Modeling Regulatory Mechanisms inIL-6 Signal Transduction in Hepatocytes

Abhay Singh, Arul Jayaraman, Juergen Hahn

Department of Chemical Engineering, Texas A&M University, College Station,Texas 77843-3122. telephone): (979) 845 3568; e-mail: hahn@tamu.edu

Received 20 February 2006; accepted 10 May 2006

Published online 2 June 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.21026

Abstract: Cytokines like interleukin-6 (IL-6) play an impor-tant role in triggering the acute phase response of thebody to injury or inflammation. Signaling by IL-6 involvestwo pathways: Janus-associated kinases (JAK) and signaltransducers and activators of transcription (STAT 3) areactivated in the first pathway while the second pathwayinvolves the activation of mitogen-activated proteinkinases (MAPK).While it is recognized that both pathwaysplay a major role in IL-6 signal transduction, a majority ofstudies have focused on signaling through either one ofthe pathways. However, simultaneous signaling throughboth JAK/STAT and MAPK pathways is still poorlyunderstood. In this work, a mathematical model has beendeveloped that integrates signaling throughboth the JAK/STAT and the MAPK pathway. The presented model isused to analyze the effect of three molecules that areinvolved in the regulation of IL-6 signaling—SHP-2(domain containing tyrosine phosphatase 2), SOCS3(suppressor of cytokine signaling 3), and a STAT3 nuclearphosphatase (PP2)—on the dynamics of IL-6 signaltransduction inhepatocytes. Theobtained results suggestthat interactions between SHP-2 and SOCS3 influencesignaling through the JAK/STATand theMAPKpathways.It is shown that SHP-2 and SOCS3 do not just regulate thepathway that theyare known tobeassociatedwith, (SHP-2with MAPK and SOCS3 with JAK/STAT), but also have astrong effect on the other pathway. Several simulationswith SOCS3, SHP-2, and PP2 knockout cells, that is,where the signaling pathway is unable to produce theseproteins, havebeenperformed tocharacterize theeffect ofthese regulatory proteins on IL-6 signal transduction inhepatocytes. � 2006 Wiley Periodicals, Inc.

Keywords: interleukin-6; hepatocytes; mathematicalmodel; cross-talk; signal transduction; STAT; MAPK

INTRODUCTION

Systemic inflammatory mediators, such as the cytokines

interleukin-1 (IL-1), interleukin-6 (IL-6), and tumor necrosis

factor (TNF) (Baumann and Gauldie, 1994), play an

important role in the induction of the inflammatory acute

phase response (APR) in the liver upon trauma or injury. The

APR is characterized by, among others, a dramatic alteration

in the protein synthetic profile of the liver, with several

plasma acute phase proteins (APPs) being upregulated

(e.g., C-reactive protein, haptoglobin, and serum amyloid

A) or down regulated (e.g., albumin and transferrin) through

the coordinated action of inflammatory mediators. While

the APR is primarily a short-term (24–72 h) (Baumann

and Gauldie, 1994) beneficial host response to injury, an

increasing body of data has also correlated elevatedmeasures

of APR with organ failure and mortality resulting from

chronic inflammation. In particular, the ratio of increase in

C-reactive protein to decrease in albumin has been negatively

correlated to survival from systemic inflammation (Pinilla

et al., 1998). An improved understanding of the molecular

mechanisms involved in the APR can lead to improved

treatment of complications arising from chronic inflamma-

tory disorders.

The dynamics of expression and interaction of the IL-6

signaling pathway molecules is a key determinant of the

phenotypical changes characteristic of the APR. The IL-6

signaling pathway is characterized by multiple branches and

possible cross-talk and redundancies. While the dynamic

behavior of some individual molecules in this pathway is

known, comprehensive system dynamics are still poorly

understood. In this work, we focus on the molecular

mechanisms involved in the regulation of IL-6 signaling

during the hepatic APR. Signal transduction by the IL-6

family of cytokines involves the activation of two major

pathways: the JAK /STATand theMAPKpathways (Heinrich

et al., 1998, 2003) that lead to a wide range of cellular

responses, including inflammation, growth, differentiation,

and apoptosis. Signaling through the JAK/STAT pathway

involves the binding of gp130 (glycoprotein 130), JAK, and

transcription factor STAT3. The MAPK pathway is linked to

the JAK/STAT pathway through SHP-2 binding to the (IL6-

gp80-gp130-JAK)2 complex. The activation of SHP-2 is a

crucial event for signaling through the MAPK pathway (Lai

et al., 1999). In addition to acting as an adaptor protein for

the MAPK pathway, SHP-2 acts as a phosphatase for the

JAK/STAT pathway and regulates this pathway (Kim and

Baumann, 1999; Schaper et al., 1998). The dual role of

SHP-2 suggests possible interactions between the JAK/STAT

and the MAPK pathways. However, the involvement of both

�2006 Wiley Periodicals, Inc.

Correspondence to: J. Hahn

JAK/STAT and MAPK pathways in IL-6 signaling has only

been studied in few cases (Schaper et al., 1998) and the

interactions between the two pathways as well as the role

played by SHP-2 in IL-6 signal transduction are not clearly

understood.

It is well established that SOCS3 acts as an inhibitor

for signal transduction through the JAK/STAT pathway

(Fischer et al., 2004; Heinrich et al., 1998, 2003). However,

SOCS3 has an effect on signaling through the MAPK

pathway (Lehmann et al., 2003; Schmitz et al., 2000) through

phosphorylation of SHP-2.

In this work, we have comprehensively analyzed the

interaction between the JAK/STATand the MAPK pathways

by developing a kinetic model that considers signaling

through both pathways. The developed model is used to

analyze the interactions between the two pathways and

investigate the role of SHP-2 in signal transduction. The

influence of SOCS3 on signal transduction has also been

evaluated by simulation of the developed model. The results

obtained through simulations have been compared with

available results from the literature and were found in

good agreement with semi-quantitative experimental obser-

vations.

MODEL DESCRIPTION

The kinetic model (Fig. 1) developed in this work is based on

the IL-6 cytokine signaling pathway presented in Heinrich

et al. (2003). The JAK/STAT part of the signal transduction

pathway and the model parameters have been adopted from

Yamada et al. (2003) while the MAPK signaling pathway is

mainly based on the work presented by Schoeberl et al.

