The effect of natural selection on the propagation of protein expression noise to bacterial growth

In bacterial cells, protein expression is a highly stochastic process. Gene expression noise moreover propagates through the cell and adds to fluctuations in the cellular growth rate. A common intuition is that, due to their relatively high noise amplitudes, proteins with a low mean expression level are the most important drivers of fluctuations in physiological variables. In this work, we challenge this intuition by considering the effect of natural selection on noise propagation. Mathematically, the contribution of each protein species to the noise in the growth rate depends on two factors: the noise amplitude of the protein’s expression level, and the sensitivity of the growth rate to fluctuations in that protein’s concentration. We argue that natural selection, while shaping mean abundances to increase the mean growth rate, also affects cellular sensitivities. In the limit in which cells grow optimally fast, the growth rate becomes most sensitive to fluctuations in highly abundant proteins. This causes abundant proteins to overall contribute strongly to the noise in the growth rate, despite their low noise levels. We further explore this result in an experimental data set of protein abundances, and test key assumptions in an evolving, stochastic toy model of cellular growth.Author summary: Gene expression in bacterial cells is intrinsically stochastic: copy numbers of all proteins vary between genetically identical cells, even in a homogeneous environment. Such noise in gene expression affects metabolic fluxes and even propagates to the cellular level. Indeed, also the growth rate of individual cells, an important proxy for fitness, fluctuates strongly. This beckons the question as to which protein species contribute most to the noise in the cell’s growth rate. We here derive general mathematical predictions stating that if cells have been optimised by evolution to grow fast, abundant protein species contribute most to the noise in the growth rate. This result is counter-intuitive, because the noise levels in the expression of those highly expressed proteins are small.