SCHOLARLY REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE
MD DEGREE AT HARVARD MEDICAL SCHOOL
UNDERSTANDING VARIATION IN
MACROPHAGE CELL DEATH FOLLOWING
M. TUBERCULOSIS INFECTION: A
SYSTEMS BIOLOGY APPROACH
ROBERT CRUTCHER
SUPERVISED BY:
BREE ALDRIDGE, PHD, DEPARTMENT OF MOLECULAR BIOLOGY AND
MICROBIOLOGY, TUFTS UNIVERSITY SCHOOL OF MEDICINE
AND
SUZANNE GAUDET, PHD, DEPARTMENT OF GENETICS,
HARVARD MEDICAL SCHOOL / DANA FARBER CANCER INSTITUTE
1 MARCH 2017
Abstract
Title: Understanding Variation in Macrophage Cell Death following M. tuberculosis Infection: A Sys-
tems Biology Approach
Purpose: Macrophage apoptosis is considered an innate immune strategy of last resort in M. tuber-
culosis infection, while necrotic cell lysis is considered a feature of bacterial virulence. We built a
mathematical model to investigate cell death decisions in mycobacterial infection, focusing on the role
of the transcription factor NF-kB and the lipid mediators PGE2 and LXA4. The purpose of our model
is to investigate proposed mechanisms, discern quantitative relationships among cell mediators, and to
generate new testable hypotheses.
Methods: We built a differential equation-based, mass-action kinetics model using PySB, an open-
source software for biochemical modeling. We simulated our model using a personal computer.
Results: We show how osmotic stress can account for experimental observations of necrosis due to mi-
tochondrial dysfunction. We recapitulate the finding that PGE2 suppresses this dysfunction, and show
how membrane repair pathways may prevent necrosis even for moderate degrees of mitochondrial in-
jury. We show how a threshold level of LXA4-mediated PGE2 suppression is required to cause necrosis.
Our simulations suggest that threshold LXA4 activity may also be required to induce apoptotic death.
We also show how TNF and IL-10 shift the balance of cell death towards apoptosis and necrosis, respec-
tively.
Conclusions: To our knowledge, we are the first to formulate a mechanistic model for the events lead-
ing to necrotic cell lysis downstream of mitochondrial dysfunction. In addition to investigating the
quantitative implications of existing hypotheses, our model also generates a novel hypothesis that the
pro-necrotic mediator LXA4 may also be required for apoptosis, via attenuation of NFkB-mediated pro-
survival pathways. This would represent an elegant mechanism for the selective application of apoptosis
as an immune response. Future work should further elucidate the biochemical pathways linking bacterial
virulence to LXA4 production and LXA4 to the suppression of PGE2.
2
Contents
1 Introduction 4
2 Student Role 7
3 Methods 7
4 Results 7
5 Discussion, Limitations, Conclusions, and Suggestions for Future Work 15
6 Acknowledgements and References 19
7 Figures 23
8 Appendix: Reaction Lists 34
Glossary of Abbreviations
Mtb: Mycobacterium tuberculosis IKK: IKK Kinase
PGE2: Prostaglandin E2 MAPK: Mitogen Activated Protein Kinase
LXA4: Lipoxin A4 EARM: Extrinsic Apoptosis Reaction Model
Cox-2: Cyclooxygenase-2 DISC: Death-Inducing Signaling Complex
5-LO: 5-Lipoxygenase TNF: Tumor Necrosis Factor
MPT: Mitochondrial Permeability Transition IP3: Inositol Triphosphate
MOMP: Mitochondrial Outer Membrane Perme- ER: Endoplasmic Reticulum
abilization ROS: Reactive Oxygen Species
cAMP: Cyclic AMP TLR: Toll-Like Receptor
PKA: Protein Kinase A 5-LO: 5-Lipoxygenase
Syt-7: Synaptotagmin-7 BCG: Bacille Calmette Guérin
NF-kB: Nuclear Factor - kappa B
IkB: Inhibitor of kappa B
3
1 Introduction
1.1 The Importance of Cell Death in Mtb Infection
Tuberculosis remains a significant global health challenge, infecting 10.4 million and claiming the lives
of 1.8 million per year, with over 95% of deaths occurring in low- and middle-income countries.1
Even the most antibiotic-sensitive strains of the pathogen Mycobacterium tuberculosis (Mtb) require
six months of multi-drug therapy to treat.1 One reason for Mtb’s success as a pathogen is its long history
of co-evolution with the human immune system, especially with the alveolar macrophage, its princi-
pal host cell.2 The study of host-pathogen interactions therefore represents an important frontier in the
search for novel Mtb treatments.
Recently, it has become evident that host cell death plays an important role in the innate immune
response to Mtb infection. When a macrophage is unable to eradicate its bacterial burden, apoptosis is
considered host-beneficial as it sequesters the bacteria within the apoptotic body, enhances antigen pre-
sentation, and provides a second opportunity at bacterial killing by a subsequent phagocyte.2 Necrosis,
a mode of cell death characterized by cell lysis, is considered beneficial to the pathogen as it results in
bacterial dissemination.2 The inflammatory response triggered by necrosis is also an essential feature of
the granuloma formation responsible for the clinical hallmarks of tuberculosis.3 That the mode of host
cell death might influence the outcome of infection is supported by evidence that more virulent strains
of mycobacteria cause a greater degree of necrosis, implying that pathogenic Mtb are able to subvert
the biochemical cascades driving host-programmed cell death.2 On the other hand, when any strain of
mycobacteria infect macrophages in vitro, a mosaic of apoptosis and necrosis is observed, suggesting
that variability in the host cell plays a role as well.2
The literature on host-cell death in Mtb infection has focused largely on the roles of the eicosanoids
prostaglandin E2 (PGE2) and lipoxin A4 (LXA4).4 Both are lipid mediators derived from arachidonic
acid (AA). PGE2 is produced in high quantities by cyclooxygenase 2 (Cox-2) in macrophages infected
with avirulent mycobacteria.4 In virulent infection, Cox-2 / PGE2 is suppressed. Instead, LXA4 is in-
duced, produced by the enzyme 5-lipoxygenase (5-LO).4 The balance between these two mediators has
been shown to correlate with the balance of cell death. Specifically, PGE2 prevents necrosis by two
mechanisms: prevention of mitochondrial permeability transition (MPT), and promotion of membrane
repair.2 MPT is the term for the permeabilization of the inner mitochondrial membrane that leads to
uncoupling of the electron transport chain.5 In virulent infection, MPT occurs in tandem with mitochon-
drial outer membrane permeabilization (MOMP) that leads to caspase activation and apoptotic death.2 In
the presence of high abundances of PGE2, however, MPT is suppressed, leading to the isolated activation
of MOMP and apoptotic pathways.5 In both cases MOMP is Bax-dependent, indicating that the the un-
4
derlying cause of apoptosis is the same in avirulent vs. virulent infection.5 Interestingly, the magnitude
of MOMP in high-PGE2 states is decreased, which may be explained by the absence of MOMP-MPT
crosstalk or anti-apoptotic PGE2 effects.5 PGE2 has been shown to prevent MPT via its EP2 receptor,
which signals through cAMP / protein kinase A (PKA).4 By contrast, PGE2-mediated membrane repair
occurs via the EP4 receptor, which signals via the PI3K / AKT pathway.6 EP4 signaling induces the
expression of synaptotagmin-7 (Syt-7), a calcium sensor which repairs damage to the plasma membrane
via efferocytosis of lysosomes to the cell surface.6
The mechanisms by which Cox-2 / PGE2 signaling is induced - or suppressed, in the case of virulent
infection - have also been partially elucidated. Cox-2 is synthesized early in infection by co-ordinate
activity of the transcription factor NF-kB and p38 mitogen-activated protein kinase (MAPK).7 Cox-
2 then amplifies its own expression in a positive feedback loop involving PGE2 / EP4 / PI3K / AKT
signaling. By contrast, LXA4 has been shown to suppress Cox-2 / PGE2 signaling.2
Despite all that is known, there is much that is not known.about the pathways leading to the balance
of eicosanoids in avirulent vs. virulent infection. We do not know exactly how EP2 signaling leads to
suppression of MPT, or how EP4 signaling leads to expression of Syt-7. In the Mtb literature, we do not
know how PGE2-mediated PI3K / AKT activation feeds back to generate additional Cox-2 expression.
In other contexts, AKT has been shown to activate Cox-2 signaling via NF-kB.8,9 The mechanism of
LXA4 suppression of Cox-2 signaling in Mtb infection is also unknown. In other contexts, LXA4
exerts its anti-inflammatory effects via inhibition of NF-kB10, although the pathway leading to NF-
kB suppression is unclear.10. Finally, we do not know how virulent mycobacteria induce host cell
LXA4 production, or what virulence factors are involved.
1.2 Studying Mtb-Induced Cell Death with Mathematical Modeling
With its many intersecting, partially understood pathways, the topic of cell death in Mtb infection is an
ideal system to study using a mathematical model. The purpose of such a model is to synthesize the
proposed mechanisms of the experimental literature, discern quantitative relationships among key cell
mediators, and to generate new testable hypotheses by simulation. For simpler systems, these steps are
often intuitive, and proceed implicitly: biological observations lead naturally to mechanistic conclusions
and to new questions. However, for a system as complex as the one described above - encompassing
gene expression, cytokine signaling, lipid mediators and cell death cascades - the process of formulating
a mechanistic model and generating new hypotheses is aided by a rigorous mathematical approach.
We therefore conducted a thorough search of the literature on Mtb-induced cell death to synthesize
what has been observed as well as the mechanisms that have been proposed to explain these observations.
We assembled these mechanisms into a single model, which we discuss in sections 4.1 and 4.2 and
5
display in the diagrams in section 7.1. We then encoded these mechanisms with mathematics so that
we could simulate our model in silico. We wanted our model simulations to not only reproduce the old
observations from proposed mechanisms but also suggest new observations and even new mechanisms
that could be discerned by future experiments. The questions we wanted to answer with our model
include the following:
1. What is the mechanism of MPT in Mtb-induced cell death and how does MPT bring about necrotic
cell death?
