  Stochasticity is both exploited and controlled by cells. Although the
intrinsic stochasticity inherent in biochemistry is relatively well understood,
cellular variation, or 'noise', is predominantly generated by interactions of
the system of interest with other stochastic systems in the cell or its
environment. Such extrinsic fluctuations are nonspecific, affecting many system
components, and have a substantial lifetime, comparable to the cell cycle (they
are 'colored'). Here, we extend the standard stochastic simulation algorithm to
include extrinsic fluctuations. We show that these fluctuations affect mean
protein numbers and intrinsic noise, can speed up typical network response
times, and can explain trends in high-throughput measurements of variation. If
extrinsic fluctuations in two components of the network are correlated, they
may combine constructively (amplifying each other) or destructively
(attenuating each other). Consequently, we predict that incoherent feedforward
loops attenuate stochasticity, while coherent feedforwards amplify it. Our
results demonstrate that both the timescales of extrinsic fluctuations and
their nonspecificity substantially affect the function and performance of
biochemical networks.
