title: Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module.
abstract: We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernández et. al [13], and are useful since take account to inherent variability of gene expression. We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler [7]. We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector representing concentration of molecules. We apply a convergence result from stochastic jump processes to deterministic trajectories and present a bifurcation analysis for the associated dynamical system. We show that non-symmetric module under study can exhibit very rich behaviours, including the empirical oscillations described by repressilator.
authors: Institute of Mathematics and Statistics, Universidade de São Paulo, Rua do Matao, 1010, CEP 05508-090, Sao Paulo, Brazil. email: manuelg@ime.usp.br.
authors: Manuel
authors: M
authors: Gonzalez-Navarrete
mesh_terms: D025461:Feedback, Physiological; D015870:Gene Expression / Q000502:physiology*; D008954:Models, Biological; D013269:Stochastic Processes