  It has been generally recognized that stochasticity can play an important
role in the information processing accomplished by reaction networks in
biological cells. Most treatments of that stochasticity employ Gaussian noise
even though it is a priori obvious that this approximation can violate physical
constraints, such as the positivity of chemical concentrations. Here, we show
that even when such nonphysical fluctuations are rare, an exact solution of the
Gaussian model shows that the model can yield unphysical results. This is done
in the context of a simple incoherent-feedforward model which exhibits perfect
adaptation in the deterministic limit. We show how one can use the natural
separation of time scales in this model to yield an approximate model, that is
analytically solvable, including its dynamical response to an environmental
change. Alternatively, one can employ a cutoff procedure to regularize the
Gaussian result.
