Abstract
Protein synthesis is the most expensive process in fast-growing bacteria. Experimentally observed growth rate dependencies of the translation machinery form the basis of powerful phenomenological growth laws; however, a quantitative theory on the basis of biochemical and biophysical constraints is lacking. Here, we show that the growth rate-dependence of the concentrations of ribosomes, tRNAs, mRNA, and elongation factors observed in Escherichia coli can be predicted accurately from a minimization of cellular costs in a mechanistic model of protein translation. The model is constrained only by the physicochemical properties of the molecules and has no adjustable parameters. The costs of individual components (made of protein and RNA parts) can be approximated through molecular masses, which correlate strongly with alternative cost measures such as the molecules’ carbon content or the requirement of energy or enzymes for their biosynthesis. Analogous cost minimization approaches may facilitate similar quantitative insights also for other cellular subsystems.
Highlights
Protein synthesis is the most expensive process in fast-growing bacteria
We use this mechanistic description of translation to find the combination of the concentrations of mRNA, ribosomes, elongation factors, and tRNAs that results in minimal cellular costs in the given condition
We find that a theoretical minimization of the combined cellular costs of the translation machinery components leads to accurate predictions for their abundances, the resulting elongation rate, and the RNA/protein ratio
Summary
Cost minimization in a mechanistic model of translation. To test our hypothesis, we constructed a translation model consisting of 274 biochemical reactions, including 119 reactions with nonlinear kinetics. To allow a meaningful comparison between predictions and experiment, we estimated the experimental concentration of ribosomes actively involved in elongation (Methods) Cost minimization predicts these experimental estimates with high accuracy across the full range of assayed growth rates; observed values deviate from predictions on average by GMFE = 14% (Fig. 3d). Relating the predicted total RNA (ribosomal RNA + tRNA + mRNA) with measured protein concentrations[28] results in a near-linear relationship, accurately matching observed values at high to intermediate growth rates (μ > 0.3 h−1; Fig. 5a). At low growth rates (μ = 0.12 h−1), predictions of RNA and proteins allocated to an optimally efficient translation machinery (including deactivated ribosomes) account for 13% of total dry mass, rising almost linearly to 49% at high growth rates (μ = 1.9 h−1; Supplementary Fig. 3). The predicted elongation rates closely match the experimental data[32] over a broad range of growth rates (Fig. 5b)
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