Abstract
We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal–response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Sibilia, M., Steinbach, J.P., Stingl, L., Aguzzi, A. & Wagner, E.F. A strain-independent postnatal neurodegeneration in mice lacking the EGF receptor. EMBO J. 17, 719–731 (1998).
Kim, H. & Muller, W.J. The role of the EGF receptor family in tumorigenesis and metastasis. Exp. Cell Res. 253, 78–87 (1999).
Hackel, P.O., Zwick, E., Prenzel, N. & Ullrich, A. Epidermal growth factor receptors: critical mediators of multiple receptor pathways. Curr. Opin. Cell. Biol. 11, 184–189 (1999).
Mueller G., et al. Regulation of Raf-1 kinase by TNF via its second messenger ceramide and cross-talk with mitogenic signalling. EMBO J. 17, 732–742 (1998).
Gibson, S., Tu, S., Oyer, R., Anderson, S.M. & Johnson, G.L. Epidermal growth factor protects epithelial cells against Fas-induced apoptosis. J. Biol. Chem. 274, 17612–17618 (1999).
Moghal, N. & Sternberg, P.W. Multiple positive and negative regulators of signalling by the EGF receptor. Curr. Opin. Cell. Biol. 11, 190–196 (1999).
Schlessinger, J. & Ullrich, A. Growth factor signalling by receptor tyrosine kinases. Neuron 9, 383–391 (1992).
Hubbard, S.R., Mohammadi, M. & Schlessinger, J. Autoregulatory mechanisms in protein–tyrosine kinases. J. Biol. Chem. 273, 11987–11990 (1998).
Batzer, A.G., Blaikie, P., Nelson, K., Schlessinger, J. & Margolis, B. The phosphotyrosine interaction domain of Shc binds an LXNPXY motif on the epidermal growth factor receptor. Mol. Cell. Biol. 15, 4403–4409 (1995).
Buday L. & Downward, J. Epidermal growth factor regulates p21 ras through the formation of a complex receptor, Grb2 adaptor protein and Sos nucleotide exchange factor. Cell 48, 611–620 (1993).
Keilhack, H. et al. Phosphotyrosine 1173 mediates binding of the protein–tyrosine phosphatase Shp-1 to the epidermal growth factor receptor and attenuation of receptor signaling. J. Biol. Chem. 273, 24839–24846 (1998).
Wang, Z., Tung, P.S. & Moran, M.F. Association of p120rasGAP with endocytic components and colocalization with epidermal growth factor receptor in response to EGF stimulation. Cell Growth Diff. 7, 123–133 (1996).
Morrison, D.K. & Cutler, R.E. The complexity of Raf-1 regulation. Curr. Opin. Cell. Biol. 9, 174–179 (1997).
Marshall C.J., Specificity of receptor tyrosine kinase signaling: transient versus sustained extracellular signal-regulated kinase activation. Cell 80, 179–185 (1995).
Cadena, D.L., Chan, C. & Gill, G.N. The intracellular tyrosine kinase domain of the epidermal growth factor receptor undergoes a conformational change upon autophosphorylation. J. Biol. Chem. 269, 1–6 (1994).
Carter, R.E. & Sorkin, A. Endocytosis of functional epidermal growth factor receptor green fluorescent protein chimera. J. Biol. Chem. 273, 35000–35007 (1998).
Waterman, H., Levkowitz, G., Alroy, I. & Yarden, Y. The RING finger of c-Cbl mediates desensitation of the EGF receptor. J. Biol. Chem. 274, 22151–22154 (1999).
Di Guglielmo, G.M., Baass, P.V., Ou, W.-J., Posner, B.I. & Bergeron, J. Compartmentalization of Shc, Grb2 and mSos and hyperphosphorylation of Raf-1 by EGF but not insulin in liver parenchyma. EMBO J. 13, 4269–4277 (1994).
Huang, C.-Y.F. & Ferrell, J.E. Ultrasensitivity in the mitogen-activated protein cascade. Proc. Natl. Acad. Sci. USA 93,10078–10083 (1996).
Tyson, J.J., Novak, B., Odell, G.M., Chen, K. & Thron, C.D. Chemical kinetic theory: understanding cell-cycle regulation. Trends Biochem. Sci. 21, 89–96 (1996).
Haugh, J.M. & Lauffenburger, J.M. Analysis of receptor internalisation as a mechanism for modulation signal transduction. J. Theor. Biol. 195, 187–218 (1998).
Ni, T.C. & Savageau, M.A. Application of biochemical systems theory to metabolism in human red blood cells. Signal propagation and accuracy of representation. J. Biol. Chem. 271, 7927–7941 (1996).
Saso, K., Moehren, G., Hagashi, K. & Hoek, J. B. Differential inhibition of epidermal growth factor signaling pathways in rat hepatocytes by long-term ethanol treatment. Gastroenterology 112, 2073–2088 (1997).
Waters, S.B. et al. Insulin and epidermal growth factor receptors regulate distinct pools of Grb2-Sos in the control of Ras activation. J. Biol. Chem. 271, 18224–18230 (1996).
