Model analysis of diﬀerence between EGF pathway and FGF pathway
Satoshi Yamada,a,* Takaharu Taketomi,b,1
and Akihiko Yoshimurab,1
a
Advanced Technology R&D Center, Mitsubishi Electric Corporation, 8-1-1, Tsukaguchi-Honmachi, Amagasaki, Hyogo 661-8661, Japan
b
Medical Institute of Bioregulation, Kyushu University, 3-1-1, Maidashi, Higashi-ku, Fukuoka 812-8582, Japan
Received 6 January 2004
Abstract
The diﬀerence in time course of Ras and mitogen activated protein kinase (MAPK) cascade by diﬀerent growth factors is
considered to be the cause of diﬀerent cellular responses. We have developed the computer simulation of Ras-MAPK signal
transduction pathway containing newly identiﬁed negative feedback system, Sprouty, and adaptor molecules. Unexpectedly, negative
feedback system did not profoundly aﬀect time course of MAPK activation. We propose the key role of ﬁbroblast growth
factor receptor substrate 2 (FRS2) in NGF/FGF pathway for sustained MAPK activation. More Grb2–SOS complexes were recruited
to the plasma membrane by binding to membrane-bound FRS2 in FGF pathway than in EGF pathway and caused sustained
activation of ERK. The EGF pathway with high concentration of EGF receptor also induced sustained MAPK activation,
which is consistent with the results in the PC12 cell overexpressing the EGF receptors. The simulated time courses of FRS2
knock-out cells were consistent with those of the reported experimental results.
Ó 2004 Elsevier Inc. All rights reserved.
Keywords: Epidermal growth factor; Nerve growth factor; Fibroblast growth factor; Fibroblast growth factor receptor substrate 2
Signal transduction pathways are concerned with
many cellular events including cell proliferation, differentiation,
survival, and apoptosis. Even the same
stimulation induces diﬀerent cellular responses depending
on cell types and stimulation time, although
their signals are transduced through the same receptor
and pathways. The growth factor receptors belonging
to the family of protein–tyrosine kinase receptors also
regulate cell growth, survival, and diﬀerentiation. These
tyrosine kinases activate several signal transduction
pathways, i.e., Janus kinase (JAK)/signal transducer
and activator of transcription (STAT), phospholipase
Cc (PLCc), phosphatidylinositol 3 kinase (PI3K), and
Ras-mitogen activated protein kinase (MAPK) path-
ways.
The MAPK cascade initiated by Ras is a conserved
pathway from yeast to human. It is activated by many
growth factors and stimuli, and induced several
responses. Activation of the MAPK cascade by receptor
tyrosine kinases (RTKs), such as the epidermal growth
factor (EGF) receptor, is initiated by binding of Shc and
Grb2 to the phosphorylated tyrosine residues of the
receptor. The complex of Grb2 and SOS activates Ras
by GTP loading. Ras-GTP recruits Raf1 to the plasma
membrane [1,2]. Then, Raf1 is phosphorylated and
activated by not well-deﬁned kinases with complex
regulatory mechanisms [3–5]. Activated Raf then phosphorylates
and activates the dual-speciﬁc kinase MEK,
which phosphorylates and activates MAPK. This RasMAP
kinase cascade is strictly regulated by several
ways; for example, activation of Ras-GAP, phosphorylation
of Raf, and inducible MAP kinase phosphatases
(MKPs). Recently, we cloned a family of novel membrane-bound
molecules, Spreds, which are related to
Sprouty [6]. Spreds and Sproutys are shown to be negative
regulators for several types of growth factor-induced
MAPK activation, including the ﬁbroblast
growth factor (FGF) and EGF [7,8]. Four Sprouty homologs
are found in mammals. Vertebrate Sproutys
have also been implicated in the negative-feedback
*
Corresponding author. Fax: +81-6-6497-7728.
E-mail addresses: Yamada.Satoshi@wrc.melco.co.jp (S. Yamada),
ttake@bioreg.kyushu-u.ac.jp (T. Taketomi), yakihiko@bioreg.
kyushu-u.ac.jp (A. Yoshimura).
1
Fax: +81-92-642-6825.
0006-291X/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.bbrc.2004.01.009
Biochemical and Biophysical Research Communications 314 (2004) 1113–1120
BBRC
www.elsevier.com/locate/ybbrc
regulation of FGF-signaling in embryogenesis [9,10] and
angiogenesis [11].
