Skip to content


  • Research Article
  • Open Access

Reaction-Diffusion Modeling ERK- and STAT-Interaction Dynamics

EURASIP Journal on Bioinformatics and Systems Biology20062006:85759

  • Received: 8 December 2005
  • Accepted: 30 August 2006
  • Published:


The modeling of the dynamics of interaction between ERK and STAT signaling pathways in the cell needs to establish the biochemical diagram of the corresponding proteins interactions as well as the corresponding reaction-diffusion scheme. Starting from the verbal description available in the literature of the cross talk between the two pathways, a simple diagram of interaction between ERK and STAT5a proteins is chosen to write corresponding kinetic equations. The dynamics of interaction is modeled in a form of two-dimensional nonlinear dynamical system for ERK—and STAT5a —protein concentrations. Then the spatial modeling of the interaction is accomplished by introducing an appropriate diffusion-reaction scheme. The obtained system of partial differential equations is analyzed and it is argued that the possibility of Turing bifurcation is presented by loss of stability of the homogeneous steady state and forms dissipative structures in the ERK and STAT interaction process. In these terms, a possible scaffolding effect in the protein interaction is related to the process of stabilization and destabilization of the dissipative structures (pattern formation) inherent to the model of ERK and STAT cross talk.


  • Partial Differential Equation
  • Protein Interaction
  • Kinetic Equation
  • System Biology
  • Pattern Formation

[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38]

Authors’ Affiliations

Section of Biodynamics and Biorheology, Institute of Mechanics and Biomechanics, Bulgarian Academia of Sciences, Acad. G. Bonchev Street, bl. 4, Sofia, 1113, Bulgaria


