower to
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dissociate from or phosphorylate the sites on ITAM A, resulting in more LCK bound to the
site (Figure 3-10B).

Figure 3-10: LCK binding and protection of partially phosphorylated ITAMs allows
for slowly phosphorylated ITAM sites to reach higher steady state phosphorylation
levels.
(A, C, E) Heat maps showing the model predictions for the percent of doubly
phosphorylated CD3ζ ITAMs at steady state as a function of LCK binding for each of
the two tyrosine sites on ITAM A (A), ITAM B (C), and ITAM C (E) with initial
conditions of 10,000 LCK/µm
2
, 10,000 CD3ζ/µm
2
, 10,000 ZAP-70/µm
2
. LCK binding
was altered while maintaining the model fits shown in Figure 3-3 and Figure 3-7 by
changing the LCK dissociation and catalytic rates together along the contour lines
shown in Figure 3-8. Red dashed areas indicate the parameter region in which ITAM
A is significantly less phosphorylated than ITAMs B and C, representing the 21 kDa
form of CD3ζ.
(B, D, F) Heat maps showing the maximum percent of bound LCK in the system at steady
state as a function of LCK binding for each of the two tyrosine sites on ITAM A (B),
ITAM B (D), or ITAM C (F).
97
Since the phosphatases can only act on ITAMs without bound LCK, this results in
more protection of partially phosphorylated ITAM A, allowing the necessary time for LCK
to create doubly phosphorylated ITAM A. As more LCK binds to ITAM site A2, less of it
is available to bind and protect ITAMS B and C. Therefore, as the binding of LCK to ITAM
A increases, the steady state phosphorylation of ITAMs B and C are reduced. Similar
effects can be seen for changes to the LCK kinetics on ITAM B (Figure 3-10C, D) and
ITAM C (Figure 3-10E, F). This analysis shows that LCK binding and protection of
partially phosphorylated ITAMs is the dominant mechanism in the model that allows for
ITAM sites that are phosphorylated at a slower rate to become more phosphorylated at
steady state. Altogether, the model predictions presented thus far enable a better
understanding of how LCK binds to and phosphorylates the CD3ζ intracellular domain.

2.4.7. CD28 tyrosine sites are phosphorylated more slowly than CD3ζ
tyrosine sites
Next, we investigated how the addition of a co-stimulatory domain, like CD28,
could influence CAR phosphorylation. To test this, we inserted the intracellular domain of
CD28 at the N-terminal of CD3ζ (28ζ), the same configuration typically used in the CAR
constructs evaluated in pre-clinical studies and clinical trials (Figure 3-11A). CD28 has
four tyrosine sites, each of which can be phosphorylated by LCK. We again used phospho-
proteomic mass spectrometry to quantify the site-specific phosphorylation levels of 28ζ.
Figure 3-11B shows the sequence and trypsin cut sites of the CD28 intracellular domain,
in which the second and third tyrosine sites in CD28 (Y206 and Y209) are both on the same
peptide after trypsin digestion. Therefore, to individually measure the phosphorylation
98
rates of these two sites, we made two more proteins with a tyrosine to phenylalanine
mutation at each of these sites (28ζ-Y206F, and 28ζ-Y209F).

Figure 3-11: CD28 tyrosine sites are phosphorylated more slowly than CD3ζ tyrosine
sites.
(A) Schematic of the His-tagged CD28-CD3ζ recombinant protein.
(B) Sequence of CD28 intracellular domain with trypsin cut sites denoted. Individual
tyrosine sites are labeled in different colors.
(C) Experimental data (dots) and model fit (lines) for CD28 tyrosine site phosphorylation
on wildtype CD28-CD3ζ, CD28-Y206F-CD3ζ, and CD28-Y209F-CD3ζ. Error bars
represent the standard deviation of two technical replicates normalized by site-specific
standard curves.
(D) Substrate specificity of individual CD28 tyrosine sites, as calculated from the model
fits in (C). 50 rounds of model fitting gave nearly identical calculations of substrate
specificities.

99
Interestingly, our measurements indicate that Y209 phosphorylation is required for
the phosphorylation of Y206. Figure 3-11C shows the individual CD28 tyrosine site
phosphorylation time courses for each of the three CD28-CD3ζ recombinant proteins.
From these graphs, we can see that there is no significant phosphorylation of the Y206 site
without prior phosphorylation of Y209 (teal lines).
The estimated substrate specificities provide insight into the effects of particular
CD28 tyrosine sites. We fit the phosphorylation measurements with a computational model
that includes CD28 and estimated the substrate specificities for each site. The model fits
the data well (Figure 3-11C, lines). In agreement with the literature (Hui et al., 2017), all
tyrosine sites on CD28 are phosphorylated more slowly than the CD3ζ tyrosine sites. The
model calculated substrate specificities for each of these sites are shown in Figure 3-11D.
From the Y206F and Y209F mutants, we can see that mutating these sites reduces the
overall phosphorylation rates of the CD28 protein, with the Y209F mutation displaying the
strongest effect. This indicates that Y209, and to a lesser extent Y206, play a significant
role in either the recruitment or phosphorylation activity of LCK toward CD28.

2.4.8. CD28 increases the phosphorylation rate of CD3ζ
CD28 influences the overall phosphorylation rate of CD3ζ, as well as the individual
phosphorylation rate of site C2. Figure 3-12A shows the phosphorylation time courses
(dots) and model fits (lines) of CD3ζ ITAM sites on the three CD28-CD3ζ recombinant
proteins. Wildtype CD28 increases the overall phosphorylation rate of all CD3ζ tyrosine
sites, making it difficult to distinguish a specific order of phosphorylation in the 28ζ
recombinant protein. Similar to the CD28 results shown in Figure 3-11C, this change in
100
substrate specificity is largely dependent on the presence of CD28-Y209, and, to a lesser
extent, CD28-Y206. This can also be seen in the estimated substrate specificity values
(Figure 3-12B).
In addition to shifting the overall substrate specificity of the protein as a whole,
CD28 also changes the relative order of the CD3ζ tyrosine site phosphorylation rates. Site
C2, which had one of the lowest substrate specificities in the CD3ζ-only recombinant
protein (Figure 3-3F), has one of the highest substrate specificities on the CD28-CD3ζ
proteins (Figure 3-12B). This relative change in the phosphorylation rate order is not
influenced by mutations at site Y206 or Y209, as the substrate specificity of this site
relative to the other sites does not change with the CD28 mutants.

101

Figure 3-12: CD28 can affect the phosphorylation of CD3ζ sites.
(A) Experimental data (dots) and model fit (lines) for CD3z ITAM phosphorylation on
wildtype CD28-CD3ζ, CD28-Y206F-CD3ζ, and CD28-Y209F-CD3ζ. Error bars
represent the standard deviation of two technical replicates normalized by site-specific
standard curves.
(B) Substrate specificity of individual CD28 tyrosine sites as calculated from the model
fits in (A). 50 rounds of model fitting gave nearly identical calculations of substrate
specificities.
(C) Heat maps showing the percent of doubly phosphorylated CD3ζ ITAMs on the 28ζ
protein at steady state as a function of the dephosphorylation activity (x-axis) and ZAP-
70 dissociation rate (y-axis) for initial conditions of 10,000 LCK/µm
2
, 10,000
CD3ζ/µm
2
, 10,000 ZAP-70/µm
2
. The red dashed area indicates the parameter region in
which ITAM A is significantly less phosphorylated than ITAMs B and C, representing
the 21 kDa form of CD3ζ. The black dashed area indicates the parameter region in
which all ITAMs are phosphorylated at a similar level, representing the 23 kDa form
of CD3ζ.
(D) Time course of 28ζ ITAM phosphorylation. Lines are the model response for the
parameters indicated by the red dot in (C), shaded regions are the 95% confidence
interval of the model response for the parameters within the red dashed area of (C).
(E) Time course of 28ζ ITAM phosphorylation. Lines are the model response for the
parameters indicated by the black dot in (C), shaded regions are the 95% confidence
interval of the model response for the parameters within the black dashed area of (C).
102
2.4.9. CD28 may decrease the threshold of CD3ζ ITAM activation
To explore how the CD28-driven changes to the relative order of CD3ζ tyrosine
phosphorylation would influence the steady state phosphorylation of the ITAMs, we
returned to our ZAP binding dephosphorylation model. Using the phosphatase and ZAP-
70 binding parameters from the CD3ζ model, we varied the LCK binding and catalytic
rates, as we did in Figure 3-10, to verify that the same mechanism of LCK binding was
still important in this system (Figure 3-13). We then chose a set of LCK parameters that
would allow the 21 kDa form of CD3ζ to emerge while still fitting our 28ζ ITAM
phosphorylation data (parameters listed in in Table 3-1).

103

Figure 3-13: CD28-CD3ζ LCK binding model analysis.
(A, C, E) Heat maps showing the percent of doubly phosphorylated CD3ζ ITAMs at
steady state as a function of LCK binding for each of the two tyrosine sites on ITAM
A (A), ITAM B (C), and ITAM C (E). LCK binding was altered while maintaining
the model fits shown in Figure 3-12 by changing the LCK dissociation and catalytic
rates together along the contour lines shown in Figure 3-8. Red dashed areas indicate
the parameter region in which ITAM A is significantly less phosphorylated than
ITAMs B and C, representing the 21 kDa form of CD3ζ.
(B, D, F) Heat maps showing the maximum percent of bound LCK in the system over
time as a function of LCK binding for each of the two tyrosine sites on ITAM A (B),
ITAM B (D), and ITAM C (F).

104
We next varied the phosphatase and ZAP-70 binding parameters, as we did in
Figure 3-9A, using the 1:1:1 initial condition ratio for LCK:CD3ζ:ZAP-70. Figure 3-12C
shows the resulting steady state phosphorylation levels of each ITAM on 28ζ. The red
dashed region shows that the 21 kDa form of CD3ζ is produced in the same parameter
region as it was in the CD3ζ-only model in Figure 3-9A, again highlighting the robustness
of the model predictions. The time course of the phosphorylation level for this parameter
region is shown in Figure 3-12D. Interestingly, however, with the increase to the
phosphorylation rate of CD3ζ site C2, we now see that even with the low ZAP-70 ratio,
about 30% of CD3ζ can become fully phosphorylated at low phosphatase activity. This
percentage is limited only by the 3:1 ration of CD3ζ ITAM binding sites to ZAP-70
molecules. The time course for this region is shown in Figure 3-12E. These results
indicate that the increase in phosphorylation rates of CD3ζ on the 28ζ protein may result
in a lower activation threshold for the 28ζ CAR phosphorylation, as CD3ζ on this protein
may be able to become fully phosphorylated in the presence of lower ZAP-70
concentrations or higher phosphatase activity.