Ras-MAPK pathway is shown to be important for
both cell proliferation and diﬀerentiation, and the
strength or duration of MAP kinases is suggested to
determine the cell fate. For example, EGF induces cell
division in PC12 cells, but nerve growth factor (NGF) or
FGF induces the diﬀerentiation of these cells. Although
both EGF and NGF/FGF activate MAPK cascade,
EGF causes transient activation of MAPK cascade,
whilst NGF/FGF causes both transient and sustained
activation. The dynamical diﬀerence is considered to be
the cause of the diﬀerence in cell responses [12]. Cells
with overexpressed EGF receptors showed transient and
sustained activation of MAPK cascade in response to
EGF and EGF induces diﬀerentiation of these transformants
[13]. Although several computer models of
Ras-MAPK pathway were developed [14–18], none of
them clariﬁed these diﬀerences.
In order to investigate the mechanism how diﬀerent
growth factors induce diﬀerent time courses of MAP
kinase activation, we have developed a computer simulation
of the Ras-MAPK signal transduction pathways.
The EGF and FGF pathways in PC12 cells were used.
Our analysis indicates that ﬁbroblast growth factor receptor
substrate 2 (FRS2) shows the key role for the
prolonged responses in the NGF/FGF pathway.
Model description
The kinetic scheme presented in Fig. 1(1) forms the
basis for the computational analysis of the Ras-MAPK
signaling network. This network is similar to that
presented in previous models [14–18].
Brieﬂy, the ligand binding induces the receptor dimerization
and the autophosphorylation, which activates
receptor’s protein kinase activity. Phosphorylated
tyrosine residues in the cytoplasmic domain of receptors
work as binding sites for several adaptor proteins. Grb2
binds to a phosphorylated tyrosine residue of cytoplasmic
domain of receptors and recruits GTP exchange
protein for Ras, SOS. Activated Ras induces Raf
phosphorylation. However, protein kinase for Raf
phosphorylation has not been identiﬁed [3–5]. In this
model, Ras is treated as virtual protein kinase for Raf.
The phosphorylation of Raf induces MAPK cascade,
MEK, and ERK phosphorylation. Activated ERK is
translocated to the nucleus and phosphorylates several
transcription factors, one example is Elk. Activated
ERK also phosphorylates SOS and inactivates it. This
inhibition makes one of the feedback loops of this
pathway [19]. The ligand-induced endocytosis of receptors
and the signal transduction by internalized receptors
are included in EGF and FGF signal transduction
pathway similar to the previous model [16–18].
In EGF pathway, Grb2–SOS complexes were recruited
to the plasma membrane by binding to receptors
directly or via Shc (Fig. 1(2)). The ﬁbroblast growth
factor receptor substrate 2 (FRS2) was reported to be
myristylated and function as a lipid-anchored docking
protein for Grb2–SOS complex without growth factor
receptors in FGF signal transduction pathway [20,21].
FRS2 was reported to have SH2 binding site which was
phosphorylated by activated FGF receptors [20]
(Fig. 1(3)). The Grb2–SOS complex bound to phosFig.
1. Schematic representation of the computer simulation of Ras-MAPK signal transduction pathway. (1) The common pathway model between
EGF and FGF, (2) signal transduction pathway from EGF receptor to Grb2–SOS, and (3) signal transduction pathway from FGF receptor to Grb2–
SOS. In this model, arrows with dot symbols denote enzymatic reactions where enzymes are shown at the line to the dot symbols, and the name
containing “P” usually denotes the phosphorylated type, e.g., “RafP” denotes the phosphorylated type of “Raf,” the complex of some proteins is
usually described in hyphen, e.g., the complex of “GFR2P” and “GS” is described in “GFR2P-GS.”
1114 S. Yamada et al. / Biochemical and Biophysical Research Communications 314 (2004) 1113–1120
phorylated FRS2, which is not bound to FGF receptor
but directly bound to the plasma membrane via its
myristyl group, also activates Ras-GDP. The concentration
of FRS2 has not been precisely known, but we
speculate that the amount of FRS2 is greater than FGF
receptor, because FRS2 is a downstream ampliﬁer of
the FGF receptor signaling. The FRS2 was also reported
to act as an adaptor protein in NGF signaling
pathway [22].
Sprouty is induced by Ras-MAPK signal transduction
pathway. We found Sprouty did not inhibit EGF
pathway, but did inhibit FGF pathway [8]. Although its
inhibitory mechanism has not been clariﬁed, Sprouty
did not inhibit the Ras activation, but inhibited the Raf
activation [8]. In this model, Sprouty is included in the
FGF pathway only and it binds to Raf to inhibit the Raf
activation.