2. What is the quantitative relationship between PGE2, LXA4, and the balance of apoptosis and
necrosis?
3. If LXA4 acts by attenuating NF-kB signaling, what is the impact of LXA4 on NF-kB mediated,
anti-apoptotic signaling? How might this potentially pro-apoptotic role for LXA4 be reconciled
with the paradigm that it is a pro-necrotic mediator?
4. What is the effect of the cytokine milieu on the balance of apoptosis and necrosis?
To answer these questions, we built a mathematical model using mass-action kinetics, a well-
established principle relating the rate of progression of a chemical reaction to its reactant concentrations.
This convention allows a network of biochemical pathways to be translated into a system of ordinary
differential equations, which can then be be solved using computational methods (for an example, see
Figure 1 on page 23). The solution to this system represents the evolution of the biochemical network
over time. To build our mass-action model, we first built a model for the late apoptotic and necrotic
cell death pathways downstream of mitochondrial dysfunction, then built a model for the earlier cell
signaling pathways that direct eicosanoid synthesis. We merged these two models to explore the impact
of the eicosanoid balance on cell death. Our model recapitulates many experimental findings from the
mechanisms proposed by the Mtb literature. In areas where mechanistic detail in the literature is scarce,
we propose plausible mechanisms to explain experimental observations. Our model also investigates the
quantitative dynamics of the mechanisms proposed by the literature, which are hard to capture with ex-
perimental tools such as small-molecule perturbations. We show that threshold levels of Syt-7 induction
are required to “switch” the cell between states of negligible and significant membrane damage, and that
threshold abundances of LXA4, by extension, switch cell fate between apoptosis and necrosis. We also
propose the novel hypothesis that a lower threshold of LXA4 may be required to induce apoptosis, by
inhibition of NF-kB-mediated pro-survival signaling. Finally, we ask how the effects of exogenous TNF
and IL-10 might alter the dynamics of our system.
6
2 Student Role
I reviewed the literature described above and constructed the mathematical model described in section
4.1 and section 4.2. I also conducted all simulations as described in section 4. In future work, other
members of the Aldridge lab will conduct experiments based on these model simulations prior to sub-
mission for publication.
3 Methods
We constructed and simulated our model using PySB, an open-source software for mass action kinetics
modeling in the Python 2.7 programming language. We modified the PySB source code to allow for
non-mass action terms in the differential equation matrix, which is required of our model’s mechanism
of NF-kB inhibition by LXA4. All model instances were solved with the “vode” ordinary differential
equation solver in NumPy, an open-source, python-based module for scientific computing, per the de-
fault settings of PySB. All model instances simulate a 24-hour infection. Building the model involved
both the construction of a chemical reaction network to encode proposed mechanisms from the litera-
ture, and the choice of reaction rate parameters and initial conditions such that our network recapitulated
experimental observations. The construction of the model network from the literature is discussed in sec-
tions 4.1 - 4.2 and the choice of parameters is discussed in section the appendix section 8.2. The full
model reaction list is presented in sections 8.3 - 8.7.
4 Results
4.1 Building Our Model for Cell Death
To build our model for cell death, we started with EARM 1.3, a published model for mitochondrial
apoptosis (see Figure 2 on page 23 for illustration and section 8.3 for reaction list).11 The EARM path-
way begins with the formation of the Death-Inducing Signaling Complex (DISC). As its name suggests,
DISC is formed from activated cell surface receptors such as the Tumor Necrosis Factor (TNF) receptor
and initiates programmed cell death.12 DISC triggers the activation of initiator caspase-8, which causes
the pro-apoptotic protein Bax to oligomerize at the mitochondrion, forming pores to cause MOMP.11
MOMP enables translocation of cytochrome C from the mitochondrion to the cytosol, which leads to
downstream Caspase-3 activation and, finally, cleavage of PARP, the Caspase-3 substrate that EARM
uses as a marker for apoptotic death.11
To this reaction network, we added pathways for MPT and necrosis. We wanted our model to reflect
the following observations from the literature:
7
1. MPT is dependent on calcium influx at the mitochondrion4
2. MOMP and MPT occur simultaneously in virulent mycobacterial infections4
3. Mitochondrial dysfunction caused by MPT leads to necrosis via depletion of ATP as well as
membrane damage2,13
4. PGE2 / EP2 signaling prevents necrosis by suppressing MPT4
5. Syt-7 induction prevents necrosis by activating endosome-mediated membrane repair2
Many gaps remain in our knowledge of the pathways leading from MPT to necrosis in Mtb infec-
tion. We therefore searched PubMed for other papers in the cell death literature that provided plausible
mechanisms to satisfy these observations. We found a well-described mechanism by which cytochrome
C released during MOMP engages IP3 receptors on the endoplasmic reticulum (ER), leading to release
of intracellular calcium stores.14 Calcium then acts as a second messenger to co-ordinate permeabiliza-
tion events among a cell’s many mitochondria (see Figure 3 on page 24 for illustration). This pathway
satisfies observations 1 and 2. To create a pathway linking MPT, ATP depletion, membrane damage,
and necrotic cell lysis, we invoked a mechanism of osmotic stress (see Figure 4 for illustration). Cells
regulate their tonicity by active transport of ions, including sodium, across the plasma membrane.15
With ATP depletion, this active transport is disrupted, leading to accumulation of sodium inside the cell.
Plasma membrane damage also leads to passive diffusion of sodium down its concentration gradient into
the cell.15 Water follows sodium into the cell, leading to cell swelling and lysis.15
We wrote reactions to simulate the ATP-dependent efflux of sodium by ion pumps along with pas-
sive sodium influx (see section 8.4 for reaction list). We also wrote reactions modeling the conversion
of functional mitochondria to MPT, as a function of mitochondrial calcium loading. While functional
mitochondria produce ATP to power osmotic homeostasis, mitochondria that have undergone perme-
ability transition hydrolyze ATP13. While the pathway linking MPT to membrane damage is unclear,
our model uses the MPT-dependent generation of reactive oxygen species (ROS), which damage many
cell components including membranes, as an effector mechanism.16,17
Recall that PGE2 prevents MPT via the EP2 / cAMP / PKA pathway.4 In other contexts it has been
postulated that PKA prevents MPT by direct phosphorylation of the permeability transition pore, and we
employ this mechanism in our model.18 We also write reactions to model Syt-7 activation by increases in
cytosolic calcium, and Syt-7-mediated efferocytosis of endosomal membranes to restore ROS-damaged
plasma membrane. The induction of Syt-7 expression is discussed below.
8
4.2 Building Our Model for Inflammatory Signaling
To model the pathways leading to induction (or suppression) of Cox-2 and its product PGE2, we began
with D2FC, a published model for NF-kB signaling.19 D2FC simulates the activation of NF-kB by the
kinase IKK, along with the multiple negative feedback loops by which NF-kB autoregulates its activity.
We expanded on D2FC to model interactions between NF-kB subunits p50 and p65, which are important
to our simulations in section 4.6. We also developed a novel, mass-action model of RNA transcription.
This module was constructed to address compatibility with our modeling software PySB as well as to
model the interaction between multiple transcription factors. A more complete description of our NF-kB
model is available in Figure 5 on page 25, along with an illustration of our inflammatory signaling model
in Figure 6. Refer to sections 8.5 - 8.7 in the appendix for model reactions lists.
Initial activation of NF-kB in our model occurs via Toll-like receptors (TLR) in response to bacterial
products.20 This occurs via activation of the kinase TAK1, which activates IKK and induces transloca-
tion of NF-kB to the nucleus.20,21 TAK1 also activates MAPK, which increases the activity of nuclear
NF-kB.20 TNF is among the targets of NF-kB signaling.20 The activated TNF receptor on the cell sur-
face, TNFR1, is capable of activating TAK1 and downstream NF-kB in a redundant pathway to TLR
signaling.12 Subsequently, the TNFR1 receptor undergoes internalization to form the DISC, the trigger
for MOMP and MPT in our model for cell death12. Cells also express the TNFR2 receptor which is dis-
tinguished from TNFR1 by its lack of pro-death signaling.22 While TNFR2 induces signal transduction
in its own right, we do not model these pathways, instead using TNFR2 to competitively inhibit TNFR1
activation.22 We also include reactions for the generation of paracrine TNF from the inflammatory mi-
lieu surrounding our simulated cell, which we distinguish from the autocrine TNF which is produced by
our cell.
NF-kB also activates the transcription of Cox-2 mRNA. Per the literature, this transcript has a short
half-life but is stabilized by MAPK signaling.23 The enzyme phospholipase A2 (PLA2) is activated by
MAPK and produces arachidonic acid (AA) from membrane lipids.24 Cox-2 catalyzes the conversion
of arachidonic acid to PGE2.4 Competing with Cox-2 for a common AA substrate, the enzyme 5-
lipoxygenase (5-LO) produces LXA4.4
As described above, PGE2 engages the EP4 receptor to activate the PI3K / AKT pathway. The
Mtb literature demonstrates that EP4 signaling is required to generate a positive feedback loop of Cox-
2 /PGE2 induction, although the pathway between EP4 and Cox-2 is not clear.7 In many other contexts,
AKT has been shown to induce NF-kB signaling via phosphorylation of IKK, and we use this mechanism
in our model to complete the induction loop.8,9
LXA4 signals through the ALX receptor.25 While we could not find substantial information on the
pathways connecting this receptor to its anti-inflammatory effects, it is generally believed that LXA4
9
acts by downregulating NF-kB signaling.10 To model this, we defined a function for IKK activity that
is inversely proportional to the quantity of LXA4 (see section 8.7 in the appendix). Thus, PGE2 and
LXA4 negatively regulate each other via two mechanisms: amplification / attenuation of NF-kB ac-
tivity, and by competition between Cox-2 and 5-LO for a common arachidonic acid substrate. To this
network of reciprocal regulation, we added a third well-described mechanism: inhibition of 5-LO by
PKA phosphorylation.26 This helps suppress 5-LO activity as Cox-2 is induced.
