Noise in a small genetic circuit that undergoes bifurcation

Based on the consideration of Boolean dynamics, it has been hypothesized that cell types may correspond to alternative attractors of a gene regulatory network. Recent stochastic Boolean network analysis, however, raised the important question concerning the stability of such attractors. In this paper a detailed numerical analysis is performed within the framework of Langevin dynamics. While the present results confirm that the noise is indeed an important dynamical element, the cell type as represented by attractors can still be a viable hypothesis. It is found that the stability of an attractor depends on the strength of noise related to the distance of the system to the bifurcation point and it can be exponentially stable depending on biological parameters.