Optimal proteome allocation and the temperature dependence of microbial growth laws

Abstract

Although the effect of temperature on microbial growth has been widely studied, the role of proteome allocation in bringing about temperature-induced changes remains elusive. To tackle this problem, we propose a coarse-grained model of microbial growth, including the processes of temperature-sensitive protein unfolding and chaperone-assisted (re)folding. We determine the proteome sector allocation that maximizes balanced growth rate as a function of nutrient limitation and temperature. Calibrated with quantitative proteomic data for Escherichia coli, the model allows us to clarify general principles of temperature-dependent proteome allocation and formulate generalized growth laws. The same activation energy for metabolic enzymes and ribosomes leads to an Arrhenius increase in growth rate at constant proteome composition over a large range of temperatures, whereas at extreme temperatures resources are diverted away from growth to chaperone-mediated stress responses. Our approach points at risks and possible remedies for the use of ribosome content to characterize complex ecosystems with temperature variation.

Fig. 1. Outline of the coarse-grained model.

Proteins are divided into four main sectors: metabolic proteins (at mass fraction m, in units g/g prot) which convert substrate (s) into precursors (p), ribosomal proteins (r) which synthetize proteins, chaperones (c) which fold proteins, and house-keeping proteins (q). Within the protein sectors, apart from the chaperones, we distinguish between folded and unfolded proteins, as indicated by the indices f and u, respectively. Solid arrows refer to mass flows and dashed arrows to catalytic (enzymatic) activities.

Fig. 2. Calibration of the coarse-grained resource allocation model with experimental data for E. coli.

a Proteome allocation to different sectors in % of total protein mass for seven conditions, namely growth in chemostat at 37 ^oC (dilution rates of 0.12/h, 0.2/h, 0.35/h, and 0.5/h), and in batch (exponential phase) at 37 ^oC and 42 ^oC in glucose minimal medium, and at 37 ^oC in rich medium (data from ref. ). b Specific growth rate as a function of temperature in glucose minimal and rich media (data from refs. ^,, respectively).

Fig. 3. Protein sector content for ribosomal proteins and chaperones as a function of specific growth rate, varying with temperature (left) or substrate limitation (right).

a Ribosomal protein mass fraction. Top: model prediction. Down: Level of the ribosomal protein S1 in E. coli for different temperatures in glucose rich medium (left), and for different media at 37 ^∘C, relative to glucose-rich medium at 37 ^∘C^,. For each point, color represents temperature (see colorbar). b Chaperone mass fraction. Same legend as (a) for the chaperone GroEL.

Fig. 4. Microbial growth laws accounting for temperature effects.

a Growth law between growth rate and RNA content, without (left) and with (right) Arrhenius correction (Eqs. (9)–(10)) for S. cerevisiae. The Arrhenius correction greatly improves the linear regression, as witnessed by the increase of adjusted R² from 0.706 to 0.982. Open symbols: batch; closed symbols: chemostat. For each point, color represents temperature (see colorbar). b Nutrient status as a function of the ribosome content. Left: the gray line represents the theoretical relationship valid for non-extreme temperatures (from Eq. (12)). At extreme temperatures, the slope changes due to chaperone burden (Eq. (11)). A decrease in ribosome content relative to a control (black dot) could be due to a substrate limitation and/or temperature stress. Right: nutrient status as a function of the nucleic acid to protein ratios for Candida utilis. The only point above the optimal temperature for growth, marked by x, was identified as an outlier and removed from the linear regression, showing a possible effect of temperature stress in line with our prediction.