ARTICLES nature cell biology Prediction and validation of the distinct dynamics of transient and sustained ERK activation Satoru Sasagawa1,4, Yu-ichi Ozaki1,4, Kazuhiro Fujita2 and Shinya Kuroda1,2,3,5 To elucidate the hidden dynamics of extracellular-signal-regulated kinase (ERK) signalling networks, we developed a simulation model of ERK signalling networks by constraining in silica dynamics based on in vivo dynamics in PC12 cells. We predicted and validated that transient ERK activation depends on rapid increases of epidermal growth factor and nerve growth factor (NGF) but not on their final concentrations, whereas sustained ERK activation depends on the final concentration of NGF but not on the temporal rate of increase. These ERK dynamics depend on Ras and Rapl dynamics, the inactivation processes of which are growth-factor-dependent and -independent, respectively. Therefore, the Ras and Rapl systems capture the temporal rate and concentration of growth factors, and encode these distinct physical properties into transient and sustained ERK activation, respectively. Transient and sustained extracellular-signal-regulated kinase (ERK) activation regulate cell fates, such as growth and differentiation, in PC12 cells1. Extracellular stimuli, such as epidermal growth factor (EGF) and nerve growth factor (NGF), induce transient, and transient and sustained ERK activation, respectively14. EGF-dependent ERK activation involves tyrosine phosphorylation of the EGF receptor (EGFR), SOS-dependent Ras activation58, followed by activation of Raf and mitogen-activated protein kinase (MEK, also known as ERK kinase), which leads to ERK activation'. In turn, ERK activation is terminated by EGFR internalization, followed by degradation1011, recruitment of Ras GTPase-activating protein (GAP) to the plasma membrane where Ras is located1213, and ERK-dependent feedback inhibition of SOS1415, resulting in transient ERK activation. NGF-dependent ERK activation consists of transient and sustained ERK activation. NGF induces tyrosine phosphorylation of TrkA, a subunit of NGFR1. Transient ERK activation by NGF depends on Ras, in a similar way to EGF-dependent ERK activation16. Sustained ERK activation involves slow and sustained activation of Rapl (refs 16-19), which is mediated by sustained TrkA activation20. Activated Rapl activates B-Raf, followed by activation of MEK, leading to sustained ERK activation16'17'21'22. Recent studies have provided practical molecular frameworks of EGF-and NGF-dependent ERK signalling networks1,18,1'; however, the dynamics of transient and sustained ERK activation remains to be elucidated. Therefore, we used an integrated approach of in silico kinetic simulation232' and in vivo dynamics measurements of cross-talk points that are cooperatively regulated by upstream or downstream networks, as the dynamics of cross-talk points critically determine that of the whole networks. In addition, we used a single cell line — PC 12 cells — because in vivo dynamics differ between cell lines due to different expression levels of molecules. We predicted and validated that the Ras and Rapl systems specifically capture the temporal rate and concentration of growth factors, and encode these distinct physical properties of growth factors into transient and sustained ERK activation, respectively. RESULTS Modelling of ERK signalling networks Based on the literature, we first developed a block diagram of ERK signalling networks (Fig. 1, and see Supplementary Information, Fig. SI). We determined kinetic parameters based on earlier experimental observations and some assumptions, then further constrained parameters on the basis of in vivo dynamics in PC12 cells (see Supplementary Information, Table SI). We measured the in vivo tyrosine phosphorylation of EGFR and TrkA in a dose-dependent manner, using EGF and NGF, respectively, as constant stimulation of growth factors is first transformed into different temporal patterns at the receptor level (Fig. 1, boxes). The in vivo tyrosine phosphorylation of EGFR and TrkA were transient and sustained, respectively (Fig. 2a, b, upper panels)18,19,30. We next measured the in vivo dynamics of the cross-talk points of the ERK signalling networks (Fig. 1, boxes). Following stimulation, SOS is recruited to the plasma membrane where SOS activates Ras31. It is subsequently inhibited by ERK-dependent phosphorylation32,33, leading to the dissociation of SOS from the complex with Grb2, resulting in a decline of Ras activation32,33. Therefore, SOS is a cross-talk point of ERK-dependent negative-feedback inhibition32,33. Mobility shifts in SOS reflect its phosphorylation undergraduate Program for Bioinformatics and Systems Biology, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan, department of Computational Biology, Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan. 3PREST0, Japan Science and Technology Agency, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. "These authors contributed equally to this work. correspondence should be addressed to S.K. (e-mail: skuroda@is.s.u-tokyo.ac.jp) Published online: 27 March 2005; DOI: 10.1038/ncbl233 NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group 365 ARTICLES J xRap1-GAP c-Raf B-Raf N / MEK I-PP2A rJL>_ - ERK -MKP3 Figure 1 Schematic overview of EGF- and NGF-dependent ERK signalling networks. Arrows and bars indicate stimulatory and inhibitory interactions, respectively. In vivo and in silico dynamics of the indicated molecules were measured (boxes; see Fig. 2, and see also Supplementary Information, Fig. S2). All the biochemical reactions and parameters are provided in Supplementary Information, Fig.SI and TableSl, respectively. MKP3, MAP kinase phosphatase 3; PP2A, protein phosphatase 2A. state, which can be regarded as an inactive state of SOS32'33. The in vivo mobility shifts of SOS, in response to EGF and NGF, were correlated with ERK activation1832'33 (Fig. 2e, f, and see Supplementary Information, Fig. S2). Signals downstream of the receptors diverge into Ras and Rapl activities, then merge again into ERK activation16'17 via successive Raf and MEK activation9'34. These small GTPases are activated by the conversion of GDP-bound forms to GTP-bound forms35. The in vivo activation of Ras was transient in response to both stimuli (Fig. 2c, upper panel)18'19. The EGF stimulus did not induce sufficient activation of Rapl, whereas the NGF stimulus induced sustained activation of Rapl (Fig. 2d, upper panel)18'19. The EGF stimulus induced transient ERK phosphorylation in vivo (Fig. 2e, upper panel), whereas the NGF stimulus induced transient and sustained ERK phosphorylation in vivo (Fig. 2f, upper panel)18'19. We fixed the parameters by constraining the corresponding in silico dynamics on the basis of the above in vivo dynamics (Fig. 2, lower panels, and see Supplementary Informtion, Table S1). Of note, transient ERK activation did not always correlate with tyrosine phosphorylation of EGFR, especially at low doses of EGF in vivo and in silico (Fig. 2a, e), whereas the sustained ERK activation was nearly proportional to the tyrosine phosphorylation of TrkA in vivo and in silico (Fig. 2b, f, and see below). The in silico EGF-dependent