Huang-Ferrell Model of MAPK Signaling

Molecular studies of cell communication systems lead to models with multiple free parameters. Analysis of dynamical behavior of these models presents considerable challenge. We have developed a computational approach for the efficient exploration of dynamic behavior in such models and applied this method to the model of the Mitogen Activated Protein Kinase cascade, a signaling network conserved in all eukaryotes. Previous analysis of this model suggested that it works as a reversible switch. We have shown that it can also function as an irreversible switch and as a clock(Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling, Qiao, Liang, Nachbar Robert B., Kevrekidis Ioannis G., and Shvartsman Stanislav Y. , PLoS Computational Biology 3(9):e184 (2007)).
(A) Schematic of the MAPK cascade, reproduced from [26], 1996. The full MAPK cascade consists of ten enzymatic reactions where each step is modeled by mass action; it can be described by an ODE system consisting of 15 variables and 37 parameters. The distinguished (bifurcation) parameter, pb ∈ R+, is the cascade input (the total concentration of E1). The 36-dimensional vector of the remaining model parameters (p ∈ R+36) consists of 30 rate constants and six total concentrations).
(B) Schematic of the sampling/continuation approach. The components of the remaining model parameters are generated from the 36-dimensional vector of predefined base values (pc ∈ R+36) and the random variables ɛi that are uniformly distributed in [−q, q], where q is the size of the uncertainty interval: pi = pci × 5ɛi, i = 1, 2, … 36.