The protein translation machinery is expressed for maximal efficiency inEscherichia coli

Abstract

9Protein synthesis is the most expensive process in fast-growing bacteria 1,2 . The economic 10 aspects of protein synthesis at the cellular level have been investigated by estimating 11 ribosome activity 3-5 and the expression of ribosomes 3,6 , tRNA 7-9 , mRNA 2 , and elongation 12 factors 10,11 . The observed growth-rate dependencies form the basis of powerful 13 phenomenological bacterial growth laws 5,12-16 ; however, a quantitative theory allowing us to 14 understand these phenomena on the basis of fundamental biophysical and biochemical 15principles is currently lacking. Here, we show that the observed growth-rate dependence of 16 the concentrations of ribosomes, tRNAs, mRNA, and elongation factors in Escherichia coli 17 can be predicted accurately by minimizing cellular costs in a detailed mathematical model of 18 protein translation; the mechanistic model is only constrained by the physicochemical 19properties of the molecules and requires no parameter fitting. We approximate the costs of 20 molecule species through their masses, justified by the observation that cellular dry mass 21 per volume is roughly constant across growth rates 17 and hence represents a limited 22resource. Our results also account quantitatively for observed RNA/protein ratios and 23 ribosome activities in E. coli across diverse growth conditions, including antibiotic stresses. 24Our prediction of active and free ribosome abundance facilitates an estimate of the 25 deactivated ribosome reserve 14,18,19 , which reaches almost 50% at the lowest growth rates. 26 We conclude that the growth rate dependent composition of E coli's protein synthesis 27 machinery is a consequence of natural selection for minimal total cost under 28 physicochemical constraints, a paradigm that might generally be applied to the analysis of 29 resource allocation in complex biological systems. 30

An optimal growth law for RNA composition and its partial implementation through ribosomal and tRNA gene locations in bacterial genomes

“…In terms of dry mass allocation, translation is the most expensive process in fast-growing bacteria [2,40]. As evidenced by comparison of diverse data to a detailed biochemical model of translation, the allocation of cellular resources across components of the E. coli translation system minimizes their total dry mass concentration at a given protein production rate [37]. This result indicates that natural selection favored the parsimonious allocation of cellular resources to the translation machinery in E. coli .…”

“…To calculate the optimal TC/ribosome ratio in E. coli , we use the measured protein concentration P [45], set the turnover number k cat to the maximal observed translation rate [2], and set the Michaelis constant K m to its diffusion limit [5] (Methods; see also Ref. [37]). Fig.…”

“…In recent work, we have shown that the growth-rate dependent composition of the translation machinery in E. coli is accurately described by predictions based on detailed reaction kinetics and the numerical minimization of the total mass of all participating molecules [37]. This minimization was motivated by the observation that the cellular dry mass density is approximately constant across growth conditions [54]; the minimization of the energy consumed or the enzyme mass required for the production of the different molecules led to almost identical results [37].…”

“…rRNA forms the central part of the catalyst of peptide elongation, while tRNA forms the core of the substrate; together, they account for the bulk of cellular RNA [2]. Their cytosolic concentrations at different growth rates in E. coli are well described by an optimality assumption [9,36,37]. Moreover, chromosomal gene positions in E. coli are known to affect the expression of both tRNA and rRNA genes [38,39]; both types of genes are located closer to oriC in fast compared to slowly growing bacteria, with rRNA genes positioned closer to oriC than tRNA genes in most examined fast-growing bacteria [27].…”

Optimal density of bacterial cells

“…The molecules in these two sectors have very different size distributions: each ribosome is 65 times larger than the median enzyme size (2,600kDa (2) vs. 40kDa (3)), and tRNAs are about 300 times larger than typical metabolites (26kDa (4) vs. 89Da, the mass of alanine). The allocation of dry mass between the two sectors of the cellular economy can be summarized by a single parameter, the growth rate μ , with the dry mass fraction of the ribosomal sector increasing almost linearly with μ (1, 5). Accordingly, the ribosome-rich cytosol at fast growth in nutrient-rich environments and the ribosome-meager cytosol at slow growth in nutritionally poor environments exhibit very different distributions of molecule sizes.…”