transient ERK phosphorylation mainly depended on Ras activation, whereas the in silico NGF-dependent transient and sustained ERK phosphorylation depended on Ras and Rapl activation, respectively16,17 (see Supplementary Information, Fig. S3h, i). We further examined the dynamics without changing parameters. Prediction and validation of the distinct ERK dynamics Constant stimulation of growth factors is generally used for in vivo dynamics measurements (Fig. 3a, b, upper panels, solid lines). However, under physiological conditions, concentrations of growth factors are likely to gradually increase in a spatiotemporal-dependent manner. Therefore, we predicted ERK activation in response to various increasing rates of EGF and NGF (Fig. 3a, b, upper panels). Although constant EGF stimulus induced transient ERK activation, transient ERK activation gradually decreased as the temporal rates of EGF decreased in silico (Fig. 3a, middle panel). Importantly, the slow stimulus did not induce sufficient transient ERK activation (Fig. 3a, middle panel, green dashed line). By contrast, a similar sustained ERK activation was induced by both increasing and constant NGF stimuli in silico (Fig. 3b, middle panel). However, transient ERK activation gradually decreased as the temporal rates of NGF decreased. Therefore, transient ERK activation depends on the temporal rates of EGF and NGF, whereas sustained ERK activation can respond to both increasing and constant NGF stimuli and depends on the final concentrations. This difference is due to the distinct activation and inactivation mechanisms of Ras and Rapl (see below). We next attempted to validate this in silico prediction by measuring in vivo dynamics. As predicted, transient ERK activation decreased as the temporal rate of EGF decreased in vivo (Fig. 3a, lower panel). The slow stimulus did not induce sufficient transient ERK activation (Fig. 3a, lower panel, green dashed line). As the temporal rate of EGF decreased, the peak concentration of transient ERK phosphorylation decreased in silico (Fig. 3c). By contrast, a similar sustained ERK activation was induced by both increasing and constant NGF stimuli in vivo (Fig. 3b, lower panel). However, transient ERK activation gradually decreased as the temporal rates of NGF decreased, which was also consistent with the in silico prediction. Sustained ERK activation depends on the final concentrations of NGF, irrespective of constant or increasing stimulation in silico (Fig. 3d). We further performed stepwise increases and decreases of stimuli to predict in silico dynamics and to validate the dynamics of ERK activation in vivo (Fig. 4). The stepwise increase of EGF successively triggered transient ERK activation in silico and in vivo (Fig. 4a). The initial constant EGF stimulus (0.5ngml_1) triggered efficient transient ERK activation, and the additional constant EGF stimulus (lOngml1) again triggered transient ERK activation, indicating that the rapid increase of EGF, rather than a threshold or absolute concentration, induces transient ERK activation. A stepwise decrease of NGF, however, induced sustained ERK activation that was similar to that seen in response to the final concentration, rather than the initial concentration, of NGF in silico and in vivo (Fig. 4b)36. Therefore, these results clearly indicate that transient ERK activation depends on the rapid temporal rates of growth factors but not on their final concentrations, whereas sustained ERK activation depends on the final concentration of NGF but not on its temporal rate of increase. Distinct temporal dynamics of Ras and Rapl activation We explored the mechanisms underlying the distinct dynamics of transient and sustained ERK activation in silico (Fig. 5). Transient ERK activation, which requires a rapid increase of stimuli, is due to the mechanism of Ras activation. Transient Ras activation decreased as the temporal rate of growth factors decreased (Fig. 5a, lower panel). The slow EGF stimulus did not induce sufficient transient Ras activation (Fig. 5a, green dashed line in lower panel). Transient Ras activation is determined by the balance between activation and inactivation processes. Deletion of Ras-GAP activity resulted in sustained Ras activation (see Supplementary Information, Fig. S3), indicating that Ras-GAP is crucial for the rapid termination of transient Ras activation. Inhibition of either EGFR internalization or ERK-dependent feedback inhibition of SOS did not affect transient Ras activation (see Supplementary Information, Fig. S3). Therefore, transient Ras 366 NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group ARTICLES Figure2 In vivo and in silico dynamics of ERK signalling networks. In vivo (upper panel) and in silico (lower panel) tyrosine phosphorylation of epidermal growth-factor receptor (EGFR; a) and TrkA (b), activation of Ras (c) and Rapl (d), and EGF- (e) and nerve growth factor (NGF)- (f) dependent phosphorylation of ERK. Insets in c show transient Ras activation within lOmin after stimulation. The thick line, thin line, thin dashed line, thin dash-dotted line and thin dotted line indicate the responses with a constant 50, 10, 5, 1 and O.Sngmh1 of either EGF or NGF, respectively, except for Ras and Rapl activation. For Ras and Rapl activation, lOngmh1 of EGF or NGF was used. The results are representative of three independent experiments. Images of the original gels of the immunoblotting are shown in Supplementary Information, Fig.S2. activation is substantially regulated by the activity balance between SOS31 and Ras-GAP12'13 in the in silico model. The rapid stimuli, as the constant stimuli, initially led to fast SOS recruitment (Fig. 5a, upper panel) and then to slow Ras-GAP recruitment in silico (Fig. 5a, middle panel), resulting in sufficient transient Ras activation in silico (Fig. 5a, lower panel). Although the slow stimuli led to the same processes, differences in activity between SOS and Ras-GAP were extended and decreased in silico, resulting in the disappearance of transient Ras activation. The apparent time constants of SOS and Ras-GAP recruitment mainly depended on the time constants of binding of She to phosphorylated EGFR, and of phosphorylation and dephosphorylation of Dok, respectively, in silico (data not shown). The amplitudes of SOS and Ras-GAP recruitments mainly depended on the affinities of She to SOS-Grb2, and of phosphorylated Dok to Ras-GAP, respectively, and also on the initial concentrations of She and Ras-GAP, respectively, in silico (data not shown). Consistent with this in silico prediction, the in vivo recruitment of SOS to the membrane fraction preceded that of Ras-GAP in response to the constant EGF stimulus (Fig. 5c). Therefore, transient Ras activation depends on a temporal rate of growth factors. In contrast to Ras-GAP, Rap 1 -GAP was constant regardless of the stimuli in silico. An apparent negative-feedback inhibition and stimuli-dependent inactivation process has not been found in the Rapl activation process, and therefore Rapl activation simply responded to the C3G activity, which depended on sustained TrkA phosphorylation (Fig. 5b). Therefore, Rapl can respond to both an increase and a decrease ofNGF