(2002). Only the Shc-dependent pathway of the Schoeberl

et al. (2002) model has been adopted for this work as the

implemented structure of the pathway has been taken from

the work by Heinrich et al. (2003). The assumption has been

made to replace Shcwith SHP-2 in themodel as both proteins

exhibit a similar response for stimulation by IL-6. Another

assumptionwas that the signal transduction pathways and the

kinetic parameters were taken from various sources in the

literature for this model (Heinrich et al., 2003; Schoeberl

et al., 2002; Yamada et al., 2003). The pathway model of

Figure 1. Signal transduction in hepatocytes induced by IL-6.A:Marks the reaction to be knocked out for a SOCS3knockout cell;B:Marks the reaction to be

knocked out for cells where theMAPK is inactive;C:Marks the reaction to be eliminated for a PP2 knockout cell. [Color figure can be seen in the online version

of this article, available at www.interscience.wiley.com.]

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Biotechnology and Bioengineering. DOI 10.1002/bit

Yamada et al. (2003) and Schoeberl et al. (2002) do not

involve STAT3 in hepatocytes, butwere derived for STAT1 in

hepatocytes or STAT3 in HeLa cells, respectively. However,

kinetic parameters and sub-model structures from these

signaling models have been adopted assuming that the

signaling transduction pathways are conserved in cells

(Kholodenko, 2000).

In the presented model IL-6 attaches to its receptor gp80,

which is referred to as the non-signaling part of the receptor.

The signaling part of the receptor gp130 binds to protein

tyrosine kinases of the JAK family. The IL-6/gp80 complex

then binds to the gp130/JAK compound and as a result the

IL6-gp80-gp130-JAK complex is formed. This binding

results in the dimerization of the IL6-gp80-gp130-JAK

complex forming (IL6-gp80-gp130-JAK)2 (Heinrich et al.,

1998, 2003; Roth et al., 1997). gp130 becomes tyrosine

phosphorylated as a result of dimerization and the phos-

phorylated dimer serves as the starting point for both the

JAK/STAT and the MAPK pathway.

In the JAK/STAT pathway, the phosphorylated dimer

recruits the transcription factor STAT3 which is also tyrosine

phosphorylated. The phosphorylated STAT3 dissociates

from the receptor complex (IL6-gp80-gp130-JAK)2 and

undergoes dimerization. The dimerized STAT3 complex

translocates to the nucleus where some of it binds to its

consensus target sequence in the promoter/enhancer

regions of IL-6 target genes (such as haptoglobin and a2-macroglobulin) (Heinrich et al., 1998, 2003). The nuclear

STAT3 dimer is dephosphorylated and exported back to

the cytosol for another phosphorylation–dephosphorylation

cycle (Heinrich et al., 1998, 2003; ten Hoeve et al., 2002).

In addition to activating the STAT3 transcription factor for

the JAK/STAT pathway, the phosphorylated gp130 also

recruits SHP-2 which subsequently undergoes phosphoryla-

tion. The activated SHP-2 is essential for signaling through

the MAPK pathway (Heinrich et al., 2003; Schaper et al.,

1998; Schmitz et al., 2000). The phosphorylated SHP-2

interacts with Grb2 (growth factor receptor bound protein)

and SOS (son of sevenless). The binding of Grb2 and SOS to

the receptor complex leads to the activation of RAS, which

further leads to the activation of the MAPK cascade

(Heinrich et al., 2003). Three phosphatases Phosp1,

Phosp2, and Phosp3 are considered in the MAPK pathway

that influence the activation of Raf, MEK, and ERK,

respectively.

Signal transduction through the JAK/STAT pathway is

regulated by twoways—SOCS3 is induced by the JAK/STAT

pathway and binds to the activated (IL6-gp80-gp130-JAK)2,

thereby inhibiting the phosphorylation of STAT3 and regulat-

ing IL-6 signaling; in addition to SOCS3, signal transduction

through the JAK/STAT pathway is also regulated by SHP-2

and two STAT3 phosphatases, PP1 and PP2. SHP-2 acts as a

phosphatase for the (IL6-gp80-gp130-JAK*)2 complex and

inactivates it (Heinrich et al., 1998, 2003; Levy and Darnell,

2002; ten Hoeve et al., 2002). The phosphatases PP1 and PP2

influence the activation of STATin the cytosol and the nucleus,

respectively. The nuclear phosphatase PP2, also known as

TC45,dephosphorylatesSTAT3 in the nucleuswhich results in

STAT3 being returned to the cytosol (Levy and Darnell, 2002;

ten Hoeve et al., 2002).

The only regulatory mechanisms in the MAPK pathway

that were modeled are given by the phosphatases Phosp1,

Phosp2, and Phosp3. These regulate the activity of RAF,

MEK, and ERK, respectively (Schoeberl et al., 2002).

Most of the reactions in the model are represented by

mass-action kinetics with a few exceptions where Michae-

lis–Menten kinetics are used. The reason for the use of

mass-action kinetics for most parts of the model is that in

signal transduction pathways the condition that the substrate

concentration is much larger than the enzyme concentration

is usually not satisfied (Yamada et al., 2003). There are

68 state variables in the presentedmodel, resulting in asmany

ordinary differential equations. The differential equation for

a particular component (A) is written as:

Rate of change

of component

ðAÞ

0@

1A ¼

Amount of ðAÞformed in all

reactions

0@

1A�

Amount of ðAÞconsumed in all

reactions

0@

1A

dNA

dt¼

XvA;produced �

XvA;consumed

where vA represents the rate of formation/consumption of

species A in a particular reaction.

The presented model is implemented inMATLAB and the

model is solved using the ODE15s subroutines. A detailed

description of the signaling pathway is provided in

Figure A.1 in Appendix I and the model equations are

provided in Appendix II.

RESULTS

The gp80 receptor and the gp130 receptor concentration in

the cell are assumed constant at 5,000 receptors/cell and 500

receptors/cell, respectively (Baumann et al., 1988; Roth

et al., 1997). Further, hepatocytes are assumed to be

continuously exposed to 10 ng/mL of IL-6 for 24 h. IL-6

binds to the receptor gp80 with low affinity (Kd¼ 500 pM)

and the IL-6-gp80 complex further binds to the gp130

receptor (Roth et al., 1997). IL-6 binding to the receptor

eventually results in dimerization and phosphorylation of the

IL6-gp80-gp130-JAK complex. The phosphorylated com-

plex (IL6-gp80-gp130-JAK*)2 reaches a maximal concen-

tration within 15 min of IL-6 binding (Fig. 2). Subsequently,

the STAT3C (STAT3 in the cytosol) transcription factor

undergoes phosphorylation (Fig. 3A) and dimerization. The

dimerized STAT3 (STAT3C*-STAT3C*) translocates to the

nucleus approximately 10min after signal induction by IL-6.

