The interplay between stochasticity and regulation in a coarse-grained model of gene expression, metabolism, and growth

Abstract

Recent time-lapse microscopy experiments on bacterial growth have shown large cell-to-cell variations in growth rate and protein expression levels. Earlier experiments at the population level have shown that the expression of different classes of protein is tightly regulated to achieve fast growth in various conditions. We have built a coarse-grained model of bacterial metabolism that incorporates both the stochasticity of protein production and division, and the regulation that optimises growth. We introduce novel variables that quantify the coupling from gene expression to growth, which we call growth control coefficients. Analysis of the system in the optimal state shows that stochasticity in the growth rate has its main cause in the stochasticity of frequently occurring proteins, even though these fluctuate relatively little. The global regularity of protein expression is explained by optimising the system for growth rate. We include a regulatory mechanism in our model that achieves this in close approximation. The regulation also counteracts the growth-inhibiting effects of stochasticity, by lowering the amplitude and decorrelation time of fluctuations in the protein concentrations. We use the model to compute crosscorrelations between protein expression and growth rate. The resulting graphs reproduce several features present in their experimental counterparts.