stimulus and the activation of Rap 1 depends on the final concentration of NGF (Fig. 5b). Consistent with this in silico prediction, sustained Rap 1 activation was observed in response to both constant and increasing NGF stimuli in vivo (Fig. 5b, lower panel). We also found that sustained Ras or Rapl activation can lead to sustained ERK activation in silico (see Supplementary Information, Fig. S3), and sustained EGFR phosphorylation induced by EGF (10 ng ml-1) in the presence of MG-132 (ref. 37), a proteasome inhibitor, increased sustained Ras, Rapl and ERK activation in vivo (see Supplementary Information, Fig. S4). These results indicate that the growth-factor-dependent fast SOS and slow Ras-GAP activation regulates transient Ras activation, and that the growth-factor-dependent C3G activation with the constant Rapl-GAP activity regulates sustained Rapl activation. NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group 367 Figure3 Distinct dynamics of transient and sustained ERK activation. For epidermal growth factor (EGF, a) and nerve growth factor (NGF, b), the indicated stimuli (upper panels) were given and the extracellular-signal-regulated kinase (ERK) phosphorylation in silico (middle panels) and in vivo (lower panels) was plotted. The constant and increasing stimuli, and the corresponding responses are indicated by solid and dashed lines, respectively. The images of the original gels in a and b are shown in Supplementary Information, Fig. S2. (c) The temporal rate of EGF-dependent ERK phosphorylation in silico. The indicated EGF stimuli (inset) were given and the transient ERK activation was plotted, (d) The in silico sustained ERK phosphorylation at 60min. Solid and dashed lines indicate ERK phosphorylation at 60min with constant and increasing NGF stimuli, respectively. The increasing stimuli are represented as the NGF concentrations at 60min. Mechanisms of the Ras and Rapl systems To facilitate understanding of the dynamics of the Ras and Rapl systems, we developed simple Ras and Rapl models downstream of phospho-rylated receptors (Fig. 6; see also Methods.) In the simple Ras model, Ras activation and inactivation were approximated by reactions with pR (phosphorylated receptor)-GEF and by reaction with pR-GAP, respectively (Fig. 6a, equtions (3)-(5). We simplified the equations further by substituting variables with dimensionless variables, yielding equations (3')-(5'), where GEF, GAP, Ras and Rapl are dimensionless representations of pR-GEF, pR-GAP, Ras-GTP and Rapl-GTP, respectively. We found that the simple Ras model, with equivalent parameters in the in silico model, was similar to the in silico dynamics of Ras activation (Fig. 6b red line, see also Fig. 7a). Here, q is the relative rate constant of GAP activation compared with GEF activation (see Supplementary Information, Fig. S5), and therefore q < 1 and q > 1 indicate the conditions in which GEF activation is faster and slower than GAP activation, respectively. The apparent transient peak of Ras was observed with q < 1, but not with q > 1, in response to constant pR stimulation (Fig. 6b). Furthermore, transient Ras activation, defined by Ras, . , (see Supplementary Information, ' transient v rr / Fig. S5), was induced in a temporal rate (r)-dependent manner in pR increase (Fig. 6c). By contrast, in the simple Rapl model (see below), transient Rapl activation was not observed under any condition (data not shown). This result supports the idea that the fast SOS and subsequent slow Ras-GAP activation enables the Ras system to capture the temporal rate of stimulation. We also developed a simple Rapl model, in which Rapl activation and inactivation were approximated by reaction with pR-GEF and by reaction with constant GAP, respectively (Fig. 6d). We derived equation (1) for Rapl activation at steady state from equations (3') and (4') (Fig.6e): (1 +Ke) pR+Ke (1) 368 NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group ARTICLES Time (min) Time (min) Figure4 In silico and in vivo ERK activation in response to stepwise increases of EGF and to stepwise decreases of NGF. (a) The indicated stepwise increase of epidermal growth factor (EGF) stimulus (inset) was performed and extracellular-signal-regulated kinase (ERK) phosphorylation in silico (upper panel) and in vivo (lower panel) was plotted. The solid red line indicates the stepwise increases in EGF stimulus (0.5-lOngmh1). The dashed blue and green lines indicate 0.5 and lOngmh1 of constant EGF stimuli, respectively, (b) The indicated stepwise decrease of nerve growth factor (NGF) or constant NGF stimulus (inset) was performed and ERK phosphorylation in silico (upper panel) and in vivo (lower panel) was plotted. The solid blue and cyan lines indicate the stepwise decreases of NGF stimuli (5-1 ngmh1 and 5-0 ngmh1, respectively). The dashed blue and cyan lines indicate 5 and 1 ngmh1 of constant NGF stimuli, respectively. The images of the original gels in a and b are shown in Supplementary Information, Fig. S2. where pR is given by a constant, a (see Methods). Under the conditions, such as a « 1, in which the GEF activation was not saturated (Fig. 5b; also see Supplementary Information, Fig. S5), equation (1) can be approximated by: Rap1=P^ Ke This approximation clearly highlights the characteristics of Rapl activation at steady state, which is proportional to pR (Fig. 6e). This result supports the idea that constant Rapl-GAP activity, with stimulation-dependent C3G activation, enables the Rapl system to capture the final concentration of stimulation. We also derived equation (2) for Ras activation at steady state: Ras = 1 1+pKe 1+pR 1+pxpR (2) where pR is given by a constant, a, and p is the constant, which is the ratio of the dissociation constants between pR for GEF and pR for GAP (Fig. 6f). Under the conditions of a «1 and pa «1, whereby the GEF and GAP activations were not saturated (Fig. 5a; also see Supplementary Information, Fig. S5), equation (2) can be approximated by: Ras= 1 1+pKe (2') This approximation clearly highlights the characteristics of Ras activation at steady state, which becomes constant and independent of pR (Fig. 6f). The slope of the plot of Ras activation, which corresponds to 0 10 20 30 40 50 60 Time (min) 10 20 30 40 50 Time (min) Time (min) Figure5 Distinct dynamics of EGF- and NGF-dependent Ras and Rapl activation. The same stimuli as those shown in Fig. 3 were given, and (a) the epidermal growth factor (EGF)-dependent active fractions of SOS (upper panel), Ras-GAP (middle panel) and Ras (lower panel), and (b) the nerve growth factor (NGF)-dependent active fractions of C3G (upper panel), Rapl-GAP (middle panel) and Rapl (lower panel) were plotted in silico, except that closed and open circles in b (lower panel) indicate the activated Rapl in vivo in response to constant and increasing NGF stimuli (5 ngmh1 at 60min), respectively. Lines and colours are the same as in Fig. 3. Images of the original gels of the immunoblotting are shown in the inset, (c) In vivo recruitment of SOS and Ras-GAP to the membrane fraction in response to constant EGF stimulus. A constant EGF stimulus (10 ngmh1) was given, and the amounts of SOS (blue) and Ras-GAP (red) in the