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

Abstract

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

arXiv comment43 pages, 4 figures

References in corpus (13)

• Analytical distributions for stochastic gene expression
• A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays
• Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
• Colored extrinsic fluctuations and stochastic gene expression
• Mutual information between in- and output trajectories of biochemical networks
• Exact distributions for stochastic gene expression models with bursting and feedback
• Steady-state fluctuations of a genetic feedback loop: an exact solution
• Mitochondrial Variability as a Source of Extrinsic Cellular Noise
• How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
• Stochastic Simulation of Biomolecular Networks in Dynamic Environments
• The linear-noise approximation and the chemical master equation exactly agree up to second-order moments for a class of chemical systems
• The dynamics of simple gene-network motifs subject to extrinsic fluctuations
• System size expansion using Feynman rules and diagrams

Cited by in corpus (2)

• Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF-$\beta$ signaling
• Information transmission in a two-step cascade: Interplay of activation and repression