Parameter values and initial concentrations were set
according to the values in the previous models [15,16].
But the models with such parameters did not show the
time courses to ﬁt observed time courses of EGF signal
transduction pathway. Those values were set to ﬁt
the experimental data of EGF stimulation by using
the genetic algorithm [23]. In FGF pathway, the
same parameter values except those for FRS2 reactions
were used.
In this kinetic analysis, Michaelis–Menten equation is
not used, because in the signal transduction pathway the
condition that the substrate concentration is much larger
than the enzyme is not usually satisﬁed [24]. The
transcription, translation, and translocation are approximated
by the equations used in [24]. Detailed
chemical reactions and their parameters are described in
Appendix A. These reactions are described in the differential
equations and solved mathematically by using
Runge–Kutta–Gill method [24]. The simulation program
was written in C by us, utilizing commonly used
subroutine [24].
Results and discussion
The binding of growth factors induces receptor dimerization
and the activation of their tyrosine kinase
activity. The phosphorylated tyrosine residues work as
the binding sites for several adaptor proteins having SH2
or SH3 domains. The Grb2 protein is one such adaptor
protein. The SOS protein binds to plasma-membranebound
Grb2 (bound to growth factor receptors in EGF
pathway or to FRS2 in FGF pathway) and activates
membrane-bound RasGDP by exchanging GDP with
GTP. The activated Ras activates MAPK cascade (RafMEK-ERK1).
The phosphorylated MAPK (ERK1)
reached a maximum in 5–10 min and then decreased by
the inhibitory phosphorylation of SOS by ERK1. In EGF
pathway, phosphorylated ERK1 disappeared in 30–
60 min. However, in FGF pathway, ERK activation was
maintained for more than 2 h as shown in Fig. 2. Fig. 3
demonstrates that the simulated time course shows the
above characteristics and the diﬀerence between EGF
pathway (Fig. 3 left panel) and FGF pathway (Fig. 3 right
panel). First, we thought that the induction of negative
regulators may make the diﬀerence between MAPK activities
in response to EGF and FGF. In FGF pathway,
induced Sprouty inhibits Raf activation by binding to
Ras–Raf complexes. Fig. 3 also shows the time course of
Sprouty knock-out cells (dotted line), which were simulated
by setting the mRNA synthesizing rate as 0, where
the phosphorylation of ERK1 lasted for a longer time,
activated Ras decreased faster than in the normal condition.
This phenomenon can be explained by the Sprouty
binding to Ras–Raf complexes. Ras–Raf–Sprouty complexes
are considered to exist for a longer time [11].
However, the presence or absence of Sprouty could not
explain the strong sustained activation of MAPK.
It has been shown that phosphorylated FRS2 functions
as an anchoring protein for Grb2 without binding to
receptors. The diﬀerence between EGF pathway model
and FGF one is the participation of FRS2 in FGF pathway,
but not in EGF pathway. In order to clarify the
FRS2’s role, the dependency on FRS2 initial concentration
was investigated. Figs. 4B and D shows the dependency
on FRS2 concentration. In the case of lower FRS2
concentration, the time course of FGF pathway was
similar to that of EGF pathway (compare Fig. 4B with
Fig. 3K). Therefore, the prolonged phosphorylation of
Elk or ERK1 was considered to be due to more Grb2–
SOS complexes in plasma membrane which bound to the
phosphorylated membrane-bound FRS2. On the other
hand, the concentration of Shc in EGF pathway had no
eﬀect on the time course (Figs. 4A and C).
Although more sustained activities were observed
without the receptor internalization, the diﬀerence between
those with the internalization and those without
was small (data not shown). The internalization could
not explain the strong sustained activation of MAPK.
The time course of FRS2 knock-out cells showed no
sustained activation (Fig. 5A) and low sensitivity to low
concentration of FGF (Figs. 5A and B), which was
consistent with the reported time course of FRS2
Fig. 2. Time course of MAPK (ERK) activation in response to EGF
and FGF. Mouse embryonic ﬁbroblasts (MEFs) were stimulated with
25 ng/ml EGF or bFGF for indicated periods. Cell extracts were prepared
and analyzed with immunoblotting with anti-phosphoMAPK
(ERK) (upper panel) and anti-ERK2 (lower panel).