2.5. Discussion
In this study, we used phospho-proteomic mass spectrometry and computational
modeling to quantitatively assess the mechanism of CD3ζ and CD28 intracellular
phosphorylation in a CAR construct. By measuring the phosphorylation of individual
tyrosine sites on CD3ζ and CD28 over time, we showed that the six sites on CD3ζ and four
sites on CD28 are phosphorylated at different rates. Individual CD3ζ point mutations
showed that the site-specific kinetics are largely independent, and therefore removing one
105
site will not greatly influence phosphorylation at any of the other sites. Additionally,
attaching CD28 to the N-terminal of CD3ζ increased the overall phosphorylation rate of
the protein, and particularly increased the relative rate of phosphorylation at the C2 ITAM
site.
Interestingly, we did not see any effect of acidic lipid concentration on the
phosphorylation rates of CD3ζ tyrosine sites. Previous studies have reported different
effects of acidic lipids on CD3-family protein phosphorylation. Several studies have
indicated that acidic lipids in the plasma membrane can control aberrant phosphorylation
of CD3ε and CD28 in unstimulated cells through binding of basic residues in the protein
to acidic lipids in the plasma membrane (Aivazian and Stern, 2000; Dobbins et al., 2016;
Gagnon et al., 2012). In addition, Hui and Vale saw that ZAP-70 tandem SH2 domains
were able to bind more quickly as CD3ζ became phosphorylated in a system containing
10% acidic POPS lipids compared to 0% POPS lipids (Hui and Vale, 2014). In our system,
changing the concentration of acidic POPS lipids on the liposome surface (even up to 45%
POPS) did not change the rate of phosphorylation of the protein as a whole or the relative
phosphorylation rate order of the individual sites. Therefore, we believe that the acidic lipid
concentration does not directly affect the phosphorylation of CD3ζ; but, as Hui and Vale
showed, it may influence the binding kinetics of downstream proteins like ZAP-70 by more
readily recruiting these proteins to membrane regions with acidic lipids.
We constructed a computational model to further investigate the mechanisms that
lead to CD3ζ phosphorylation. With the model, we were able to calculate site-specific
phosphorylation parameters, such as the LCK substrate specificity, that are difficult to
measure experimentally. Previous studies have attempted to use CD3ζ phospho-tyrosine
106
specific antibodies to qualitatively define the phosphorylation order of individual ITAM
sites (Kersh, 1998); but, the similarity between ITAM sites limited the antibody specificity,
preventing solid conclusions regarding the phosphorylation order. In 2003, Housden et al.
used synthetic peptides that each contained one ITAM tyrosine to measure the preference
of LCK for each site through radioactive phosphate incorporation. Interestingly, the LCK
substrate specificity order they found (A1>C1>C2>B1>A2>B2) differs from ours
(A1>B2>B1>A2≥C2≥C1) (Housden et al., 2003). Their experiments were performed in
solution, not in a two-dimensional lipid-bound configuration, and each single tyrosine-
bearing peptide was phosphorylated independently. Therefore, their study did not account
for conformational, steric, and competitive factors that may influence the phosphorylation
rates at different sites. However, the authors did use mass spectrometry to measure full
length recombinant protein CD3ζ phosphorylation and found that, at intermediate time
points, ITAM site A1 was significantly more phosphorylated than the other sites, which is
consistent with our data. To our knowledge, our work is the first study to specifically
quantify the individual phosphorylation kinetics of all six CD3ζ ITAM tyrosine sites on
the same protein in a two-dimensional lipid-bound setting.
Our model provides novel insights into the effects of LCK-CD3ζ interactions. Our
modeling results confirm a random order of LCK phosphorylation of CD3ζ, validating
previous studies in the literature based on average CD3ζ protein phosphorylation
(Mukhopadhyay et al., 2016). Additionally, we were able to provide a possible mechanistic
explanation for how the slowly phosphorylated ITAMs B and C become more
phosphorylated than ITAM A at steady state in the 21 kDa form of CD3ζ (van Oers et al.,
2000; Pitcher et al., 2003). The model indicates that, while the rates of phosphorylation
107
and dephosphorylation are important, the binding events that protect the ITAMs from
dephosphorylation are also important. These effects of LCK binding predicted by our
model have also been hypothesized in previously published models based on experimental
data (Sjölin-goodfellow et al., 2015).
Importantly, LCK is not the only protein that could bind and protect these single
ITAM sites. In future work, the model can be applied to include the binding of other
proteins in the T cell activation pathway that can bind to single ITAM sites, allowing us to
study a range of molecular interactions and their effects on CAR phosphorylation. These
modeling results, as well as the site-specific quantification results, indicate that protein-
protein binding interactions, the two-dimensional protein arrangement, and the
arrangement of the tyrosine sites on CD3ζ may all play a role in determining the different
substrate specificities of LCK toward each ITAM site.
CD28 also plays an important role in the CAR structure, both by adding its co-
stimulatory signaling and modulating the phosphorylation rates of CD3ζ. We showed that
adding CD28 to the N-terminal of CD3ζ increases the overall phosphorylation of CD3ζ,
and this is largely dependent on CD28-Y209. This site has been implicated in the
recruitment of LCK to the immunological synapse in endogenous T cells through binding
of the SH2 domain on LCK (Hofinger and Sticht, 2005). Here, we validate the importance
of this site as a strong recruiter of LCK, and its potential role in the strong activation of
CD28-bearing CAR proteins.
Interestingly, CD28-Y209 is phosphorylated much more slowly than any of the
sites on CD3ζ. In fact, when all of the CD3ζ sites are 100% phosphorylated, only about
25% of the CD28-Y209 sites have been phosphorylated. This leads us to hypothesize that
108
unphosphorylated Y209 plays a role in recruiting LCK to the system. Perhaps this site is
able to bind and recruit LCK more readily than other sites but, given its lower affinity for
the catalytic pocket of LCK, it can be outcompeted by other sites on the same protein. More
work needs to be done to decouple the binding preferences that lead to LCK recruitment
from the catalytic activity of the protein-substrate pairs.
We used our computational model to explore the effects of the CD28-dependent
increase and reordering of CD3ζ ITAM phosphorylation. The model predicts that
increasing the phosphorylation rate of ITAM site C2 in the presence of CD28 could allow
the maximal level of ITAM C phosphorylation to increase above that of the CD3ζ-only
protein. This effect appears to be independent of phosphorylation at CD28 site Y209,
indicating that another mechanism, such as the folding of the CD3ζ protein chain, must
contribute to the increased phosphorylation at this particular site. The results also predict
that this increase in the C2 site phosphorylation kinetics could allow CD3ζ on the 28ζ CAR
protein to become fully phosphorylated at a lower signaling threshold, potentially adding
to the stronger T cell activation of the 28ζ CAR compared to CD3ζ alone.

2.6. Conclusion
Taken together, this work provides new insights into the activation of CAR-T cells
through quantitative phospho-proteomic experiment and computational modeling. Our
model predicts how the separate actions of protein binding and catalytic activity influence
CD3ζ ITAM phosphorylation. In addition to producing novel measurements and a
modeling framework that explains experimental observations, our work generates new
109
hypotheses regarding protein phosphorylation that can be applied to better engineer CARs
that more optimally activate T cells for therapeutic purposes.

2.7. Acknowledgements
The authors would like to thank the lab of Ronald Vale at UCSF for providing the
recombinant protein plasmids. This work was supported by the National Cancer Institute
of the National Institutes of Health under Award Numbers F31CA200242 (to J.A.R.),
R01EB017206, R01CA170820, and P01CA132681 (to P.W.)

110

111

3.

Chapter 4

ERK activation in CAR T cells is amplified by CD28-mediated increase in
CD3ζ phosphorylation

Portions of this chapter are adapted from a manuscript by:
Jennifer A. Rohrs, Elizabeth Siegler, Pin Wang, and Stacey D. Finley

In Preparation.

112
3.1. Abstract
4. Chimeric antigen receptors (CARs) are engineered receptors that mediate T cell
activation. To do so, CARs are comprised of a variety of different activating and co-
stimulatory domains derived from endogenous T cells. These intracellular domains initiate
signaling required for T cell activation, including ERK activation through the MAPK
pathway. The mechanisms by which co-stimulatory domains on CARs influence this
signaling are not clear. Therefore, we have constructed a computational mechanistic model
of CAR-mediated activation of ERK in T cells. We model anti-CD19 CARs bearing the
CD3ζ domain alone or in combination with CD28. We compared our model of CD3ζ
activation to experimental data and find that it qualitatively reproduces the effects of
modifications to various proteins in the signaling pathway on the ERK response time. We
then used an ensemble modeling approach to explore a variety of mechanisms of how
CD28 co-stimulation enhances the predicted ERK response time, including binding of
adaptor molecules and changes to the CD3ζ activation kinetics. We validated the model
predictions using experimental measurements of ERK activation in Jurkat T cells
engineered with anti-CD19 CARs. Specifically, we confirmed that CD28 primarily
influences ERK activation by modifying the phosphorylation kinetics of CD3ζ. The model
also generates new hypotheses involving the influence of negative feedback by the
phosphatase SHP1 on the effect of CD28 co-stimulation. Thus, this model is a framework
that can be used to gain insights into the mechanism of CAR T cell activation and produce
new testable hypotheses.

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4.1. Introduction
Chimeric antigen receptor (CAR) engineered T cells have recently been approved
for the treatment of CD19 positive B cell malignancies (Mullard, 2017). They have been
extremely successful for these tumors, but it has been difficult to extend CAR T cell
therapies to other types of cancer, specifically solid tumors (Morgan et al., 2010). To better
engineer CAR T cells to fight cancer, we need to improve our understanding of how these
modified receptors activate T cells.
CARs typically include an extracellular antibody-derived binding domain linked to
a transmembrane domain and a number of different intracellular signaling domains
(Sadelain et al., 2013). These signaling domains are derived from endogenous T cells and
typically include CD3ζ, a part of the endogenous T cell receptor (TCR), and a co-
stimulatory domain, like CD28. It is clear that T cells require this secondary signaling
through a co-stimulatory receptor, but the mechanisms through which co-stimulatory
domains influence T cell activation are not clear (Bretscher, 1999). Additionally, it is not
clear how CAR signaling differs from endogenous T cell receptor signaling (Harris et al.,
2018).
Computational mechanistic models can be used to test hypotheses about molecular
signaling mechanisms. These models have been used in the past to study endogenous T
cell activation, providing insights into important activation and feedback mechanisms that
help control the sensitivity and specificity of TCR activation (Altan-Bonnet and Germain,
2005; Das et al., 2009; Lever et al., 2017; Sjölin-goodfellow et al., 2015). These models
generally assume that T cell activation is derived directly from the TCR CD3ζ signaling
domain, while neglecting the effects of the co-stimulatory domains. Therefore, the
114
immunology field has developed a fairly clear picture of the signaling events downstream
of CD3ζ, but there is a lack of understanding of the effects of co-stimulation.
Recently, we have used phospho-proteomic mass spectrometry to quantify the site-
specific phosphorylation kinetics of CARs containing CD3ζ with or without CD28 (Rohrs
et al., 2018). This data showed that CD3ζ immunoreceptor tyrosine-based activation motifs
(ITAMs) are phosphorylated independently, in a random order, and with distinct kinetics.
Adding the CD28 co-stimulatory domain increased the rate of CD3ζ phosphorylation by
an average of 500-fold. However, our kinetic data do not explain how this increase in CD3ζ
phosphorylation affects downstream signaling. More generally, it is not clear how CD28
signaling influences downstream T cell activation. We are particularly interested in
activation of the MAPK signaling pathway, leading to ERK phosphorylation, as this
pathway helps mediate T cell proliferation.
Upon T cell activation, ERK exhibits a digital (on/off) response. Typically, when
ERK is measured as a readout of T cell activation, the percent of ERK positive cells in a
population is measured. The response time of the population can then be calculated based
on the fit of the phosphorylation time course to a standard sigmoidal curve. This response
time is equal to the time it takes to reach half of the maximal level of phosphorylation. In
our model, we assume that the deterministic differential equations are representative of the
average response of the T cell population. Therefore, we directly compare the ERK
response time in the model to the half maximal cellular population response time. This
comparison has previously been shown to relate well (Altan-Bonnet and Germain, 2005).
To explain how the CAR intracellular domains influence ERK response time, we
constructed a mechanistic computational model of T cell activation by CARs containing
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the CD3ζ domain alone or in combination with CD28. We showed that model is able to
reproduce known effects of various intracellular protein perturbations on ERK response
time following T cell activation. Additionally, we used an ensemble modeling approach to
predict the effects of various mechanisms of CD28 co-stimulation (Brännmark et al., 2010).
Experimental measurements of ERK response in CAR engineered T cells validated the
model hypothesis that CD28 activates ERK primarily through modifications of CD3ζ
phosphorylation kinetics. The model also generates additional hypotheses that can be used
to guide new experiments. Overall, this modeling study enriches our understanding of CAR
T cell co-stimulatory activation and allows for the improved development of CAR-
engineered T cells.

