We study by means of analytical calculation and stochastic simulations how intrinsic noise modifies the bifurcation diagram of gene regulatory processes that can be effectively described by the Langevin formalism. In a general context, our study raises the intriguing question of how biochemical fluctuations redesign the epigenetic landscape in differentiation processes. We have applied our findings to a general class of regulatory processes that includes the simplest case that displays a bistable behavior and hence phenotypic variability: the genetic auto-activating switch. Thus, we explain why and how the noise promotes the stability of the low-state phenotype of the switch and show that the bistable region is extended when increasing the intensity of the fluctuations. This phenomenology is found in a simple one-dimensional model of the genetic switch as well as in a more detailed model that takes into account the binding of the protein to the promoter region. Altogether, we prescribe the analytical means to understand and quantify the noise-induced modifications of the bifurcation points for a general class of regulatory processes where the genetic bistable switch is included.
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