Ueki, K. et al. Feedback regulation of mitogen-activated protein kinase kinase kinase activity of c-Raf-1 by insulin and phorbol ester stimulation. J. Biol. Chem. 269, 15756–15761 (1994).
Haugh J.M., Schooler, K., Wells, A., Wiley H.S. & Lauffenburger, D.A. Effect of epidermal growth factor receptor internalisation on regulation of the phospholipase C γ1 signaling pathway. J. Biol. Chem. 274, 8958–8965 (1999).
Burke, P., Schooler, K. & Wiley, H.S. Regulation of epidermal growth factor receptor signaling by endocytosis and intracellular trafficking. Mol. Biol. Cell. 12, 1897–1910 (2001).
Traverse, S. et al. EGF triggers neuronal differentiation of PC 12 cells that overexpress the EGF receptor. Curr. Biol. 4, 694–701 (1994).
Bray, D. Intracellular signaling as a parallel distributed process. J. Theor. Biol. 143, 215–231 (1990).
Kalb, A., Bluethmann, H., Moore, M.W. & Lesslauer, W. Tumor necrosis factor receptors (Tnfr) in mouse fibroblasts deficient in Tnfr1 or Tnfr2 are signaling competent and activate the mitogen-activated protein kinase pathway with differential kinetics. J. Biol. Chem. 271, 28097–28104 (1996).
Eigen, M. Diffusion control in biochemical reactions. In Quantum statistical mechanics in the natural sciences. (eds. Kursunoglu, B. et al.) 37–61 (Plenum, New York; 1974).
Rechenberg, I. Evolutionsstrategie '94. (Frommann-Holzboog, Stuttgart;1994).
Corbalan-Garcia, S., Margarit, S.M., Galron, D., Yang, S.-S. & Baar-Sag, D. Regulation of Sos activity by intramolecular interactions. Mol. Cell. Biol. 18, 880–886 (1998).
Sermon, B.A., Lowe, P.N., Strom, M. & Eccleston, J.F. The importance of two conserved arginine residues for catalysis by the Ras GTPase-activation protein, neurofibromin. J. Biol. Chem. 273, 9480–9485 (1998).
Sydor, J.R., Engelhard, M., Wittinghofer, A., Goody, R.S. & Herrmann, C. Transient kinetic studies on the interaction of Ras and the Ras-binding domain of c-Raf-1 reveal rapid equilibration of the complex. Biochemistry 37, 14292–14299 (1998).
El-Masri, H.A. & Portier, C.J. Replication potential of cells via the protein kinase C-MAPK pathway: application of a mathematical model. Bull. Math. Biol. 61, 379–398 (1999).
Starbuck, C. & Lauffenburger, D.A. Mathematical model for the effects of epidermal growth factor receptor trafficking dynamics on fibroblast responses. Biotechn. Prog. 8,132–143 (1992).
Lund, K.A., Opresko, L.K., Starbuck, C., Walsh, B.J. & Wiley, H. Quantitative analysis of the endocytic system involved in hormone-induced receptor internalisation. J. Biol. Chem. 265, 15713–15723 (1990).
Wang, Z. & Moran, M.F. Requirement for the adapter protein Grb2 in EGF receptor endocytosis. Science 272, 1935–1945 (1996).
Hansen, S.H., Sandvig, K. & van Deurs, B. The preendosomal compartment comprises distinct coated and noncoated endocytotic vesicle populations. J. Cell. Biol. 113, 731–741 (1991).
Wiley, H.S. Anomalous binding of epidermal growth factor to A431 cells is due to the effect of high receptor densities and a saturable endocytic system. J. Cell. Biol. 107, 801–810 (1991).
Martin-Fernandez, M.L., Clarke, D.T., Tobin, J. & Jones, G.R. Real-time studies on the interactions between epidermal growth factor and its receptor during endocytic trafficking. Cell. Mol. Biol. 46, 1103–1112 (2000).
Berkers, J.A., van Bergen en Henegouwen, P.M. & Boonstra, J. Three classes of epidermal growth factor receptors on HeLa cells. J. Biol. Chem. 266, 922–927 (1991).
Sako, Y., Minoguchi, S. & Yanagida, T. Single molecule imaging of EGFR signaling on the surface of living cells. Nat. Cell Biol. 2, 168–172 (2000).
Chung, J.C., Sciaky, N. & Gross, D.J. Heterogeneity of epidermal growth factor binding kinetics on individual cells. Biophys. J. 73,1089–1102 (1997).
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 interactions J. Biol. Chem. 270, 4334–4340 (1995).
Kholodenko, B.N., Demin, O.V., Moehren, G. & Hoek, J.B. Quantification of short term signaling by the epidermal growth factor receptor. J. Biol. Chem. 274, 30169–30181 (1999).
Author information
Authors and Affiliations
Corresponding author
Supplementary information
Supplementary Figure 1.