4.2. Methods
4.2.1. Construction of a mechanistic computational model of CAR T cell
activation
We constructed a model of CAR T cell activation based on our previous modeling
work, as well as other models and experimentally measured kinetic data and parameters in
the literature. The full model includes models of LCK autoregulation (Rohrs et al., 2016a),
CAR phosphorylation (Rohrs et al., 2018), LAT signalosome formation, CD45
phosphatase activity, Ras activation (Das et al., 2009), MAPK pathway activation
(Birtwistle et al., 2012), and SHP1 negative feedback (Altan-Bonnet and Germain, 2005).
Overall, the model presented in this work includes signaling initiated by antigen binding
to the CAR and culminates in phosphorylation of ERK. The steps used to unite these
elements into a single model are described below.
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LCK autoregulation – We have previously developed a mass action based model
of LCK autoregulation (Rohrs et al., 2016a). However, due to the size of the complete CAR
signaling model, we needed to simplify this model of LCK to reduce the computational
complexity. To do this, we altered the interactions between various phosphorylated forms
of LCK from mass action kinetics to Michaelis-Menten kinetics. This greatly reduced the
number of ordinary differential equations, as the different phosphorylated species of LCK
no longer need to form dimers before the autophosphorylation reactions can be catalyzed.
To allow the model to match with the experimental data, CSK interactions were kept as
mass action. This agrees with mechanistic data in the literature, which shows that CSK can
bind to the phosphorylated Y394 residue on LCK (Bougeret et al., 1996). The model
parameters were fit together to the same data from Hui and Vale used to fit the original
model (Hui and Vale, 2014). Fitting was done using particle swarm optimization (PSO),
described below. The best fits and parameters values are shown in Figure 4-1.

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Figure 4-1: Minimal LCK model reduction. Our model of LCK regulation (Rohrs et al.,
2016a) was refit to data from Hui and Vale (Hui and Vale, 2014) using Michaelis-Menten
kinetics for all LCK-LCK interactions and mass action kinetics for all CSK-LCK
interactions. The best fits (top) and parameter values (bottom) are shown.

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CAR phosphorylation – We next combined the LCK regulation model with our
model of LCK activation of the CD3ζ and CD28 CAR intracellular signaling domains
(Rohrs et al., 2018). We used the measured substrate specificities for each tyrosine site
from the published paper and held all of the dissociation rates at 1×10
6
min
-1
. The original
version of this model only accounted for active pY394-LCK phosphorylation. To
incorporate the other phosphorylated forms of LCK, we assumed that doubly
phosphorylated and unphosphorylated LCK both had the same binding kinetics as active
LCK and half of the catalytic activity, as measured by Hui and Vale (Hui and Vale, 2014).
As a simplification to the system, and based predictions from our LCK model (Rohrs et al.,
2016a) that the catalytic activity of pY505-LCK is several orders of magnitude lower than
pY394-LCK, we assumed that inactive pY505-LCK is not catalytically active, and
therefore, does not interact with LCK substrates.
LAT signalosome – In the LAT signalosome, we include only proteins that directly
relate to the activation of the ERK and the MAPK pathway (Braiman et al., 2006; Brownlie
and Zamoyska, 2013; Nag et al., 2009), as activated ERK is a key downstream species that
characterizes T cell activation. For these interactions, all of the binding parameters, with
the exception of parameters for IL-2-inducible T cell kinase (ITK), were taken from
measurements in the literature. That is, we set either the association or dissociation rate
parameter (kon, and koff) or the dissociation constant (KD) for each specific interaction
(Houtman et al., 2004). The binding rates of unphosphorylated and phosphorylated ZAP-
70 to doubly phosphorylated CD3ζ ITAMs were taken from Katz et al. (Katz et al., 2017).
The catalytic activities of LCK and ZAP-70 were fit to in vitro experimental data in the
presence of CD45, described below (Hui et al., 2017). For ITK, the binding rates were not
119
available, but our sensitivity analysis showed that these parameters did not significantly
influence the ERK response. Therefore, we assumed that ITK can bind to SLP76 with a
relatively low KD of 100 molecules/µm
2
, and its catalytic activity toward PLCg is assumed
to be 1 min
-1
with a Michaelis-Menten constant of 100 molecules/µm
2
.
CD45 phosphatase – Before stimulation, the model species are allowed to reach
steady state in the presence of CD45, which is able to dephosphorylate all tyrosine sites in
the model. However, the two-dimensional substrate-specific catalytic rates of CD45
dephosphorylation are not available in literature. There are measurements of CD45
dephosphorylation for a subset of the species in the model in solution (Felberg and Pauline,
1998; Peters et al., 2003), but it has been shown that the catalytic rates in solution can be
vastly different from those on a two dimensional membrane (Furlan et al., 2014; Hui and
Vale, 2014). Therefore, to more accurately parameterize these interactions, we first fit the
catalytic rates of LCK toward ZAP-70, ZAP-70 toward LAT and SLP76, and CD45 toward
all proteins in the data. These parameters were fit to data from Hui et al. 2017 (Hui et al.,
2017).
To do this, we simulated our model using only the species included in the
experiments performed by Hui and coworkers. The initial conditions for these species were
set according to the equivalent molecules/µm
2
value listed in the Hui et al. supplemental
information. All other species’ initial concentrations in our model were set to 0. We then
recorded the model outputs of the normalized phosphorylation of various species at 30
minutes for a range of different CD45 concentrations, mimicking the experiments
performed by Hui et al. We fit the model to their data, keeping the CD45 Michaelis-Menten
constants at 100 molecules/µm
2
, a value on the same order of magnitude as the protein
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concentrations. The model repeatedly converged on a single set of catalytic rates that best
fit the data. To better refine the model fits, starting from the best-fit catalytic rates, we next
allowed the CD45 Michaelis-Menten constants and the CD45 catalytic rates to vary. In this
case, the model converged at several local minima, with several of the parameter sets
converging at the same global minima. This fitting procedure provided a set of parameter
values that enabled the model to match the available experimental data. These parameter
values were used throughout the simulations.
Ras activation – The mechanism of Ras-GTP activation was adapted from a model
by Das et al. (Das et al., 2009). The original model was parameterized based on data in the
literature of proteins interacting in solution, and it was compared to data on a much longer
time course than our model of CAR T cell activation. Therefore, for this model to agree
with the other parameters in our model, all time dependent parameters were scaled to be
on the same scale as the other interactions in the model. Additionally, the binding affinity
of SOS toward RAS-GTP was scaled to account for the closer proximity on the two-
dimensional T cell intracellular surface. We then tuned the amount of RasGAP
phosphatase, such that the MAPK pathway could only be activated by both SOS and
RasGRP together, but not either mechanism alone.
MAPK pathway – The MAPK pathway and its parameters were directly adapted
from the Birtwistle et al. model, using the zero feedback case (Birtwistle et al., 2012). This
pathway includes the three-layer phosphorylation cascade involving Raf, Mek, and ERK.
SHP1 negative feedback – The last mechanism we included in the model was
negative feedback through the phosphatase SHP1, which can be turned off by positive
feedback from activated ERK, first modeled by Altan-Bonnet and Germain (Altan-Bonnet
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and Germain, 2005). To reduce the computational complexity that arises from SHP1
binding to the six different singly phosphorylated ITAM sites, we modified the recruitment
of SHP1 so that its association rate to the membrane signaling region is proportional to the
concentration of singly phosphorylated ITAMs, and its dissociation rate is proportional to
the concentration of unphosphorylated or ZAP-70 bound ITAMs.

4.2.2. Parameter fitting
A particle swarm optimization (PSO) algorithm was used to fit the model to
experimental data (Iadevaia et al., 2010). We allowed the catalytic rates to vary on a log
scale from 10
-1
-10
4
min
-1
, and the Michaelis-Menten constants varied from 10
1
-10
6

molecules/µm
2
. The objective functions minimized the sum of the squared errors between
the model outputs and the experimental data. We also ensured that, for each model system
being fit, the chosen fit parameter set allowed for maximal phosphorylation of the system
within the time of the of the simulation. To do this, we added an additional term to the
objective function that calculated the difference between 100% and the percent
phosphorylation of each site measured in the model at the end of the simulation (30 minutes
based on the experimental time from (Hui et al., 2017)). The PSO algorithm was run at
least 20 times for each set of parameters being fit. The parameter sets with the lowest error
were selected for use in the model.

4.2.3. Sensitivity analysis
The extended Fourier amplitude sensitivity test (eFAST) has been described in
detail previously (Marino et al., 2008), and we have applied this approach in our previous
122
work (Rohrs et al., 2016a, 2016b). Briefly, eFAST is a global variance-based sensitivity
analysis that can identify which model parameters have the most significant effect on a
given model output. In this method, a set of model parameters are varied at the same time,
with different frequencies, and the model output is calculated. The Fourier transform of the
model output is then compared to the various frequencies with which the parameters were
varied. A model output’s sensitivity to a given parameter of interest is proportional to the
normalized Fourier transform peak of the model output at the frequency with which that
parameter was varied. This is referred to as the individual sensitivity index (Si). The extent
of higher order interactions between parameters can then be estimated by calculating the
Fourier transform peaks of frequencies other than those of the individual frequency and
harmonics of the parameter of interest, giving the total sensitivity index (STi). A greater
total index compared to first-order index indicates that a parameter is more important in
combination with other parameters than alone.
We implemented the eFAST method using MATLAB code developed by Kirschner
and colleagues (Marino et al., 2008). We analyzed the parameters in nine groups, allowing
each parameter to vary 10-fold up and down from its baseline value.