S. Yamada et al. / Biochemical and Biophysical Research Communications 314 (2004) 1113–1120 1115
knock-out cells [20]. In FGF pathway, since growth
factor receptors act as a kinase for FRS2, FGF pathway
shows hyper sensitivity to FGF concentration.
Another way to increase membrane-bound Grb2–
SOS is to increase receptor concentration (normal concentration
is 26 nM, the concentration is changed from
0.26 nM to 2.6 lM). Fig. 6 shows the dependency on the
initial receptor concentration. As the initial concentration
of EGF receptor increases, phosphorylation of
MAPK is prolonged (Figs. 6A and C). This characteristic
is consistent with the experimental responses of cells
in which EGF receptor is overexpressed [12]. On the
contrary, the increase in FGF receptor shows no increase
in prolonged MAPK activation (Figs. 6B and D).
Fig. 3. Simulated time course of Ras-MAPK activation over 4 h continuous exposure to EGF (A, C, E, G, I, K) and FGF (B, D, F, H, J, L). The time
course of GS (Grb2–SOS complex) bound to plasma membrane via EGFR (A) or phosphorylated FRS2 (B), activated Ras (RasT) (C,D), phosphorylated
Raf (E,F), phosphorylated MEK (G,H), phosphorylated ERK (I,J), and phosphorylated Elk (K,L). The time courses of Sprouty knockout
cells are also shown (dashed line in B, D, F, H, J, L).
1116 S. Yamada et al. / Biochemical and Biophysical Research Communications 314 (2004) 1113–1120
Fig. 4. Dependency on Shc and FRS2 concentration. (A,B) The time course of phosphorylated Elk for various concentrations (1/100–100 times) of
Shc in EGF pathway (A) and FRS2 in FGF pathway (B). The bold line shows the time course of the normal condition. (C,D) The dependency of the
peak concentration (s) and steady state (3 h) concentration (d) on Shc in EGF pathway (C) and on FRS2 in FGF pathway (D).
Fig. 5. Comparison of the time course of FRS2 knock-out cells with those normal cells. (A) The time course of phosphorylated ERK in the normal
cells (solid line) and in the FRS2 knock-out cells (dashed line) stimulated by various FGF concentrations (0.005, 0.05, 0.5, and 5 nM). (B) The
dependency on FGF concentration of peak values of phosphorylated ERK in the normal cells (s), that in the FRS2 knock-out cells (Ã), the steady
state values (3 h) in the normal cells (d), and that in the FRS2 knock-out cells (j).
S. Yamada et al. / Biochemical and Biophysical Research Communications 314 (2004) 1113–1120 1117
Conclusions
Through a quantitative analysis of a computer simulation
of Ras-MAPK signal transduction pathway, we
have presented the key role of FRS2 in FGF pathway.
In FGF pathway, more Grb2–SOS are recruited to the
plasma membrane via phosphorylated FRS2 than those
bound to receptors in EGF pathway. From our simulation
study, the key diﬀerence between FGF pathway
and EGF pathway is the concentration of Grb2–SOS
complex bound to the plasma membrane. The increase
in EGF receptor concentration is another way to increase
membrane-bound Grb2–SOS. The model with
the high EGF receptor concentration showed prolonged
phosphorylation of ERK1 or Elk similar to FGF
pathway, which was consistent with the result of the cell
with overexpressed EGF receptors. FRS2 knock-out
cells showed only transient activation, which was consistent
with the experimental results [20]. Since the FRS2
was also reported to act as an adaptor protein in NGF
signaling pathway [22], NGF signaling pathway is considered
to have the same mechanism as FGF pathway.
Fig. 6. Dependency on receptor concentration. The time course of phosphorylated Elk for various concentrations (1/100–100 times) of EGFR (A)
and FGFR (B). The dependency of the peak concentration (s) and steady state (3 h) concentration (d) in EGF pathway (C) and FGF pathway (D).
Appendix A. Chemical reactions and their parameter values
First and second rate constants are expressed in units of sÀ1
and 106
MÀ1
sÀ1
, respectively. The dissociation constants
(kd) for binding reactions are also written in parentheses in units of nM. Initial concentrations of proteins are expressed
in units of nM.
The following reactions are EGF pathway.
[EGF] + [R] $ [EGFR] k1 ¼ 100., kÀ1 ¼ 0:06 (kd1 ¼ 0:6)
2[EGFR] $ [EGFR2] k2 ¼ 10., kÀ2 ¼ 0:1 (kd2 ¼ 10.)
