Fitness costs of noise in biochemical reaction networks and the evolutionary limits of cellular robustness

Gene expression is inherently noisy, but little is known about whether noise affects cell function or, if so, how and by how much. Here I present a theoretical framework to quantify the fitness costs of gene expression noise and identify the evolutionary and synthetic targets of noise control. I find that gene expression noise reduces fitness by slowing the average rate of nutrient uptake and protein synthesis. This is a direct consequence of the hyperbolic (Michaelis-Menten) kinetics of most biological reactions, which I show cause \"hyperbolic filtering\", a process that diminishes both the average rate and noise propagation of stochastic reactions. Interestingly, I find that transcriptional noise directly slows growth by slowing the average translation rate. Perhaps surprisingly, this is the largest fitness cost of transcriptional noise since translation strongly filters mRNA noise, making protein noise largely independent of transcriptional noise, consistent with empirical data. Translation, not transcription, then, is the primary target of protein noise control. Paradoxically, selection for protein-noise control favors increased ribosome-mRNA binding affinity, even though this increases translational bursting. However, I find that the efficacy of selection to suppress noise decays faster than linearly with increasing cell size. This predicts a stark, cell-size-mediated taxonomic divide in selection pressures for noise control: small unicellular species, including most prokaryotes, face fairly strong selection to suppress gene expression noise, whereas larger unicells, including most eukaryotes, experience extremely weak selection. I suggest that this taxonomic discrepancy in selection efficacy contributed to the evolution of greater gene-regulatory complexity in eukaryotes.\n\nARTICLE SUMMARYGene expression is a probabilistic process, resulting in random variation in mRNA and protein abundance among cells called \"noise\". Understanding how noise affects cell function is a major problem in biology. Here I present theory demonstrating that gene expression noise slows the average rate of cell division. Furthermore, by modeling stochastic gene expression with non-linearity, I identify novel mechanisms of cellular robustness. However, I find that the cost of noise, and therefore the strength of selection favoring robustness, decays faster than linearly with increasing cell size. This may help explain the vast differences in gene-regulatory complexity between prokaryotes and eukaryotes.