4.2.4. Cell lines and reagents
Jurkat T cells (ATTC TIB-152) and K562 cells (ATCC CCL-243) were maintained
in 5% CO2 environment in RPMI (GIBCO) media supplemented with 10% fetal bovine
serum, 1% penicillin-streptomycin, and 2 mM L-glutamine. Alexa-488 conjugated
antibody against doubly phosphorylated ERK (clone E10) was purchased from Cell
Signaling Technology. Anti-HA antibody (AB9110) was purchased from Abcam. Alexa-
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647 conjugated Goat anti-rabbit secondary antibody was purchased from Thermo
Scientific. PE conjugated anti-CD19 (clone HIB19) was purchased from Biolegend.

4.2.5. Stable transduction of CAR and CD19 expressing cell lines
The construction of a lentiviral plasmid containing an HA-tagged anti-CD19 CAR
bearing the CD28 transmembrane domain and CD28 and CD3ζ intracellular domains was
constructed based on a previously reported CD19 CAR (Milone et al., 2009). The codon
optimized CD19 single-chain fragment variable (scFv) sequence and human CD8 hinge
region (aa 138-184) was synthesized by Integrated DNA Technologies (Coralville, IA).
The CD19/CD8 hinge gene block was amplified by PCR and added upstream of the
transmembrane and intracellular domains of human CD28 (aa 153-220) followed by the
intracellular domain of human CD3ζ (aa 52-164). The CD8 leader sequence and HA-tag
were inserted upstream of the CD19 scFv to allow for labeling and detection of CAR-
expressing cells. To make the lentiviral vector, this sequence was inserted downstream of
the human ubiquitin-C promoter in the lentiviral plasmid pFUW using Gibson assembly,
as previously described (Dai et al., 2012).
To make the CD3ζ-only CAR, PCR was used to amplify the sequence from the N-
terminal of the CAR construct through the scFv region, as well as the CD3ζ intracellular
domain. The codon optimized CD8 transmembrane domain sequence was synthesized by
IDT-DNA and inserted between the scFv and CD3ζ PCR products using PCR. The CAR
gene fragment was then reinserted into the lentiviral plasmid using Gibson assembly.
Lentiviral vectors were prepared by transient transfection of 293T cells using a
standard calcium phosphate precipitation protocol, as described previously (Dai et al.,
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2012). The viral supernatants were harvested 48 hours post-transfection and filtered
through a 0.45 µm filter (Corning, Corning, NY). For transduction, Jurkat T cells were
mixed with fresh viral supernatant and centrifuged for 90 minutes at 1050xg at room
temperature. A stable CD19 expressing K562 line was generated in a similar way by
transducing parental K562 cells with a lentiviral vector encoding the cDNA of human
CD19, as described previously.
To get populations of cells that express the transduced protein at different levels,
CAR-expressing Jurkat T cells and CD19-expressing K562 cells were sorted into high,
medium, and low populations. To do this, the cells were stained with fluorophore-
conjugated antibodies. T cells were first stained with anti-HA antibody for 30 minutes at
4°C, followed by three washes with PBS. The cells were then stained with a secondary
alexa-647 conjugated anti-rabbit antibody for 15 minutes at 4°C, followed by three more
washed with PBS. CD19 cells were stained with PE conjugated anti-CD19 followed by
three washed with PBS. All stained cells were then sorted into the three groups using the
BD SORP FACS Aria I cell sorter at the USC stem cell flow cytometry core. The mean
expression levels of the CAR and CD19 cell populations were quantified using the 6 Peak
Rainbow Calibration Particles (Spherotech), as described previously (Wu and Finley,
2017).

4.2.6. T cell stimulation and ppERK analysis
CAR expressing Jurkat T cells were stimulated by either HA antibody or CD19
expressing cells. For antibody stimulation, 0.1x10
6
CAR expressing cells were incubated
with various amounts of anti-HA antibody in 200 µl in 96 well plates in a 37°C water bath.
125
For cellular stimulation, 0.1x10
6
CAR expressing Jurkat T cells were combined with
0.1x10
6
CD19 expressing K562 cells in 200 µl in 96 well plates. After the cells were mixed,
they were centrifuged at 1000xg for 10 seconds before moving directly into a 37°C water
bath. Doubly phosphorylated ERK was measured as described previously (Altan-Bonnet
and Germain, 2005). Briefly, to fix the intracellular stimulation reactions after a given
amount of time, cells were moved to an ice bath, and ice cold 16% paraformaldehyde
solution was added to a final concentration of 4% for 20 minutes. The cells were then
centrifuged and resuspended in 100% ice cold methanol. The cells were incubated at -20°C
for at least 30 minutes, followed by 3 washes in 200 µl FACS staining buffer (5% FBS in
PBS). Cells were then stained with fluorophore conjugated phospho-ERK antibody for 30
minutes at 4°C in the dark, followed by 3 washes with 200 µl PBS. Fluorescence signal
was analyzed using the Miltenyi Biotec flow cytometer and all FACS data was analyzed
using FlowJo software. Small Jurkat cells were distinguishable from the large K562 target
cells based on their low autofluorescence in the forward and side scatter channels.

4.2.7. Experimental data curve fitting
Graphpad Prism was used to fit the phosphorylated ERK response time from our
experimental data to a standard sigmoidal curve, using the non-linear regression curve fit
function.

126
4.3. Results
4.3.1. Model of CAR ERK activation
We constructed a computational mechanistic model that describes the early CAR
signaling events leading to T cell activation. We specifically predict how the CAR mediates
ERK activation through the MAPK pathway. Studies have indicated that, while the
activation of CARs and TCRs follow different mechanisms and kinetics, the signaling
events initiated downstream are not significantly different (Harris et al., 2018). Therefore,
to construct our model, we combined four mechanistic signaling modules: (I) CAR-specific
phosphorylation based on our previously published models, (II) phosphatase activity, (III)
a LAT signalosome, and (IV) a MAPK pathway that leads to ERK activation (Figure 4-
2). To characterize the model, we first explored signaling primarily through the CD3ζ CAR
stimulatory domain. This allowed us to compare our model to previously developed models
in the literature, which largely simplify the TCR to only account for the CD3ζ domain.

127

Figure 4-2: Schematic of signaling model through ERK activation incorporating
models from literature. Arrow and bars indicate activating and inhibitory interactions,
respectively. Dashed lines denote the same species in multiple Modules.
Module I: LCK regulation, autophosphorylation, and phosphorylation of the CAR
intracellular signaling domains and ZAP-70.
Module II: CD45 and SHP1 phosphatase activity. CD45 is constitutively active in
resting T cells, but it is excluded from the signaling area upon CAR binding to its ligand.
SHP1 is recruited to the area by singly phosphorylated CD3ζ ITAMs and is activated by
LCK.
Module III: The LAT signalosome forms when ZAP-70 binds to doubly
phosphorylated ITAMs and becomes phosphorylated by LCK. It can then phosphorylate
sites on LAT and SLP76. Phosphorylated sites on LAT can bind proteins Grb2, GADS,
and PLCg. Grb2 can bind to SOS, while GADS binds to SLP76 and the kinase ITK. ITK
can then phosphorylate and activate PLCg.
Module IV: PLCg and SOS can activate Ras-GDP to Ras-GTP. Ras-GTP can be
inactivated by RasGAP. Once activated, RAS-GTP can activate the MAPK pathway,
which leads to ERK activation. Doubly phosphorylated ERK can phosphorylate LCK at a
protection site, which prevents LCK from associating with SHP1, resulting in a positive
feedback loop.
128
Module I focuses on LCK autoregulation and its phosphorylation of the CAR
intracellular signaling domains and ZAP-70. We first adapted our model of LCK
autoregulation and inhibitory phosphorylation by the kinase CSK to reduce the
computational complexity (Rohrs et al., 2016a). The second model in this module was
adapted from work from our lab to quantify the kinetics of CAR intracellular domain
phosphorylation by LCK (Rohrs et al., 2018). Our published computational quantification,
paired with novel in vitro phospho-proteomic mass spectrometry, specifically identified
the phosphorylation rates of individual tyrosine sites. This work also revealed that the
addition of CD28 increases the rate of CD3ζ ITAM phosphorylation, which will be used
later in the present study to explore how CD28 affects downstream signaling in the T cell
activation system.
In module II, we modeled the activity of phosphatases known to play a role in T
cell activation. This module influences both modules I and III. We included two main
phosphatases that act throughout the whole model of T cell activation: CD45 and SHP1.
CD45 is constitutively active in T cells and prevents unstimulated T cell activation. SHP1
activity is induced upon phosphorylation of the TCR. To explore its effects on CAR
activation, we included a mechanism of negative feedback through phosphatase SHP-1
recruitment, first modeled by Altan-Bonnet and Germain (Altan-Bonnet and Germain,
2005). SHP1 is recruited to singly phosphorylated CD3ζ ITAMs (from module I), where it
can be activated by LCK. SHP1 can then dephosphorylate various proteins in the signaling
cascades in module I and III.
Module III, the LAT signalosome, links the output of module I (phosphorylated
CAR receptors) to the input of module IV (active SOS and PLCg). Module III begins with
129
ZAP-70 binding to doubly phosphorylated ITAMs on CD3ζ, from module I. ZAP-70 can
then be phosphorylated by LCK at several sites. This phosphorylation has a variety of
effects: holding ZAP-70 in an open conformation, increasing ZAP-70 catalytic activity,
and allowing ZAP-70 to dissociate from CD3ζ (Katz et al., 2017; Sjölin-goodfellow et al.,
2015). Once free and activated, ZAP-70 can go on to phosphorylate LAT. Phosphorylated
LAT can bind to adaptor molecules, GADS and Grb2, which in turn bind to other
downstream signaling proteins, such as SLP76, ITK, and the inputs to module IV, SOS and
PLCg.
Module IV focuses on MAPK pathway activation. To initiate this pathway, we
adapted a model of Ras-GDP to Ras-GTP conversion by SOS and RasGRP from Das et al.
(Das et al., 2009). Their model details the allosteric regulation of SOS by active Ras, which
results in a positive feedback loop that can transform the analog phosphorylation events
derived from TCR or CAR activation to a digital ERK response. The RAS-GTP output of
this model was used as the input to a MAPK cascade parameterized by Birtwistle et al.
(Birtwistle et al., 2012), resulting in doubly phosphorylated ERK. Active ERK also feeds
back to modules I and II as it can phosphorylate LCK at a protection site, which prevents
interactions with the phosphatase SHP1, as first modeled by Altan-Bonnet and Germain
(Altan-Bonnet and Germain, 2005).
Together, these modules constitute a mechanistic description of what are thought
to be the most important interactions in the binary decision of T cells to activate ERK.
Below, we explore the model in more detail and make predictions about the mechanisms
through which the individual signaling domains on CARs influence the ERK response.

