Regulatory control and the costs and benefits of biochemical noise

Abstract

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.

Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biology

References in corpus (2)

• Stochastic fluctuations in metabolic pathways
• Optimal signal processing in small stochastic biochemical networks

Cited by in corpus (10)

• Information capacity of genetic regulatory elements
• DNA looping provides stability and robustness to the bacteriophage lambda switch
• Probing the limits to microRNA-mediated control of gene expression
• Noise expands the response range of the Bacillus subtilis competence circuit
• The effect of phenotypic selection on stochastic gene expression
• Complete integrability of information processing by biochemical reactions
• Non-genetic variability: survival strategy or nuisance?
• Asymptotic decoupling of population growth rate and cell size distribution
• Competition between transient oscillations and early stochasticity in exponentially growing populations
• Exactly Solvable Population Model with Square-Root Growth Noise and Cell-Size Regulation