[EGFR2] ! [EGFR2P] k3 ¼ 2:014
[EGFR2P] + [SHP] $ [EGFR2P-SHP] k4 ¼ 3:114, kÀ4 ¼ 0:2 (kd4 ¼ 64:22)
[EGFR2P-SHP] ! [EGFR2] + [SHP] k5 ¼ 0:2661
[EGFR2P] + [Shc] $ [EGFR2P-Shc] k6 ¼ 43:75, kÀ6 ¼ 0:6 (kd6 ¼ 13:72)
[EGFR2P-Shc] ! [EGFR2P-ShcP] k7 ¼ 0:5838
[EGFR2P] + [ShcP] $ [EGFR2P-ShcP] k8 ¼ 4:481, kÀ8 ¼ 0:3 (kd8 ¼ 66:95)
1118 S. Yamada et al. / Biochemical and Biophysical Research Communications 314 (2004) 1113–1120
[ShcP] + [SHP] $ [ShcP-SHP] k4, kÀ4 (kd4)
[ShcP-SHP] ! [Shc] + [SHP] k5
[EGFR2P-ShcP] + [GS] $ [EGFR2P-ShcP-GS] k9 ¼ 4:922, kÀ9 ¼ 0:045 (kd9 ¼ 9:143)
[EGFR2P] + [GS] $ [EGFR2P-GS] k10 ¼ 2:734, kÀ10 ¼ 0:025 (kd10 ¼ 9:143)
[RasD] + [EGFR2P-GS] $ [EGFR2P-GS-RasD] k11 ¼ 202:9, kÀ11 ¼ 0:18 (kd11 ¼ 0:887)
[EGFR2P-GS-RasD] ! [EGFR2P-GS] + [RasT] k12 ¼ 0:1434
[RasD] + [EGFR2P-ShcP-GS] $ [EGFR2P-ShcP-GS-RasD] k11, kÀ11 (kd11)
[EGFR2P-ShcP-GS-RasD] ! [EGFR2P-ShcP-GS]+[RasT] k12
[RasT] + [GAP] $ [RasT-GAP] k13 ¼ 2:854, kÀ13 ¼ 0:96 (kd13 ¼ 336:4)
[RasT-GAP] ! [GAP] + [RasD] k14 ¼ 7:760
[Raf] + [RasT] $ [Raf-RasT] k15 ¼ 1:754, kÀ15 ¼ 0:05 (kd15 ¼ 28:51)
[Raf-RasT] ! [RasT] + [RafP] k16 ¼ 0:07624
[RafP] + [PP] $ [RafP-PP] k17 ¼ 4:908, kÀ17 ¼ 0:4 (kd17 ¼ 81:50)
[RafP-PP] ! [PP] + [Raf] k18 ¼ 0:3665
[MEK] + [RafP] $ [MEK-RafP] k19 ¼ 9:196, kÀ19 ¼ 0:9 (kd19 ¼ 97:87)
[MEK-RafP] ! [MEKP] + [RafP] k20 ¼ 1:693
[MEKP] + [RafP] $ [MEKP-RafP] k19, kÀ19 (kd19)
[MEKP-RafP] ! [MEKPP] + [RafP] k20
[MEKPP] + [XPP] $ [MEKPP-XPP] k21 ¼ 2:060, kÀ21 ¼ 0:4 (kd21 ¼ 194:1)
[MEKPP-XPP] ! [MEKP] + [XPP] k22 ¼ 0:2752
[MEKP] + [XPP] $ [MEKP-XPP] k21, kÀ21 (kd21)
[MEKP-XPP] ! [MEK] + [XPP] k22
[ERKc] + [MEKPP] $ [ERKc-MEKPP] k23 ¼ 0:318, kÀ23 ¼ 0:9 (kd23 ¼ 2832.)
[ERKc-MEKPP] ! [ERKPc] + [MEKPP] k24 ¼ 0:1002
[ERKPc] + [MEKPP] $ [ERKPc-MEKPP] k23, kÀ23 (kd23)
[ERKPc-MEKPP] ! [ERKPPc] + [MEKPP] k24
[ERKPPc] + [MKP] $ [ERKPPc-MKP] k25 ¼ 0:239, kÀ25 ¼ 0:4 (kd25 ¼ 1676.)