membrane fractions were measured. The in vivo activated Ras in Fig. 2c were also plotted (green). The images of the original gels in c are shown in Supplementary Information, Fig. S2. the order of the reactions from pR to Ras activation, was lower than that of Rapl activation under the conditions, such as a «1 andpa «1 (Fig. 6e, f), thereby characterizing the distinct dynamics between the Ras and Rapl activation at steady state. Next, we confirmed the above characteristics in silico (Fig. 7). Responses of transient Ras activation versus the indicated values of q and r in silico were very similar to those in the simple Ras model (Figs 6b, c;7a, b), where q, r and Ras denote the relative rate constant of ' 1 transient Ras-GAP activation compared with SOS activation, increasing the rate of phosphorylated EGFR and the relative peak amplitude of transient Ras activation, respectively (see Supplementary Information, Fig. S5). These results indicate that the simple Ras model retains the essential characteristics of transient Ras activation in silico. We also confirmed that the simple Rapl and Ras models represent the same characteristics of Rapl and Ras activation at steady state in silico. The slopes of the plot of Rapl activation versus both phosphorylated receptors at steady state were very similar at lower doses in silico (Fig. 7c). The slopes of the plots of Ras activation versus both phospho- NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group 369 ARTICLES pR-GEF pR+GEF *3 Q--- pR+GAP s pR-GAP pR + GEF pR-GEF GDP-Ras GTP-Ras GDP-Rap1 GTP-Rap1 GAP (constant) Figure6 Characteristics of Ras and Rapl activation in the simple Ras and Rapl models, (a) Simple Ras model, in which pR-dependent GEF and GAP activation regulate Ras activation, (b) Constant pR stimulation was given, and Ras was plotted against the indicated values of q. Here, time denotes tlk2. (c) Rastmnssent was plotted against the indicated values of rand q, where Ras4 and /-indicate the relative peak amplitude of transient Ras transient ^ ^ activation and the increasing rate of pR, respectively (see Supplementary Information, Fig. S5). Red lines in b and c indicate Ras activation with the equivalent parameters in the in silico model, (d) Simple Rapl model, in which the pR-dependent GEF activation with constant GAP activity regulates Rapl activation, (e) Rapl activation at steady state derived from equation (1), where pR is given by a constant, a. (f) Ras activation at steady state derived from equation (2), where pR is given by a constant, a. rylated receptors at steady state were also similar at lower doses in silico (Fig. 7c). However, the slopes of the plots of Ras activation were lower than those of Rap 1 activation at the lower doses, at which GEF and GAP activations were not saturated (Fig. 5a, b). These in silico characteristics are consistent with the results in the simple Rapl and Ras models (Fig. 6e, f), indicating that the simple Rapl and Ras models also retain essential characteristics of Rapl and Ras activation at steady state in silico. Inhibition of Ras activation at higher doses of both phosphor-ylated receptors depended on the negative-feedback inhibition of SOS; the deletion of the negative-feedback inhibition of SOS resulted in the disappearance of this inhibition at higher doses without affecting Ras activation at lower doses (Fig. 7c). It is also possible that the negative-feedback inhibition of SOS regulates Ras activation even at lower doses in vivo, and further study is necessary to address this issue. We also predicted the dynamics of ERK activation at steady state against the phosphorylated receptors in silico. The slope of the plot of ERK activation versus the phosphorylated EGFR at steady state was lower than that versus the phosphorylated TrkA (Fig. 7d). ERK activation at steady state consisted of Ras- (Fig. 7d, dotted lines) and Rapl- (Fig. 7d, dashed line) dependent ERK activation in silico. Ras-dependent ERK activation Phosphorylated EGFR (iiM) 0.00001 0.0001 0.001 0.01 0.1 Phosphorylated EGFR (iiM) Phosphorylated TrkA (iiM) Phosphorylated TrkA (iiM) EGF (ng mr) + MG132 ■ 0 01 0 0S 0 1 0 5 1 ? Phosphorylated EGFR Phosphorylated ERK2 | NGF (ng ml-1) 0.01 0.05 0.1 0.5 1 2 5 Phosphorylated TrkA [J Phosphorylated ERK2| — ^r-M»»' Phosphorylated receptor (AU) Figure7 Transient Ras activation, and Ras, Rapl and ERK activation at steady state, (a) A constant phosphorylated epidermal growth-factor receptor (EGFR) stimulus was given, and the in silico Ras activation was plotted against the indicated values of q. (b) Ras was plotted against the indicated values of rand q in silico. Red lines in a and b indicate Ras activation with the original parameters in the in silico model, (c) In silico Ras and Rapl activation at steady state against the constant phosphorylated EGFR are shown in red and cyan, and those against the constant phosphorylated TrkA are shown in pink and blue, respectively. Dashed lines indicate Ras activation without negative-feedback inhibition of SOS. (d) In silico extracellular-signal-regulated kinase (ERK) activation at steady state against the constant phosphorylated EGFR and TrkA are shown with red and blue solid lines, respectively. Dashed and dotted lines indicate Rapl-dependent ERK activation (without Ras activation) and Ras-dependent ERK activation (without Rapl activation), respectively. Circles indicate the intersecting points of Ras- and Rapl-dependent ERK activation, (e) In vivo ERK phosphorylation was plotted against phosphorylated EGFR (red) and TrkA (blue) at 30min. Lines were estimated by the least squares method, (f) The corresponding gel images of the results from e. Arrowheads in c-e indicate the points of the phosphorylated receptors induced by 1 ngmh1 of EGF (in the absence of MG-132) and NGF, respectively. became dominant at lower doses of the phosphorylated receptors, below the intersecting points (Fig.7d). In turn, Rapl-dependent ERK activation became dominant at higher doses of the phosphorylated receptors, above the intersecting points (Fig. 7d). The curves of Ras-dependent ERK activation were similar, whereas those of Rap 1 -dependent ERK activation were different. The distinct Rap 1 activation against both phosphorylated receptors is due to the distinct affinities of fibroblast growth factor receptor substrate 2 (FRS2) to both receptors (see below). We validated the distinct properties of sustained ERK activation in vivo. The slope of the plot of the ERK activation versus the phosphorylated EGFR was lower than that versus the phosphorylated TrkA (Fig. 7e, f), which is consistent with the in silico prediction. 