130
4.3.2. Sensitivity analysis
To better understand how the model parameters interact with one another and
influence the output of doubly phosphorylated ERK response time, we conducted a
sensitivity analysis using the extended Fourier amplitude sensitivity analysis (eFAST)
method (Marino et al., 2008). This global sensitivity analysis allows us to identify the
parameters that the model output is sensitive to both individually, with the first order
sensitivity index (Si), and in combination, with the total sensitivity index (S Ti). This
analysis is particularly important for large models, like the one presented here, which
incorporate many different mechanisms of feedback and other complex interactions.
We analyzed the model parameters in nine groups: initial concentrations,
LCK/CSK parameters, CD3ζ parameters, kinase parameters, binding parameters, CD45
parameters, SHP1 parameters, RAS parameters, and MAPK parameters. The results are
shown in Figure 4-3. We only list the parameters whose sensitivity indices are statistically
significant. There is at least one parameter in each group that does significantly influence
ERK response time. Additionally, all of the influential parameters have a higher total
sensitivity index than first order index. This indicates that, even if all the parameters in a
group are not significantly influential on their own, they do all still interact together to
affect the output.

131

Figure 4-3: First order (Si) and Total (STi) sensitivity indexes of model parameters.
The parameters were separated into nine groups, listed on the left. The total number of
parameters in each group (n) is listed under the group name. An eFAST sensitivity analysis
was performed on each group, and only the parameters whose sensitivity indices were
significantly significant are shown.

132
Not surprisingly, the species and parameters closest to ERK in the model have more
of an affect on its response time. Of the initial concentrations, only Ras, the activator of
the MAPK pathway, and its direct modifiers, RasGRP and RasGAP, are influential.
Although SOS can also activate Ras directly, its sensitivity indices are not statistically
significant. This is due to the mechanism of activation, in which RasGRP activity produces
a graded response of Ras, which is able to prime SOS through binding of active Ras-GTP
at an allosteric site. Once activated, SOS quickly and efficiently initiates the complete
activation of the MAPK pathway. Therefore, this initial response from RasGRP, along with
the inhibitory effects of RasGAP, control the time at which this switch occurs.
The most influential parameters in the model are the upstream parameters that
involve LCK and ZAP-70 kinase activity. These are the main kinetic drivers of T cell
activation, and it is not surprising that the activities of these proteins have a strong effect
on how quickly the T cells are able to respond and activate ERK. As the model progresses
downstream, there are a higher number of statistically significant sensitive parameters
(about a quarter of the parameters in the MAPK and Ras activation subsets compared to
about a tenth or less of the parameters in the kinase, and phosphatase groups). However,
even though some downstream parameters are influential, each one is less influential than
the upstream parameters. Taken together, this highlights the interconnected nature of the
model, where the final output depends on each step of the pathway to produce a response.

4.3.3. Model fit to experimental data
We first fit the model to experimental data to obtain a robust mathematical
framework to predict T cell activation leading to ERK phosphorylation. The majority of
133
the model parameters come directly from measurements in the literature or from previously
published models. However, several of the parameters were not well defined, either
because they had not been measured experimentally, they had conflicting values after being
fit to the specific assumptions of previous models, or they did not account for the two-
dimensional nature of the interactions specifically modeled here. This was particularly true
of the activation rates of ZAP-70, the catalytic activity of ZAP-70, and the phosphatase
activity in the system, parameters shown to significantly influence ERK response time in
our sensitivity analysis. To better constrain these parameters, we fit the model to published
measurements obtained using an in vitro system of recombinant proteins interacting on a
two-dimensional liposomal membrane (Hui et al., 2017). Hui et al. used this system,
combining twelve proteins involved in T cell activation, to measure nine different protein
phosphorylation states in the presence of varying amounts of CD45.
We extracted this data and fit the model to it, as described in the Methods section.
Figure 4-4A shows the best fit of the median values for these global minimum sets. The
parameter distributions are shown in Figure 4-4B. The median values of these best-fit
parameters were used for the rest of the simulations.

134

Figure 4-4: A subset of the model parameters were fit to data from Hui et al (2017).
A) The model fits (lines) to experimental data (dots) are shown without CSK (left)
and with CSK (right).
B) Best fits parameter values for catalytic rates (top) and Michaelis-Menten
constants (bottom).

135
4.3.4. Model recreates experimental results from the literature
Using the calibrated model, we sought to validate the model by reproducing
experimental observations of T cell ERK activation from the literature. We first
investigated the role of the phosphatase CD45. The role of CD45 is particularly important
in modulating CAR activation, due to the tight binding between the CARs extracellular
domain and the antigen of interest. Whereas TCRs normally bind to MHC presented
antigen peptides with affinities in the micromolar range, the scFvs on CARs typically bind
to their targets in the nanomolar range (Harris et al., 2018). The difference between these
affinities indicates that the unbinding and rebinding events that result in a kinetic
proofreading mechanism of TCR activation may not play a significant role in CAR
activation. However, it has been shown that both CARs and TCRs form immunological
synapses, which can exclude phosphatases with large extracellular domains, like CD45,
from the binding region (Leupin et al., 2000; Mukherjee et al., 2017). In fact, excluding
CD45 is sufficient to activate the TCR in T cells (Chang et al., 2016).
Therefore, we used the model to investigate how CD45 affects downstream ERK
phosphorylation. In particular, we predict the interplay between the amounts of CD45 and
CD3ζ. Figure 4-5A shows the model simulated ERK response time for varying amounts
of CD45 and CD3ζ. For high CD45 concentrations, ERK is not activated. For a given CD3ζ
concentration, once CD45 is below its activation threshold value, the amount of CD45 does
not greatly influence the response time. On the other hand, the ERK response time is
asymptotically dependent on the amount of CD3ζ that can be activated. This model
behavior is in agreement with experimental data in the literature. Therefore, in our model,
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we initiate signaling by removing CD45, assuming that all of the CAR in the simulation is
strongly bound to the antigen and able to signal.

Figure 4-5: The model can reproduce known effects of T cell signaling in the
literature.
A) Effects of changing CD3ζ and CD45 concentration on ERK response time.
B) Predicted concentrations of LCK species. The model was first allowed to reach
steady state with zero CD3ζ and 100 molecules/µm
2
CD45. At t=0, CD45 was
set to 0 and CD3ζ was set to 1000 molecules/µm
2
and the simulation was run
for 100 minutes, by which time, the system had reached steady state.
C) The model can qualitatively match the expected changes in ERK response time
due to changes to various intracellular signaling molecules. The baseline ERK
response time of the unaltered model is shown in black. The model was then
simulated with varying amounts of CSK, as well as alterations to the indicated
LCK tyrosine sites to mimic a tyrosine to phenylalanine mutation. Model results
that qualitatively match the expected ERK response are shown in green, and
results that do not match the experimental results are shown in red.

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We next explored how LCK phosphorylation state changes within the model.
Figure 4-5B shows how the phosphorylation state of LCK changes over time. Before
stimulation (at t=0; not shown due to the log scale for the x-axis), 90% of the LCK is
unphosphorylated due to the activity of CD45, whereas approximately 5.5% is in the active
pY394 form and 4.5% is doubly phosphorylated. Negligible amounts of LCK are in the
inhibited pY505 form. Upon stimulation, unphosphorylated LCK rapidly
autophosphorylates at Y394 to become more fully activated. At the same time, LCK more
slowly autophosphorylates at Y505, and CSK phosphorylates active pY394-LCK at Y505.
Together, these events lead to a steady increase in doubly phosphorylated LCK.
Additionally, as LCK activates the negative feedback of SHP1, SHP1 can dephosphorylate
LCK at Y394. This leads to a later peak of inhibited pY505 LCK. These simulations agree
with evidence in the literature measuring the amount of phosphorylated LCK in resting T
cells (Ballek et al., 2015) and showing that both Y394 and Y505 phosphorylation increase
near the T cell activating receptors over time (Philipsen et al., 2017). Additionally, it
provides new evidence for the dynamics of LCK regulation upon T cell activation.
We next aimed to validate that the model could reproduce known modifications of
ERK activation in the literature. To do this, we tested how different mutations to upstream
signaling molecules influence downstream ERK response time (Figure 4-5C). Schoenborn
et al. modified CSK experimentally to produce a form of the protein that can specifically
bind to a small molecule inhibitor (Schoenborn et al., 2011). They showed that inhibiting
CSK resulted in faster ERK activation in a population of T cells. When we remove CSK
from the model, we see that ERK response time increases by about 0.25 minutes, in
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agreement with the findings from Schoenborn and coworkers. Conversely, when we double
the amount of CSK we see that ERK response time slows.
Similar experiments were done by Philipsen et al. to test the ERK response to
various LCK tyrosine to phenylalanine mutants expressed in LCK negative Jurkat T cells
(Philipsen et al., 2017). They found that LCK-Y394F greatly reduced the amount of ERK
positive cells at three minutes, while LCK-Y505 slightly increased the amount of ERK
positive cells. Implementing these two mutations in our model shows that Y394F increased
ERK response time while Y505F decreased it. Since our model does not incorporate
stochasticity, we cannot directly measure the percentage of positive cells. However, these
trends agree with the experimental findings.
In another comparison, our model predicts a faster ERK response time for the LCK
double mutant, compared to wild type LCK. Interestingly, experiments show that this
double mutant reduces the percentage of doubly phosphorylated ERK cells (Philipsen et
al., 2017). In their paper, Philipsen and colleagues hypothesize that this is due to the
catalytic activity of LCK unphosphorylated at Y394. One reason for this discrepancy is
related to the catalytic activity of LCK. Philipsen and colleagues believe that the activity
of unphosphorylated LCK is closer to the Y394F mutant, which has a catalytic activity
significantly lower than pY394 LCK. However, in our model we assume that this form of
LCK has a catalytic activity half that of pY394, based on from experimental measurements
by Hui and Vale (Hui and Vale, 2014). With the exception of this case, the molecular
interactions included in the model match different sets of experimental data and
observations, giving high confidence in the model’s predictive ability. Therefore, we
applied the model to explore how the CAR signaling domains influence ERK activation.
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4.3.5. Tuning of SHP1 negative feedback
In our model, we assume that the intracellular signaling events downstream
of CD3ζ activation are the same for the TCR and CARs. As such, our CAR signaling model
incorporates a similar form of SHP1 negative feedback that has been shown to play an
important role in TCR signaling. This response has been modeled in TCR signaling
previously (Altan-Bonnet and Germain, 2005). We explored this feedback in the model by
recording ERK response time for various levels of CD3ζ CAR over a range of SHP1
feedback strengths. To vary SHP1 feedback, we changed the binding affinity of SHP1 to
singly phosphorylated CD3ζ ITAMs. The resulting effects on the ERK response time are
show in Figure 4-6A. From this heat map, we can see that, for strong SHP1 feedback and
low CD3ζ, SHP1 is able to completely prevent ERK activation. As CAR concentration
increases for high SHP1 feedback, as well as in intermediate SHP1 feedback levels, the
ERK response time first decreases and then increases. This is more clearly shown in Figure
4-6B (blue line), which shows the effect of changing CD3ζ concentration when the SHP1
association rate is 10 µm
2
molecules
-1
min
-1
. When SHP1 feedback strength is low, this
longer ERK response for high CD3ζ is not seen, indicating that it is the feedback of SHP1
that is responsible for this shift in the ERK response time trend (Figure 4-6B, orange line).

