Abundant proteins contribute strongly to noise in the growth rate of optimally growing bacteria

In bacterial cells, protein expression is a highly stochastic process. At the same time, physiological variables such as the cellular growth rate also fluctuate significantly. A common intuition is that, due to their relatively high noise amplitudes, proteins with a low mean expression level are the most important causes of these fluctuations on a larger, physiological scale. Noise in highly expressed proteins, whose stochastic fluctuations are relatively small, is often ignored. In this work, we challenge this intuition by developing a theory that predicts the contribution of a proteins expression noise to the noise in the instantaneous, cellular growth rate. Using mathematical analysis, we decomposed the contribution of each protein into two factors: the noise amplitude of the protein, and the sensitivity of the growth rate to fluctuations in that proteins concentration. Next, we incorporated evolution, which has shaped the mean abundances of growth-related proteins to optimise the growth rate, causing protein abundances, but also cellular sensitivities to be non-random. We show that in cells that grow optimally fast, the growth rate is most sensitive to fluctuations in highly abundant proteins. This causes such proteins to overall contribute strongly to the noise in the growth-rate, despite their low noise levels. The results are confirmed in a stochastic toy model of cellular growth.