Kinetic scheme of the EGF receptor-induced MAP kinase cascade induced by an Shc-dependent and an Shc-independent pathway. Each component is identified by a specific number (blue). Blue numbers in brackets specify the components after internalization. The arrows represent the reaction rates specified in Supplementary Table 1 and characterized by green numbers v1-v62. The second green number identifies reaction rates after internalization. (PDF 16 kb)
Supplementary Figure 2.
Biochemical reaction schemes of internalization by coated pit-dependent and -independent pathways. The internalization steps modeled for the compounds in Figure 1 are illustrated separately in this figure to avoid confusing additional arrows. (A) Receptor internalization in the Shc pathway initiated by the association of a coated-pit protein (Prot) to the components identified by the blue numbers (identical to those in Fig. 1). After dissociation of Prot, the components are identified by the same numbers as the blue numbers in brackets of Figure 1. v115, v118, v121, v124 are equivalent to k4. Prot-associated components 91, 92, 93, 94 are not depicted in Figure 1. (B) Receptor internalization in the Grb2 pathway initiated by the coated-pit protein (Prot) identified according to the same principle as in (A). v106, v109, and v112 are equivalent to k4 and v107, v110, v113 are identical to k5. Prot-associated components 7, 88, 89, 90 are not depicted in Figure 1. (C) Internalization in both pathways by a (Prot)-independent step. v102, v103, v104, v108, v111, v114, v117, v120, v123, are the same as k6. (PDF 2 kb)
Supplementary Figure 3.
Time course of ERK-1/2 phosphorylation and c-fos activation in HeLa cells after EGF stimulation. (A) Kinetics of ERK activation. HeLa cells were serum-starved for 24 h and then incubated with different concentrations of EGF for times indicated. Protein samples were blotted onto nitrocellulose membranes and probed for the phosphorylated forms of ERK-1/2 as described in the main text Experimental Protocol. Vinculin was used as an internal standard to normalize protein levels. The different panels show western blots of the time-dependent ERK-1/2 (p42/p44) phosphorylation after stimulation with decreasing amounts of EGF, as indicated. For all concentrations, the value for ERK-1/2 activation at 50 ng/ml EGF after 3 min was used as internal standard for maximal ERK phosphorylation. These experiments were done with the same passage of HeLa cells within 1 day, and were repeated four times with similar results. (B) Induction of c-fos expression after EGF treatment. HeLa cells were serum-starved for 24 h and then incubated with different concentrations of EGF for 1 h as indicated. Immunocytochemistry was done using anti-c-fos rabbit polyclonal antibody as described in the main text Experimental Protocol. Levels of c-fos protein were evaluated by counting the percentage of c-fos-labeled nuclei of duplicate populations of 500 cells for each EGF concentration indicated. Each experiment was repeated twice with similar results. (PDF 156 kb)
Supplementary Figure 4.
Curves from Figure 2A (green line) and F (blue line) for 0.5 ng/ml EGF calculated as percentage of total are combined. (PDF 7 kb)
Supplementary Figure 5.
Graphic representation of variability of association (A) and dissociation (B) rates using fixed initial conditions as shown in Supplementary Table 2. Thin horizontal lines represent the values used in the current model; vertical lines between thick bars show the possible variability of parameters on a logarithmic scale leading to the same solution. (PDF 10 kb)
Supplementary Figure 6.
Parameter variation for two different sets of initial conditions. A second model was calculated assuming underestimated initial conditions, leading to the same solution as in the original model. Compared to the molecule numbers shown in Supplementary Table 2, initial conditions were reduced as follows: Shc, 1/10; SOS, 1/3; Raf, 1/22; MEK, 1/500; ERK, 1/500; phosphatase 1 and 2, ¼; and phosphatase 3, 1/140. Circles indicate the parameters of the presented model from Supplementary Table 1. Crosses within the circles indicate no change of the parameter. Vertical lines between circles and crosses indicate the change of association rates (A) and dissociation rates (B) necessary to obtain the same solution. (PDF 15 kb)
Supplementary Figure 7.
Determination of concentrations of signaling proteins as described in the main text Experimental Protocol. (PDF 90 kb)
Rights and permissions
About this article
Cite this article
Schoeberl, B., Eichler-Jonsson, C., Gilles, E. et al. Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat Biotechnol 20, 370–375 (2002). https://doi.org/10.1038/nbt0402-370
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/nbt0402-370
This article is cited by
-
Knowledge-based mechanistic modeling accurately predicts disease progression with gefitinib in EGFR-mutant lung adenocarcinoma
npj Systems Biology and Applications (2023)
-
p-mTOR, p-ERK and PTEN Expression in Tumor Biopsies and Organoids as Predictive Biomarkers for Patients with HPV Negative Head and Neck Cancer
Head and Neck Pathology (2023)
-
Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics
Bulletin of Mathematical Biology (2023)
-
A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws
BMC Bioinformatics (2022)
-
Scalable reaction network modeling with automatic validation of consistency in Event-B
Scientific Reports (2022)