We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, which was invented by Elowitz and Leibler. We propose an alternative approach to model the dynamical behaviors  , that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take account to inherent variability of gene expression. We  consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector in the thermodynamic limit . We apply a convergence result from  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 behaviors , including the empirical oscillations described by repressilator.
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 Fern\'andez et. al (2009), 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 (2000). 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.
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analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, which was invented by Elowitz and Leibler. We propose an
study an
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of biological feedback loop
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analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler (2000). We
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in the thermodynamic limit
representing concentration of molecules
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stochastic
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behaviors
behaviours