After being considered as a nuisance to be filtered out, it became increasingly clear that noises play a complex role, often fully functional, for biochemical networks. The influence of intrinsic and extrinsic noises on these networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations should be bounded. In the first part of this work we consider Gillespie-like stochastic models of nonlinear networks (i.e. networks affected by intrinsic stochasticity) where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. As an application, in the second part of this contribute we investigate the influence of both amplitude and autocorrelation time of an harmonic noise on a genetic toggle switch. We show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises.