We also model the inducible expression of Syt-7, the calcium sensor that is important for membrane
repair. We know that PGE2 induces Syt-7 via the EP4 receptor, although the identity of the proximal
transcription factor or factors is not known.6 For simplicity, our model assumes that this occurs via
NF-kB.
A final gene product that NF-kB induces in our model is Bcl-2. This anti-apoptotic mediator helps
MOMP by inhibiting Bax oligomerization, as encoded in EARM.11 Bcl-2 induction is an important
example of the pro-survival signaling of NF-kB that occurs alongside the production of cytokines e.g.
TNF that trigger cell death.27 We wanted our model to investigate how LXA4-mediated attenuation of
NF-kB affected this signaling and how this might affect the cell death network. In addition to Bcl-2,
NF-kB upregulates many other anti-apoptotic mediators, including FLIP and XIAP, apoptosis inhibitors
which are also encoded in EARM. For this model, we chose to focus on Bcl-2 because its mitochondrial
localization enables it to impact both MOMP and MPT. Indeed, our literature review revealed a role for
Bcl-2 in blocking MPT in addition to its well-known anti-apoptotic effects.28
4.3 Simulating Cell Death: Osmotic Stress, Suppression of MPT by PKA,
and the Syt-7 Switch
We began simulating our model network by testing its mechanism of calcium-induced MPT, triggered by
ER calcium release downstream of MOMP. We were able to control the degree of MPT by modulating
the quantity of ER calcium ions over four orders of magnitude. Relatively low calcium stores caused
little MPT whereas higher calcium stores caused proportional increases in mitochondrial disruption (see
Figure 7a on page 26).
Next, we tested our osmotic stress model of necrosis in response to various degrees of MPT. We
were able to distinguish the roles of ATP depletion and plasma membrane damage by modulating the
degree of ROS production by MPT. In the absence of membrane damage, ATP depletion alone was able
to cause significant amounts of osmotic stress only at maximal levels of MPT. When membrane damage
was considered, significant osmotic stress occurred at more moderate degrees of MPT. The amount of
osmotic stress for at any given amount of MPT was dependent on the rate of ROS production. (Figure
7c)
10
We next examined the role of PGE2-dependent mechanisms in the prevention of necrosis. Recall
that our model encodes PKA as the inhibitor of MPT downstream of the EP2 receptor, and that Syt-7
helps prevent necrosis by initiating membrane repair. We set ER calcium stores at a moderately high
level (7.0 x 106 ions) and modulated the abundance of PKA to observe the effect on MPT inhibition.
From what we encoded in our model we expected PKA to suppress MPT. Indeed, this is the case (see
Figure 7b). What is harder to glean from the experimental literature, and even from the mechanisms
encoded in our model, is the quantitative relationship between PKA and MPT. Our simulations predict
that high PKA abundances suppress MPT, whereas low to moderate PKA abundances are associated
with significant MPT.
We went on to investigate the effects of PKA-mediated MPT inhibition and Syt-7-mediated mem-
brane repair on osmotic stress. Our simulations revealed an interesting relationship between these two
anti-necrotic mechanisms that we did not predict from the experimental literature. (Figure 7d). For each
Syt-7 abundance across a wide range of values, there is a critical abundance of PKA above which the
cell sees little osmotic stress, approximating the ideal case of no membrane damage. Below this critical
value, there is a dramatic increase in the rate of change of osmotic stress as PKA decreases. Stated suc-
cinctly, Syt-7 acts a switch between states of negligible membrane damage and significant membrane
damage.
To further explore Figure 7d, consider a horizontal line representing the threshold osmotic stress
required to cause cell lysis (Figure 8). Three regions of PKA / Syt-7 “phase space” become apparent.
High abundances of PKA are sufficient to prevent necrosis through suppression of MPT, even in the
absence of membrane repair. Low abundances of PKA result in a degree MPT sufficient to cause necrosis
by ATP depletion alone, even in the absence of membrane damage. For intermediate abundances of
PKA, the fate of the cell depends on Syt-7 mediated membrane repair, remaining intact only if membrane
damage is suppressed.
4.4 Simulating Inflammatory Signaling Pathways: Reciprocal Regulation of
PGE2 and LXA4
We next evaluated the performance of our model for inflammatory cell signaling pathways that activate
PKA and Syt-7 downstream of PGE2. Our model recapitulates the experimental observation that p38
MAPK is essential for the generation of a positive feedback loop of Cox-2 expression, which is sustained
by EP4 signaling. We showed this by modulating the reaction rate constants controlling the activity of
p38 and EP4 (Figure 9).
Next, we used our model to investigate the production of PGE2 and LXA4 and the effect on down-
stream mediators. Because little is known about how virulent mycobacteria induce LXA4 production,
11
as a proxy for bacterial virulence, we modulated the abundance of 5-LO to control the rate of LXA4
synthesis. From what is known from the experimental literature, we expected high abundances of PGE2
to occur at low levels of 5-LO, and high abundances of LXA4 to occur at higher levels of 5-LO. When
we varied 5-LO levels over a 100-fold range, our model produced the time courses shown in Figure
10. At low levels of 5-LO, LXA4 abundances peak early. As Cox-2 is induced, LXA4 is suppressed.
This LXA4 suppression is mediated by competition for substrate between 5-LO and Cox-2 as well as
inhibition of 5-LO activity by PKA, downstream of EP2. At higher levels of 5-LO, the amount of LXA4
generated at early time points is sufficient to suppress Cox-2 induction by the attenuation of NF-kB.
We next investigated the role of 5-LO / LXA4 signaling in the inhibition of important determinants of
cell death. By attenuating NF-kB signaling and Cox-2 induction, high abundances of LXA4 suppress the
production of PGE2, the activity of PKA, and the expression of Syt-7. LXA4 also attenuates production
of TNF and downstream activation of DISC, the trigger for apoptosis. Analyzing Figure 11, one can see
3 distinct patterns of LXA4-mediated attenuation. NF-kB and its downstream gene products (TNF, Cox-
2, and Syt-7) are significantly but not completely suppressed at high abundances of 5-LO. This reflects
residual NF-kB activation by TLR and TNF signaling in the absence of PGE2. By contrast, PGE2
production and the downstream activation of PKA are completely suppressed. This reflects the fact
that 5-LO inhibits PGE2 formation by competing for AA substrate in addition to the LXA4-mediated
attenuation of Cox-2 induction. Finally, relative to other species DISC formation is only moderately
attenuated at higher abundances of 5-LO. This may be because TNF is not completely suppressed by
LXA4, and the TNF produced at even the highest abundances of 5-LO still triggers moderate amounts
of DISC formation.
We further explored the reciprocal regulation of PGE2 and LXA4 by modulating the production of
arachidonic acid (AA). Our goal in these simulations was to further distinguish the roles of our model’s
two encoded mechanisms of PGE2 suppression: LXA4-mediated attenuation of NF-kB, and competi-
tion between 5-LO and Cox-2 for a common AA substrate. We hypothesized that a decrease in AA
production would increase the importance of the second of these two mechanisms. Conversely, we hy-
pothesized that increasing AA abundance would make the first mechanism relatively more important.
We examined the impact of AA perturbations on the abundances of PGE2 and LXA4 as well as the
abundances of the two principal determinants of necrosis, PKA and Syt-7 (Figure 12). We found that
increasing AA production increased the abundance of both PGE2 and LXA4, and that decreasing AA
production decreased the abundance of each. We also found that each perturbation had different effects
on PKA and Syt7. Increasing AA production increased PKA activation, while decreasing AA produc-
tion attenuated PKA activation. These effects occurred at all 5-LO abundances. By contrast, the effect
of AA modulation on Syt-7 expression depended on the abundance of 5-LO. For high 5-LO abundances,
12
increasing AA production attenuated Syt-7 expression, while decreasing AA production enhanced Syt-7
expression - effects opposite to those on PKA. For low 5-LO abundances, both over- and underproduc-
tion of AA resulted in a decrease in Syt-7 expression.
We can explain these results in terms of the proximal control points on PKA and Syt-7 encoded by
our model. The proximal determinant of Syt-7 expression in our model is NF-kB activity, therefore Syt-
7 suppression occurs exclusively via LXA4-mediated attenuation of NF-kB. The proximal determinant
of PKA activation is PGE2 abundance, therefore the attenuation of PKA activity due to 5-LO occurs via
5-LO competition for AA in addition to NF-kB attenuation. In this light, a perturbation that increased
both PGE2 and LXA4 abundance would indeed be expected to amplify PKA activation while attenuating
Syt-7 expression. The exception to this expectation - the simulated finding that the intermediate value
of AA production maximized Syt-7 expression only for low 5-LO abundances - is explained by the
more distal effect of increased PGE2 abundance on NF-kB amplification. The strength of this distal
PGE2 effect outweighs the more proximal LXA4 affect only at low 5-LO abundances, where LXA4
production is small.
4.5 Threshold Levels of LXA4 Production are Required for Necrosis and Apoptosis
We combined our models for inflammatory signaling and cell death to investigate the effects of PGE2
and LXA4 on apoptosis and necrosis. As above, we control LXA4 production by modulating abundances
of 5-LO. At low levels of LXA4 production, cells see little osmotic stress relative to baseline (Figure 13).
Beyond a critical value of 5-LO, cells see high levels of osmotic stress. The switch-like behavior of 5-
LO / LXA4 reflects the quantitative dynamics of the mechanisms we explored in section 4.3. Recalling
figure 7d, LXA4 suppresses PKA and Syt-7 to the critical point where MPT and membrane damage
cannot be suppressed, resulting in a sharp transition in phase space to necrosis.
We next investigated the impact of 5-LO / LXA4 signaling on the timing of apoptosis and necrosis.
In particular, we wanted to know whether necrosis could occur before or after apoptosis. This ordering
is significant, as apoptosis is both bactericidal and allows the dead cell to be consumed by adjacent
phagocytes. Apoptotic cells which subsequently lyse are said to undergo “secondary necrosis,” which is
thought to be the natural outcome for apoptotic cells that are not consumed by other cells.29 In the case
of Mtb infection, both primary and secondary necrosis may result in bacterial dissemination.