The nuclear STAT3 complex (STAT3N*-STAT3N*) reaches

a maximal concentration in about 1 h, rapidly decays, and

attains a new steady state after about 5 h (Fig. 3A). These

findings are consistent with the ones reported in Jayaraman

et al. (2000) where STAT3-mRNA attains a new steady state

on continuous exposure to IL-6.

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Role of SOCS3

SOCS3 appears about 30 min after the IL-6 binding and

reaches a maximal concentration after about 2 h (Fig. 3B).

SOCS3 inhibits the signal transduction in the JAK/STAT

pathway by inhibiting the phosphorylation of STAT3 and as a

result the translocated STAT3 dimer concentration in the

nucleus decreases significantly after reaching a maximum

(Fig. 3A). In order to further examine the influence of SOCS3

on signal transduction through the JAK/STAT pathway, we

simulated a SOCS3 knockout cell model (Fig. 1 with

pathwaymarked by ‘‘A’’). Dynamic simulations were carried

out for the same conditions investigated for the regular cell

model. The responses of STAT3 and translocated nuclear

STAT3 in SOCS3 knockout cells are shown in Figure 4.

These responses are remarkably different when compared to

the graphs shown in Figure 3A. Fischer et al. (2004) have

reported similar observations of STAT3 activity in wild type

and permanent activation of STAT3 in SOCS3-deficient

hepatocyte cell.

Role of SHP-2

SHP-2 is not only one of the main components for initiating

the MAPK pathway, it also acts as an inhibitor for the JAK/

STAT pathway. SHP-2 dephosphorylates the (IL6-gp80-

gp130-JAK*)2 complex and thereby inhibits the phosphor-

ylation of STAT3C as shown in Figure 1 (the SHP-2 knockout

cell is given by Figure 1 where the reaction marked with a

‘‘B’’ is suppressed).

Enhanced activation of STAT3 in the cytosol and in the

nucleus STAT3N*-STAT3N* is observed for simulations of

cells where SHP-2 phosphorylation is blocked (Fig. 5). The

maximal level of STAT3N*-STAT3N* in the above case

reaches 300 nM (Fig. 5) compared to 42 nM in normal

hepatocytes (Fig. 3A). Essentially, signaling through the

JAK/STAT pathway is enhanced when the MAPK pathway

cannot be activated due to blocking of SHP-2 phosphoryla-

tion. These results are consistent with the observations of

Schaper et al. (1998) who observed that overexpression of a

phosphatase-inactive SHP-2 mutant in HepG2 cells resulted

in enhanced STAT activation and a 20-fold induction in the

expression of an acute phase protein (a2-macroglobulin)

promoter-luciferase reporter plasmid.

The influence of SHP-2 concentration on signal transduc-

tion is further analyzed by varying the initial concentration of

SHP-2 in the range of 0–100 nM as is shown in Figure 6.

The maximal level of activated STAT3 in the cytosol

(Fig. 6A) and the nucleus (Fig. 6B) varies depending on the

SHP-2 initial concentration in the cell. The cell shows a

‘‘largest dip’’ in the value of activated STAT3C for low initial

concentrations of SHP-2. Additionally, it can be concluded

Figure 2. Dynamic response of phosphorylated complex (IL6-gp80-

gp130-JAK*)2 induced by 10 ng/mL of IL-6 for 24 h. [Color figure can be

seen in the online version of this article, available at www.interscience.

wiley.com.]

Figure 3. Dynamic response of STAT3 in the cytosol, nuclear STAT3N*-

STAT3N* (A), and SOCS3 (B) concentration for stimulation with 10 ng/mL

of IL-6 for 24 h. [Color figure can be seen in the online version of this article,

available at www.interscience.wiley.com.]

Singh et al.: Modeling Regulatory Mechanisms 853

Biotechnology and Bioengineering. DOI 10.1002/bit

that there is a stronger long-term activation of STAT3C, the

lower the initial SHP-2 concentration.

In a next step the effect of SOCS3 on the phosphorylation of

SHP-2 is investigated. As shown in the earlier results, SOCS3

appears about 30min after IL-6 binds to the receptor (Fig. 3B).

As SOCS3 influences the phosphorylation of SHP-2, the

concentration of phosphorylated SHP-2 decreases after

reaching a maximal level about 1 h after IL-6 stimulation

of the cell (Fig. 7 (top)). SHP-2 acts as an adaptor protein for

the MAPK pathway and its phosphorylation is essential for

initiation of the MAPK pathway. Therefore, in the presence

of SOCS3 signal transduction through theMAPK pathway is

down regulated. However, in order to corroborate these

observations simulations have also been carried out in

SOCS3 knockout cells. In the absence of SOCS3, phos-

phorylated SHP-2 shows sustained activation (Fig. 7 (top)).

Such sustained activation of SHP-2 can lead to increased

signaling through the MAPK pathway as illustrated in

Figure 7 (bottom). Note that the long-term Raf* concentra-

tion reaches a value in a SOCS3 knockout cell that is three

times as large as the one for a normal cell, even though both

concentrations are relatively small.

Due to the effect on SHP-2 it can be concluded that SOCS3

has a regulatory effect on the MAPK pathway in addition to

its effect on the JAK/STAT pathway.

Role of PP2

The nuclear phosphatase PP2 plays an important role in

the JAK/STAT pathway as it causes deactivation of the phos-

Figure 4. Dynamic response of STAT3 in the cytosol and nuclear

STAT3N*-STAT3N* in SOCS3 knockout cells for stimulation with 10 ng/

mL of IL-6 for 24 h. [Color figure can be seen in the online version of this

article, available at www.interscience.wiley.com.]

Figure 5. Dynamic response of STAT3 in the cytosol and nuclear

STAT3N*-STAT3N* for signal transduction induced by IL-6 for 24 h. with

no phosphorylation of SHP-2. [Color figure can be seen in the online version

of this article, available at www.interscience.wiley.com.]

Figure 6. Dynamic response for signal transduction induced by IL-6 for

24 h. with SHP-2 initial concentration varied in the range of 0–100 Nm.

A: STAT3 in the cytosol B: nuclear STAT3N*-STAT3N*. [Color figure canbe seen in the online version of this article, available at www.interscience.

wiley.com.]

854 Biotechnology and Bioengineering, Vol. 95, No. 5, December 5, 2006

DOI 10.1002/bit

phorylated STAT3 dimer in the nucleus. This deactivation is

an important step for returning STAT3 to the cytosol for

another phosphorylation–dephosphorylation cycle. There-

fore, we developed a PP2 knockout cell model (Fig. 1; the

pathway marked with a ‘‘C’’) to further study the effect that

PP2 has on signal transduction.