[ERKPPc-MKP] ! [ERKPc] + [MKP] k26 ¼ 0:1298
[ERKPc] + [MKP] $ [ERKPc-MKP] k25, kÀ25 (kd25)
[ERKPc-MKP] ! [ERKc] + [MKP] k26
[GS] + [ERKPPc] $ [GS-ERKPPc] k27 ¼ 8:898, kÀ27 ¼ 1. (kd27 ¼ 112:4)
[GS-ERKPPc] ! [GSP] + [ERKPPc] k28 ¼ 0:0426
[GSP] + [GPP] $ [GSP-GPP] k29 ¼ 0:147, kÀ29 ¼ 0:4 (kd29 ¼ 2725.)
[GSP-GPP] ! [GS] + [GPP] k30 ¼ 0:01928
[ERKPPc] ! [ERKPPn] k31 ¼ 0:0002
[Elk] + [ERKPPn] $ [Elk-ERKPPn] k32 ¼ 2:, kÀ32 ¼ 1. (kd32 ¼ 500.)
[Elk-ERKPPn] ! [ElkP] + [ERKPPn] k33 ¼ 0:05
[ElkP] + [PPN] $ [ElkP-PPN] k34 ¼ 1:, kÀ34 ¼ 0:2 (kd34 ¼ 200.)
[ElkP-PPN] ! [Elk] + [PPN] k35 ¼ 0:01
[ERKPPn] + [PPN] $ [ERKPPn-PPN] k34, kÀ34 (kd34)
[ERKPPn-PPN] ! [ERKPn] + [PPN] k35
[ERKPn] + [PPN] $ [ERKPn-PPN] k34, kÀ34 (kd34)
[ERKPn-PPN] ! [ERKn] + [PPN] k35
[ERKPn] ! [ERKPc] k36 ¼ 0:01
[ERKn] ! [ERKc] k37 ¼ 0:05
[EGFR] ! [EGFR]i d[EGFR]i/dt ¼ k38*(e1 þ ð1 À e1Þ Ã ð1 À expðÀ3t=T1ÞÞ)*[EGFR] k38 ¼ 0:0024, e1 ¼ 0.12,
T1 ¼ 195.
[R]![R]i d[R]i/dt ¼ k39*(e1 þ ð1 À e1Þ*(1 À expðÀ3t= T1Þ))*[R] k39 ¼ 0:00012, e1, T1
d/[R]i/dt ¼ Àk40[R]i k40 ¼ 0:005
In FGF pathway, reactions concerning with Shc are excluded and reactions for FRS2 and for Sprouty are included.
Other reactions except additional reactions below are same as reactions in EGF pathway. EGF in reactions should be
exchanged into FGF for FGF pathway.
[FRS] + [FGFR2P] $ [FGFR2P-FRS] k50 ¼ 43:75, kÀ50 ¼ 0:6 (kd50 ¼ 13:72)
[FGFR2P-FRS] ! [FRSP] + [FGFR2P] k51 ¼ 2:584
[FRSP] + [SHP] $ [FRSP-SHP] k52 ¼ 0:4, kÀ52 ¼ 0:2 (kd52 ¼ 500.)
[FRSP-SHP] ! [FRS] + [SHP] k53 ¼ 0:01
S. Yamada et al. / Biochemical and Biophysical Research Communications 314 (2004) 1113–1120 1119
[FRSP] + [GS] $ [FRSP-GS] k54 ¼ 10:94, kÀ54 ¼ 0:1 (kd54 ¼ 9:143)
[RasD] + [FRSP-GS] $ [FRSP-GS-RasD] k11, kÀ11 (kd11)
[FRSP-GS-RasD] ! [FRSP-GS] + [RasT] k12
d[mRNASn]/dt ¼ k55a[ElkP]/(k55b + [ElkP]) k55a ¼ 0:01 nM/s, k55b ¼ 50 nM
[mRNASn] ! [mRNASc] k56 ¼ 0:001
d[Sprouty]/dt ¼ k57[mRNASc] k57 ¼ 0:02
d[mRNASc]/dt ¼ Àk58[mRNASc] k58 ¼ 0:0005
d[Sprouty]/dt ¼ Àk59[Sprouty] k59 ¼ 0:0001
[Sprouty] + [Raf] $ [Raf-Sprouty] k60 ¼ 1., kÀ60 ¼ 0:1 (kd60 ¼ 100.)
[Sprouty] + [Raf-RasT] $ [Raf-RasT-Sprouty] k60, kÀ60 (kd60)
[Raf-Sprouty] + [RasT] $ [Raf-RasT-Sprouty] k15, kÀ15 (kd15)
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