Applications of Little's Law to stochastic models of gene expression

被引:30
作者
Elgart, Vlad [1 ]
Jia, Tao [1 ]
Kulkarni, Rahul V. [1 ]
机构
[1] Virginia Polytech Inst & State Univ, Dept Phys, Blacksburg, VA 24060 USA
来源
PHYSICAL REVIEW E | 2010年 / 82卷 / 02期
关键词
PROTEIN EXPRESSION; MOLECULE; NOISE; DEGRADATION; CHANCE; CELLS; RNA;
D O I
10.1103/PhysRevE.82.021901
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 [等离子体物理]; 070301 [无机化学];
摘要
The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of messenger RNA (mRNA) fluctuations ("Poisson" and "telegraph" processes) have been proposed in stochastic models of gene expression. Both Poisson and telegraph scenario models explain experimental observations of noise in protein levels in terms of "bursts" of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression. To illustrate this, we consider a model for regulation of protein expression bursts by small RNAs. For a broad range of parameters, we derive analytical expressions (validated by stochastic simulations) for the mean protein levels as the levels of regulatory small RNAs are varied. The results obtained show that the degree of transcriptional bursting can, in principle, be determined from changes in mean steady-state protein levels for general stochastic models of gene expression.
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页数:6
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