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It is well known that the kinetics of an intracellular biochemical network isstochastic. This is due to intrinsic noise arising from the random timing ofbiochemical reactions in the network as well as due to extrinsic noise stemmingfrom the interaction of unknown molecular components with the network and fromthe cell's changing environment. While there are many methods to study theeffect of intrinsic noise on the system dynamics, few exist to study theinfluence of both types of noise. Here we show how one can extend theconventional linear-noise approximation to allow for the rapid evaluation ofthe molecule numbers statistics of a biochemical network influenced byintrinsic noise and by slow lognormally distributed extrinsic noise. The theoryis applied to simple models of gene regulatory networks and its validityconfirmed by comparison with exact stochastic simulations. In particular weshow how extrinsic noise modifies the dependence of the variance of themolecule number fluctuations on the rate constants, the mutual informationbetween input and output signalling molecules and the robustness offeed-forward loop motifs.

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise