Abstract
We introduce a novel model construction, cascaded games, that is intended to allow us to study the notion of steady states algebraically and structurally. The model construction is inspired by the chemical underpinning and the prevailing conceptualisation of mitogen-activated protein kinase (MAPK) cascades. To analyse the models, we use the recent notion of change-of-mind equilibria. We exemplify our proposal with gene regulation and MAPK cascades, capturing basic as well as advanced issues such as prophage induction and tauopathy causation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alberts, B., Johnson, A., Julian, L., Raff, M., Roberts, K., Walter, P.: Molecular Biology of the Cell. In: Garland Science, 4th edn. Taylor and Francis Group, London (2002)
Atsumi, S., Little, J.W.: Role of the lytic repressor in prophage induction of phage lambda as analyzed by a module-replacement approach. PNAS 103 (2006)
BioCarta. BioCarta, http://www.biocarta.com
Bradford Cannon, W.: The Wisdom of the Body, W.W. Norton, New York (1932)
Chettaoui, C., Delaplace, F., Lescanne, P., Vestergaard, M., Vestergaard, R.: Rewriting game theory as a found. for state-based models of gene regulation. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol. 4210, Springer, Heidelberg (2006)
Comperts, B.D., Kramer, I.M., Tatham, P.E.R. (eds.): Signal Transduction. Elsevier, Amsterdam (2004)
Chen, Z., et al.: MAP kinase. Chemical Review 101, 2449–2476 (2001)
Feijoo, C., Campbell, D.G., Jakes, R., Goedert, M., Cuenda, A.: Evidence that phosphorylation of the microtubule-associated protein tau by SAPK4/p38d at Thr50 promotes microtubule assembly. J. Cell Sc., 118 (2005)
Ferrer, I.: Stress kinases involved in tau phosphorylation in Alzheimer’s disease, tauopathies and APP transgenic mice. Neurotoxicity Research, 6 (2004)
Ferrer, I., Gomez-Isla, T., Puig, B., Freixes, M., Ribe, E., Dalfo, E., Avila, J.: Current advances on different kinases involved in tau phosphorylation, and implications in Alzheimer’s disease and tauopathies. Curr. Alz’s R., 2 (2005)
Gilman, A., Arkin, A.P.: Genetic “code”: Representations and dynamical models of genetic components and networks. Annu Rev Genomics Hum Genet. 3 (2002)
Gong, C.-X., Liu, F., Grundke-Iqbal, I., Iqbal, K.: Dysregulation of protein phosphorylation/dephosphorylation in Alzheimer’s disease. J. of Biomed, Biotech (2006)
GuimerĂ , R., Sales-Pardo, M.: Form follows function: the architecture of complex networks. Molecular Systems Biology 2(42) (2006)
Haddad, J.J.: Mitogen-activated protein kinases and the evolution of Alzheimer’s: a revolutionary neurogenetic axis for therapeutic intervention. Progress in Neurobiology 73 (2004)
Harsanyi, J.C., Nash, J.F., Selten, R.: The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, for their pioneering analysis of equilibria in the theory of non-cooperative games (1994)
Kanehisa, M., et al.: KEGG, MAP signaling pathway - homo sapiens (human), http://www.genome.jp/kegg/
Kauffman, S.A.: The Origins of Order: Self-Organization and Selection in Evol. OUP (1993)
Kiriakis, J.M., Avruch, J.: Mammalian mitogen-activated protein kinase signal transduction pathways activated by stress and inflammation. Physiological Reviews, 81 (2001)
Kuhn, H.W.: Extensive games and the problem of information. Contributions to the Theory of Games II, Reprinted in [20] (1953)
Kuhn, H.W. (ed.): Classics in Game Theory. Princeton Uni. Press, Princeton (1997)
Manning, A.M., Davis, R.J.: Targeting JNK for therapeutic benefit: From junk to gold? Nature Reviews Drug Discovery 2, 554–565 (2003)
Maturana, H.R., Varela, F.J.: Autopoiesis and Cognition: The Realization of the Living. D. Reidel Publishing, Dordrecht (1980)
Nash, J.F.: Non-Cooperative Games PhD thesis. Princeton University, Princeton (1950)
Nash, J.F.: Non-cooperative games. Annals of Mathematics, 54, Reprinted in [20]; published version of [23] (1951)
Oda, K., Matsuoka, Y., Funahashi, A., Kitano, H.: A comprehensive pathway map of epidermal growth factor receptor signalling. Mol. Sys. Bio. (2005)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, Cambridge (1994)
Pearson, G., Robinson, F., Gibson, T.B., Xu, B., Karandikar, M., Berman, K., Cobb, M.H.: Mitogen-activated protein (MAP) kinase pathways: Regulation and physiological fynctions. Endocrine Reviews 22, 153–183 (2001)
Pei, J.-J., Gong, C.-X., An, W.-L., Winblad, B., Cowburn, R.F., Grundke-Iqbal, I., Iqbal, K.: Okadaic-acid-induced inhibition of protein phosphatase 2A produces activation of mitogen-activated protein kinases ERK1/2, MEK1/2, and p70S6, similar to that in Alzheimer’s disease. Am. J. Path 163 (2003)
ProteinLounge. Proteinlounge databases, http://www.proteinlounge.com
Qi, M., Elion, E.A.: MAP kinase pathways. Journal of Cell Science 116, 3569–3572 (2003)
Rous, P.P., Blenis, J.: ERK and p38 MAPK-activated protein kinases: a family of protein kinases with diverse biologcal functions. Microbio and MBR 68, 320–344 (2004)
Le Roux, S., Lescanne, P., Vestergaard, R.: A discrete Nash theorem with quadratic complexity and dynamic equilibria. Technical Report IS-RR-2006-006, JAIST (May 2006)
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. Nature Biotechnology 20 (2002)
Senachak, J., Vestergaard, M., Vestergaard, R.: Rewriting game theory applied to protein signalling in MAPK cascades TechReport IS-RR-2006-007, JAIST (Unpublished, May 2006)
Tarjan, R.E.: Depth first search and linear graph algorithms. SIAM JoC, 146–160 (1972)
Thieffry, D., Thomas, R.: Dynamical behaviour of biological regulatory networks–II. immunity control in bacteriophage lambda. Bull Math Biol. 57(2) (1995)
Thomas, R., Kaufman, M.: Multistationarity, the basis of cell differentiation and memory I: Structural conditions of multistationarity and other nontrivial behavior. Chaos 11(1) (2001)
Upstate. Cell signaling, MAPK pathway, http://www.cellsignaling.com
Vestergaard, R.: A constructive approach to sequential Nash equilibria. IPL 97, 46–51 (2006)
Voet, D., Voet, J.G.: Biochemistry. John Wiley and Sons, Inc., West Sussex (1995)
Watson, J.D., Baker, T.A., Bell, S.P., Gann, A., Levine, M., Losick, R.: Molecular Biology of the Gene, 5th edn. The Benjamin/Cummings Publishing Company (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Senachak, J., Vestergaard, M., Vestergaard, R. (2007). Cascaded Games. In: Anai, H., Horimoto, K., Kutsia, T. (eds) Algebraic Biology. AB 2007. Lecture Notes in Computer Science, vol 4545. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73433-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-73433-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73432-1
Online ISBN: 978-3-540-73433-8
eBook Packages: Computer ScienceComputer Science (R0)