We also wanted to know how LXA4 might impact anti-apoptotic mediators induced by NF-kB, and
how perturbation of these pathways might alter the timing and balance of cell death. To determine
times of cell death, we defined species-based thresholds for both apoptosis and necrosis. Following the
convention of the EARM model, we say that apoptosis has occurred when over 50% of PARP has been
cleaved by activated caspase-3. Similarly, we say that necrosis occurs when the amount of intracellular
13
sodium - our necrosis model’s marker of osmotic stress - has exceeded 10 times its resting value.
We simulated the time to apoptosis and necrosis over a range of 5-LO abundances (Figure 14). For
this simulation, we also varied the rate constant controlling the magnitude of the NF-kB-mediated induc-
tion of Bcl-2 expression. Recall that Bcl-2 is an anti-apoptotic protein which prevents the oligomeriza-
tion of Bax at the mitochondrion. For every level of Bcl-2 induction, necrosis occurs at approximately
the same threshold abundance of 5-LO. Near this threshold, necrosis occurs after apoptosis; at higher
abundances of 5-LO, necrosis occurs before apoptosis. Furthermore, for higher levels of Bcl-2 induction
necrosis occurs at later time points at every abundance of 5-LO.
The timing of apoptosis is also dependent both on the strength of NF-kB-mediated Bcl-2 induction
and LXA4 production by 5-LO. In our simulations, apoptosis occurred at later time points at higher lev-
els of Bcl-2 induction as well as at lower abundances of 5-LO, reflecting the fact that LXA4 attenuated
Bcl-2 abundances downstream of NF-kB. In fact, at the highest level of Bcl-2 induction we tested, a
threshold abundance of 5-LO was required to achieve apoptosis in the 24-hour window of our simula-
tion. This threshold was much lower than that required to induce necrosis. This scenario represents an
elegant mechanism for apoptosis as an immune strategy of last resort. If a threshold LXA4 abundance
is required to induce apoptosis, then macrophages will only undergo programmed cell death in response
to pathogens that upregulate LXA4 and put the cell at risk for necrosis.
4.6 The Impact of Cytokines TNF and IL-10 on Cell Death
Finally, we used our model to investigate the impact of cytokines on cell death. We added a synthesis
reaction to our model to simulate TNF production by the inflammatory milieu, which is secreted by
adjacent cells and which acts on our simulated cell in a paracrine manner. This is in contrast to the TNF
which is produced by our simulated cell and acts in an autocrine manner. We also examined the effect of
the TNFR2 receptor which has been implicated in Mtb infection as a way for the pathogen to attenuate
TNF signaling. We investigated the effect of p50 overexpression and the consequent inhibition of NF-
kB activity by p50/p50 homodimers, a reported mechanism of IL-10 anti-inflammatory signaling.30 For
good measure, we simulated the effect of p50 underexpression as well.
In our model, the addition of paracrine TNF had little effect on NF-kB activation and Syt-7 expres-
sion (Figure 15). Paracrine TNF had a somewhat larger impact on PKA, signifying an amplification of
the TNF signal in the pathways linking NF-kB activation and PGE2 production. When we examined
the effect of exogenous TNF on cell death, we found that it increased the threshold 5-LO abundance
required to cause necrosis. This is likely a PKA-mediated effect. TNF did not change the 5-LO thresh-
old for apoptosis, but it reduced the time to achieve either mode of cell death at a given level of LXA4
production. The robust apoptotic threshold in this simulation is consistent with the aforementioned rela-
14
tionship between paracrine TNF and Syt-7: the apoptotic threshold in our model is determined by Bcl-2
induction, and both Bcl-2 and Syt-7 expression are directly downstream of NF-kB in our model. The
decreased time to apoptosis occurs downstream of increases in the abundance DISC. TNFR2 expression
had the opposite effects, including a very mild attenuation of Syt-7, a more appreciable attenuation of
PKA, a decrease in the 5-LO abundance required to cause necrosis and an increase in the time to achieve
necrosis.
There are two possible explanations for the simulated finding that NF-kB and its downstream gene
products are insensitive to modulations in TNF. The first lies with the model network, which includes
three different stimuli for NF-kB activation: TLR signaling, TNF signaling, and PGE2 / EP4 signaling.
In this context, NF-kB activation may be robust to changes in TNF in light of the other two parallel
pathways. The second explanation is that our model’s reaction rate parameters render NF-kB insensitive
to TNF perturbations even though the reaction network itself is capable of more sensitivity. Indeed, we
parameterized our model to maximize the sensitivity of PGE2-mediated NF-kB activation, which lies at
the heart of the reciprocal regulation of PGE2 and LXA4.
We next investigated the effect of p50 expression on cell death. Increasing the expression of p50
decreased expression of Syt-7 as well as activation of PKA. Accordingly, susceptibility to necrosis
was seen at lower abundances of 5-LO. Apoptosis was also observed at far low abundances of 5-LO.
Interestingly, underexpression of p50 also resulted in attenuation of PKA and Syt-7 and decreased 5-
LO thresholds for apoptosis and necrosis. These findings indicate that there is an optimal rate of p50
expression that maximizes NF-kB activity. Too little p50 synthesis decreases the quantity of active
p65 / p50 heterodimers, while too much p50 synthesis disproportionately increases the quantity of p50
homodimers that inhibits NF-kB signaling.
5 Discussion, Limitations, Conclusions, and Suggestions for Future Work
We built a mathematical model to study the cell signaling networks of apoptosis and necrosis in macrophages
infected with M. tuberculosis. The purpose of our model is to study the mechanisms proposed by the
experimental literature in silico, to elucidate quantitative relationships between key mediators, and to
generate testable hypotheses for future experiments.
To our knowledge, our model is the first to formulate a mechanism for necrosis caused by Mito-
chondrial Permeability Transition, which is important to many pathological processes. That mechanism
is based on the concept of osmotic stress, which is caused by the synergistic effects of ATP depletion
and membrane damage. Our model recapitulated the experimental observation that two different mech-
anisms downstream of Prostaglandin E2 prevent necrosis in Mtb infection: the EP2 / PKA pathway,
which prevents MPT, and the EP4 / Syt-7 pathway, which engages membrane repair. On further in-
15
vestigation, we found that Syt-7 acts as a switch between states of negligible membrane damage and
significant membrane damage. For every level of Syt-7 induction, there was a critical value of PKA at
which this switch point occurred. Very high abundances of PKA completely suppressed MPT and were
sufficient to prevent necrosis. However, for more moderate abundances of PKA, Syt-7-mediated mem-
brane repair determined whether a cell died by apoptosis or necrosis. We hypothesize that membrane
repair may act as a buffer against necrosis, preventing cell lysis even in the face of moderate amounts of
MPT.
We also modeled the cell signaling pathways that lead to the induction of Cox-2 / PGE2 signaling.
Our model reproduced the experimental observation that Cox-2 is induced in a positive feedback loop
that is generated by p38 MAPK and sustained by the PGE2 / EP4 / NF-kB pathway. Our model also
recapitulates the observation that LXA4 suppresses Cox-2 / PGE2 signaling. We showed that LXA4-
mediated attenuation of NF-kB was a plausible explanation for this observation. However, many gaps
in our knowledge remain. While many papers in the literature demonstrate that LXA4 attenuates NF-kB
signaling, our literature review did not a reveal a detailed pathway explaining how this occurs. Similarly,
while LXA4 production is a well-documented consequence of mycobacterial virulence, our literature
review did not reveal a pathway linking a virulence factor to LXA4 synthesis. Future work should
focus on elucidating these pathways. For the purposes of this model, we simulated LXA4 production in
virulent mycobacterial infections by over-expressing the 5-LO enzyme responsible for LXA4 synthesis.
When we combined our models for PGE2 production and cell death, we found that a threshold level
of 5-LO / LXA4 signaling was required to cause necrosis. Under certain conditions, a lower threshold
of 5LO / LXA4 signaling was also required to cause apoptosis by attenuating the NF-kB-mediated
upregulation of anti-apoptotic mediators such as Bcl-2. On its face, this result seems to be at odds with
the paradigm that casts PGE2 as a ”pro-apoptotic” mediator and LXA4 as a “pro-necrotic” mediator.2
In fact, in many other contexts PGE2 is described as an anti-apoptotic mediator, which is consistent
with our simulation.31 An LXA4 requirement for apoptosis also provides an elegant mechanism for
programmed cell death as an immune strategy of last resort. It ensures that macrophage only undergo
apoptosis in response to pathogens that pose a risk for necrosis.
Finally, we used our model to modulate TNF as well as p50 expression, the latter a hypothesized
mechanism of IL-10. We altered production of paracrine TNF - and of the TNF decoy receptor TNFR2
- to amplify or attenuate TNF signaling. We found that paracrine TNF had only a minor effect on
the upregulation of PKA and Syt-7. This is because TNF activation of NF-kB is redundant to TLR and
PGE2-mediated activation of NF-kB in our model. It is possible that our model undervalues the impact of
TNF relative to these parallel pathways. Paracrine TNF modestly increased the 5-LO / LXA4 threshold
required to induce necrosis. While TNF did not alter the LXA4 threshold required to induce apoptosis
16
in our model, it decreased the time to both apoptotic and necrotic cell death at every abundance of 5-LO.
It has been reported that virulent mycobacteria blunt TNF signaling by upregulating the production of
the inhibitory TNFR2 receptor. Predictably, the effects of TNFR2 expression were equal and opposite
those of paracrine TNF production: a mild attenuation of PKA and Syt-7 and a decrease in the threshold
5-LO / LXA4 required of necrosis, with a global increase in the time to both apoptotic and necrotic
cell death. Interestingly, both p50 over- and underexpression blunted NF-kB signaling and downstream
PKA / Syt-7 activity and decreased the 5-LO / LXA4 thresholds for both apoptosis and necrosis. This
finding suggests that there is an optimal ratio of p65 and p50 expression for NF-kB activity, and that
perturbation of this ratio in either direction attenuates NF-kB.
