The protein translation machinery is expressed for maximal efficiency in Escherichia coli

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.

Fig. 1. Schematic overview of the translation model.

A reduced pathway for elongation with amino acids cysteine (aminoacyl-tRNA Cys) and glutamine (aa-tRNA Gln1, Gln2) is represented in Systems Biology Graphical Notation. Initiation: free (unbound) ribosome gets converted to active ribosome, modulated by mRNA. Termination: active ribosome converts back to free ribosome at a rate fixed by the desired protein production rate. Active ribosome state transition: active ribosome instantaneously binds to codons (61 codons in full model, 4 here) at the fractions set by the specified proteome composition. Ternary complex formation: charged tRNAs (40 aa-tRNAs in full model, 3 here), replenished from a pool, combine with EF-Tu*GTP to form ternary complexes (40 TCs in the full model). Kinetic parameters of these reversible processes depend on the aa-tRNA. Elongation: labeled ribosome binds with the cognate TC to elongate the protein with the respective amino acid. The ribosome returns to its active state and EF-Tu*GDP is released. Other products of this reaction, such as deacylated tRNA, are not modeled. Nucleotide exchange (see right panel): EF-Tu*GDP is reactivated to EF-Tu*GTP in a sequence of steps modeled by reversible mass action kinetics. GTP and GDP pools are modeled with fixed concentrations. The nucleotide exchange is supported by EF-Ts, and the main flux is carried through the complexes formed by EF-Tu with EF-Ts.

Fig. 2. Predicted vs. observed concentrations in a glucose-limited chemostat.

Growth rate μ = 0.35 h⁻¹ (for other conditions, see Supplementary Fig. 1). The solid line shows the expected identity, whereas the upper and lower dashed lines show prediction errors of 2x and 0.5x, respectively. Predictions for ribosome, EF-Tu, EF-Ts, mRNA, and total tRNA are highly accurate, with Pearson’s R² = 0.99 and geometric mean fold-error GMFE = 1.13, i.e., predictions based purely on a physico-chemical model and the assumption of cost minimization are on average 13% off. Predictions for individual tRNA species are somewhat less accurate, GMFE = 1.64. Experimentally determined concentrations of the ribosome (averaged over all ribosomal proteins), EF-Tu, and EF-Ts are from ref. . mRNA and tRNA concentrations are interpolated values based on growth rates. Source data are provided as a Source Data file.

Fig. 3. Growth rate dependence of predicted (red lines) and observed concentrations.

a EF-Tu, R² = 0.79, GMFE = 1.27. b EF-Ts, R² = 0.79, GMFE = 1.25. c Total ribosome concentration (arithmetic means across ribosomal proteins). d Actively elongating ribosomes, estimated from data in c according to ref. (see Methods). Circles indicate normal conditions, triangles indicate stress conditions. Source data are provided as a Source Data file.

Fig. 4. Estimated fraction of deactivated ribosomes.

The deactivated fraction reaches almost 50% for the lowest growth rate assayed in ref. and drops rapidly towards zero at higher growth rates. Source data are provided as a Source Data file.

Fig. 5. Growth rate dependences of total RNA/protein ratio and ribosome activity.

a Predicted total RNA concentration (mRNA + tRNA + rRNA) relative to observed total protein concentration at different cellular growth rates (red line) compared to experimental observations^,; R² = 0.97, GMFE = 1.12. b Predicted (red line) and experimentally determined elongation rates of actively translating ribosomes (ribosome activities); R² = 0.93, GMFE = 1.06. At the lowest assayed growth rates, non-growth-related translation—which is not included in the model—may become comparable to growth-related translation; at these growth rates, the numerical optimization of our model did not converge (μ < 0.1 h⁻¹), and thus the red lines are not extended into this region. Source data are provided as a Source Data file.