Format

Send to

Choose Destination
See comment in PubMed Commons below
Proc Natl Acad Sci U S A. 2008 Nov 11;105(45):17256-61. doi: 10.1073/pnas.0803850105. Epub 2008 Nov 6.

Analytical distributions for stochastic gene expression.

Author information

1
Centre for Non-linear Dynamics, Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, Canada, H3G 1Y6.

Abstract

Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance, but also the distribution of protein numbers. We assume that proteins decay substantially more slowly than their mRNA and confirm that many genes satisfy this relation by using high-throughput data from budding yeast. For a two-stage model of gene expression, with transcription and translation as first-order reactions, we calculate the protein distribution for all times greater than several mRNA lifetimes and thus qualitatively predict the distribution of times for protein levels to first cross an arbitrary threshold. If in addition the fluctuates between inactive and active states, we can find the steady-state protein distribution, which can be bimodal if fluctuations of the promoter are slow. We show that our assumptions imply that protein synthesis occurs in geometrically distributed bursts and allows mRNA to be eliminated from a master equation description. In general, we find that protein distributions are asymmetric and may be poorly characterized by their mean and variance. Through maximum likelihood methods, our expressions should therefore allow more quantitative comparisons with experimental data. More generally, we introduce a technique to derive a simpler, effective dynamics for a stochastic system by eliminating a fast variable.

PMID:
18988743
PMCID:
PMC2582303
DOI:
10.1073/pnas.0803850105
[Indexed for MEDLINE]
Free PMC Article
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for HighWire Icon for PubMed Central
    Loading ...
    Support Center