When PP2 knockout cells are stimulated with IL-6, signal

transduction is strongly inhibited as the phosphorylated

STAT3 dimer in the nucleus is not deactivated. As a result,

the concentration of STAT3 in the cytosol continuously

decreases with time (Fig. 8A), while the STAT3N*-

STAT3N* concentration increases (Fig. 8A) and reaches a

new steady state concentration. These results are in line with

the western blot analysis reported in ten Hoeve et al. (2002)

which shows sustained activation of nuclear phosphorylated

STAT3 in nuclear STAT3 phosphatase null cell. Since STAT3

in the cytosol is an essential component for signaling through

the JAK/STAT pathway, signal transduction is strongly

inhibited in PP2 knockout cells.

It should be noted that the implementedmodel does not take

into account de novo synthesis of STAT3 in the cytosol, which

would have the effect of increasing nuclear STAT3 over time

as compared to the results shown in Figure 8A. Since the

amount of nuclear STAT3 reaches a high level in PP2knockout

cells, a large amount of SOCS3 is generated and the SOCS3

concentration approaches a steady state within 24 h as shown

in Figure 8B.

A comparison between the rate of STAT3 transported into

the nucleus is shown in Figure 9 as this is an indicator of the

activation of the JAK/STATpathway. It can be concluded that

SOCS3 knockout cells have a higher activation than regular

hepatocytes, while PP2 knockout cells show less activity in

the JAK/STAT pathway.

DISCUSSION

The model was developed by aggregating several parts of

the signaling pathways that had previously been published

in the literature (Schoeberl et al., 2002; Yamada et al., 2003).

The assumption has been made that these individual parts of

the pathways can be modeled together without requiring

changes to the parameters. While comparisons of the

simulated behavior of individual proteins have been made

to semi-quantitative data from the literature, an experimental

investigation of the dynamic protein profiles is currently

under way.

Discussion of SimulationResults for Hepatocytes

The dynamic response of STAT3 as predicted by the

simulation is inline with results reported in the literature

(Fischer et al., 2004). The strong initial increase in the con-

centration of nuclear STAT3 in our simulations is remarkably

consistent with the dynamics of nuclear STAT3 in HepG2

cells upon continuous exposure to IL-6 (Fischer et al., 2004).

The authors also observed a second peak of activated STAT3

in the nucleus, which is also observed in our simulations. Our

simulation results indicate that the short-term SOCS3 levels

in response to IL-6 are approximately five-fold greater than

the long-term levels seen at 24 h. These simulation results

are consistent with the mRNA data from IL-6 stimulated

adipocytes reported by Fasshauer et al. (2004) who observed

an approximately 10-fold higher values in the short-term

response as compared to the long-term response. Both our

simulations and the adipocyte data clearly show an initial

Figure 7. Dynamic responses of (a) phosphorylated SHP-2 (SHP-2*) and (b) Raf* for signal transduction inducedby 10 ng/mLof IL-6 for 24 h in normal and

SOCS3 knockout cells. [Color figure can be seen in the online version of this article, available at www.interscience.wiley.com.]

Singh et al.: Modeling Regulatory Mechanisms 855

Biotechnology and Bioengineering. DOI 10.1002/bit

increase in SOCS3 levels, with minimal change after 8 h of

IL-6 stimulation.

These results indicate the validity of the developed model,

at least with respect to the JAK/STAT arm of the IL-6

signaling pathway in hepatocytes.

Role of SOCS3

While simulations of SOCS3 knockout cells were mainly

performed to characterize the effect of SOCS3 on IL-6

signal transduction during the hepatic APR, a quantitative

understanding of IL-6 signaling in SOCS3 knockout

cells could also have broader impact, as SOCS3 has been

shown to be involved in certain types of cancer as well

(He et al., 2004; Niwa et al., 2005). Our simulations with

SOCS3 knockout cells predict sustained activation of nuclear

STAT3N*-STAT3N* upon IL-6 stimulation as compared

to normal cells (855 nM after 24 h for SOCS3 knockout

cells versus 960 nM for normal cells; see Figures 4

and 3A), which in turn, indicates increased signaling through

the JAK/STAT pathway. These results are consistent with

those of Niwa et al. (2005) who suggest that methylation

silencing of SOCS3 expression (i.e., analogous to SOCS3

knockout cells) resulted in higher JAK/STAT pathway

activity.

The simulations results are validated when comparisons

are made to the Western blot data reported in Lang et al.

(2003) for the dynamic profile of phosphorylated nuclear

STAT3 concentrations for regular cells and SOCS knockout

cells stimulated by IL-6 measured at 25, 100, and 400 min.

The results show that the (semi-quantitative) concentration

of phosphorylated nuclear STAT3 in regular cells and in

SOCS knockout cells follows the results shown in Figures 3A

and 4.

Role of SHP-2

The sustained activation of SHP-2 shown in the simulation

will result in sustained signaling through the MAPK

pathway. Simulations results for variations in the SHP-2

concentration showed that absence of SHP-2 will result in no

signaling through the MAPK pathway and in increased

signaling through the JAK/STAT pathway. From the

presented results, it can be concluded that both SHP-2 and

SOCS3 act as inhibitors for the JAK/STAT part of the

signaling pathway, however, each utilizes a different

process for the inhibition (Lehmann et al., 2003). While

SOCS3 inhibits the JAK/STAT pathway by binding to

the (IL6-gp80-gp130-JAK)2 complex and thereby inhibits

phosphorylation of STAT3 in the cytosol, SHP-2 inhibits

the JAK/STAT pathway by dephosphorylation of the

Figure 8. Dynamic response of STAT3 in the cytosol, nuclear STAT3N*-

STAT3N* (A) and SOCS3 (B) in PP2 knockout cell for signal transduction

induced by 10 ng/mL of IL-6 for 24 h. [Color figure can be seen in the online

version of this article, available at www.interscience.wiley.com.]

Figure 9. STAT3 influx of the nucleus for normal hepatocyte cells, SOCS3

knockout cells, and PP2 knockout cells. [Color figure can be seen in the

online version of this article, available at www.interscience.wiley.com.]

856 Biotechnology and Bioengineering, Vol. 95, No. 5, December 5, 2006

DOI 10.1002/bit

(IL6-gp80-gp130-JAK*)2 complex. Moreover, it can be

deduced that SOCS3 and SHP-2 do not act independent of

each other in IL-6 signaling, but are functionally connected

and influence signaling through the JAK/STAT and the

MAPK pathways. Our simulation results on the functional

link between SOCS3 and SHP-2 are consistent with the

experimental observations of Schmitz et al. (2000). In this

study, the authors reported that impaired SHP-2 activation in

HepG2 cells resulted in enhanced SOCS3 induction and

suggest that the SOCS3 activation may be a result of

compensation for the reduced SHP-2 activity. Together, our

simulation support the hypothesis proposed by Schmitz et al.