370 NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group ARTICLES Growth factor ERK activation Figure8 The distinct temporal dynamics of transient and sustained ERK activation via Ras and Rapl activation. The Ras and Rapl systems specifically capture the distinct properties of growth factors — the temporal rate and final concentration — and thereby encode these physical properties of growth factors into transient and sustained ERK activation, respectively. Therefore, these in silico and in vivo results clearly indicate the distinct dynamics of ERK activation against the phosphorylated EGFR and TrkA at steady state. DISCUSSION The crucial difference between EGF- and NGF-dependent ERK activation is the absence or presence of sustained ERK activation, which depends on sustained Rapl activation. One of the most crucial differences came from the different affinities of FRS2 for the phosphorylated receptors in this model. The affinity of FRS2 for phosphorylated TrkA was higher than that for phosphorylated EGFR (see Supplementary Information, Table SI). Reduction of the affinity of FRS2 for phosphorylated TrkA reduced sustained Rapl activation (see Supplementary Information, Fig. S3). The amplitude of Rapl activation in response to NGF became similar to that in response to EGF when the affinities of FRS2 for both phosphorylated receptors were set at 200 nM (see Supplementary Information, Fig. S3j, solid and dashed green lines), indicating that the affinity of FRS2 for the phosphorylated receptor determines the amplitude of Rap 1 activation. Another crucial difference was the different dynamics of tyrosine phosphorylation of the receptors. NGF induced sustained tyrosine phosphorylation of TrkA (Fig. 2b), whereas EGF induced transient tyrosine phosphorylation of EGFR due to rapid internalization and degradation (Fig. 2a; also see Supplementary Information, Fig. S3). It should also be noted that, from downstream of the adaptor proteins to ERK, both the topology of the network and the kinetic parameters are identical regardless of the stimuli, indicating that the difference between EGF- and NGF-dependent ERK activation is due to different dynamics upstream of the adaptor proteins. We showed that the temporal rate and final concentration of growth factors are specifically captured by the Ras and Rapl systems via transient Ras and sustained Rapl activation, and then encoded into transient and sustained ERK activation, respectively (Fig. 8). This difference between the Ras and Rapl systems came from their distinct inactivation processes — slower and constant GAP activity, respectively. This finding also indicates the existence of similar physiological roles of other stimulation-dependent negative regulators38, such as other GAPs (for example, Rho-GAP), protein tyrosine phosphatases (for example, SHP) and lipid phosphatases (for example, SHIP and PTEN). We should emphasize that each in silico network should be regarded as representative of similar redundant processes, rather than as a complete description. For example, FRS2 is only an adaptor protein for Rap 1 activation in the current in silico model; however, this protein implicitly represents another adaptor protein, ARMS, which performs a similar function39. In conclusion, combining in silico and in vivo analyses facilitates systematic understanding of the underlying properties of signalling networks. METHODS Numerical simulation of biochemical reactions. All reactions were repre sented by molecule-molecule interactions and enzymatic reactions23. We used a GENESIS simulator (version 2.2) with a Kinetikit interface for solving the ordinary differential equations with a time step of 10 ms23. Block diagram and parameters. The model consisted of 22 molecules and 106 rate constants. The rate constants consisted of 70 and 36 rate constants for molecule-molecule interactions and enzymatic reactions, respectively. The biochemical reactions and the rate constants that were used in the study are shown in Supplementary Information, Fig.SI and TableSl, respectively. The GENESIS script of our in silico model is also available as a text file on our website (http:// www.kurodalab.org/info/ERK.g). Cell culture and growth-factor treatments. PC12 cells (kindly provided by Masato Nakafuku, Cincinnati Children's Hospital Medical Center, Ohio) (8 x 105) were starved in DMEM for 16 h, then stimulated with the indicated concentrations of NGF (Invitrogen, Carlsbad, CA) or EGF (Roche, Indianapolis, IN). Increasing stimuli of EGF and NGF were added by use of a microsyringe pump (KD Scientific, Holliston, MA) with a continuous lOiilmin-1 flow rate into 2 ml of the cultured media. Immunoblotting. Cell lysates were subjected to standard SDS-PAGE (acrylamide: bis=29.5:l) or low-bis SDS-PAGE (acrylamide:bis=144:l) for the separation of phosphorylated and non-phosphorylated ERK, and then transferred to nitrocellulose membrane. The membranes were probed with anti-phospho EGFR (Y1068) antibody (1:1,000; Cell Signaling Technology, Beverly, MA), anti-phospho TrkA (Y490) antibody (1:1,000; Cell Signaling Technology), anti-SOS 1 antibody (1:1,000; Upstate, Charlottesville, VA) or anti-ERKl/2 antibody (1:1,000; Cell Signaling Technology). Anti-phospho ERK1/2 (T202/Y204) antibody (1:1000; Cell Signaling Technology) was used due to its higher sensitivity compared with that of anti-ERKl/2 antibody, and the ratio of phosphorylated to non-phosphorylated ERK2 was estimated by comparison at the same point (5ngmf1 NGF) using anti-ERKl/2 antibody (Fig. 7f). Horseradish peroxidase (HRP)-conju-gated secondary antibodies (Amersham Biosciences, Piscataway, NJ) were used at 1:5,000 and an enhanced chemiluminescence (ECL) detection kit (Amersham Biosciences) was used for HRP detection. Ras and Rapl pull-down assay. Ras and Rapl activation was measured by an affinity pull-down assay using glutathione S-transferase (GST)-c-Rafl (1-149 amino acids) or GST-RalGDS (767-867 amino acids) (kindly provided by Akira Kikuchi, Hiroshima University, Japan) as described elsewhere40. The small NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group 37T ARTICLES GTPases bound to the beads were subjected to SDS-PAGE, followed by immu-noblotting with monoclonal anti-Ras (1:500; BD biosciences, Franklin Lakes, NJ) or anti-Rap 1 (1:500; BD biosciences) antibodies. Recruitment of SOS and Ras-GAP to the membrane fractions. PC 12 cells were stimulated with a constant rate of 10 ng mh1 EGF, and cells were lysed by sonication at the indicated time with a buffer containing 50 mM Tris-HCl (pH7.5), 200 mM sucrose, 2.5 mM MgCl2,10 mM NaF, 1 mM sodium orthovanadate, 1 mM difhio-threitol and 10(Xgmh' leupeptin and aprotinin. After the membrane and cytosol fractions were separated by centrifugation at 100,000g for 30 min, the amounts of SOS and Ras-GAP in both fractions were measured by western blotting. The simple Ras and Rapl models. In the simple Ras model in Fig. 6a, the derivatives of pR-GEF and pR-GAP, and GTPase-GTP (Ras or Rapl) are given by: d[pR-GEF] dt d[pR-GAP] dt ' 0 (Fig. 6c, Fig. 7b and Supplementary Information, Fig. S5). The increasing EGF stimuli led to the SOS and RasGAP activation in a dose-dependent manner in EGF (Fig. 5a), indicating that the SOS and GAP activation were not saturated in silico. The equivalent conditions in the simple models can be obtained by a< < 1 and pa< < 1. At steady state, the concentrations of the activated GEF, GAP and GTPase become constant. Therefore, by setting the equations (3') to (5') equal to zero, we obtain equation (2). Similarly, we obtain equation (1) from equations (3') and (5'), where GAP is always constant {GAP= 1). Note that all values in Fig. 6b, c, e, f are dimensionless. In Fig. 7a, b, we numerically measured the time constants of SOS and RasGAP