Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

Autor(es)

Fernandez, Roberto ^[1] ; Fontes, Luiz R. ^[2] ; Neves, E. Jordao ^[2]

Afiliação do(s) autor(es)

^[1] Univ Rouen, CNRS, UMR 6085, Lab Math Raphael Salem, F-76801 St Etienne - France

^[2] Univ Sao Paulo, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 136, n. 5, p. 875-901, SEP 2009.
• Citações Web of Science: 4

Resumo

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module. (AU)

• Processo FAPESP: 04/07276-2 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Luiz Renato Gonçalves Fontes
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 06/03227-2 - Expressão gênica em tumores do estômago e do esôfago: da biologia ao diagnóstico
• Beneficiário: Luiz Fernando Lima Reis
• Linha de fomento: Auxílio à Pesquisa - Temático