Sistemas de partículas interagentes dependentes de tipo e aplicações ao estudo de redes de sinalização biológica / Type-dependent interacting particle systems and their applications in the study of signaling biological networks

AUTOR(ES)
DATA DE PUBLICAÇÃO

2011

RESUMO

We study type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. The original 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. In the thermodynamic limit it was proved that, within arbitrary finite time-intervals, the path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. The behavior of the associated dynamical system may include bifurcations, associated to phase transitions in the statistical mechanical setting. Our aim is to extend the spin model with Glauber dynamics, to allow multiple spin-flips. In the biological context we included situations in which molecules of different types simultaneously change their internal states. Using several methods, such as large deviations and coupling, we prove the convergence theorem.

ASSUNTO(S)

almost sure convergence biological signaling network campo médio convergência quase certa density-profile process dinâmica estocástica não reversível dynamical system mean field modelo de spins estocástico dependente de tipo non-reversible stochastic dynamics processo de perfil de densidade rede de sinalização biológica sistema dinâmico type-dependent stochastic spin model

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