The chief limitation of our model is that our model predictions are only as accurate as its reaction
network, and the parameterization of that network by our choices for reaction rate constants and species
initial conditions. At many points in our reaction network the mechanisms proposed by the literature are
incomplete, which introduces the potential for error in our simulations. A second source of error is the
possibility that other pathways, not considered by our model, critically alter the dynamics of our reaction
network. Failure to account for such pathways would affect the accuracy of our predictions. Finally,
even if our reaction network is a reasonable model for our biological system in question. our model’s
reaction rate parameters must reasonably approximate the kinetics of binding, catalysis, synthesis, and
degradation of the species in our network. Large errors in these parameters also affect the accuracy
of our predictions. A potential example of this source of error can be found in section 4.6, where we
discuss how NF-kB activation in our model is relatively insensitive to TNF modulations, contrary to our
expectations based on our literature review and our model’s reaction network.
Despite these limitations, our model reproduces several key findings of the experimental literature,
and proposes new hypotheses which can be evaluated by future experimental work. We propose os-
motic stress as a mechanism of necrosis downstream of MPT; future experiments should evaluate its
validity. We show how Syt-7-mediated membrane repair may act as a buffer against necrosis, allowing
cells to tolerate some degree of MPT below a critical point where cell fate abruptly switches to necro-
sis. Future experiments should further investigate the synergistic relationship between PKA-mediated
suppression of MPT and membrane repair. Our model also shows that LXA4-mediated suppression of
NF-kB is a plausible mechanism for the suppression of Cox-2 / PGE2 anti-necrotic signaling. How-
ever, the mechanisms linking LXA4 to NF-kB inhibition - and those linking bacterial virulence factors
to LXA4 upregulation - remain obscure. Future work should seek to better understand these pathways
in order to build a more comprehensive model of cell death. We propose the novel hypothesis that, in
addition to causing necrosis, LXA4 may also be required to cause apoptosis via parallel inhibition of
NF-kB-mediated, anti-apoptotic signaling. Future experiments should address this question. Finally, fu-
17
ture work should address the impact of cytokines including TNF and IL-10 on cell death. In particular,
the importance of TNF on NF-kB activation should be further characterized relative to parallel pathways
that activate this central transcription factor during Mtb infection.
We conclude by proposing three specific experiments to test some of the simulated results of our
model. A core hypothesis of our model is that crosstalk between Cox-2 signaling and NF-KB signaling
accounts for the differences in PGE2 and LXA4 observed in virulent vs. avirulent mycobacterial in-
fection. One might test this hypothesis by measuring abundances of PGE2, LXA4, and nuclear NF-kB
in in vitro infections of THP-1 macrophages with the virulent Mtb auxotrophe compared to the aviru-
lent Bacille Calmette-Guérin (BCG). Based on modeling results, we would expect BCG infection to be
associated with high abundance of NF-kB and PGE2 and low abundance of LXA4, while auxotrophe in-
fection should be associated with high LXA4 and low NF-kB / PGE2. One might further test the nature
of NF-kB and eicosanoid crosstalk by modulating both pathways to look for expected perturbations in
their counterpart. Aspirin is an anti-inflammatory drug that acetylates Cox-2, causing it to cease PGE2
production and initiate production of an analog of LXA4.32 Adding purified aspirin to BCG-infected
macrophages should, according to our simulation, decrease PGE2 abundances as well as NF-kB activa-
tion. Conversely, we would expect an experimental perturbation that enhanced NF-kB activation - such
as the addition of an inhibitors of IkB or A20 - to also increase the PGE2 / LXA4 ratio in macrophages
infection with Mtb auxotrophe.
A second finding from our model simulations is that some amount of LXA4 may be required to
attenuate anti-apoptotic NF-kB signaling in order for apoptosis to occur. This hypothesis may be eval-
uated by comparing levels of apoptosis in 5-LO-deficient macrophages vs. wild-type macrophages in
in vitro infections with both virulent and avirulent mycobacteria. Based on our model simulations we
would expect a greater portion 5-LO deficient macrophages to remain viable compared to wild-type. A
second method of evaluating this hypothesis is via the aspirin model described above. We would expect
more apoptosis as well as necrosis to occur when aspirin is added to in vitro macrophage infections with
mycobacteria.
A third interesting finding from our model simulations is that there may be an optimal level of p50
expression that maximizes NF-kB activation. Recall that both over- and underexpression of p50 leads to
decreased levels of NF-kB signaling, the former causing an excess of inhibitory p50/p50 homodimers,
the latter causing a deficit of active p65/p50 heterodimers. This hypothesis could be tested by modulating
p50 production using siRNA and observing the effect on targets of NF-kB gene transcription.
18
6 Acknowledgements and References
We are grateful to Alex Histed, Trever Smith, and Anne Jenney for help with the in vitro experiments
that will accompany this project, and to Amy Thurber and William Chen for helpful discussions.
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7 Figures
7.1 Model Diagrams and Illustrations
k
←−fE + S → kE : S −−c→ E + P
kr
d[E]
= −kf [E][S] + (kr + kc)[E : S]
dt
d[S]
= −kf [E][S] + kr[E : S]
dt
d[E : S]
= kf [E][S]− (kr + kc)[E : S]
dt
d[P ]
= kc[E : S]
dt
Figure 1: An Example of Mass Action Kinetics. Shown above is a simple mass-action model for
the enzymatic conversion of a substrate S to product P. kf , kr, kc are rate constants for the binding and
catalytic activity of the enzyme E.
Figure 2: A Diagram for EARM, a Published Model for Mitochondrial Apoptosis. Death ligands
e.g. TNF lead to the formation of the the Death Induced Signaling Complex (DISC), which triggers the
apoptosis pathway. EARM encodes negative regulators of apoptosis including FLIP, Bcl-2, and XIAP.
23
Figure 3: A Diagram for Mitochondria-ER Crosstalk During Cell Death. To trigger MPT, our
model encodes a well-described mechanism in which cytochrome C released during MOMP activates
IP3 receptors, causing release of ER calcium stores into the cytosol. In the absence of PGE2-mediated
protection, calcium influx into susceptible mitochondria causes MPT.
Figure 4: A Diagram for our Necrosis Model. MPT causes uncoupling of the electron transport chain
and the cessation of ATP production. ATP is required to maintain cellular ion gradients. With ATP
depletion, cell swelling and lysis occurs secondary to increases in intracellular sodium. Membrane
damage downstream of MPT accelerates this process. PGE2-dependent mechanisms protect against
necrosis: PKA prevents MPT, while Syt-7 trafficks lysosomes to the cell membrane to repair damage.
24
Figure 5: A Diagram for our Model of NF-kB Signaling. A: Active NF-kB is a dimer of p65 and p50 subunits.
p50 is cleaved from an inactive precursor. A byproduct of this cleavage, p105, acts to sequester p65 (note:
controversy exists in the literature as to whether p105 itself is the inactive precursor or its cleaved product.) p50
can also homodimerize and competitively inhibit NF-kB binding to target genes. B: At rest, NF-kB is sequestered
in the cytoplasm by the “inhibitor of kB” (IkB). IkB Kinase (IKK) phosphorylates and degrades IkB and p105,
freeing NF-kB to translocate to the nucleus. MAPK phosphorylation of p65 further increases its transcriptional
activity. C: NF-kB autoregulates its activity by inducing IkB as well as A20, which inhibits IKK.
Figure 6: A Diagram for our Model of Eicosanoid Signaling. NF-kB and MAPK are activated first by Toll-
Like Receptors. Targets of NF-kB that we model include: TNF, a cytokine that activates NF-kB / MAPK as well
as cell death cascades; Cox-2, which synthesizes PGE2, and Syt-7, important for membrane repair. MAPK also
induces Cox-2 by stabilizing its mRNA. Cox-2 synthesizes PGE2 from AA, which amplifies its own induction by
further activation of NF-kB. 5-LO competes with Cox-2 for AA substrate to produce LXA4. which suppresses
Cox-2 / PGE2 induction via attenuation of NF-kB.
25
7.2 Model Simulations
In Figure 7 below we show key simulations of our model for necrosis. In plots (a) and (c) we modulate
mitochondrial permeability transition (MPT) by varying the level of ER calcium stores. In plots (b)
and (d) we fix ER calcium stores and modulate PKA abundances to inhibit MPT. In (c), we see that
ATP depletion alone is sufficient to cause osmotic stress at high levels of MPT, whereas the addition
of membrane damage allows osmotic stress to occur at moderate levels of MPT. In (d), we see that for
every Syt-7 abundance there is a critical value of PKA where cells undergo a “switch” between states of
negligible and significant osmotic stress.
(a) (b)
(c) (d)
Figure 7: Simulations of our Model for Necrosis. (a-b) Response curves showing the percentage of
mitochondrial permeability transition (%MPT) as a function of mitochondrial calcium ion concentration
(a) and PKA abundance (b). (c) Response curves showing fold increases in intracellular sodium ions (a
marker for osmotic stress) as a function of MPT, for various levels of plasma membrane damage. (d)
Response curves showing fold increases in intracellular sodium ions as a function of PKA abundance,
for various levels of Syt-7 abundance.
26
Figure 8: Syt-7 Abundance Determines the Mode of Cell Death at Moderate Abundances of PKA.
Dashed curves plot fold changes of intracellular sodium as a function of PKA abundance in the presence
(+) and absence (x) of membrane damage. The horizontal line shows an osmotic stress threshold for
necrosis. Colored boxes show regions of PKA phase space where cell death occurs via necrosis (red),
apoptosis (green), or either apoptosis / necrosis depending on Syt-7 abundance (yellow).
(a) (b)
Figure 9: Optimal Induction of Cox-2 Requires Both p38 and EP4 Signaling. Response curves
showing Cox-2 abundance as a function of (a) p38 MAPK activity and (b) EP4 activity.
27
As a proxy for Mtb virulence, we scanned abundances of 5-lipoxygenase (5-LO) to modulate the rate
of LXA4 production. High 5-LO abundances suppress Cox-2 induction via NF-kB attenuation. At
lower-abundances of 5-LO, Cox-2 is induced and suppresses LXA4 via PGE2 (see below).
(a) (b)
(c)
Figure 10: Reciprocal Regulation of PGE2 and LXA4 Occurs via NF-kB in our Model for
Eicosanoid Signaling. (a-c) Time courses for the induction of (a) LXA4, (b) PGE2, and (c) NF-kB
for various abundances of 5-LO.
