  After being considered as a nuisance to be filtered out, it became recently
clear that biochemical noise plays a complex role, often fully functional, for
a genetic network. The influence of intrinsic and extrinsic noises on genetic
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 are clearly bounded. In this paper we
consider Gillespie-like stochastic models of nonlinear networks, i.e. the
intrinsic noise, 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.
  We investigated the influence of both amplitude and autocorrelation time of a
extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of
noisy enzymatic reactions, which we show to be applicable also in co-presence
of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle
and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ 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.
