Coevolutionary information, protein folding landscapes, and the thermodynamics of natural selection

Significance Natural protein sequences, being the result of random mutation coupled with natural selection, have remarkable properties that are not typical of unselected random sequences, including the ability to robustly fold to an organized structure that is needed to function. We estimate the selection temperature, the effective temperature at which sequences were selected by evolution, for eight protein families and compare these values with experimental data for folding temperatures of proteins in each family. The selection temperature measures the importance of maintaining the stability and structural specificity of the folded state on the evolutionary process. For all families, the selection temperature is below physiological temperature, indicating that maintaining the structural integrity of the folded state is an important constraint on evolution. The energy landscape used by nature over evolutionary timescales to select protein sequences is essentially the same as the one that folds these sequences into functioning proteins, sometimes in microseconds. We show that genomic data, physical coarse-grained free energy functions, and family-specific information theoretic models can be combined to give consistent estimates of energy landscape characteristics of natural proteins. One such characteristic is the effective temperature Tsel at which these foldable sequences have been selected in sequence space by evolution. Tsel quantifies the importance of folded-state energetics and structural specificity for molecular evolution. Across all protein families studied, our estimates for Tsel are well below the experimental folding temperatures, indicating that the energy landscapes of natural foldable proteins are strongly funneled toward the native state.