  1. Beltrami E: Mathematics for Dynamic Modeling. Academic Press, Boston, Mass, USA; 1987.MATHGoogle Scholar
  2. Eungdamrong NJ, Iyengar R: Modeling cell signaling networks. Biology of the Cell 2004,96(5):355-362. 10.1016/j.biolcel.2004.03.004View ArticleGoogle Scholar
  3. Khurana S, Kreydiyyeh S, Aronzon A, et al.:Asymmetric signal transduction in polarized ileal -absorbing cells: carbachol activates brush-border but not basolateral-membrane -PLC and translocates PLC- only to the brush border Biochemical Journal 1996,313(2):509-518.View ArticleGoogle Scholar
  4. Holdaway-Clarke TL, Feijo JA, Hackett GR, Kunkel JG, Hepler PK: Pollen tube growth and the intracellular cytosolic calcium gradient oscillate in phase while extracellular calcium influx is delayed. Plant Cell 1997,9(11):1999-2010.View ArticleGoogle Scholar
  5. Lam H, Matroule J-Y, Jacobs-Wagner C: The asymmetric spatial distribution of bacterial signal transduction proteins coordinates cell cycle events. Developmental Cell 2003,5(1):149-159. 10.1016/S1534-5807(03)00191-6View ArticleGoogle Scholar
  6. Belenkaya TY, Han C, Yan D, et al.: Drosophila Dpp morphogen movement is independent of dynamin-mediated endocytosis but regulated by the glypican members of heparan sulfate proteoglycans. Cell 2004,119(2):231-244. 10.1016/j.cell.2004.09.031View ArticleGoogle Scholar
  7. Lengyel I, Epstein IR: A chemical approach to designing Turing patterns in reaction-diffusion systems. Proceedings of the National Academy of Sciences of the United States of America 1992,89(9):3977-3979. 10.1073/pnas.89.9.3977MATHView ArticleGoogle Scholar
  8. Alber M, Glimm T, Hentschel HGE, Kazmierczak B, Newman SA:Stability of -dimensional patterns in a generalized Turing system: implications for biological pattern formation. Nonlinearity 2005,18(1):125-138. 10.1088/0951-7715/18/1/007MATHMathSciNetView ArticleGoogle Scholar
  9. Pawson T, Raina M, Nash P: Interaction domains: from simple binding events to complex cellular behavior. FEBS Letters 2002,513(1):2-10. 10.1016/S0014-5793(01)03292-6View ArticleGoogle Scholar
  10. Shuai K: Modulation of STAT signaling by STAT-interacting proteins. Oncogene 2000,19(21):2638-2644. 10.1038/sj.onc.1203522View ArticleGoogle Scholar
  11. Alexander WS: Suppressors of cytokine signalling (SOCS) in the immune system. Nature Reviews Immunology 2002,2(6):410-416.Google Scholar
  12. Cacalano NA, Sanden D, Johnston JA: Tyrosine-phosphorylated SOCS-3 inhibits STAT activation but binds to p120 RasGAP and activates Ras. Nature Cell Biology 2001,3(5):460-465. 10.1038/35074525View ArticleGoogle Scholar
  13. Buitenhuis M, Coffer PJ, Koenderman L: Signal transducer and activator of transcription 5 (STAT5). International Journal of Biochemistry and Cell Biology 2004,36(11):2120-2124. 10.1016/j.biocel.2003.11.008View ArticleGoogle Scholar
  14. Wood TJJ, Sliva D, Lobie PE, et al.: Mediation of growth hormone-dependent transcriptional activation by mammary gland factor/stat 5. Journal of Biological Chemistry 1995,270(16):9448-9453. 10.1074/jbc.270.16.9448View ArticleGoogle Scholar
  15. Pircher TJ, Petersen H, Gustafsson J-A, Haldosen L-A: Extracellular signal-regulated kinase (ERK) interacts with signal transducer and activator of transcription (STAT) 5a. Molecular Endocrinology 1999,13(4):555-565. 10.1210/me.13.4.555View ArticleGoogle Scholar
  16. Blume-Jensen P, Hunter T: Oncogenic kinase signalling. Nature 2001,411(6835):355-365. 10.1038/35077225View ArticleGoogle Scholar
  17. Boulton TG, Yancopoulos GD, Gregory JS, et al.: An insulin-stimulated protein kinase similar to yeast kinases involved in cell cycle control. Science 1990,249(4964):64-67. 10.1126/science.2164259View ArticleGoogle Scholar
  18. Boulton TG, Nye SH, Robbins DJ, et al.: ERKs: a family of protein-serine/threonine kinases that are activated and tyrosine phosphorylated in response to insulin and NGF. Cell 1991,65(4):663-675. 10.1016/0092-8674(91)90098-JView ArticleGoogle Scholar
  19. Takahashi K, Vel Arjunan S, Tomita M: Space in systems biology of signaling pathways - towards intracellular molecular crowding in silico. FEBS Letters 2005,579(8):1783-1788. 10.1016/j.febslet.2005.01.072View ArticleGoogle Scholar
  20. Kholodenko BN, Brown GC, Hoek JB: Diffusion control of protein phosphorylation in signal transduction pathways. Biochemical Journal 2000,350(3):901-907. 10.1042/0264-6021:3500901View ArticleGoogle Scholar
  21. Bhalla US: Signaling in small subcellular volumes. I. Stochastic and diffusion effects on individual pathways. Biophysical Journal 2004,87(2):733-744. 10.1529/biophysj.104.040469View ArticleGoogle Scholar
  22. Schnell S, Turner TE: Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Progress in Biophysics and Molecular Biology 2004,85(2-3):235-260. 10.1016/j.pbiomolbio.2004.01.012View ArticleGoogle Scholar
  23. Swameye I, Müller TG, Timmer J, Sandra O, Klingmüller U: Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling. Proceedings of the National Academy of Sciences of the United States of America 2003,100(3):1028-1033. 10.1073/pnas.0237333100View ArticleGoogle Scholar
  24. Ketteler R, Heinrich AC, Offe JK, et al.: A functional green fluorescent protein-tagged erythropoietin receptor despite physical separation of JAK2 binding site and tyrosine residues. Journal of Biological Chemistry 2002,277(29):26547-26552. 10.1074/jbc.M202287200View ArticleGoogle Scholar
  25. Kolch W: Meaningful relationships: the regulation of the Ras/Raf/MEK/ERK pathway by protein interactions. Biochemical Journal 2000,351(2):289-305. 10.1042/0264-6021:3510289View ArticleGoogle Scholar
  26. Georgiev N, Petrov V, Nikolova E: Systems biology of cell signalling pathways. Proceedings of the 10th Jubilee National Congress on Theoretical and Applied Mechanics, Varna, Bulgaria, September 2005 2: 120-123.Google Scholar
  27. Berg HC: Random Walks in Biology. Princeton University Press, Princeton, NJ, USA; 1993.Google Scholar
  28. Nagorcka BN, Mooney JR: From stripes to spots: prepatterns which can be produced in the skin by a reaction-diffusion system. IMA Journal of Mathematics Applied in Medicine and Biology 1992,9(4):249-267. 10.1093/imammb/9.4.249MATHView ArticleGoogle Scholar
  29. Painter KJ, Maini PK, Othmer HG: Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis. Proceedings of the National Academy of Sciences of the United States of America 1999,96(10):5549-5554. 10.1073/pnas.96.10.5549View ArticleGoogle Scholar
  30. Iooss G, Joseph DD: Elementary Stability and Bifurcation Theory. 2nd edition. Springer, New York, NY, USA; 1990.MATHView ArticleGoogle Scholar
  31. Tichonov AN: Systemy differentsialnyh uravneniy, soderjashchie malye parametry pri proizvodnyh. Matematicheskiy Sbornik 1952,31(3):575-586.Google Scholar
  32. Turing AM: The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B 1952, 237: 37-72. 10.1098/rstb.1952.0012View ArticleGoogle Scholar
  33. Pircher TJ, Flores-Morales A, Mui AL-F, et al.: Mitogen-activated protein kinase kinase inhibition decreases growth hormone stimulated transcription mediated by STAT5. Molecular and Cellular Endocrinology 1997,133(2):169-176. 10.1016/S0303-7207(97)00164-0View ArticleGoogle Scholar
  34. Stewart S, Sundaram M, Zhang Y, Lee J, Han M, Guan K-L: Kinase suppressor of Ras forms a multiprotein signaling complex and modulates MEK localization. Molecular and Cellular Biology 1999,19(8):5523-5534.View ArticleGoogle Scholar
  35. Schaeffer HJ, Catling AD, Eblen ST, Collier LS, Krauss A, Weber MJ: MP1: a MEK binding partner that enhances enzymatic activation of the MAP kinase cascade. Science 1998,281(5383):1668-1671.View ArticleGoogle Scholar
  36. Teis D, Wunderlich W, Huber LA: Localization of the MP1-MAPK scaffold complex to endosomes is mediated by p14 and required for signal transduction. Developmental Cell 2002,3(6):803-814. 10.1016/S1534-5807(02)00364-7View ArticleGoogle Scholar
  37. Bray D, Lay S: Computer-based analysis of the binding steps in protein complex formation. Proceedings of the National Academy of Sciences of the United States of America 1997,94(25):13493-13498. 10.1073/pnas.94.25.13493View ArticleGoogle Scholar
  38. Levchenko A, Bruck J, Sternberg PW: Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. Proceedings of the National Academy of Sciences of the United States of America 2000,97(11):5818-5823. 10.1073/pnas.97.11.5818View ArticleGoogle Scholar


© Nikola Georgiev et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.