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Evolution of proteins in bacteria and archaea living in different conditions leads to significant correlations between amino acid usage and environmental temperature. The origins of these correlations are poorly understood, and an important question of protein theory, physics-based prediction of types of amino acids overrepresented in highly thermostable proteins, remains largely unsolved. Here, we extend the random energy model of protein folding by weighting the interaction energies of amino acids by their frequencies in protein sequences and predict the energy gap of proteins designed to fold well at elevated temperatures. To test the model, we present a novel scalable algorithm for simultaneous energy calculation for many sequences in many structures, targeting massively parallel computing architectures such as graphics processing unit. The energy calculation is performed by multiplying two matrices, one representing the complete set of sequences, and the other describing the contact maps of all structural templates. An implementation of the algorithm for the CUDA platform is available at http://www.github.com/kzeldovich/galeprot and calculates protein folding energies over 250 times faster than a single central processing unit. Analysis of amino acid usage in 64-mer cubic lattice proteins designed to fold well at different temperatures demonstrates an excellent agreement between theoretical and simulated values of energy gap. The theoretical predictions of temperature trends of amino acid frequencies are significantly correlated with bioinformatics data on 191 bacteria and archaea, and highlight protein folding constraints as a fundamental selection pressure during thermal adaptation in biological evolution. [ABSTRACT FROM AUTHOR]

The distribution of fitness effects (DFEs) of new mutations across different environments quantifies the potential for adaptation in a given environment and its cost in others. So far, results regarding the cost of adaptation across environments have been mixed, and most studies have sampled random mutations across different genes. Here, we quantify systematically how costs of adaptation vary along a large stretch of protein sequence by studying the distribution of fitness effects of the same ≈2,300 amino-acid changing mutations obtained from deep mutational scanning of 119 amino acids in the middle domain of the heat shock protein Hsp90 in five environments. This region is known to be important for client binding, stabilization of the Hsp90 dimer, stabilization of the N-terminal-Middle and Middle-C-terminal interdomains, and regulation of ATPase–chaperone activity. Interestingly, we find that fitness correlates well across diverse stressful environments, with the exception of one environment, diamide. Consistent with this result, we find little cost of adaptation; on average only one in seven beneficial mutations is deleterious in another environment. We identify a hotspot of beneficial mutations in a region of the protein that is located within an allosteric center. The identified protein regions that are enriched in beneficial, deleterious, and costly mutations coincide with residues that are involved in the stabilization of Hsp90 interdomains and stabilization of client-binding interfaces, or residues that are involved in ATPase–chaperone activity of Hsp90. Thus, our study yields information regarding the role and adaptive potential of a protein sequence that complements and extends known structural information. [ABSTRACT FROM AUTHOR]

Protein evolution proceeds by a complex response of organismal fitness to mutations that can simultaneously affect protein stability, structure, and enzymatic activity. To probe the relationship between genotype and phenotype, we chose a fundamental paradigm for protein evolution, folding, and design, the (βα)8 TIM barrel fold. Here, we demonstrate the role of long‐range allosteric interactions in the adaptation of an essential hyperthermophilic TIM barrel enzyme to mesophilic conditions in a yeast host. Beneficial fitness effects observed with single and double mutations of the canonical βα‐hairpin clamps and the α‐helical shell distal to the active site revealed an underlying energy network between opposite faces of the cylindrical β‐barrel. We experimentally determined the fitness of multiple mutants in the energetic phase plane, contrasting the energy barrier of the chemical reaction and the folding free energy of the protein. For the system studied, the reaction energy barrier was the primary determinant of organism fitness. Our observations of long‐range epistatic interactions uncovered an allosteric pathway in an ancient and ubiquitous enzyme that may provide a novel way of designing proteins with a desired activity and stability profile. [ABSTRACT FROM AUTHOR]

Protein evolution proceeds by a complex response of organismal fitness to mutations that can simultaneously affect protein stability, structure, and enzymatic activity. To probe the relationship between genotype and phenotype, we chose a fundamental paradigm for protein evolution, folding, and design, the (βα) 8 TIM barrel fold. Here, we demonstrate the role of long-range allosteric interactions in the adaptation of an essential hyperthermophilic TIM barrel enzyme to mesophilic conditions in a yeast host. Beneficial fitness effects observed with single and double mutations of the canonical βα-hairpin clamps and the α-helical shell distal to the active site revealed an underlying energy network between opposite faces of the cylindrical β-barrel. We experimentally determined the fitness of multiple mutants in the energetic phase plane, contrasting the energy barrier of the chemical reaction and the folding free energy of the protein. For the system studied, the reaction energy barrier was the primary determinant of organism fitness. Our observations of long-range epistatic interactions uncovered an allosteric pathway in an ancient and ubiquitous enzyme that may provide a novel way of designing proteins with a desired activity and stability profile., (© 2020 The Authors. Protein Science published by Wiley Periodicals LLC on behalf of The Protein Society.)