461 research outputs found
Analytical distributions for stochastic gene expression
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 slower than their mRNA and confirm
that many genes satisfy this relation 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 promoter fluctuates between inactive and active
states, we can find the steady-state protein distribution, which can be bimodal
if promoter fluctuations 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.Comment: Supplementary information can be found on PNAS websit
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