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Figure 4-6: SHP1 negative feedback in CD3ζ CAR stimulated T cells.
A) Effects of changing CD3ζ and SHP1 association rate on ERK response time.
Blue and orange lines indicate the SHP1 association rate used in 5B.
B) ERK response time as a function of CD3ζ concentration when SHP1 association
rate is 10 µm
2
molecules
-1
min
-1
(blue line), or 0.1 µm
2
molecules
-1
min
-1
(orange
line).

4.3.6. Comparison of CD28 signaling mechanisms
The results presented above demonstrate how we have used this model to explore
the effects of the first-generation CAR bearing only the CD3ζ activating domain.
However, studies have shown that, for full activation, CARs need at least one co-
stimulatory signal, most commonly CD28 (Bretscher, 1999). Therefore, we next expanded
the model to better understand how CD28 signaling influences T cell activation. CD28 has
been shown to bind to several different proteins that are also involved in the LAT
signalosome. Specifically, phosphorylated tyrosine sites and proline-rich regions on CD28
can bind to the adaptor proteins Grb2 and GADS (Higo et al., 2014). As these proteins can
recruit and bind to other proteins that lead to ERK activation, we tested how these binding
mechanisms affected downstream ERK activation. Additionally, our previous work to
quantify CAR phosphorylation kinetics showed that the presence of CD28, without any
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downstream binding proteins, increases the rate of CD3ζ phosphorylation (Rohrs et al.,
2018). Therefore, we explored the effects of each of these possible ways that CD28
influences CAR-mediated T cell signaling. To do so, we used an ensemble modeling
approach where we modeled each of these mechanisms independently and then combined
them to predict how they affect ERK response time (Brännmark et al., 2010).
We investigated the effects of three mechanisms involving CD28: Grb2 binding to
CD28, GADS binding to CD28, and CD28-mediated enhancement of LCK activity. These
mechanisms are shown in Figure 4-7A-C. If Grb2 binds to CD28 in the same way that it
binds to LAT, then it will be able to recruit SOS to the signaling area, which can activate
Ras and the MAPK pathway directly (Figure 4-7A) (Schneider et al., 1995). If GADS is
able to bind to CD28 in the same way that is binds to LAT, then it will be able to recruit
SLP76 and ITK, thus increasing the amount of ITK in the signaling region (Figure 4-7B).
Additionally, it is possible that ITK can bind to CD28 on its own, without the adaptor
proteins (Tian et al., 2015). ITK can then activate its substrate PLCg on LAT, leading to
Ras and MAPK pathway activation (Braiman et al., 2006). To implement these two
mechanisms, we used values of protein binding to CD28 from the literature (Higo et al.,
2014), and assumed that all other interactions would have the same parameters as the same
interactions on the LAT signalosome. The third mechanism uses the kinetic rates calculated
in our previous model of phosphorylation of the individual CD3ζ ITAM sites in the
presence of CD28. In this mechanism, the increased phosphorylation rate of CD3ζ allows
for faster recruitment of ZAP-70 and therefore faster activation of the LAT signalosome
and the MAPK pathway (Figure 4-7C).
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Figure 4-7: Ensemble models of CD28 ERK activation mechanisms.
A) CD28 can bind to Grb2, which binds to SOS and activates MAPK pathway and
ERK.
B) CD28 can bind to GADS, which binds to SLP76 and ITK. ITK can then activate
PLCg on the LAT signalosome, which activates MAPK pathway and ERK.
C) The presence of CD28 on the N-terminal of CD3ζ has been shown to increase
the rate of CD3ζ phosphorylation by LCK. This leads to faster assembly of the
LAT signalosome and activation of the MAPK pathway and ERK.
D) ERK response time as a function of CD3ζ concentration for the ζ (black) or 28ζ
CAR in which the only effect of CD28 is its binding to Grb2 (yellow).
E) ERK response time as a function of CD3ζ concentration for the ζ (black) or 28ζ
CAR in which the only effect of CD28 is its binding to GADS (orange).
F) ERK response time as a function of CD3ζ concentration for the ζ (black) or 28ζ
CAR in which the only effect of CD28 is to increase the rate of phosphorylation
of CD3ζ (blue).
G) ERK response time as a function of CD3ζ concentration for the ζ (black) or 28ζ
CAR in which CD28 is able to bind to both Grb2 and GADS as well as
increasing the rate of CD3ζ phosphorylation (red).
H) ERK response time as a function of CD3ζ concentration for model simulations
without SHP1 for the ζ (black) or 28ζ CAR in which the only effect of CD28 is
its binding to Grb2 (yellow).
I) ERK response time as a function of CD3ζ concentration for model simulations
without SHP1 for the ζ (black) or 28ζ CAR in which the only effect of CD28 is
to increase the rate of phosphorylation of CD3ζ (blue).
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We simulated the model with each CD28 mechanism individually and in various
combinations. Figure 4-7D-F shows the predicted ERK response time as a function of
CAR concentrations for each of these mechanisms compared to the CD3ζ-only model.
Both Grb2 and GADS binding showed similar effects, greatly speeding up the ERK
response time at high CAR concentrations with no significant difference at low CAR
concentrations. However, the response for Grb2 binding is slightly more profound due to
the stronger switch-like effect of SOS activation of Ras, compared to the more graded
activation by PLCg. In contrast, the effect of the increased rate of CD3ζ phosphorylation
was significantly different, showing a nearly constant decrease in response time in the
presence of CD28 over all CAR concentrations. The combined effects of all three
mechanisms of CD28 signaling is shown in Figure 4-7G. This shows that the effects of
Grb2 and GADS binding are largely redundant, producing a similar level of response as
each one independently. The effect of the kinetic changes to CD3ζ was largely additive,
speeding up the response times of the binding effects for all CAR concentrations. The pair-
wise combinations also showed the same effects, with the binding events together showing
a similar response as each one independently and the CD3ζ kinetic effects showing an
additive response (Figure 4-8).

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Figure 4-8: Model predictions for ERK response due to pair-wise combinations of
CD28 signaling mechanisms. (Left) ERK response time as a function of CD3ζ
concentration for the ζ (black) or 28ζ CAR in which CD28 is able to bind to Grb2 and
GADS (cyan). (Middle) ERK response time as a function of CD3ζ concentration for the
ζ (black) or 28ζ CAR in which CD28 is able to bind to GADS and increase CD3ζ
phosphorylation rate (purple). (Right) ERK response time as a function of CD3ζ
concentration for the ζ (black) or 28ζ CAR in which CD28 is able to bind to Grb2 and
increase CD3ζ phosphorylation rate (green).

We next sought to better understand how these mechanisms were influenced by the
negative feedback from SHP1, as the results presented above for the CD3ζ CAR showed
SHP1 to be important in determining the ERK response time as a function of CD3ζ
concentration. We tested each of these mechanisms in the model in the absence of SHP1
(Figure 4-7H-I). Figure 4-7H shows the response of SOS binding to CD28 in the absence
of SHP1 in the CD3ζ-only CAR (“ζ”) compared to the CD28-CD3ζ CAR (“28ζ”). This
binding mechanism does not greatly depend on SHP1 feedback, as the trends of the binding
are the same as what happens in the presence of SHP1 (Figure 4-7D). Specifically, Grb2
binding increases the response rate only at high CAR concentrations. The CD3ζ kinetic
mechanism, however, does depend on SHP1 negative feedback (Figure 4-7I). Here we
see that for low CAR concentration, the CD28-CD3ζ CAR has a faster ERK response time
than the CD3ζ-only CAR, but for higher CAR concentrations, without SHP1 negative
feedback, this effect is lost.
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4.3.7. Experimental data of ERK activation in CAR T cells
Finally, we performed experimental studies to validate the model predictions for
the effect of CD28 on ERK response time. Here, we used lentiviral vectors to create stable
Jurkat T cell lines expressing HA-tagged anti-CD19 ζ or 28ζ CARs at various levels.
Figure 4-9A shows a diagram of the CAR constructs used. Once expressed, CAR positive
cells were sorted into three populations according to their CAR expression levels: high
expressing cells (H), medium expressing cells (M), and low expressing cells (L) (Figure
4-9B). The same was done to make CD19 target-expressing K562 stable cell lines (19H,
19M, and 19L) (Figure 4-9C). The mean CAR and CD19 expression was quantified for
comparison to the model (Supplemental Figure 4-10).

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Figure 4-9: Experimental validation of CAR activated ERK response time.
A) Schematic of the CAR lentiviral vectors. Sequences encoding anti-CD19 CARs
were inserted downstream of the Ubi promoter in the FUW lentiviral vector.
B) CAR expression in Jurkat T cells. CARs were expressed using lentiviral vectors
and the resulting populations were sorted into high (green), medium (blue) and
low (red) expressing populations. The grey area shows the isotype control
staining.
C) CD19 expression in K562 cells. CD19 was expressed using a lentiviral vector
and the resulting population was sorted into high (green), medium (blue) and
low (red) expressing populations. The grey area shows the isotype control
staining.
D) The percent of ppERK-positive 28ζ CAR T cells over time after stimulation
with various amount of anti-HA antibody. The lines show a sigmoidal curve fit
to the data (dots).
E) ERK response time for different amounts of anti-HA antibody stimulation. The
dots represent the IC50 values of the curves fit in panel (D).
F) ERK response time for different CAR and CD19 expressing populations. High,
medium, and low CAR expressing cell populations were mixed at a 1:1 ratio
with high, medium, and low CD19 K562 cell populations, and the percentage
of ERK positive cells was measured over time. A sigmoidal curve was fit to the
time course data, and the IC50 ERK response time was calculated.
G) Medium expressing ζ CAR cells and 28ζ CAR cells were mixed with various
amounts of medium expressing CD19 K562 cells, and the ERK response was
measured over time. The data was then fit to a sigmoidal curve, and the IC50
ERK response time was calculated.
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Figure 4-10: Quantification of CAR surface expression. CAR expressing populations
of Jurkat T cells were stained with rabbit anti-HA antibody followed by alexa-647
conjugated anti-rabbit and analyzed by flow cytometry. Mean fluorescence was compared
to a standard curve of Rainbow calibration beads to quantify the average CAR expression
levels.

