Abstract
Bacterial ribosomes are composed of one-third protein and two-thirds RNA by mass. The predominance of RNA is often attributed to a primordial RNA world, but why exactly two-thirds remains a long-standing mystery. Here we present a quantitative analysis, based on the kinetics of ribosome self-replication, demonstrating that the 1∶2 protein-to-RNA mass ratio uniquely maximizes cellular growth rates in E.coli. A previously unrecognized growth law, and an invariant of bacterial growth, also follow from our analysis. The growth law reveals that the ratio between the number of ribosomes and the number of polymerases making ribosomal RNA is proportional to the cellular doubling time. The invariant is conserved across growth conditions and specifies how key microscopic parameters in the cell, such as transcription and translation rates, are coupled to cellular physiology. Quantitative predictions from the growth law and invariant are shown to be in excellent agreement with E.coli data despite having no fitting parameters. Our analysis can be readily extended to other bacteria once data become available.
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