activation, t0„0 and t„ at which time constant EGF stimulation induced 50% ' SOS Ras-GAP of their maximal activation in silico, respectively. We defined q = tsos/t GAi, which represents the relative rate constant of the RasGAP activation compared to the SOS activation. Indicated values of q were obtained by changing t GAp without changing tsos. For simplicity, the negative feedback inhibition of SOS by ERK was blocked for the analysis in Fig. 7a, b, because the transient Ras activation was not dependent on the negative feedback (Supplementary Information, Fig. S3). We also set [phosphorylated EGFR] = 0.0018 (pM), which corresponds to the phosphorylated EGFR concentration induced by 1 ngmh1 of EGF for constant stimulation (Fig. 7a), and the increasing phosphorylated EGFR stimulus was given by [phosphorylatedEGFR]=0.0018{l-exp(-r(t/Tsos))} (pM), where r corresponds to the increasing rate of phosphorylated EGFR (Fig. 7b). Supplementary information is available on the Nature Cell Biology website. ACKNOWLEDGEMENTS We thank K. Kaibuchi, Y. Gotoh, M. Kawato and M. Arita for critically reading this manuscript, and R. Kettunen and R. Kunihiro for their technical assistance. This work was supported in part by a grant in-aid for scientific research from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and by a grant in-aid from Uehara Memorial Foundation. COMPETING FINANCIAL INTERESTS The authors declare that they have no competing financial interests. 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A unique pathway for sustained neurotrophin signaling through an ankyrin-rich membrane-spanning protein. EM BO J. 23, 2358-2368 (2004). 40. de Rooij, J. & Bos, J. L. Minimal Ras-binding domain of Raf 1 can be used as an activation-specific probe for Ras. Oncogene 14, 623-625 (1997). NATURE CELL BIOLOGY VOLUME 7 | NUMBER 4 | APRIL 2005 ©2005 Nature Publishing Group 373 a pro_EGFR © I EGF—^@ L.EGFR H ® L.dEGFR dpEGFR [{S| FMdpEGFR + c-Cbl —^© + [{S|F}.]dpEGFR.c-Cbl + [{S I F}.]dpEGFR.c-Cbl.ubiq © I ^[{S|fH pro tea so me [{S| F}.]dpEGFR[.c-Cbl] c-Cbl Dok pDok dpEGFR[.C-Cbl] dpEGFR[.C-Cbl] S —-© {FRS2 I pFRS2}—-® S.dpEGFR[.c-Cbl] {FRS2 | pFRS2}.dpEGFR[.c-Cbl] Shc.dpEGFR[.c-Cbl] FRS2.dpEGFR[.c-Cbl] ® © + t pShc.dPEGFR[.c-Cbl] pFRS2.dpEGFR[.c-Cbl] Sand Fdenote {She | [Grb2.SOS.]pShc} and {FRS2 I [Crk.C3G.]pFRS2}, respectively. Kuroda Fig. Sla © 2005 Nature Publishing Group b pro_TrkA {pTrkA | pTrkA_endo> ® ® * I NGFR S.{pTrkA | pTrkA_endo} t NGF—*- © I {pTrkA I pTrkA_endo} L.NGFR J + {FRS2 I pFRS2}—-© ® + + {FRS2 I pFRS2}.{pTrkA | pTrkA_endo} pTrkA [{SI F}-]pTrkA © t [{S I /=}.]pTrkA_endo t degradation Shc.{pTrkA I pTrkA_endo} I ® pShc.{pTrkA | pTrkA_endo} FRS2.{pTrkA | pTrkA_endo} ® I pFRS2.{pTrkA | pTrkA_endo} [{SI F}.]pTrkA [{S | F}.]pTrkA © Dok pDok degradation Sand Fdenote {She | [Grb2.SOS.]pShc} and {FRS2 I [Crk.C3G.]pFRS2}, respectively. Kuroda Fig. S1b © 2005 Nature Publishing Group {SOS I pSOS) pShC[.pRTK ] * ( Grb2 — © Grb2.SOS—© I \ Grb2.{SOS I pSOS} Grb2.SOS.pShc[.pfl7if ] Grb2.SOS.pShc. pRTKm Ras.GDP Ras.GTP [Grb2.SOS.]pShc \ ®—[Grb2.S0S] + She dppERK dppERK [Grb2.]pSOS ® SOS pSOS Grb2.S0S[.pShc] Grb2,pS0S [Grbz!]SOS [pShc] pDok pDok Ras.GTP I + + RasGAP —*- © © © I + + p Do k. RasGAP Dok Ras.GDP [{B-Raf I c-Raf}] [{B-Raf I c-Raf}.] Ras.GDP Ras.GTP pRTKm and pRTK denote {dpEGFR[.c-Cbl] | pTrkA} and {dpEGFR[.c-Cbl] | pTrkA | pTrkA_endo}5 respectively. Kuroda_Fig. S1c © 2005 Nature Publishing Group C3G pFRS2.p/?TCC + + Crk —Crk.C3G —© + + Crk.C3G Crk.C3G.pFRS2.pfl7K pFR£2 Crk.C3G.pFRS2.pflr/fe FRS2 Rapl.GDP Rapl.GTP Rapl.GTP RaplGAP © + Rapl.GDP [B-Raf.] Rapl.GTP Rapl.GDP [B-Raf] pflTTCeand pRTK denote {dpEGFR[.c-Cbl] | pTrkA_endo} and {dpEGFR[.c-Cbl] I pTrkA | pTrkA_endo}, respectively. Kuroda Fig. S1d © 2005 Nature Publishing Group Ras.GTP Ras.GTP I 4 c-Raf — © B-Raf—© i \ c-Raf.Ras.GTP B-Raf.Ras.GTP {MEK I pMEK} {pMEK | ppMEK} {MEK|pMEK} {pMEK | ppMEK} [.ERK] [.ERK] [.ERK] [.ERK] Rapl.GTP 4 B-Raf—^ ® B-Raf.Rapl.GTP H PP2A {pMEK I ppMEK} {MEK | pMEK} [.ERK] [.ERK] {MEK I pMEK} {pMEK | ppMEK} [.ERK] [.ERK] ppMEK.ERK I ©—^ ppMEK + ppERK + 4 ® MKP3 {MEK I pMEK I ppMEK} 4 ERK—-© 4 {MEK I pMEK J ppMEK}.ERK MKP3 ppERK dppERK ppERK ERK dppERK ERK Kuroda_Fig. S1e © 2005 Nature Publishing Group Notation of Figure SI Circles with arrows denote molecule-molecule interactions. Boxes with round arrows denote enzymatic reactions. Rate constants (Numbered circles or boxes) and concentrations of molecules are shown in Supplementary Information, Table SI. Periods between molecules denote non-covalent binding, p and pp denote monophosphorylated and diphosphorylated molecules, respectively, d denotes a dimerised molecule. [ ] denotes an optional component(s) of the complex which shares the same kinetic parameters. For example, [pShc.[Sos.Grb2.]]pEGFR indicates either pEGFR alone, pShc.pEGFR, or pShc.Sos.Grb2.pEGFR. { | } denotes an exclusive component which shares the same kinetic parameters. For example, {SOS|pSOS} indicates either SOS or pSOS. Figure Sla Tyrosine phosphorylation of EGFR and recruitment of adaptor proteins to EGFR. Binding of EGF to EGFR triggers the dimerisation of the receptors, resulting in autophosphorylation of the receptors1. Phosphorylated EGFR binds adaptor proteins including She2, c-Cbl3'4 and FRS25, and phosphorylates these adaptor proteins and Dok6. EGFR complexed with c-Cbl is ubiquitinated and degraded by proteasome7"9. S and F denote {She | [Grb2.Sos.]pShc} and {FRS2 | [Crk.C3G.]pFRS2}, respectively. Figure Sib Tyrosine phosphorylation of TrkA and recruitment of adaptor proteins to TrkA. Binding of NGF to NGFR, consisting of TrkA and p75, triggers autophosphorylation of TrkA10. Phosphorylated TrkA binds adaptor proteins including 1112 1315 She ' and FRS2 " , and phosphorylates the adaptor proteins and Dok. Because the binding of She and FRS2 to TrkA compete14'15, She and FRS2 exclusively bind TrkA in this model. Activated TrkA complexed with adaptor proteins is internalised to endosome where Rapl is activated16. Internalisation of TrkA in this model is © 2005 Nature Publishing Group represented as a single exponetial decay, however, this implicitly represents the PI-3 kinase dependent internalisation of the TrkA17. S and F denote {She | [Grb2.Sos.]pShc} and {FRS2 | [Crk.C3G.]pFRS2}, respectively. Figure Sic Activation of Ras. Grb2 and SOS complex18"23 is recruited to phosphorylated She bound to EGFR2 or TrkA1112 and catalyse GDP/GTP exchange 18 23 24 25 reaction of Ras " . Activated ERK phosphorylates SOS ' and phosphorylated SOS 26 27 28 29 30 dissociates from the complex with She ' . Sprouty ' and Spred have recently been shown to be involved in negative feedback inhibition of Ras. In this model, ERK-dependent negative feedback inhibition of SOS implicitly represents Sprouty-dependent negative feedback inhibition because these pathways can be computationally regarded as similar pathways. RasGAP recruited to phosphorylated Dok6 facilitates intrinsic GTPase reaction of Ras31. Ras.GTP is also inactivated by intrinsic GTPase activity31. pRTKm andpRTK denote {dpEGFR[.c-Cbl] | pTrkA} and {dpEGFR[.c-Cbl] | pTrkA | pTrkA_endo}, respectively. Figure Sid Activation of Rapl. Crk and C3G complex32 is recruited