(2000) that the inhibitory role of SHP-2 on IL-6 signaling, in

part, is through the recruitment of SOCS3 to the IL-6 receptor

complex.

Our simulation results are further validated when compar-

isons are made to the Western blot data reported in

Lang et al. (2003) for the dynamic profile of SHP-2

concentrations for regular cells and SOCS knockout cells

stimulated by IL-6. The results show that the concentration

of phosphorylated SHP-2 is about the same after 25 min

after stimulation for both types of cells. However, the SHP-2

concentration after 100 and 400 min clearly indicates that

the SOCS3 knockout cell has a significantly higher

concentration of SHP-2 at these time points than the regular

cell. These results validate the simulation results shown in

Figure 7.

Furthermore, the results shown in the bottom plot of

Figure 7 illustrate that while SOCS3 knockout cells have a

higher activity in the MAPK pathway, that the long-

term concentration of phosphorylated RAF is quite small

for both cell types and the results are indistinguishable from

one another in an experimental setting. These results are

inline with experimental observations made by Lang et al.

(2003) that the increase in SHP-2 phorphorylation did not

seem to be linked to the downstream increase in MAPK

activation.

Role of PP2

Yamada et al. (2003) have observed that the effect of SOCS

knockout cells and PP2 knockout cells on the dynamics of

STAT1 in cells are similar.While our investigation deals with

STAT3, the underlying structure of the signal transduction

network is nevertheless the same for the two proteins;

therefore, we compared the effect of SOCS3 and PP2

knockout cells on STAT3 activation. We found that SOCS3

knockout cells have a higher activation than regular

hepatocytes, while PP2 knockout cells show a reduced

amount of signaling through the JAK/STAT pathway. As

such, preventing SOCS3 formation in cells has the opposite

effect on the amount rate of STAT3 translocating to the

nucleus compared to PP2 knockout cells. However, this is not

to be confused with the amount of IL-6 regulated transcrip-

tion of APP genes taking place in those cells: both SOCS3

knockout cells and PP2 knockout cells have a high nuclear

STAT3 concentration that will lead to an increased

transcription rate (Schaper et al., 1998).

Limitations of the Implemented Model

All the presented results are affected by the assumptions

made while developing the model. As such any conclusions

drawn from a simulation study can only be as good as the

assumptions underlying the model. It is important to list

these assumptions as they form the basis for future

improvements:

The developed model focuses only on signal transduction in

the cytosol and translocation of STAT3 dimers to the

nucleus and STAT3 monomer to the cytosol. All other

import/export across the nuclear membrane has been

ignored with the exception of SOCS3-mRNA to the cytosol.

Therefore, the JAK/STAT pathway is not extended beyond

the translocation of STAT3 and production of SOCS3 and

the MAPK pathway has ERK as the end point. The only

transcriptional up-regulation term included is the expression

of SOCS3 as it directly influences the dynamics of the JAK/

STAT pathway.

De novo synthesis of transcription factors (including auto-

regulatory effects), protein turnover in the cytosol, and

receptor recycling have not been included in the current

model.

Due to these assumptions it is not possible tomake statements

about redundancy of the pathways for the APR as the

transcription of APR proteins has not been modeled. Future

work will include validation of the model, fitting of model

parameters, and investigation/implementation of the parts of

the APR that cannot be modeled at this point in time.

CONCLUSIONS

In this work a kinetic model for signal transduction of

hepatocytes stimulated by IL-6 has been presented. The

model includes signal transduction occurring via the JAK/

STAT and the MAPK pathways. The model has been shown

to predict behavior qualitatively inline with experimental

studies found in the literature.

The presented model was used to investigate the effect of

SHP-2, SOCS3, and PP2 on signal transduction induced by

IL-6. Simulations carried out with the model show that

SOCS3 acts as an inhibitor for the JAK/STAT pathway and it

also down regulates the phosphorylation of SHP-2 and

presumably inhibits signaling through theMAPK pathway. It

has also been illustrated that while SHP-2 plays an important

function for signaling through MAPK pathway, that SHP-2

downs regulates signaling through the JAK/STAT pathway.

It can be further concluded from the presented results that

SHP-2 and SOCS3 are functionally linked to each other.

They influence signal transduction through the JAK/STATas

well as the MAPK pathway.

Singh et al.: Modeling Regulatory Mechanisms 857

Biotechnology and Bioengineering. DOI 10.1002/bit

PP2 was found to play an important role for signal

transduction through the JAK/STAT pathway. Themodel of a

PP2 knockout cells was unable to eject STAT3 from the

nucleus which resulted in a low STAT3 concentration in the

cytosol and very high levels of SOCS3. As a result the model

of the knockout cell showed strongly reduced signaling

through the JAK/STAT pathway. At the same time, the level

of protein transcription expression is high in PP2 knockout

cells due to a high concentration of nuclear STAT3 (Schaper

et al., 1998).

APPENDIX-I

Appendix-I A.1. Reaction network for IL-6 induced signal transduction in hepatocytes. The blue text represents the JAK/STAT branch of the signaling

pathway and green text represents the MAPK branch of the pathway. The red text in the signaling network represents pathway common to the JAK/STATand

MAPK branches. [Color figure can be seen in the online version of this article, available at www.interscience.wiley.com.]

858 Biotechnology and Bioengineering, Vol. 95, No. 5, December 5, 2006

DOI 10.1002/bit

APPENDIX-II

Model Equations:

