Noise robustness and metabolic load determine the principles of central dogma regulation*

Protein expression levels optimize cell fitness: Too low of an expression level of essential proteins slows growth by compromising the function of essential processes, whereas the overexpression of proteins slows growth by increasing the metabolic load. This trade-off naively predicts that the cell maximizes its fitness by a Goldilocks principle in which cells express just enough protein for function; however, this strategy neglects the significance of the inherent stochasticity of the gene expression process which leads to significant cell-to-cell variation in protein numbers. How does the cell ensure robust growth in the face of the inherent stochasticity of these central dogma processes? To explore the consequences of noise in the expression of hundreds of essential genes, we build a minimal model where the trade-off between metabolic cost and growth robustness can be analyzed analytically. The model predicts that growth-rate maximization leads to a highly-asymmetric cost-benefit analysis which drives the optimal protein expression levels far above what is required on average, with low-expression essential proteins expressed at more than 10-fold what is required for growth in the typical cell. This robustness mechanism naturally explains the surprisingly strong buffering effect observed in essential protein depletion experiments and leads to a second qualitative prediction: there is a lower floor on the transcription level of essential genes corresponding to one message per cell cycle. We show that nearly all essential, but not non-essential, genes obey this limit in three evolutionarily-divergent model organisms: Escherichia coli, yeast, and human. The model also pre- dicts that the optimal translation efficiency is roughly proportional to message abundance, predicting the observed relation between proteome fraction and message abundance in eukaryotic cells. This optimal translation efficiency predicts a non-canonical scaling of gene expression noise with protein abundance, which we show is observed in yeast. Together, these results reveal that noise robustness and metabolic load determine the global regulatory principles that govern central dogma function.