to phosphorylated FRS2 bound to the receptors14'33, and catalyse GDP/GTP exchange reaction of Rapl34. RaplGAP facilitates intrinsic GTPase activity of Rapl35. Rapl.GTP is also inactivated by its intrinsic GTPase activity31. Recruitment of Crk and C3G complex to TrkA may involve other adaptor proteins including SFLP16'36, Gab216 and pl30CAS16'37. In this model, FRS2-dependent recruitment of Crk and C3G complex to TrkA implicitly represents these similar pathways. pRTKe and pRTK denote {dpEGFR[.c-Cbl] | pTrkAendo} and {dpEGFR[.c-Cbl] | pTrkA | pTrkAendo}, respectively. © 2005 Nature Publishing Group Figure Sle Activation of Raf, MEK and ERK. GTP-bound forms of Ras and Rap 1 interact with c-Raf38"43 and B-Raf44"46, and B-Raf47'48, respectively, and activated c-Raf and B-Raf phosphorylate MEK. Phosphorylation of MEK at S218 and S222 (rat MEK1) results in activation of MEK49"51. Phosphorylated MEK is dephosphorylated by PP2A52"55. Unphosphorylated ERK forms complex with MEK56'57. Activated MEK phosphorylates ERK at T183 and Y185 (rat ERK2) and this dual phosphorylation leads to activation58'59 release from the complex with MEK60, and dimerisation61 of ERK. Phosphorylated ERK is dephosphorylated by MKP362'63. 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Signal. 16, 769-779 (2004). © 2005 Nature Publishing Group SUPPLEMENTARY INFORMATION pEGFR Acbvalcd Rax b pTAA MGh I.^.r.l 9 SOS r * * ir ■ h SÜ3 himx'i r r T t lllf V ■connlant 6GF J'iillTJFSJI' . — — — «r v — Tl.] 1^ w*fm-r---- 4rW «Ii.I muyh im ECiF D" If }B3T4e If m <.-5r.}Uimi.n^ » jajh^— * f»! s 11 ]m kj.;, :r 1.4ns»iinPiin__ "MÜH JJ-^ izciiiinnrii'n^,., *-".^iiJiftiri. - - - _ En f 'f irjffJf«:«: 1 InfniLUnui «~ -_ — C —-•■ - 3 a :r,^- 2 as [■ I- f if Ii- J-j vr aa->o^ni — ----tK5 "-flQilTil » ■fa m * * ■■ ■■■ffiSa I! 1 h—lM«*i BM-I .--— -t »- i-i- 1 FigureS2 Images of the original gels in Fig. 1, Fig. 2, Fig. 3 and Fig. 4. (a) phosphorylated EGFR at Y1068 (pEGFR) (Fig. 2a), (b) phosphorylated TrkA at Y490 (pTrkA) (Fig. 2b), (c) activated Ras (Fig. 2c), (d) activated Rap1 (Fig.2d), (e) EGF-induced phosphorylated and nonphosphorylated ERK2 (pERK2 and ERK2) (Fig.2e), (f) NGF-induced phosphorylated and nonphosphorylated ERK2 (Fig.2f), (g) EGF-induced SOS mobility shift in vivo (upper panel) and in silico (lower panel), (h) NGF-induced SOS mobility shift in vivo (upper panel) and in silico (lower panel), (i) constant and increasing EGF stimuli-induced ERK2 activation (Fig. 3a), (j) constant and increasing NGF stimuli-induced ERK2 activation (Fig. 3b), (k) a stepwise increase of EGF stimuli-induced ERK2 activation (Fig. 4a), (I) a stepwise decrease of NGF stimuli-induced ERK2 activation (Fig. 4b), and (m) constant EGF stimuli-induced SOS and Ras GAP recruitment to the membrane fractions (Fig. 5c). Since the temporal patterns of phosphorylated ERK1 and ERK2 were always similar (data not shown), phosphorylated ERK2 per total ERK2 were plotted for all figures. 3 © 2005 Nature Publishing Group WWW.NATURE.COM/NATURECELLBIOLOGY SUPPLEMENTARY INFORMATION FigureS3 In silico roles of molecules in Ras, Rap1 and ERK activation. Roles of the indicated molecules in Ras and Rap1 activation in silico (a-g). (a) The pathway indicated by a red bar was blocked and Ras and Rap1 activations were plotted as follows. Constant EGF stimuli were given in the presence or absence of either RasGAP (b), EGFR internalisation (c, f) and ERK-dependent feedback inhibition of SOS (d), and Ras activation (b-d) and Rap1 activation (f) were plotted. Solid line, normal conditions; dashed line, in the absence of the indicated pathway. The inset in d is the transient Ras activation within 15 min after stimulation, (e) Constant NGF stimuli were given in the presence or absence of Rap1 GAP, and Rap1 activation was plotted. Red, green and blue lines indicate the ERK phosphorylation with constant 50, 5 or 1 ng/ml of either EGF or NGF stimuli, respectively, (g) Constant EGF stimulus (1 ng/ml) was given in the presence or absence of EGFR internalisation, the Ras or the Rap1 activation, and the ERK activation were plotted. Green solid line; normal conditions; green dashed line, in the absence of EGFR internalisation; red dotted line, in the absence of EGFR internalisation and Ras activation; blue dotted line, in the absence of EGFR internalisation and Rap1 activation. The roles of Ras and Rap1 in EGF- and NGF-dependent ERK activation in silico (h-j). Concentration of the activated Ras or Rap1 was fixed at the basal level, and then simulations were run with (h) EGF (10 ng/ml) and (i) NGF (10 ng/ml), and phosphorylation of ERK was plotted. Blue line, normal conditions; green line, without Rap1 activation; red line, without Ras activation, (j) Rap1 activation depends on the affinity of FRS2 for the phosphorylated receptors. The dissociation constant of FRS2 for phosphorylated TrkA was set at 20, 50, 100, 200, 500 or 1000 nM. Then, the constant NGF stimulus (10 ng/ml) was given and the activation of Rap1 was plotted. The black, blue, cyan, green, orange and red lines indicate the Rap1 activation with 20, 50, 100, 200, 500 or 1000 nM of the dissociation constant of FRS2 for phosphorylated TrkA, respectively. Green dashed line indicates the Rap1 activation in response to EGF (10ng/ml) in silico where the affinity of FRS2 for phosphorylated EGFR was 200 nM (Fig. 2d). Note that 20 and 200 nM were the original dissociation constants of FRS2 for phosphorylated TrkA and EGFR in silico, respectively (TableSI). WWW.NATURE.COM/NATURECELLBIOLOGY © 2005 Nature Publishing Group 4 SUPPLEMENTARY INFORMATION 10 14,1 2 I S* FigureS4 Sustained Ras, Rap1 and ERK activation in response to the sustained phosphorylated EGFR. (a, b) Fifty uM of MG-132, a proteasome inhibitor, was added for 1 h, then PC12 cells were stimulated with EGF (10ng/ml). After stimulation, phosphorylated EGFR (a) and phosphorylated ERK2 (b) were measured. Blue and red lines indicate the responses in the presence or absence of MG-132, respectively. MG-132 alone did not affect the amounts of total and phosphorylated EGFR during incubation for 120 min (data not shown). Sustained Ras (c) and Rap1 (d) activation in the presence of MG-132 at 30 min after stimulation under the same conditions in (a). 