dx1

dt¼ �kf0x1uþ kr0x2

dx2

dt¼ kf0x1u� kr0x2 þ kr2x6 � kf2x2x5

dx3

dt¼ �kf1x3x4 þ kr1x5

dx4

dt¼ �kf1x3x4 þ kr1x5

dx5

dt¼ kf1x3x4 � kr1x5 � kf2x2x5 þ kr2x6

dx6

dt¼ kf2x2x5 � kr2x6 � 2kf3x

26 þ 2kr3x7

dx7

dt¼ kf3x

26 � kr3x7 � k4x7 þ k10x16 þ k10x32

dx8

dt¼ k4x7 � kf5x8x9 þ kr5x11 þ k6x11 � kf7x8x10 þ kr7x12

� kf9x8x15 þ kr9x16 � kf21x29x8 þ kr21x30 þ kf37x39

� kr37x8x46 þ kf39x40 � kr30x45x8 þ kf32x41 � kr32x44x8

dx9

dt¼ �kf5x8x9 þ kr5x11 þ k12x18 � kf13x9x10

þ kr13x14 þ k17x22 � kf5x9x30 þ kr5x31 þ k10x32

dx10

dt¼ k6x11 � kf7x8x10 þ kr7x12 � 2kf8x

210

þ 2kr8x13 � kf11x10x17 þ kr11x18 � kf13x9x10 þ kr13x14

dx11

dt¼ kf5x8x9 � kr5x11 � k6x11

dx12

dt¼ kf7x8x10 � kr7x12

dx13

dt¼ kf8x

210 � kr8x13 � kf11x13x17 þ kr11x19 � k14x13

dx14

dt¼ k12x19 þ kf13x9x10 � kr13x14

dx15

dt¼ �kf9x8x15 þ kr9x16 þ k10x16

� kf9x15x31 þ kr9x32 þ k10x32 þ Vmx46

Km þ x46

dx16

dt¼ kf9x14x8 � kr9x16 � k10x16 � kf34x16 þ kr34x39

dx17

dt¼ �kf11x10x17 þ kr11x18 þ k12x18

� kf11x13x17 þ kr11x19 þ k12x19

dx18

dt¼ kf11x10x17 � kr11x18 � k12x18

dx19

dt¼ kf11x13x17 � kr11x19 � k12x19

dx20

dt¼ k14x13 � kf60x20 þ kr60x

221 � kf15x23x20 þ kr15x27

dx21

dt¼ 2kf60x20 � 2kr60x

221

� kf15x23x21 þ kr15x28 þ kf61x24 � kr61x21x22

dx22

dt¼ k16x28 þ kf61x24 � kr61x21x22 � k17x22

dx23

dt¼ �kf15x21x23

þ kr15x28 þ k16x28 � kf15x20x23 þ kr15x27 þ k16x27

dx24

dt¼ k16x27 � kf61x24 þ kr61x21x22

dx25

dt¼ k18ax20

k18b þ x20� k19x25

dx26

dt¼ k19x25 � k22x26

dx27

dt¼ kf15x23x20 � kr15x27 � k16x27

dx28

dt¼ kf15x23x21 � kr15x28 � k16x28

dx29

dt¼ k20x26 � k23x29

� kf21x29x8 þ kr21x30 þ k23x32 þ k10x32

dx30

dt¼ kf21x29x8 � kr21x30 � kf5x9x30 þ kr5x31

dx31

dt¼ kf5x9x30 � kr5x31 � kf9x15x31 þ kr9x32

dx32

dt¼ kf9x15x31 � kr9x32 � k10x32 � k23x32

Singh et al.: Modeling Regulatory Mechanisms 859

Biotechnology and Bioengineering. DOI 10.1002/bit

dx33

dt¼ k23x32

dx34

dt¼ �kf38x34x46 þ kr38x45

þ kf35x38 � kr35x34x35 � kf24x39x34 þ k24rx40

dx35

dt¼ �kf25x35x40 þ kr25x41

� kf40x35x45 þ kr40x44 þ kf35x38 � kr35x34x35

dx36

dt¼ �kf26x36x41 þ kr26x42 þ kf31x43 � kr31x36x41

dx37

dt¼ kf27x42 � kr27x37x41 � kf28x37x47 þ kr28x48

dx38

dt¼ �kf35x38 þ kr35x34x35

� kf41x38x39 þ kr41x41 þ kf33x44 � kr33x38x46

dx39

dt¼ kf34x16 � kr34x39 � kf37x39 þ kr37x8x46

� kf24x39x34 þ kr24x40 � kf41x39x38 þ kr41x41

dx40

dt¼ kf24x39x34 � kr24x40

� kf25x40x35 þ kr25x41 � kf39x40 þ kr39x45x8

dx41dt

¼ kf25x35x40 � kr25x41 � kf32x41 þ kr32x44x8 � kf26x41x36

þ kr26x42 þ kf31x43 � kr31x41x36 þ kf41x39x38 � kr41x41

� kf30x49x41 þ kr30x43 þ kf27x42 � kr27x41x37

dx42dt

¼ kf26x36x41 � kr26x42 � kf27x42 þ kr27x37x41

dx43dt

¼ kf30x41x49 � kr30x43 � kf31x43 þ kr31x36x41

dx44dt

¼ kf32x41

� kr32x44x8 � kf33x44 þ kr33x38x46 þ kf40x35x45 � kr40x44

dx45dt

¼ kf38x34x46

� kr38x45 þ kf39x40 � kr39x8x45 � kf40x35x45 þ kr40x44

dx46dt

¼ kf37x39 � kr37x8x46

� Vmx46

Km þ x46� kf38x34x46 þ kr38x45 þ kf33x44 � kr33x38x46

dx47dt

¼ �kf28x37x47 þ kr28x48 þ k43x52

dx48dt

¼ kf28x37x47 � kr28x48 � kf29x48 þ kr29x49x51

dx49dt

¼ kf29x48 � kr29x49x51 � kf30x41x49 þ kr30x43

dx50dt

¼ �kf42x50x51 þ kr42x52 þ k43x52

dx51dt

¼ kf29x48 � kr29x49x51 � kf42x50x51 þ kr42x52 � kf44x51x53

þ kr44x54 þ k45x54 þ k47x56 � kf46x55x51 þ kr46x56

dx52dt

¼ kf42x50x51 � kr42x52 � k43x52

dx53dt

¼ �kf44x51x53 þ kr44x54 þ k51x60

dx54dt

¼ kf44x51x53 � kr44x54 � k45x54

dx55dt

¼ k45x54 � kf46x51x55

þ kr46x56 þ k49x58 � kf50x55x59 þ kr50x60

dx56dt

¼ �k47x56 þ kf46x51x55 � kr46x56

dx57dt

¼ k47x56 � kf48x57x59 þ kr48x58 � kf52x57x61 þ kr52x62

þ k53x62 � kf54x57x63 þ kr54x64 þ k55x64

dx58dt

¼ kf48x57x59 � kr48x58 � k49x58

dx59dt

¼ k49x58 � kf48x57x59 þ kr48x58 � kf50x55x59

þ kr50x60 þ k51x60

dx60dt

¼ kf50x55x59 � kr50x60 � k51x60

dx61dt

¼ �kf52x57x61 þ kr52x62 þ k59x68

dx62dt

¼ kf52x57x61 � kr52x62 � k53x62

dx63dt

¼ k53x62 � kf54x57x63 þ kr54x64

þ k57x67 � kf58x63x66 þ kr58x68

dx64dt

¼ kf54x57x63 � kr54x64 � k55x64

dx65

dt¼ k55x64 � kf56x65x66 þ kr56x67

APPENDIX-II

(continued)

