  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.