28
Our model encodes two different mechanisms of 5-LO mediated attenuation of PGE2: LXA4 attenuation
of NF-kB, and competition between 5-LO and Cox-2 for arachidonic acid (AA) substrate. The latter
mechanism accounts for the difference in the response curves of PGE2 and NF-kB to scanned 5-LO
abundances shown in Figure 11 below. We further explored these two mechanisms by altering the rate
of AA production. We hypothesize that decreased AA production enhances the effects of competition
for AA substrate relative to the effects of NF-kB attenuation. In Figure 12 on the next page we found that
modulating AA production had opposite effects on the two main determinants of cell death. Increasing
AA production resulted in increased PGE2 and LXA4 abundance. In this setting, PKA activation was
enhanced while Syt-7 expression was attenuated.
Figure 11: LXA4 Attenuates Important Determinants of Cell Death. Response curves for the abun-
dances of nuclear NF-kB, TNF, Cox-2, Syt-7, PGE2, activated PKA, and DISC are shown as a function
of 5-LO abundance. Quantities for each species have been normalized to those of simulated 5-LO-
deficient cells.
29
(a) (b)
(c) (d)
Figure 12: Altering AA Abundance Results in Different Effects on PKA and Syt-7 Abundances.
(a-d) Response curves showing (a) PGE2, (b) LXA4, (c) PKA, and (d) Syt-7 abundances as a function
of 5-LO abundance for three different rates of arachidonic acid production (default rate in the model is
0.01 copies / s, green curves).
30
Our model simulations showed that a threshold level of 5-LO abundance / LXA4 production was re-
quired to generate a sufficient osmotic stress to cause necrotic cell death (Figure 13). We also found that
for high levels of NF-kB mediated induction of the anti-apoptotic mediator Bcl-2, a threshold abundance
of LXA4 was required to cause apoptosis (Figure 14).
Figure 13: Susceptibility to Necrosis Occurs Beyond a Threshold Value of LXA4 Production. Fold
change in intracellular sodium, a marker of osmotic stress, is plotted as a function of 5-LO abundance.
Figure 14: LXA4 May Be Required for Apoptosis as well as Necrosis. Response curves are shown for
the time of apoptotic (dashed lines) and necrotic cell death (solid lines) as a function of 5-LO abundance,
for three different levels of NF-kB-mediated Bcl-2 induction.
31
(a) (b)
(c)
Figure 15: Effects of TNF Perturbations on Cell Death. (a-b) Response curves for (a) PKA and
(b) Syt-7 abundances as a function of 5-LO abundance, for the cases of autocrine TNF signaling only
(blue curve - baseline model), autocrine + paracrine TNF signaling (green curve), and autocrine + TNF
inhibition by decoy TNFR2 receptors (red curve). (c) Curves showing the time to apoptotic (dashed
lines) and necrotic cell death (solid lines) as a function of 5-LO abundance, for cases of autocrine TNF
signaling only (blue curves - baseline model), autocrine + paracrine TNF signaling (green curves), and
autocrine + TNF inhibition by decoy TNFR2 receptors (red curves).
32
(a) (b)
(c)
Figure 16: Effects of p50 Over / Underexpression on Cell Death. (a-b) Response curves for (a) PKA
and (b) Syt-7 abundances as a function of 5-LO abundance, for three different levels of p50 expression.
(c) Curves showing the time to apoptotic (dashed lines) and necrotic cell death (solid lines) as a function
of 5-LO abundance, for three different levels of p50 expression.
33
8 Appendix: Reaction Lists
8.1 Conventions
For each module of our model we provide a list of reactions, along with corresponding rate parameters,
and a list of initial conditions. Initial conditions are expressed in units of copies. Rate parameters
are expressed in units of seconds−1 if there is one reactant, and (copies x seconds)−1 if there are two
reactants. We name our rate parameters with alphanumeric subscripts denoting the number and type of
the reaction to which the parameters apply. Examples are shown below.
Reaction Description Example Parameter(s)
Reversible Reactions E + S←−→ E : S, S1 ←−→ S2 kf , kr
Catalysis E : S −−→ E + P kc
Synthesis E −−→ E + P, 0 −−→ P ks
Degradation E : S −−→ E, S −−→ ∅ kd
Note that in synthesis and degradation reactions, the species responsible for the synthesis or degradation
of their substrate may be explicitly modeled or omitted. We also count as “degradation” reactions those
that return activated species to their nascent state, e.g. the de-phosporylation of a phosphorylation or
the de-activation of a receptor. A:B denotes species A bound to species B. When a reaction involves
a species that may occur in more than one state (e.g. bound / unbound, phosphorylated / unphospho-
rylated), we use the symbol A∗ to denote a “wildcard” of species A, and specify the applicable states
below the reaction. For example, the phosphorylation of IkB by phospho-IKK is shown below; IkB
may be unbound or bound to NF-kB:
IKKp + IkB∗ ←−→ IKKp:IkB∗ −−→ IKKp + IkBp∗
IkB∗ = IkB, IkB:NFkB
IkBp∗ = IkBp, IkBp:NFkB
34
8.2 Choosing Model Parameters
Here we discuss the rationale behind our choices for the model parameters presented in the following
sections.
The backbone of our model for apoptosis is EARM (section 8.3), and most rate constants and initial
conditions in this section are identical to the published version of EARM 1.3.11. We decreased the
affinity of DISC for caspase-8 (kf,3) by an order of magnitude to account for the fact that our model
produces more DISC than the stimulus in EARM. We also made the caspase cleavage reactions in EARM
ATP-dependent, to simulate the impact of mitochondrial dysfunction on the kinetics of the apoptotic
cascade. To do this we added an ATP / ADP exchange to the catalytic step of these reactions (see
reaction 9). We modified the rate constants for these reaction steps such that they recapitulate EARM
kinetics at baseline ATP levels, with ATP depletion causing a proportional decrease in catalysis rates.
For the remaining reactions in the model, we had no direct precedent to guide the choice of rate
constants. For each type of reaction (e.g. forward binding, reverse binding, catalysis), we chose values
for rate constants that closely resembled the parameters for similar reactions found in EARM. We also
drew inspiration from a published model for MAPK cascades for the many kinase reactions in our
model.33 Stratified by reaction type, most of these choices fell within a 100-fold range. Below we list
these ranges, as well as “default” values specifying the most commonly chosen parameter value by
reaction type. In the process of building the model, we started with the default values and tweaked
parameters as needed to recapitulate observations in the experimental literature.
Parameter type Range Default
Forward binding (Copies / s) 10−7 − 10−5 10−6
Reverse binding (enzyme) (1/s) 10−3 − 10−1 10−1
Reverse binding (1/s) 10−3 − 10−1 10−3
Enzymatic catalysis (1/s) 10−1 − 101 10−1
Note that we divide reverse binding rate parameters into two classes above. The first is specific
to the binding step in two-step catalytic reactions (e.g. E + S←−→ E:S −−→ E + P). One class of
parameters whose values differ substantially from that of EARM 1.3 are degradation parameters, which
are generally on the order of 10−3 s−1, whereas the default degradation rate in EARM 1.3 is 2.9 ∗ 10−6
s−1. This change was made so that the reactions in the gene transcription module (section 8.5) would
mimic the gene expression kinetics of D2FC, the published model for NF-kB signaling.19 Similarly,
for the reactions involving regulation of NF-kB by IkB and A20 in sections 8.3, 8.4, and 8.5, we chose
rate parameters that recapitulated the oscillatory dynamics of NF-kB activation observed in D2FC. We
35
should note that it is hard to compare NF-kB time courses between our model and D2FC given the
positive feedback loops in our model between NF-kB and autocrine TNF signaling, and NF-kB and
Cox-2 induction, which are not encoded in D2FC. Therefore, in the process of choosing rate parameters
for these reactions we silenced these feedback loops and modulated TNF levels, similar to the stimuli
used in D2FC (simulations not shown).
Finally, the majority of our model’s initial conditions (ICs) for species fall between 104−106 copies.
This is consistent with both EARM and D2FC. For the initial conditions of small molecules and ions we
used a search engine for biological numbers to look up reasonable values.34 Here we found references
for the abundance of ATP35, ADP:ATP ratios in viable, apoptotic and necrotic cells36, and ratios of
intracellular to extracellular sodium.37 The default abundance of ER calcium in our model we deter-
mined by scanning over several orders of magnitude, to find a level that would cause significant MPT,
as discussed in section 4.3.
36
8.3 EARM Apoptosis
This module can be simulated as a standalone model, with the necrosis module (8.4), or with all of the
modules in this appendix. In the last case, omit reaction 1 and change the I.C. for Bcl2 to 10000.
8.3.1 Initial Conditions
Species I.C. Species I.C. Species I.C. Species I.C.