860 Biotechnology and Bioengineering, Vol. 95, No. 5, December 5, 2006

DOI 10.1002/bit

dx66

dt¼ �kf56x65x66 þ kr56x67 þ k57x67

� kf58x63x66 þ kr58x68 þ k59x68

dx67

dt¼ kf56x65x66 � kr56x67 � k57x67

dx68

dt¼ kf58x63x66 � kr58x68 � k59x68

APPENDIX-III

Model Variable Description:

Variable Description

x1 gp80

x2 IL6-gp80

x3 gp130

x4 JAK

x5 gp130-JAK

x6 IL6-gp80- gp130-JAK

x7 (IL6-gp80- gp130-JAK)2x8 (IL6-gp80- gp130-JAK)2

*

x9 STAT3C

x10 STAT3C*

x11 (IL6-gp80- gp130-JAK)2*-STAT3C

x12 (IL6-gp80- gp130-JAK)2*-STAT3C*

x13 STAT3C*-STAT3C*

x14 STAT3C-STAT3C*

x15 SHP2

x16 (IL6-gp80- gp130-JAK)2*–SHP2

x17 PP1

x18 PP1-STAT3C*

x19 PP1-STAT3C*- STAT3C*

x20 STAT3N*- STAT3N*

x21 STAT3N*

x22 STAT3N

x23 PP2

x24 STAT3N-STAT3N*

x25 Mrna-SOCS3N

x26 Mrna-SOCS3C

x27 PP2-STAT3N*-STAT3N*

x28 PP2-STAT3N*

x29 SOCS3

x30 (IL6-gp80-gp130-JAK)2*–SOCS3

x31 (IL6-gp80- gp130-JAK)2*–STAT3C-SOCS3

x32 (IL6-gp80- gp130-JAK)2*–STAT3C-SOCS3-SHP2

x33 (IL6-gp80- gp130-JAK)2*–STAT3C-SHP2

x34 Grb2

x35 SOS

x36 Ras-GDP

x37 Ras-GTP

x38 Grb2-SOS

x39 (IL6-gp80- gp130-JAK)2*–SHP2*

x40 (IL6-gp80- gp130-JAK)2*–SHP2*-Grb2

x41 (IL6-gp80- gp130-JAK)2*–SHP2*-Grb2-SOS

x42 (IL6-gp80- gp130-JAK)2*–SHP2*-Grb2-SOS-Ras-GDP

x43 (IL6-gp80- gp130-JAK)2*–SHP2*-Grb2-SOS-Ras-GTP

x44 SHP2*-Grb2-SOS

x45 SHP2*-Grb2

x46 SHP2*

x47 Raf

x48 Raf-Ras-GTP

x49 Ras-GTP*

x50 Phosp1

x51 Raf*

x52 Raf*-Phosp1

x53 MEK

x54 MEK-Raf*

x55 MEK-P

x56 MEK-P-Raf*

x57 MEK-PP

x58 MEK-PP-Phosp2

x59 Phosp2

x60 MEK-P-Phosp2

x61 ERK

x62 ERK-MEK-PP

x63 ERK-P

x64 ERK-P-MEK-PP

x65 ERK-PP

x66 Phosp3

x67 ERK-PP-Phosp3

x68 ERK-P-Phosp3

APPENDIX-IV

Model Parameters:

kf0 ¼ 100� 10�3 kr0 ¼ 0:05kf1 ¼ 100� 10�3 kr1 ¼ 0:05

kf2 ¼ 20� 10�3 kr2 ¼ 0:02

kf3 ¼ 40� 10�3 kr3 ¼ 0:2

k4 ¼ 0:005

kf5 ¼ 8� 10�3 kr3 ¼ 0:8

k6 ¼ 0:4

kf7 ¼ 5� 10�3 kr7 ¼ 0:5

kf8 ¼ 20� 10�3 kr8 ¼ 0:1

kf9 ¼ 1� 10�3 kr9 ¼ 0:2

k10 ¼ 0:003

kf11 ¼ 1� 10�3 kr11 ¼ 0:2

k12 ¼ 0:003

kf13 ¼ 0:0002� 10�3 kr13 ¼ 0:2

k14 ¼ 0:005

kf15 ¼ 1� 10�3 kr15 ¼ 0:2

k16 ¼ 0:005

k17 ¼ 0:05

k18a ¼ 0:01 k18b ¼ 400

k19 ¼ 0:001

k20 ¼ 0:01

kf21 ¼ 20� 10�3 kr21 ¼ 0:1

k22 ¼ 0:0005

k23 ¼ 0:0005

kf24 ¼ 1� 10�2 kr24 ¼ 0:55

kf25 ¼ 1� 10�2 kr25 ¼ 0:0214kf26 ¼ 1:5� 10�2 kr26 ¼ 1:3

kf27 ¼ 0:5 kr27 ¼ 1� 10�4

kf28 ¼ 1� 10�3 kr28 ¼ 0:0053

kf29 ¼ 1 kr29 ¼ 7� 10�4

kf30 ¼ 7:9� 10�3 kr30 ¼ 0:3

kf31 ¼ 0:023 kr31 ¼ 2:2� 10�4

kf32 ¼ 0:1 kr32 ¼ 2:45� 10�4

kf33 ¼ 0:3 kr33 ¼ 2:1� 10�2

kf34 ¼ 6 kr34 ¼ 0:6

APPENDIX-II

(continued)Variable Description

Singh et al.: Modeling Regulatory Mechanisms 861

Biotechnology and Bioengineering. DOI 10.1002/bit

References

Baumann H, Gauldie J. 1994. The acute phase response. Immunol Today

15:74–80.

BaumannH, Isseroff H, Latimer JJ, Jahreis GP. 1988. Phorbolster modulates

interleukin 6 and interleukin 1 regulated expression of acute phase

plasma proteins in hepatoma cells. J Biol Chem 263:17390–17396.

Fasshauer M, Kralisch S, Klier M, Lossner U, Bluher M, Klein J. 2004.

Insulin resistance-inducing cytokines differentially regulate SOCS

mRNA expression via growth factor- and JAK/STAT-signaling path-

ways in 3T3-L1 adipocytes. J Endocrinol 181:129–138.

Fischer P, Lehmann U, Sobota RM, Schmitz J, Niemand C, Linnemann S,

Haan S, Behrmann I, Yoshimura A, Johnston JA, Muller-Newen G,

Heinrich PC, Schaper F. 2004. The role of the inhibitors of interleukin-6

signal transduction SHP-2 and SOCS3 foe desensitization of inter-

leukin-6 signaling. Biochem J 378:449–460.

He B, You L, Xu Z, Mazieres J, Lee AY, Jablons DM. 2004. Activity of the

suppressor of cytokine signaling-3 promoter in human non-small-cell

lung cancer. Clin Lung Cancer 5(6):366–370.

