Modeling of asymmetric gene networks functioning with different types of regulation

Abstract

We find conditions of existence of closed trajectories and describe their bifurcations for two broad classes of 3D asymmetric gene network models corresponding to two different regulation mechanisms. These results can be generalized to the case of gene networks of mixed types, where this regulation is effected either at the stages of initiation of mRNA and protein synthesis or at the stages of their degradation, and both different regulation mechanisms can appear in the same gene network. Description of the Andronov-Hopf bifurcation in these models is given as well.