5 © 2005 Nature Publishing Group WWW.NATURE.COM/NATURECELLBIOLOGY SUPPLEMENTARY INFORMATION FigureS5 Transient Ras activation in the simple Ras model, (a) Schematic representation of the GEF activation and GAP activation in response to the constant pR stimulation. Here, 1/qcan be regarded as the relative time constant of GAP activation compared to GEF activation. The dimensionless concentrations of GEF and GAP at steady state are given by a and pa, respectively. Red and blue lines indicate GAP and GEF, respectively, (b) The definition of the characteristics of the transient Ras activation. The relative amplitude of the transient Ras activation compared to that at steady state was defined by Rastransinet, which is given by Rastransinet=(Max-Equi)/Equi (Appendix). Here, the transient Ras activation was defined by Rastransinet >0. (c) Increasing pR stimulation used in Fig. 6b and c. The pR stimulation was given by pR= a{1 -exp(-rk2t)} (Appendix). Note that r corresponds to the increasing rate of pR. Time in a-c denotes t/k2. WWW.NATURE.COM/NATURECELLBIOLOGY © 2005 Nature Publishing Group 6 Table Sla Molecule-molecule interaction Reaction numbei kf (/s/u,M) kb (Is) Notes 1 1.0e-4* 1.0e-4 Constrained by in vivo dynamics of EGFR (Fig. 2a) 2 2.2833 0.0029666 1,2 3 10 0.02 3,4 4 4 0.001 3,5,6 5 0.5 0.2 On the basis of7, further constrained by in vivo dynamics of EGFR (Fig. 2a) 6 0.05 * On the basis of7, further constrained by in vivo dynamics of EGFR (Fig. 2a) 7 0.001 * Constrained by in vivo dynamics of EGFR (Fig. 2a) 8 10 0.2 3,4 9 1 * On the basis of8, further constrained by in vivo dynamics of Ras (Fig. 2c) 10 1 0.2 On the basis of9, further constrained by EGF-dependent Rapl activation (Fig. 2d) 11 1 * On the basis of9, further constrained by EGF-dependent Rapl activation (Fig. 2d) * denotes Is. Enzymatic reaction Reaction numbei Km (u»M) Vmax (Is) Notes 1 0.1 0.2 10 Initial concentration Molecule Colnit (liM) Notes EGFR 0.3 3 pro EGFR 0.3 constant 3,11 She 1 3 c-Cbl 0.5 On the basis of12, futher constrained by in vivo dynamics of EGFR (Fig. 2a) FRS2 1 13 Dok 0.3 Constrained by in vivo dynamics of Ras (Fig. 2c) 1 French, A. R., Tadaki, D. K., Niyogi, S. K. & Lauffenburger, D. A. Intracellular trafficking of epidermal growth factor family ligands is directly influenced by the pH sensitivity of the receptor/ligand interaction. J. Biol. Chem. 270, 4334-4340 (1995). 2 DeWitt, A. et al. Affinity regulates spatial range of EGF receptor autocrine ligand binding. Dev. Biol. 250, 305-316 (2002). 3 Bhalla, U. S. & Iyengar, R. Emergent properties of networks of biological signaling pathways. Science 283, 381-387 (1999). 4 Sasaoka, T., Langlois, W. J., Leitner, J. W., Draznin, B. & Olefsky, J. M. The signaling pathway coupling epidermal growth factor receptors to activation of p21ras. J. 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Table Sib Molecule-molecule interaction Reaction numbei kf (/s/liM) kb (Is) Notes 1 8.333e-4* 2.7778e-4 l 2 6.2 6.4e-5 On the basis of2, fürther constrained by in vivo dynamics of TrkA (Fig. 2b) 3 1 * Constrained by/« vivo dynamics of TrkA (Fig. 2b) 4 6.3e-4 * On the basis of1, fürther constrained by in vivo dynamics of TrkA (Fig. 2b) 5 4.2e-4 * On the basis of1, fürther constrained by in vivo dynamics of TrkA (Fig. 2b) 6 10 0.2 On the basis of, fürther constrained by in vivo dynamics of Ras (Fig. 2c) 7 5 0.1 On the basis of, fürther constrained by in vivo dynamics of Ras (Fig. 2c) 8 0.1 * On the basis of*, fürther constrained by/« vivo dynamics of Ras (Fig. 2c) 9 2 * On the basis of5, fürther constrained by/« vivo dynamics of Rap 1 (Fig. 2d) 10 0.0022 * Constrained by/« vivo dynamics of TrkA (Fig. 2b) * denotes Is. Enzymatic reaction Reaction numbei Km (u»M) Vmax (Is) Notes 1 0.1 0.02 On the basis of, further onstrained by in vivo dynamics of Ras (Fig. 2c) Initial concentration Molecule Colnit (uM) Notes TrkA 0.061894 7 pro TrkA 0.020631 constant 1 1 Jullien, J., Guili, V., Reichardt, L. F. & Rudkin, B. B. Molecular kinetics of nerve growth factor receptor trafficking and activation. J. Biol. Chem. 211, 38700-38708 (2002). 2 Mahadeo, D., Kaplan, L., Chao, M. V. & Hempstead, B. L. High affinity nerve growth factor binding displays a faster rate of association than pl40trk binding. Implications for multi-subunit polypeptide receptors. J. Biol. Chem. 269, 6884-6891 (1994). 3 Farooq, A., Plotnikova, O., Zeng, L. & Zhou, M. M. Phosphotyrosine binding domains of She and insulin receptor substrate 1 recognize the NPXpY motif in a thermodynamically distinct manner. J. Biol. Chem. 214, 6114-6121 (1999). 4 Gatti, A. 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Table Sic Molecule-molecule interaction Reaction numbei kf (/s/uJM) kb (Is) Notes 1 0.03 0.0168 i 2 10 0.2 1,2 3 0.005 * 2 4 0.002 * Constrained by in vivo dynamics of SOS (Fig. S2g, h) 5 0.12 0.01 3 6 0.002 * 1.0e-5 Constrained by in vivo dynamics of Ras (Fig. 2c) 7 1.667e-4* 4 * denotes Is. Enzymatic reaction Reaction numbei Km (u.M) Vmax (Is) Notes 1 0.02 2 5 2 25.641 1 6 3 1 10 7 Initial concentration Molecule Colnit (uM) Notes SOS 0.1 6 Grb2 1 6 RasGAP 0.1 8 Ras 0.1 6 1 Chook, Y. M, Gish, G. D., Kay, C. M, Pai, E. F. & Pawson, T. The Grb2-mSosl complex binds phosphopeptides with higher affinity than Grb2. J. Biol. Chem. 271, 30472-30478 (1996). 2 Sasaoka, T., Langlois, W. J., Leitner, J. W., Draznin, B. & Olefsky, J. M. The signaling pathway coupling epidermal growth factor receptors to activation of p21ras. J. Biol. Chem. 269, 32621-32625 (1994). 3 Kuriyan, J. & Cowburn, D. Modular peptide recognition domains in eukaryotic signaling. Annu. Rev. Biophys. Biomol. 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Biotechnol. 20, 370-375 (2002). Table Sid Molecule-molecule interaction Reaction numbei kf (/s/uM) kb (Is) Notes 1 1 0.002 i 2 1 0.2 2 3 0.005 * Constrained by in vivo dynamics of Rapl activation (Fig. 2d" 4 1.166e-4* 3 * denotes Is. Enzymatic reaction Reaction numbei Km (uM) Vmax (Is) Notes 1 0.01 0.024 On the basis of4, further constrained by in vivo dynamics of Rap 1 activation (Fig. 2d) 2 1 2 5 Initial concentration Molecule Colnit (uM) Notes C3G 0.5 Constrained by in vivo dynamics of Rapl activation (Fig. 2d" Crk 1 Constrained by in vivo dynamics of Rapl activation (Fig. 2d" Rapl 0.2 On the basis of6, further constrained by in vivo dynamics of Rap 1 activation (Fig. 2d) Rap 1 GAP 0.012 On the basis of6, further constrained by in vivo dynamics of Rap 1 activation (Fig. 2d) 1 Knudsen, B. S., Feller, S. M. & Hanafusa, H. Four proline-rich sequences of the guanine-nucleotide exchange factor C3G bind with unique specificity to the first Src homology 3 domain of Crk. J. Biol. 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U.S.A. 88, 239-243 (1991). Table Sie Molecule-molecule interaction Reaction numbei kf (/s/LtM) kb (Is) Notes 1 60 0.5 l 2 60 0.5 1,2 3 60 0.5 3 4 0.15 * 1 5 10 0.075 4 6 16.304 0.6 1 * denotes Is. Enzymatic reaction Reaction numbei Km (u.M) Vmax (Is) Notes 1 0.16 0.5 l 2 0.16 0.2 l 3 0.16 0.3 l 4 15.657 3 l 5 0.02 0.06 5 Initial concentration Molecule Colnit (u-M) Notes c-Raf 0.5 1 B-Raf 0.2 1 MEK 0.68 1 ERK 0.26 1 PP2A 0.24 1 MKP3 0.018 1,6 1 Bhalla, U. S. & Iyengar, R. Emergent properties of networks of biological signaling pathways. Science 283, 381-387 (1999). 2 Yamamori, B. et al. Purification of a Ras-dependent mitogen-activated protein kinase kinase kinase from bovine brain cytosol and its identification as a complex of B-Raf and 14-3-3 proteins. J. Biol. Chem. 270, 11723-11726 (1995). 3 Ohtsuka, T., Shimizu, K., Yamamori, B., Kuroda, S. & Takai, Y. Activation of brain B-Raf protein kinase by RaplB small GTP-binding protein. J. Biol. Chem. 271, 1258-1261 (1996). 4 Khokhlatchev, A. V. et al. Phosphorylation of the MAP kinase ERK2 promotes its homodimerization and nuclear translocation. Cell 93, 605-615 (1998). 5 Zhao, Y. & Zhang, Z. Y. The mechanism of dephosphorylation of extracellular signal-regulated kinase 2 by mitogen-activated protein kinase phosphatase 3. J. Biol. Chem. 276, 32382-32391 (2001). 6 Schoeberl, B., Eichler-Jonsson, C, Gilles, E. D. & Muller, G. Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat. Biotechnol. 20, 370-375 (2002).