Multistability and robustness of the MAPK pathway

In this paper, we propose a qualitative model of the MAPK signaling cascade and analyze its multi-stability properties. Building on our previous work, we employ Lyapunov and invariant sets theory to analyze the system. In particular we focus on the first stage of a class of MAPK cascades, known as the Mos subsystem, which is the target of a positive feedback loop. Under general assumptions, we show that the system is bistable when three equilibria are present, regardless of the specific feedback dynamics.

[1]  M. Feinberg.  Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems , 1987 .

[2]  H. Kitano.  Systems Biology: A Brief Overview , 2002, Science.

[3]  John Ian Ferrell,et al.  Detection of multi-stability , 2004 .

[4]  J E Ferrell,et al.  The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. , 1998, Science.

[5]  M. Feinberg,et al.  Structural Sources of Robustness in Biochemical Reaction Networks , 2010, Science.

[6]  Uri Alon,et al.  Input–output robustness in simple bacterial signaling systems , 2007, Proceedings of the National Academy of Sciences.

[7]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[8]  B. Kholodenko,et al.  Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades , 2004, The Journal of cell biology.

[9]  Eduardo D. Sontag,et al.  Monotone and near-monotone biochemical networks , 2007, Systems and Synthetic Biology.

[10]  J. Bodart,et al.  On the equilibria of the MAPK cascade: Cooperativity, modularity and bistability , 2007, q-bio/0702051.

[11]  Eduardo Sontag,et al.  Untangling the wires: A strategy to trace functional interactions in signaling and gene networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[12]  John A. Jacquez,et al.  Qualitative Theory of Compartmental Systems , 1993, SIAM Rev..

[13]  N. Rouche,et al.  Stability Theory by Liapunov's Direct Method , 1977 .

[14]  P. Bastiaens,et al.  Growth factor-induced MAPK network topology shapes Erk response determining PC-12 cell fate , 2007, Nature Cell Biology.

[15]  Andre Levchenko,et al.  Dynamic Properties of Network Motifs Contribute to Biological Network Organization , 2005, PLoS biology.

[16]  Franco Blanchini,et al.  Structurally robust biological networks , 2011, BMC Systems Biology.

[17]  Chi-Ying F. Huang,et al.  Ultrasensitivity in the mitogen-activated protein kinase cascade. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[18]  James E Ferrell,et al.  Simple, realistic models of complex biological processes: Positive feedback and bistability in a cell fate switch and a cell cycle oscillator , 2009, FEBS letters.

[19]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[20]  Liang Qiao,et al.  Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling , 2007, PLoS Comput. Biol..