L 4 ∗ 104 R 104 FLIP 2000 C8 10
4
BAR 1000 C 104 C 104 PARP 1063 6
Bcl2 3 ∗ 10
4 Mcl 2 ∗ 104 Bid 6 ∗ 104 Bax 8 ∗ 104
MOM 5 ∗ 105 mCytoC 5 ∗ 105 Apaf 105 C 59 10
mSmac 105 XIAP 105 ATP 108 ADP 5 ∗ 106
8.3.2 Reaction List
1. L + R←−→ L:R −−→ DISC k −7 −1 −1f,1 = 10 , kr,1 = 10 , kr,1 = 10
2. FLIP + DISC←−→ FLIP:DISC k = 10−6f,2 , k −3r,2 = 10
3. DISC + C8 ←−→ DISC:C8 −−→ DISC + C k = 10
−8
8A f,3 , k
−3 −5
r,3 = 10 , kr,3 = 10
4. C8A +BAR←−→ C8A:BAR k = 10
−6
f,4 , k
−3
r,4 = 10
5 C8A +C3 ←−→ C8A:C3 kf,5 = 10
−7, k −3r,5 = 10
C8A:C3 +ATP −−→ C8A +C3A +ADP kc,5 = 10
−8
6 C + C ←−→ C :C k = 10−73A 6 3A 6 f,6 , kr,6 = 10
−3
C3A:C6 +ATP −−→ C3A +C6A +ADP kc,6 = 10
−8
7 C6A +C8 ←−→ C6A:C8 kf,7 = 10
−7, k −3r,7 = 10
C6A:C8 +ATP −−→ C6A +C8A +ADP k
−8
c,7 = 10
8. XIAP + C3A ←−→ XIAP:C3A −−→ XIAP + C
−6
3i kf,8 = 2 ∗ 10 , kr,8 = 10
−3, kr,8 = 10
−1
9 C8A +Bid←−→ C8A:Bid k
−7 −3
f,9 = 10 , kr,9 = 10
C8A:Bid + ATP −−→ C8A + tBid + ADP kc,9 = 10
−8
10. Mcl + tBid←−→ Mcl:tBid kf,10 = 10−6, k −3r,10 = 10
11. tBid + Bax←−→ tBid:Bax −−→ tBid + Bax −7 −3A kf,11 = 10 , kr,11 = 10 , kr,11 = 1
37
12. BaxA ←−→ BaxM kf,12 = 1, kr,12 = 0.01
13. BaxM ←−→ Bax2 k
−4
f,13 = 2 ∗ 10 , kr,13 = 10−3
14. Bax2 ←−→ Bax4 kf,14 = 2 ∗ 10
−4, k −3r,14 = 10
15. Bcl2 + Bax∗ ←−→ Bcl2:Bax∗ k = 10−4f,15 , kr,15 = 10−3
Bax∗ = Bax,Bax2,Bax4
16. Bax4 +MOM←−→ Bax4:MOM −−→ MOMP k = 10
−4
f,16 , k
−3
r,16 = 10 , kr,16 = 1
17. MOMP+mCytoC←−→ MOMP:mCytoC k −8 −3f,17 = 5 ∗ 10 , kr,17 = 10
MOMP:mCytoC −−→ MOMP+ aCytoC kc,17 = 10
18. aCytoC +mSmac←−→ aCytoC:mSmac k −6 −3f,18 = 2 ∗ 10 , kr,18 = 10
aCytoC:mSmac −−→ aCytoC + aSmac kc,18 = 10
19. aCytoC←−→ cCytoC kf,19 = 1, kr,19 = 0.01
20. cCytoC + Apaf ←−→ cCytoC:Apaf k −7f,22 = 5 ∗ 10 , kr,22 = 10−3
cCytoC:Apaf −−→ cCytoC + ApafA kc,22 = 1
21. Apaf + C ←−→ Apop k = 5 ∗ 10−8 −3A 9 f,21 , kr,21 = 10
22 Apop + C3 ←−→ Apop:C3 kf,22 = 5 ∗ 10
−9, k −3r,22 = 10
Apop:C3 +ATP −−→ Apop + C3A +ADP kc,22 = 10
−8
23. aSmac←−→ cSmac kf,23 = 1, kr,23 = 0.01
24. XIAP + Apop←−→ XIAP:Apop k −6f,24 = 2 ∗ 10 , kr,24 = 10−3
25. XIAP + cSmac←−→ XIAP:cSmac k = 7 ∗ 10−6f,25 , k −3r,25 = 10
Additionally, most species in this module are degraded at a rate of 2.9 ∗ 10−6s−1. Exceptions are as
follows: PARP, cPARP,C3A:PARP (kd = 0), L,R,DISC,FLIP,FLIP:DISC (kd = 10
−3), and
ATP,ADP (see the next section). For species with initial conditions, we also create synthesis reactions
with rate ks = kd ∗ IC.
38
8.4 Necrosis
This module is an extension of EARM for necrosis pathways.
8.4.1 Initial Conditions
Species I.C. Species I.C. Species I.C. Species I.C.
PKAA scanned Syt7 scanned Ca 7 ∗ 10
6 MIM 104E
Na 107E NaPump 10
6 Mem 107 IP 53R 10
8.4.2 Reaction List
26. cCytoC + IP3R←−→ cCytoC:IP3R k
−6
f,26 = 10 , kr,26 = 0.01
cCytoC:IP3R −−→ cCytoC + IP3RA kc,26 = 1
27. IP3R
−3
A +CaE −−→ IP3RA +CaI kc,27 = 10
28. CaI ←−→ CaM kf,28 = 0.01, kr,28 = 0.01
29. IP3RA −−→ IP3R kd,29 = 10
−3
30. CaI −−→ CaE kd,30 = 10
31. CaM +MIM←−→ CaM:MIM kf,31 = 10
−7, kr,31 = 0.01
CaM:MIM −−→ CaM +MIMP kc,31 = 0.1
32. MIMP −−→ MIM kd,32 = 0.01
33. PKAA +MIM←−→ PKAA:MIM kf,33 = 2 ∗ 10
−5, kr,33 = 0.1
PKAA:MIM −−→ PKAA +MIMp kc,33 = 0.1
34. MIMp −−→ MIM k −3d,34 = 10
35. MIM∗ +ADP −−→ MIM∗ +ATP k = 104c,35
MIM∗ = MIM,MIMp
36. MIMP+ATP −−→ MIMP+ADP k 4c,36 = 10
37. MIMP −−→ MIMP+ROS ks,37 = 0.1
38. ROS −−→ ∅ kd,38 = 1
39. ATP −−→ ADP kd,39 = 4 ∗ 105
40. ROS +Mem←−→ ROS:Mem −−→ ROS +MemD kf,40 = 10
−7, kr,40 = 0.1, kr,40 = 1
39
41. CaI + Syt7←−→ Syt7
−6
A kf,41 = 10 , kr,41 = 10
−3
42. Syt7A −−→ Syt7A +MemL ks,42 = 0.05
43. MemL −−→ ∅ k
−6
d,43 = 10
44. MemL +MemD −−→ Mem k = 10
−4
c,44
45. NaE −−→ NaI kc,45 = 0.01
46. Mem +Na ←−→ Mem :Na −−→ Mem +Na k = 10−6D E D E D I f,46 , kr,46 = 0.1, kr,46 = 10
47 NaPump + NaI ←−→ NaPump:Na k = 10
−5
I f,47 , kr,47 = 0.1
NaPump:NaI +ATP −−→ NaPump + NaE +ADP k
−8
c,47 = 10
40
8.5 Gene Expression
For the lists below, let X∗ denote any member of the set {IkB,A20,TNF,COX, Syt7,Bcl2}. Likewise
let X∗∗ denote any of {TNF,COX, Syt7}. Let NFkB∗ denote any of {p65n:p50n, p65np:p50n}, and let
NFkB∗∗ denote any of {p65n:p50n, p65np:p50n, p50n:p50n}. We define dX to be the gene for species
X, and tX the mRNA.
8.5.1 Initial Conditions
Species I.C. Species I.C.
Pol 2 ∗ 105 dX∗ 2
8.5.2 Reaction List
48. NFkB∗ + dIkB←−→ NFkB∗:dIkB kf,48 = 3.69 ∗ 10−6, kr,48 = 0.3
49. NFkB∗∗ + dA20←−→ NFkB∗∗:dA20 kf,49 = 3.69 ∗ 10−6, kr,49 = 0.3
50. NFkB∗∗ + dX∗∗ ←−→ NFkB∗∗:dX∗∗ k −7f,50 = 8 ∗ 10 , kr,50 = 0.3
51. NFkB∗∗ + dBcl2←−→ NFkB∗∗:dBcl2 k = 8 ∗ 10−7f,51 , kr,51 = 0.3
52. Pol + NFkB∗:dIkB←−→ Pol:NFkB∗:dIkB kf,52 = 1.575 ∗ 10−6, kr,52 = 0.3
53. Pol + NFkB∗:dA20 ←−→ Pol:NFkB
∗:dA −520 kf,53 = 3 ∗ 10 , kr,53 = 0.3
54. Pol + p65 ∗∗ ∗∗n:p50n:dX ←−→ Pol:p65n:p50n:dX kf,54 = 4.8 ∗ 10−8, kr,54 = 0.3
55. Pol + p65np:p50n:dX
∗∗ ←−→ Pol:p65np:p50n:dX∗∗ kf,55 = 4.8 ∗ 10−6, kr,55 = 0.3
56. Pol + p65n:p50n:dBcl2←−→ Pol:p65n:p50 :dBcl2 k = 1 ∗ 10−8n f,56 , kr,56 = 0.3
57. Pol + p65np:p50n:dBcl2←−→ Pol:p65np:p50n:dBcl2 k −6f,57 = 5 ∗ 10 , kr,57 = 0.3
58. Pol:dX∗ −−→ Pol + dX∗X∗ kc,58 = 0.3
59. PolX∗ −−→ Pol + tX
∗ kc,59 = 0.3
60. tX∗ −−→ tX∗ +X∗ ks,60 = 1.5
61. 0 −−→ Bcl2 ks,61 = 1
The degradation rates for inducible gene products of NF-kB and their mRNA are as follows: tIkB :
kd = 9 ∗ 10−4; IkB : kd = 9 ∗ 10−4; tA20 : k −3d = 3 ∗ 10 ; A20 : k = 9 ∗ 10−4d ; tTNF : kd = 10−3;
TNF : k = 10−3d ; tCOX : k = 10−2; COX : k = 10−2d d ; tSyt7 : kd = 5 ∗ 10−3; Syt7 : k = 10−3d ,
tBcl2 : kd = 10
−3; Bcl2 : kd = 10−4
41
8.6 NF-kB module
This section details binding interactions among NF-kB subunits p65 and p50, as well as the inhibitors
IkB and p105. For details of IKK-mediated degradation of IkB and activation of NF-kB signaling, see
the next section.
8.6.1 Initial Conditions
We obtained the following initial conditions by silencing any source of IKK activation and letting the
module achieve a steady state. Before interrogating the full model we recommend performing this
stabilization step, especially if one alters any parameters of this module. Prior to stabilization, all initial
conditions listed below were set to 0.
