Molecular Distributions in Gene Regulatory Dynamics

Abstract

We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in degradation rates arising from low numbers of molecules. We have compared our results with an analysis of the same model systems (either inducible or repressible operons) in the absence of any stochastic effects, and shown the correspondence between behaviour in the deterministic system and the stochastic analogs. We have identified key dimensionless parameters that control the appearance of one or two steady states in the deterministic case, or unimodal and bimodal densities in the stochastic systems, and detailed the analytic requirements for the occurrence of different behaviours. This approach provides, in some situations, an alternative to computationally intensive stochastic simulations. Our results indicate that, within the context of the simple models we have examined, bursting and degradation noise cannot be distinguished analytically when present alone.

14 pages, 12 figures. Conferences: "2010 Annual Meeting of The Society of Mathematical Biology", Rio de Janeiro (Brazil), 24-29/07/2010. "First International workshop on Differential and Integral Equations with Applications in Biology and Medicine", Aegean University, Karlovassi, Samos island (Greece), 6-10/09/2010

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Cited by in corpus (13)

• Dynamic behavior of stochastic gene expression models in the presence of bursting
• Transcriptional leakage versus noise: A simple mechanism of conversion between binary and graded response in autoregulated genes
• Influence of gene copy number on self-regulated gene expression
• The Limiting Dynamics of a Bistable Molecular Switch With and Without Noise
• Existence of invariant densities for semiflows with jumps
• A Model of Gene Expression Based on Random Dynamical Systems Reveals Modularity Properties of Gene Regulatory Networks
• Exponential equilibration of genetic circuits using entropy methods
• The combined effects of Feller diffusion and transcriptional/translational bursting in simple gene networks
• Adiabatic reduction of models of stochastic gene expression with bursting
• Adiabatic reduction of a model of stochastic gene expression with jump Markov process
• Efficient stochastic simulation of gene regulatory networks using hybrid models of transcriptional bursting
• Gene expression noise is affected differentially by feedback in burst frequency and burst size
• On the bursting of gene products