Using the medium expressing the 28ζ CAR cell population (28ζM), we stimulated
the cells with various amounts of anti-HA antibody and measured the percent of doubly
phosphorylated ERK over time (Figure 4-9D). This antibody was able to stimulate ERK
in the Jurkat T cells, with increasing levels of antibody leading to higher steady state
percentages of ERK positive cells. We then fit these responses to a 4-parameter sigmoidal
curve to estimate the half maximal ERK response time for each antibody concentration,
termed the “IC50” (Figure 4-9E). From this curve, we can see that as the antibody
concentration increases, and presumably the level of bound and activating CAR, the ERK
response time of the population becomes faster. However, this changes at high antibody
concentrations, where the response time begins to slow. Comparing this graph to the ERK
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response predicted by our mathematical model in the presence of SHP1 feedback (Figure
4-6B), we see that the two graphs agree quite well. This indicates that SHP1 does play a
significant role in CAR signaling, confirming the model predictions.
We next compared ERK activation in the ζ CAR and 28ζ CAR cells stimulated with
CD19 expressing target cells. We first stimulated high, medium, and low CAR cells with
high, medium and low CD19 target cells at a 1:1 ratio and measured the ERK response
time as described above (Figure 4-9F). The ERK response time was shown to depend on
both CAR expression level and CD19 expression level, with high expressing cells
displaying faster response times than lower expressing cells. Additionally, 28ζ CARs
consistently had faster ERK response times than ζ CARs, despite the fact that the 28ζ CAR
had slightly lower expression levels (Figure 4-10).
To more directly compare the difference between CAR cells, we stimulated
medium expressing 28ζ and ζ-only CARs with different ratios of medium expressing CD19
target cells and measured the ERK response time (Figure 4-9G). Here, we see that the 28ζ
CAR has consistently faster ERK activation for all target cell ratios. Comparing this data
to the predicted CD28 model mechanisms in Figure 4-7, we can see that the mechanism
in which CD28 increases CD3ζ activation kinetics (Figure 4-7F) most accurately matches
the experimental data. Therefore, our experimental data validated the model-generated
hypothesis that CD28 primarily influences ERK activation through modifications to CD3ζ
activation and not through specific binding events of the CD28 protein itself.

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4.4. Discussion
In this study, we developed a computational mechanistic model of the signaling
events that lead to activation of CAR-engineered T cells. To our knowledge, this is the first
model to combine this level of detail of the T cell activation signaling pathways. It
incorporates 23 different proteins in the signaling pathway that leads from CAR
phosphorylation to ERK activation. We used this model to explore how the CAR CD28
co-stimulatory domain influences ERK activation. We used an ensemble modeling
approach to generate novel hypotheses for the way that three different CD28 signaling
mechanisms influence ERK activation kinetics (Mesecke et al., 2011). Experiments
quantifying ERK activation in CAR-bearing Jurkat T cells were used for model validation.
Specifically, we confirmed the importance of SHP1 negative feedback in CAR signaling
and validated the model-generated hypothesis that CD28 primarily signals through
modifying the phosphorylation rate of CD3ζ.
The model was first parameterized based on estimated values from experimental
measurements and previous models in the literature (Altan-Bonnet and Germain, 2005;
Birtwistle et al., 2012; Das et al., 2009; Higo et al., 2014; Houtman et al., 2004; Rohrs et
al., 2016a). We then performed an eFAST sensitivity analysis to determine which
parameters most strongly influence the ERK response time. From this analysis, we found
that the upstream parameters controlling various mechanisms of LCK and ZAP-70
activation were particularly important in influencing the ERK response time. These
parameters were not well defined in the literature, and therefore, we estimated their values
by fitting the LCK, ZAP-70, and CD45 catalytic rates to published experimental data (Hui
et al., 2017).
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Once the model was fully parameterized, we ensured that it could reproduce
experimental observations for ERK activation in T cells, documented in the literature. We
first confirmed that in our model, ERK does indeed become activated when the
phosphatase CD45 is removed. The model predictions agree with experimental results
showing that when CD45 is excluded from the signaling region of antigen-bound CAR and
TCR, there is ERK activation.
We then explored how the activation state of LCK changes over time. The model
predicts that before activation, CD45 activity keeps LCK in a largely inactive
conformation; however, the autophosphorylation of LCK and activity of CSK allow for
some of the LCK pool to be singly phosphorylate at Y394 and doubly phosphorylated,
while negligible amounts of LCK are in the inactive pY505 form. Previous studies have
shown that CD45 has the potential to both enhance and inhibit T cell activation signaling
(Furlan et al., 2014). Our model shows that the presence of CD45 does increase the levels
of active pY394 LCK in the system, particularly at the initial stages of CAR activation.
This is compared to CAR activation in the model without CD45, in which all of the LCK
is doubly phosphorylated (model simulations, not shown).
These novel predictions about the resting state of LCK in T cells have wider
implications for the mechanism of LCK activation in T cells. Previous studies have
attempted to show that a large amount of LCK (~40%) is in an active pY394 conformation
in resting T cells, giving rise to the “stand by” model of activation in which this active LCK
could immediately phosphorylate CD3ζ upon antigen binding to the TCR (Nika et al.,
2010). However, more recently, with the availability of more precise experimental methods
of quantification, this pool of active LCK has been demonstrated to be much smaller (~2%)
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(Ballek et al., 2015). Our model predictions more closely match this experimental result
for the relative amount of active LCK in resting T cells. We also confirm the findings from
Philipsen et al. that the total amount of phosphorylation at LCK Y394 and LCK Y505 both
increase upon T cell activation (Philipsen et al., 2017). Additionally, the model is able to
reproduce known signaling features of T cell activation that occur when CSK is inhibited
and when the amount of CD45 is altered.
The model also identifies new experimental studies that can be performed to
increase our understanding of CAR T cell activation. Model predictions match several sets
of experimental data for activation of T cells with tyrosine to phenylalanine mutant forms
of LCK. The model qualitatively shows that Y394F will decrease ERK activation (resulting
a longer response time in the model) and Y505F will increase ERK activation (resulting in
a shorter model response time). Interestingly, our model predicts that the double mutant
will speed up ERK response time, while experiments in TCR activated T cells have shown
that it actually slows the response (Philipsen et al., 2017). Although a thorough testing of
this model prediction is outside of the scope of the present study, we hypothesize that the
reason for the discrepancy could be due to the nature of the experimental study. The
experiments were performed through antibody stimulation of the TCR. This may lead to
activation through TCR clustering, rather than specific exclusion of CD45, as simulated in
our model. Therefore, more feedback mechanisms of CD45 or other TCR-specific
interactions may play a role in the outcome. Additionally, new experiments should be done
to see if the LCK mutants have the same effect on CAR T cell activation. Thus, the model
can be used to guide and design future experimental studies.
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Given the mechanistic detail of the model, we can distinguish the possible ways
that the CD28 co-stimulatory domain affects ERK response time in engineered T cells.
CD28 is known to bind to several different adaptor proteins that can recruit activators of
Ras and the MAPK pathway (Higo et al., 2014; Tian et al., 2015). Therefore, we
investigated how each of these mechanisms may influence the ERK response time. We
also tested a finding from our recent publication that CD28 increases the phosphorylation
rate of CD3ζ (Rohrs et al., 2018), which in turn could lead to more rapid LAT signalosome
formation and ERK activation (Holdorf et al., 2002). We explored each of these
mechanisms alone and in various combinations to develop model-driven hypotheses about
how each one would affect the ERK response time. We then measured the ERK response
for CD3ζ-only CAR T cells and CD28-CD3ζ CAR T cells for model validation. These
experiments confirmed and validated that the effects of increased CD3ζ phosphorylation
kinetics are the primary cause of enhanced ERK response when the CAR includes CD28.
We further explored the mechanisms of ERK activation in the model and hypothesized that
the negative feedback through SHP1 is a key factor that allows the ERK response time to
differ between CD28-CD3ζ and CD3ζ-only CAR signaling.
The insights from the model increase our understanding of how CD28 is
functioning in T cells. Specifically, the model shows that CD28 primarily works to recruit
LCK to activate the CD3ζ domain rather than contributing its own signaling mechanisms
to ERK activation. However, the model does not indicate how CD28 influences other
downstream T cell activation pathways. In the literature, CD28 has been shown to bind to
PI3K, which activates the Akt pathway (Acuto and Michel, 2003; Rudd et al., 2009).
Additionally, CD28 co-stimulation with the TCR can increase the amount of active Vav in
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the T cell (Helou et al., 2015; Muscolini et al., 2015). These mechanisms are not
specifically included in the model, but it is possible that these pathways may cross talk
with the MAPK pathway and further influence ERK activation (Costello et al., 1999; Dent,
2014). Additionally, it is not clear why CD28 signaling though Grb2 and GADS would not
influence ERK response time in T cells. We believe several possible mechanism could be
explored to explain this result: (i) the CAR structure could prevent binding of these adaptor
proteins, (ii) Grb2 and GADS bind to CD28 in a way that changes their preferred binding
partners so that they initiate different pathways when bound to CD28 than LAT, or (iii)
CD28 binds to and activates the same pathways as LAT but physical separation of CAR
signaling clusters and the LAT signalosome prevent them from interacting and influencing
the MAPK pathway. Overall, these hypotheses, stimulated by the model insights, can be
further tested experimentally to help improve our understanding of how CD28 co-
stimulatory signaling can be optimized in CAR T cells.
We acknowledge some limitations in the current model. First, the model does not
incorporate stochasticity. Specifically, we omit extrinsic noise such as variability in the
initial protein levels, assuming that our model is predicting the average response for a
population of cells. However, to more accurately model the dynamics of the population,
the model should be implemented with varying initial protein conditions to mimic
individual cells. In the future, the model can be expanded to account for such variability,
allowing a closer comparison to experimental data in which the T cells’ response is
measured as the percentage of cells with doubly phosphorylated ERK. The combination of
incorporating this stochasticity, as well as a proofreading mechanism to account for the
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phosphatase activity that can return when the CAR or TCR receptor dissociate from their
stimulatory ligands could provide more accurate predictions (Feinerman et al., 2008).
Additionally, in our model, we assume that unphosphorylated and doubly
phosphorylated LCK have half the catalytic activity as the active pY394 form of LCK. This
is based on experimental measurements from Hui and Vale using in vitro membrane-bound
recombinant LCK and CD3ζ (Hui and Vale, 2014). However, it is not clear if these relative
differences would be true for other LCK substrates, like ZAP-70, or if interactions with
other proteins could limit the availability of these sub-optimally active forms of LCK. More
work can be done in the future to reevaluate these assumptions in the model and make new
predictions that can be further tested experimentally.