Species I.C. Species I.C. Species I.C. Species I.C.
p65 8800 p50 1500 p105 6500 p65:p105 43600
p65:p50 4400 p65n:p50n 14400 p50:p50 800 p50:p50n 1600
p65n 35000 p50n 500 IkB 14400 IkBn 1700
IkB:p65:p50 43000 IkBn:p65n:p50n 900 tIkB 37 p50P 50000
8.6.2 Reaction List
62. p50P −−→ p50 + p105 kc,62 = 9 ∗ 10
−4
63. p65 + p105←−→ p65:p105 kf,63 = 3 ∗ 10−6, k = 3 ∗ 10−3r,63
64. p65 + p50←−→ p65:p50 kf,64 = 3 ∗ 10−6, k −3r,64 = 3 ∗ 10
65. p65 −6 −3n + p50n ←−→ p65n:p50n kf,65 = 3 ∗ 10 , kr,65 = 3 ∗ 10
66. p50 + p50←−→ p50:p50 kf,66 = 3 ∗ 10−6, k = 3 ∗ 10−3r,66
67. p50n + p50n ←−→ p50n:p50n kf,67 = 3 ∗ 10−6, kr,67 = 3 ∗ 10−3
68. X∗ ←−→ X∗n kf,68 = 7.8 ∗ 10−3, kr,68 = 1.56 ∗ 10−3
X∗ = p65, p50, p65:p50, p50:p50
69. IkB←−→ IkBn kf,69 = 2 ∗ 10−3, k −3r,69 = 10
42
70. IkB + p65:p50←−→ IkB:p65:p50 kf,70 = 1.2 ∗ 10−6, kr,70 = 1.5 ∗ 10−3
71. IkBn + p65n:p50n ←−→ IkBn:p65n:p50n kf,71 = 1.2 ∗ 10−6, kr,71 = 1.5 ∗ 10−3
72. IkBn:p65n:p50n −−→ IkB:p65:p50 kc,72 = 0.03
The following species are degraded at a rate of 9 ∗ 10−4s−1: p65, p50, p105, p65:p105, p65:p50,
p50:p50, IkB, IkB:p65:p50. Additionally, p65 is synthesized at a rate of 90 copies / s, and p50P is
synthesized at a rate of 45 copies / s (this value is modulated in section 4.6).
8.7 Inflammatory Cell Signaling
This module encompasses NF-kB activation, TNF signaling, and eicosanoid signaling. Note that for
reaction 92, kf,92 is not truly a rate constant but instead a function of LXA4. We define that function to
be
1
f(LXA4) = 3 ∗ 106 + 103 ∗ [LXA4]
8.7.1 Initial Conditions
As in section 8.6, we obtain the following four initial conditions by silencing IKK activation and letting
the NF-kB module achieve a steady state. Prior to stabilization the initial condition for IKK was set to
105 copies.
Species I.C. Species I.C. Species I.C. Species I.C.
tA20 27 A20 80 IKK 55200 A20 :IKK 44700
The remaining initial conditions are as follows:
Species I.C. Species I.C. Species I.C. Species I.C.
TB 1 TLR 104 TAK 106 p38 106
TNFR 104 MSK1 104 MKP 107 PLA 1052
5LO scanned EP2 104 EP4 104 PKA 105
AKT 105
43
8.7.2 Reaction List
73. TB −−→ TB+ PAMP ks,73 = 100
74. PAMP −−→ ∅ k −3d,74 = 10
75. PAMP+TLR←−→ PAMP:TLR −−→ TLR k = 10−6A f,75 , kr,75 = 0.1, kr,75 = 0.1
76. TLR −−→ TLR k = 10−3A d,76
77. TLRA +TAK←−→ TLRA:TAK k
−7
f,77 = 10 , kr,77 = 0.1
TLRA:TAK −−→ TLRA +TAKp kc,77 = 0.1
78. 0 −−→ TNFR ks,78 = 10
79. TNFR −−→ ∅ k −3d,79 = 10
80. TNF + TNFR←−→ TNF:TNFR −−→ TNFRA k = 10
−7
f,80 , kr,80 = 0.1, kr,80 = 0.1
81. TNFRA +TAK←−→ TNFRA:TAK k
−7
f,81 = 10 , kr,81 = 0.1
TNFRA:TAK −−→ TNFRA +TAKp kc,81 = 0.1
82. TNFRA −−→ DISC k = 10
−3
c,82
83. DISC −−→ ∅ k −3d,83 = 10
84. TAKp + IKK←−→ TAKp:IKK kf,84 = 3 ∗ 10−6, kr,84 = 0.3
TAKp:IKK −−→ TAKp + IKKp kc,84 = 0.3
85. A20 + IKK←−→ A20:IKK kf,85 = 3 ∗ 10−4, kr,85 = 0.03
86. 0 −−→ IKK ks,86 = 90
83. IKK∗ −−→ ∅ k −4d,83 = 9 ∗ 10
IKK∗ = IKK, IKKp,A20 :IKK
87. TAKp + p38←−→ TAKp:p38 kf,87 = 10−7, kr,87 = 0.3
TAKp:p38 −−→ TAKp + p38p kc,87 = 0.3
88. p38p +MSK1←−→ p38p:MSK1 k −6f,88 = 3 ∗ 10 , kr,88 = 0.3
p38p:MSK1 −−→ p38p +MSK1p kc,88 = 0.3
89. MKP+TAKp ←−→ MKP:TAK −6p kf,89 = 10 , kr,89 = 0.1
MKP:TAKp −−→ MKP+TAK k −3c,89 = 3 ∗ 10
90. MKP+ p38p ←−→ MKP:p38p kf,90 = 3 ∗ 10−6, kr,90 = 0.3
MKP:p38p −−→ MKP+ p38 kc,90 = 9 ∗ 10−3
44
91. MKP+MSK1p ←−→ MKP:MSK1p kf,91 = 3 ∗ 10−6, kr,91 = 0.3
MKP:MSK1p −−→ MKP+MSK1 k = 9 ∗ 10−3c,91
92. IKKp + IkB
∗ ←−→ IKKp:IkB∗ kf,92 = f(LXA4), kr,92 = 0.3
IKKp:IkB
∗ −−→ IKKp + IkB∗p kc,92 = 0.3
IkB∗ = IkB, IkB:p65:p50
93. IKKp + p105
∗ ←−→ IKK :p105∗p kf,93 = 3 ∗ 10−6, kr,93 = 0.3
IKKp:p105
∗ −−→ IKK ∗p + p105p kc,93 = 0.3
p105∗ = p105, p105 :p65
94. IkBp −−→ ∅ kd,94 = 0.3
95. p105p −−→ ∅ kd,95 = 0.3
96. IkBp:p65 :p50 −−→ p65 :p50 kd,96 = 0.3
97. p105p:p65 −−→ p65 kd,97 = 0.3
98. MSK1p ←−→ MSK1n kf,98 = 0.1, kr,98 = 10−3
99. MSK1n + p65
∗
n ←−→ MSK1 :p65 ∗n n kf,99 = 3 ∗ 10−5, kr,99 = 0.3
MSK1n:p65
∗
n −−→ MSK1n + p65 ∗np kc,99 = 0.3
p65 ∗n = p65n, p65n:p50n
100. MSK1 −5n + tCOX←−→ MSK1n:tCOX kf,100 = 10 , kr,100 = 0.1
MSK1n:tCOX −−→ MSK1n + tCOXp kc,100 = 0.1
101. tCOXp −−→ ∅ k −4d,101 = 10
102. p38p + PLA
−5
2 ←−→ p38p:PLA2 kf,102 = 10 , kr,102 = 0.1
p38p:PLA2 −−→ p38p + PLA2p kc,102 = 0.1
103. PLA2p −−→ PLA2p +AA ks,103 = 0.01
104. COX+AA←−→ COX:AA −−→ COX+ PGE2 kf,104 = 10
−6, kr,104 = 0.1, kr,104 = 0.1
105. 5LO + AA←−→ 5LO:AA −−→ 5LO + LXA4 kf,105 = 10
−5, kr,105 = 0.1, kr,105 = 0.1
106. AA∗ −−→ ∅ kd,106 = 0.01
AA∗ = AA,PGE2,LXA4
107. PGE2 + EP2←−→ PGE2:EP2 −−→ EP2
−7
A kf,107 = 10 , kr,107 = 0.1, kr,107 = 0.1
108. EP2 −3A −−→ EP2 kd,108 = 10
45
109. EP2A −−→ EP2A + cAMP ks,109 = 0.01
110. cAMP −−→ ∅ kd,110 = 0.1
111. cAMP+ PKA←−→ cAMP:PKA −−→ PKA k = 10−6A f,111 , kr,111 = 0.1, kr,111 = 0.1
112. PKAA −−→ PKA kd,112 = 10
−3
113. PKAA + 5LO←−→ PKAA:5LO k = 10
−6
f,113 , kr,113 = 0.1
PKAA:5LO −−→ PKAA + 5LOp kc,113 = 0.1
114. 5LOp −−→ 5LO k −3d,114 = 10
115. PGE2 + EP4←−→ PGE2:EP4 −−→ EP4A kf,115 = 10
−6, kr,115 = 0.1, kr,115 = 0.1
116. EP4A −−→ EP4 kd,116 = 10
−3
117. EP4A −−→ EP4A + PIP3 ks,117 = 0.1
118. PIP3 −−→ ∅ kd,118 = 0.1
119. PIP3 +AKT←−→ PIP3:AKT k
−6
f,119 = 10 , kr,119 = 0.1
PIP3:AKT −−→ PIP3 +AKTp kc,119 = 0.1
120. AKTp −−→ AKT kd,120 = 10−3
121. AKTp + IKK←−→ AKTp:IKK kf,121 = 10−5, kr,121 = 0.1
AKTp:IKK −−→ AKTp + IKKp kc,121 = 0.1
122. 0 −−→ TNF ks,122 = scanned / 0 by default
123. 0 −−→ TNFR2 ks,123 = scanned / 0 by default
124. TNF + TNFR2←−→ TNF:TNFR2 −−→ TNFR2 k = 10−7A f,124 , kr,124 = 0.1, kr,124 = 0.1
125. TNFR2∗ −−→ ∅ k = 10−3d,125
TNFR2∗ = TNFR2,TNFR2A
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