  The study of biochemical pathways usually focuses on a small section of a
protein interactions network. Two distinct sources contribute to the noise in
such a system: intrinsic noise, inherent in the studied reactions, and
extrinsic noise generated in other parts of the network or in the environment.
We study the effect of extrinsic noise entering the system through a nonlinear
uptake reaction which acts as a nonlinear filter. Varying input noise intensity
varies the mean of the noise after the passage through the filter, which
changes the stability properties of the system. The steady-state displacement
due to small noise is independent on the kinetics of the system but it only
depends on the nonlinearity of the input function.
  For monotonically increasing and concave input functions such as the
Michaelis-Menten uptake rate, we give a simple argument based on the
small-noise expansion, which enables qualitative predictions of the
steady-state displacement only by inspection of experimental data: when weak
and rapid noise enters the system through a Michaelis-Menten reaction, then the
graph of the system's steady states vs. the mean of the input signal always
shifts to the right as noise intensity increases.
  We test the predictions on two models of lac operon, where TMG/lactose uptake
is driven by a Michaelis-Menten enzymatic process. We show that as a
consequence of the steady state displacement due to fluctuations in
extracellular TMG/lactose concentration the lac switch responds in an
asymmetric manner: as noise intensity increases, switching off lactose
metabolism becomes easier and switching it on becomes more difficult.