4.5. Conclusion
Altogether, this mechanistic model of CAR-mediated T cell signaling is able to
reproduce known effects of CAR activation of the ERK/MAPK pathway and shed new
light on the mechanisms of CAR co-stimulatory signaling through CD28. The model has
provided a specific mechanism for the modification of ERK response time by CD28, which
was validated experimentally. Additionally, it provides new hypotheses for how these co-
stimulatory domain signals can be controlled through SHP1 feedback. The model can be
used to guide the development of new experiments to further analyze how CD28 signaling
on CARs differs from endogenous T cells. Thus, the model provides a framework that can
be used to better understand and optimize CAR-engineered T cell development.

155
4.6. Acknowledgements
This work was supported by the National Cancer Institute of the National Institutes
of Health under Award Numbers F31CA200242 (to J.A.R.), R01EB017206,
R01CA170820, and P01CA132681 (to P.W.)

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157

5.

Chapter 5

Conclusion

158
5.1. Summary
The computational modeling work described here has added new mechanistic
insight into the methods through which chimeric antigen receptors (CARs) are able to
activate T cells. We first explored the regulation of the main activating kinase in T cells,
LCK. In the TCR, LCK is recruited to the signaling area through the co-receptors CD8 and
CD4, but these co-receptors have not been shown to play a role in CAR activation.
Therefore, the regulation of free LCK in T cells presumably plays an important role in
CAR activation. LCK can be phosphorylated at an activating tyrosine site (Y394) and an
inhibitory tyrosine site (Y505), resulting in four different phosphorylation species with
different catalytic and binding activities. The model predicts that binding events between
LCK and its inhibitory kinase CSK play an important role in LCK phosphorylation.
Additionally, the substrate preference of the different phosphorylated forms of LCK could
act as a mechanism to maintain a constant level of LCK catalytic activity.
We next sought to better understand how LCK phosphorylates individual tyrosine
sites on CAR proteins. To measure the site-specific phosphorylation kinetics, we used an
in vitro recombinant protein system. In this system, HIS-tagged CAR intracellular
signaling domain recombinant proteins and HIS-tagged constitutively active LCK (Y505F)
were attached to a nickel-chelated liposomal membrane. They proteins were allowed to
react for various time and then subjected to phospho-proteomic mass spectrometry to
measure the percent phosphorylation of each tyrosine site on over time. We found that the
six immunoreceptor tyrosine-based activation motifs (ITAMs) on CD3ζ were
phosphorylated independently at different rates. The four tyrosine sites on CD28 were also
phosphorylated at different rates, significantly more slowly than those of CD3ζ. Most
159
interestingly, we found that including CD28 at the N-terminal of the CD3ζ domain greatly
increased the rate of CD3ζ phosphorylation. We fit this data to a mass action based
computational model to quantify the differences between the substrate specificity of LCK
for each tyrosine site. We then used the model to explain a mechanism for the appearance
of various phosphorylated forms on CD3ζ in resting T cells.
This new quantification of phosphorylation site kinetics on CAR proteins opened
up new questions about how these upstream kinetic changes influence downstream T cell
activation. To answer these questions, we combined our models of LCK autoregulation
and CAR intracellular signaling domain activation and expanded this model to account for
the molecular interactions that lead to ERK activation. In T cells, ERK is activated with
switch-like characteristics that are thought to help determine the on/off state of T cell
activation. We showed that our model, combining 23 different proteins in the signaling
pathway, is able to reproduce the effects of various protein modifications on ERK
activation response time. We then used an ensemble modeling approach to predict how
various mechanisms of CD28 co-stimulation affect the ERK response. To test these
different hypotheses, we measured ERK response time in CD3ζ or CD28-CD3ζ CAR
engineered T cells. These experiments validated the model prediction that the change in
CD3ζ phosphorylation kinetics in the presence of CD28 on the CAR is the main mechanism
influencing ERK response time. This model was also used to predict the T cell feedback
pathways that significantly influence this difference between CD3ζ-only and CD28-CD3ζ
T cell activation of ERK.

160
5.2. Future Directions
This model of CAR T cell activation has provided new insights in the mechanisms
of CAR signaling that influence the downstream ERK response in T cells; however, it can
be expanded to further explore different aspects of CAR T cell signaling to improve future
T cell therapies. One key assumption of the current model is that is reproduces the average
response of a population of T cells (Altan-Bonnet and Germain, 2005). However, ERK
activation is measured at the level of individual T cells. This results in changes to not only
ERK response time, but also the maximal number of ERK positive cells.
To explore how CAR signaling influences the number of ERK positive cells, the
model could be implemented in a stochastic manner. To do this, we could randomly vary
the initial conditions of the proteins in the system to mimic the heterogeneity in a
population of T cells. We could then run the model a number of times with these different
initial conditions and record the number of cells that activate ERK at various times. This
type of stochastic simulation had been used to better understand how co-regulation of
various proteins in T cells influence activation through the TCR (Feinerman et al., 2008),
as well at the bimodal response of the MAPK pathway (Birtwistle et al., 2012). This
stochastic implementation of the CAR signaling model could be used to answer questions
about why some CAR T cells respond better than others, and possibly provide biomarkers
for patients with T cells that might be better suited for CAR therapy.
In addition to CD28, a variety of other co-stimulatory domains have been
incorporated on CARs. This model of CAR signaling could be expanded to include other
signaling domains, like 41BB or OX40 or others. 41BB and OX40 both signal by binding
to TRAF proteins, which can influence various MAPK pathways or NFkB signaling
161
(Dempsey et al., 2003). It is also not known how these co-stimulatory domains might
influence CD3ζ phosphorylation kinetics. Unlike CD28, they are not known to recruit
LCK, so it is not likely that they will increase the rate of CD3ζ phosphorylation. On the
contrary, the added steric hindrance due to binding of adaptor proteins to these stimulatory
domains may slow CD3ζ activation. A mechanistic model including these co-stimulatory
domains could help shed light on the effects of these various mechanisms. It would also be
interesting to compare the output of different co-stimulatory signals in the model to help
determine which co-stimulatory domain leads to optimal T cell activation.
In additional to co-stimulatory domains, inhibitory T cell domains can also affect
CAR signaling. Particularly, inhibition of T cell activation through expression of PD-1 has
been shown to greatly affect T cell activity in patients (Ghoneim et al., 2016). In the clinic,
researchers have attempted to prevent this through combination therapy with anti-PD1 or
anti-PDL1; however, this is only effective if enough of the antibody drug gets to the T
cells, requiring multiple treatments and the possibility of side effects (Postow et al., 2018).
It would be ideal to be able to understand how PD-1 therapy affects CAR signaling and
design a CAR that is not affected by this negative regulation. Recent studies have made
efforts to describe the mechanism of PD1 activity through the recruitment of the
phosphatase SHP2 (Hui et al., 2017). Adding this mechanistic insight to the model, as well
as other inhibitor signaling pathways, like CTLA-4, could help with the design of more
optimal CAR therapies.
Finally, ERK is only one downstream transcription factor regulator activated by T
cell signaling. Other pathways, such at the PI3K/AKT pathway, NFkB, and NFAT
pathways all contribute to the functional response of T cells. These pathways can integrate
162
and control T cell responses such as survival, proliferation, cytokine production, and cell
killing. The ultimate goal of this work is to link the mechanistic model developed here to
a model that can use the outcome of these signaling pathways to predict the different
function response phenotypes of T cells.

5.3. Conclusion
Ultimately, the work provides a framework with which to study CAR T cell
activation. It is able to provide mechanistic insight into the function of T cell stimulatory
domains CD3ζ and CD28. Additionally, it can he used to test and generate new hypotheses
to guide future experiments. This framework can be expanded upon in the future to make
a complete model that can predict the functional results of T cell activation by different
CAR structures. The information from this modeling work can be used to design improved
CAR therapies to expand CAR T cell treatments to more patients.
163
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Abstract (if available)

Abstract Chimeric antigen receptors (CARs) are engineered receptors that mediate T cell activation. To do so, CARs are comprised of a variety of different activating and co- stimulatory domains derived from endogenous T cells. These intracellular domains initiate signaling required for T cell activation, including ERK activation through the MAPK pathway. The mechanisms by which co-stimulatory domains on CARs influence this signaling are not clear. To better understand how CAR signaling differs from T cell receptor (TCR) signaling and how the individual CAR signaling domains CD3ζ and CD28 influence the downstream activation, I have used a bottom-up modeling approach to build a framework that will allow for the exploration of the specific mechanisms of CAR T cell activation. In chapter one, I develop a computational model to better understand how the main T cell activating kinase, LCK, is autophosphoryated at its inhibitory and activating tyrosine sites. This model, trained using in vitro experimental data of LCK autophosphorylation and phosphorylation by the kinase CSK, identifies key mechanisms required for T cell regulation. In chapter two, I focused on the interaction between LCK and the CD3ζ and CD28 intracellular signaling domains of the CAR. I first collect quantitative phospho-proteomic mass spectrometry measurements to measure the phosphorylation kinetics of different CAR structures. I fit this data using a computational model of CD3ζ phosphorylation by LCK. Testing how different model structures compare to the data, I am able to confirm that these sites are phosphorylated randomly with different rates. The model also predicts that the CD3ζ sites are phosphorylated independently, which I confirm experimentally. When CD28 is added upstream of CD3ζ, the experimental data shows that the phosphorylation rates of all CD3ζ ITAM sites are increased, and the order of the site phosphorylation is altered. In light of this, I use this computational model to explain a mechanism for the appearance of differentially phosphorylated forms of CD3ζ in resting T cells and determine that protein binding to singly phosphorylated ITAM sites plays an important role in influencing the overall phosphorylation of these sites. Finally, in chapter three, I combine the LCK autoregulation and CD3ζ/CD28 phosphorylation models with downstream mechanisms from several other models in the literature to predict how CARs with or without the CD28 co-stimulatory domain affect downstream ERK activation. I use an ensemble modeling approach to explore the specific mechanisms of CD28 that contribute to ERK activation in anti-CD19 CD28-CD3ζ CAR- bearing Jurkat T cells. The model produces several hypotheses for how ERK response time could be affected by various binding events and kinetic changes initiated by CD28 co- stimulation. I then perform experiments to validate the main CD28 mechanism of activation in CAR T cells. Thus, the model provides new mechanistic insights into the functions of T cell co-stimulatory domains. Altogether, my model provides a framework with which to study CAR engineered T cell activation. In the future, the model can be further expanded to study other co- stimulatory domains, like 41-BB, and inhibitory domains, like PD-1. I envision this model as a tool to help understand and optimize CAR T cell activation to improve future CAR therapies.

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Asset Metadata

Creator Rohrs, Jennifer Ann (author)

Core Title Mechanistic model of chimeric antigen receptor T cell activation

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 07/10/2018

Defense Date 04/11/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chimeric antigen receptors,computational modeling,OAI-PMH Harvest,systems biology,T cell signaling

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wang, Pin (committee chair), D'Argenio, David (committee member), Finley, Stacey (committee member), Graham, Nicholas (committee member)

Creator Email jennifer.rohrs@gmail.com,jrohrs@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-15762

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Legacy Identifier etd-RohrsJenni-6386.pdf

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Document Type Dissertation

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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 a...

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