Heinrich PC, Behrmann I, Muller-Newen G, Schaper F, Graeve L. 1998.

Interleukin-6-type cytokine signaling through the gp130/JAK/STAT

pathway. Biochem J 334:297–314.

Heinrich PC, Behrmann I, Haan S, Hermanns HM, Muller-Newen G,

Schaper F. 2003. Principles of interleukin (IL)-6-type cytokine signaling

and its regulation. Biochem J 374:1–20.

Jayaraman A, Yarmush ML, Roth CM. 2000. Dynamics of Gene

expression in rat hepatocytes under stress. Metab Eng 2:239–251.

Kholodenko BN. 2000. Negative feedback and ultrasenstivity can bring

about oscillations in the mitogen-activated protein kinase cascades. Eur

J Biochem 267:1583–1588.

Kim H, Baumann H. 1999. Dual signaling role of the protein tyrosine

phosphate SHP-2 in regulating expression of acute-phase plasma

proteins by interleukin-6 cytokine receptors in hepatic cells. Mol Cell

Biol 19:5326–5338.

Lai CF, Ripperger J, Wang Y, Kim H, Hawleys RB. 1999. The STAT3-

independent signaling pathway by glycoprotein 130 in hepatic cells.

J Biol Chem 274:7793–7802.

Lang R, Pauleau AL, Parganas E, Takahashi Y,Mages J, Ihle JN, Rutschman

R, Murray PJ. 2003. SOCS regulates the plasticity of gp120 signaling.

Nat Immunol 4:546–550.

LehmannU, Schmitz J,WeissenbachM, Sobota RM,HortnerM, Friederichs

K, Behrmann I, Tsiaris W, Sasaki A, Schneider-Mergener J, Yoshimura

A,Neel BG,Heinrich PC, Schaper F. 2003. SHP2 and SOCS3 contribute

to Tyr-759-dependent attenuation of interleukin-6 signaling through

gp130. J Biol Chem 278:661–667.

Levy DE, Darnell JE Jr. 2002. Stats: Transcriptional control and biological

impact. Nature Review Mol Cell Biol 3:651–662.

Niwa Y, Kanda H, Shikauchi Y, Saiura Y, Matsubara K, Kitagawa T,

Yamamoto J, Kubo T, Yoshikawa H. 2005. Methylation silencing of

SOCS-3 promotes cell growth and migration of enhancing JAK/STAT

and FAK signalings in human hepatocellular carcinoma. Oncogene

24:6406–6417.

Pinilla JC, Hayes P, Laverty W, Arnold C, Laxdal V. 1998. The C-reactive

protein to prealbumin ratio correlates with the severity ofmultiple organ

dysfunction. Surgery 24:799–806.

Roth CM, Reiken SR, Le Doux JM, Rajur SB, Lu XM,Morgan JR, Yarmush

ML. 1997. Targeted antisense modulation of inflammatory cytokine

receptors. Biotechnol Bioeng 55:72–81.

Schaper F, Gendo C, Monika E, Schmitz J, Grimm C, Anhuf D, Kerr IM.

1998. Activation of the protein tyrosine phosphate SHP-2 via the

interleukin-6 signal transducing receptor protein gp130 requires

tyrosine kinase JAK1 and limits acute-phase protein expression.

Biochem J 335:557–565.

Schmitz J, Weissenbach M, Haan S, Henerich PC, Schaper F. 2000. SOCS3

exerts its inhibitory function on interleukin-6 signal transduction

through the SHP-2 recruitment site of gp130. J Biol Chem 275:

12848–12856.

Schoeberl B, Eichler-Jonsson C, Gilles ED, Muller G. 2002. Computational

modeling of the dynamics of the MAP kinase cascade activated by

surface and internalized EGF receptors. Nat Biotechnol 20:370–375.

ten Hoeve J, Ibarra-Sanchez M, Fu Y, Zhu W, Tremblay M, David M, Shuai

K. 2002. Identification of a nuclear Stat1 protein tyrosine phosphatase.

Mol Cell Biol 22:5662–5668.

Yamada S, Shiono S, Joo A, Yoshimura A. 2003. Control mechanism of

JAK/STAT signal transduction pathway. FEBS Lett 534:190–196.

APPENDIX-IV

(continued)

kf35 ¼ 0:0015 kr35 ¼ 4:5� 10�3

Vm ¼ 1:7 Km ¼ 340

kf37 ¼ 0:3 kr37 ¼ 9� 10�4

kf38 ¼ 1� 10�2 kr38 ¼ 0:55

kf39 ¼ 0:3 kr39 ¼ 9� 10�4

kf40 ¼ 3� 10�2 kr40 ¼ 0:064

kf41 ¼ 3� 10�2 kr41 ¼ 0:0429

kf42 ¼ 7:17� 10�2 kr42 ¼ 0:2

k43 ¼ 1

kf44 ¼ 1:1� 10�2 kr44 ¼ 0:01833

k45 ¼ 3:5

kf46 ¼ 1:1� 10�2 kr46 ¼ 0:01833

k47 ¼ 2:9

kf48 ¼ 1:43� 10�2 kr48 ¼ 0:8

k49 ¼ 0:058

kf50 ¼ 2:7� 10�4 kr50 ¼ 0:5

k51 ¼ 0:058

kf52 ¼ 1:1� 10�4 kr52 ¼ 0:033

k53 ¼ 16

kf54 ¼ 1:1� 10�4 kr54 ¼ 0:033

k55 ¼ 5:7

kf56 ¼ 1:4� 10�2 kr56 ¼ 0:6

k57 ¼ 0:27

kf58 ¼ 5� 10�3 kr58 ¼ 0:5

k59 ¼ 0:3

kf60 ¼ 0:5 kr60 ¼ 5� 10�3

kf61 ¼ 0:2 kr61 ¼ 0:0002� 10�3

First order rate constants are in units of s�1 and second order rateconstants are expressed in nM�1 s�1. Michaelis constants are in nM.

APPENDIX-V

Initial Conditions:

x1 gp80 8

x3 gp130 0.8

x4 JAK 12

x9 STAT3C 1000

x15 SHP2 100

x17 PP1 50

x23 PP2 60

x34 Grb2 85

x35 SOS 34

x36 Ras-GDP 19000

x47 Raf 67

x50 Phosp1 67

x53 MEK 41667

x59 Phosp2 67

x61 ERK 35000

x66 Phosp3 16667

All other initial conditions are set to zero.Initial concentrations of proteins are in units of nM.

862 Biotechnology and Bioengineering, Vol. 95, No. 5, December 5, 2006

DOI 10.1002/bit