Optimal scaling between mRNA and protein maximizes cell fitness

Gene expression regulation is crucial for cell fitness, balancing the costs of mRNA and protein synthesis with the benefits of their production. Here, we identify the optimal scaling between mRNA and protein levels that maximizes cell fitness. For highly expressed genes for which protein noise is negligible, the mRNA copy number scales with the square root of the protein copy number ( m ∼ p ^0.5 ), while for lowly expressed genes for which protein noise is significant, a linear relationship ( m ∼ p ) emerges. Simulations of in silico cells using biological parameters predict that Saccharomyces cerevisiae is close to the square-root regime while Escherichia coli is close to the linear regime, in perfect agreement with experimental measurements. We show that the universal predominance of transcription regulation in determining protein abundance is a natural result of optimal fitness, in agreement with the mRNA-protein scaling across different organisms. We also establish a constraint on the ratio between the translation and transcription rate, rationalizing the absence of highly expressed mRNAs with low translational activity. Our findings uncover a universal principle of gene expression regulation.