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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Fernandez, Roberto [1] ; Fontes, Luiz R. [2] ; Neves, E. Jordao [2]
Total Authors: 3
Affiliation:
[1] Univ Rouen, CNRS, UMR 6085, Lab Math Raphael Salem, F-76801 St Etienne - France
[2] Univ Sao Paulo, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Statistical Physics; v. 136, n. 5, p. 875-901, SEP 2009.
Web of Science Citations: 4
Abstract

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)

FAPESP's process: 04/07276-2 - Stochastic Modelling of Interacting Systems
Grantee:Luiz Renato Gonçalves Fontes
Support type: Research Projects - Thematic Grants
FAPESP's process: 06/03227-2 - Gene expression profile of tumors from the upper digestive track: from tumor biology to new diagnostic tools
Grantee:Luiz Fernando Lima Reis
Support type: Research Projects - Thematic Grants