  Simulation of biomolecular networks is now indispensable for studying
biological systems, from small reaction networks to large ensembles of cells.
Here we present a novel approach for stochastic simulation of networks embedded
in the dynamic environment of the cell and its surroundings. We thus sample
trajectories of the stochastic process described by the chemical master
equation with time-varying propensities. A comparative analysis shows that
existing approaches can either fail dramatically, or else can impose
impractical computational burdens due to numerical integration of reaction
propensities, especially when cell ensembles are studied. Here we introduce the
Extrande method which, given a simulated time course of dynamic network inputs,
provides a conditionally exact and several orders-of-magnitude faster
simulation solution. The new approach makes it feasible to demonstrate, using
decision-making by a large population of quorum sensing bacteria, that
robustness to fluctuations from upstream signaling places strong constraints on
the design of networks determining cell fate. Our approach has the potential to
significantly advance both understanding of molecular systems biology and
design of synthetic circuits.
