Stochastic branching-diffusion models for gene expression

David Cottrell, Peter S Swain, Paul F Tupper

Research output: Contribution to journalArticlepeer-review

Abstract

A challenge to both understanding and modeling biochemical networks is integrating the effects of diffusion and stochasticity. Here, we use the theory of branching processes to give exact analytical expressions for the mean and variance of protein numbers as a function of time and position in a spatial version of an established model of gene expression. We show that both the mean and the magnitude of fluctuations are determined by the protein's Kuramoto length-the typical distance a protein diffuses over its lifetime-and find that the covariance between local concentrations of proteins often increases if there are substantial bursts of synthesis during translation. Using high-throughput data, we estimate that the Kuramoto length of cytoplasmic proteins in budding yeast to be an order of magnitude larger than the cell diameter, implying that many such proteins should have an approximately uniform concentration. For constitutively expressed proteins that live substantially longer than their mRNA, we give an exact expression for the deviation of their local fluctuations from Poisson fluctuations. If the Kuramoto length of mRNA is sufficiently small, we predict that such local fluctuations become approximately Poisson in bacteria in much of the cell, unless translational bursting is exceptionally strong. Our results therefore demonstrate that diffusion can act to both increase and decrease the complexity of fluctuations in biochemical networks.
Original languageEnglish
Pages (from-to)9699-9704
Number of pages6
JournalProceedings of the National Academy of Sciences
Volume109
Issue number25
DOIs
Publication statusPublished - 2012

Keywords

  • stochastic gene expression
  • intrinsic noise

Fingerprint

Dive into the research topics of 'Stochastic branching-diffusion models for gene expression'. Together they form a unique fingerprint.

Cite this