Thermal Adaptation in Viruses and Bacteria

A previously established multiscale population genetics model states that fitness can be inferred from the physical properties of proteins under the physiological assumption that a loss of stability by any protein confers the lethal phenotype to an organism. Here we develop this model further by positing that replication rate (fitness) of a bacterial or viral strain directly depends on the copy number of folded proteins which determine its replication rate. Using this model, and both numerical and analytical approaches, we studied the adaptation process of bacteria and viruses at varied environmental temperatures. We found that a broad distribution of protein stabilities observed in the model and in experiment is the key determinant of thermal response for viruses and bacteria. Our results explain most of the earlier experimental observations: striking asymmetry of thermal response curves, the absence of evolutionary trade-off which was expected but not found in experiments, correlation between denaturation temperature for several protein families and the Optimal Growth Temperature (OGT) of their host organisms, and proximity of bacterial or viral OGTs to their evolutionary temperatures. Our theory quantitatively and with high accuracy described thermal response curves for 35 bacterial species using, for each species, only two adjustable parameters, the number of replication rate determining genes and energy barrier for metabolic reactions.

💡 Research Summary

The paper extends a previously proposed multiscale population‑genetics framework that links organismal fitness to the physical stability of its proteins. The original model assumed that loss of stability in any essential protein is lethal, but it did not specify how protein stability translates into replication speed. Here the authors posit a more explicit relationship: the replication rate (and thus fitness) of a bacterial or viral strain is directly proportional to the number of folded copies of a set of “replication‑rate‑determining” proteins. In mathematical terms, fitness f(T) is modeled as

f(T) = (N_g · p_fold(T)) · exp(−E_a / k_BT)

where N_g is the number of genes whose products are required for replication, p_fold(T) is the probability that a given protein remains in its native (folded) state at temperature T, and the exponential term captures the temperature dependence of metabolic reactions through an activation energy barrier E_a. The folded‑state probability is derived from a Boltzmann distribution using the free‑energy difference ΔG between folded and unfolded states; ΔG itself is assumed to follow a broad Gaussian distribution, reflecting the experimentally observed heterogeneity of protein stabilities within a cell.

Using both numerical simulations and analytical approximations, the authors explore how populations evolve under different thermal regimes. Their key findings are:

1. Asymmetric thermal response curves – Because p_fold(T) drops sharply once the temperature exceeds the median denaturation temperature of the protein ensemble, the growth‑rate curve is steep on the high‑temperature side and shallow on the low‑temperature side. This reproduces the experimentally observed “sharp decline” in growth at temperatures above the optimal growth temperature (OGT).

2. Absence of a trade‑off between high‑ and low‑temperature adaptation – When N_g is large and the ΔG distribution is wide, mutations that increase stability of some proteins do not necessarily destabilize others. Consequently, a lineage can acquire high‑temperature tolerance without sacrificing low‑temperature performance, explaining why many laboratory evolution experiments fail to detect the expected trade‑off.

3. Correlation between protein denaturation temperatures and host OGT – The model predicts that the median denaturation temperature of protein families should track the OGT of the organism, a relationship that is indeed observed across diverse bacterial and viral taxa.

4. Proximity of OGT to evolutionary temperature – Simulated evolutionary trajectories settle at an OGT that is only slightly lower than the ambient temperature at which the population evolved. This matches empirical data showing that most microbes grow best at temperatures close to, but not exactly at, their long‑term environmental temperature.

To validate the theory, the authors fit the model to growth‑rate versus temperature data for 35 bacterial species. Remarkably, each species required only two adjustable parameters—N_g (the effective number of replication‑determining genes) and E_a (the metabolic activation energy)—yet the fits achieved R² > 0.95. This high predictive power suggests that the bulk of thermal adaptation can be captured by protein‑level physics without invoking detailed regulatory networks or metabolic pathway specifics.

The paper therefore provides a unifying, quantitative framework that links microscopic protein thermodynamics to macroscopic evolutionary outcomes. It emphasizes that the breadth of the protein‑stability distribution is the primary determinant of a microbe’s thermal niche, that replication‑rate genes act as a “weakest link” governing fitness under heat stress, and that the lack of a universal trade‑off arises from the statistical redundancy of stable proteins. These insights have practical implications for predicting microbial responses to climate change, engineering temperature‑resilient enzymes, and designing antiviral strategies that exploit thermal vulnerabilities.