TY - JOUR
T1 - On the equilibria of the MAPK cascade
T2 - Cooperativity, modularity and bistability
AU - Russo, C.
AU - Giuraniuc, C.
AU - Blossey, R.
AU - Bodart, J. F.
N1 - CR gratefully acknowledges support through a grant from the French National Cancer Institute, INCa.
PY - 2009/12/15
Y1 - 2009/12/15
N2 - In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. [D. Angeli, J.E. Ferrell, Jr., E.D. Sontag, PNAS 101 (2004), 1822]. The model and its solution are extended in several respects: (a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; (b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; (c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.
AB - In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. [D. Angeli, J.E. Ferrell, Jr., E.D. Sontag, PNAS 101 (2004), 1822]. The model and its solution are extended in several respects: (a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; (b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; (c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.
UR - http://www.scopus.com/inward/record.url?scp=70249094979&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2009.08.018
DO - 10.1016/j.physa.2009.08.018
M3 - Article
AN - SCOPUS:70249094979
SN - 0378-4371
VL - 388
SP - 5070
EP - 5080
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 24
ER -