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      Influence of mutation bias and hydrophobicity on the substitution rates and sequence entropies of protein evolution


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          The number of amino acids that occupy a given protein site during evolution reflects the selective constraints operating on the site. This evolutionary variability is strongly influenced by the structural properties of the site in the native structure, and it is quantified either through sequence entropy or through substitution rates. However, while the sequence entropy only depends on the equilibrium frequencies of the amino acids, the substitution rate also depends on the exchangeability matrix that describes mutations in the mathematical model of the substitution process. Here we apply two variants of a mathematical model of protein evolution with selection for protein stability, both against unfolding and against misfolding. Exploiting the approximation of independent sites, these models allow computing site-specific substitution processes that satisfy global constraints on folding stability. We find that site-specific substitution rates do not depend only on the selective constraints acting on the site, quantified through its sequence entropy. In fact, polar sites evolve faster than hydrophobic sites even for equal sequence entropy, as a consequence of the fact that polar amino acids are characterized by higher mutational exchangeability than hydrophobic ones. Accordingly, the model predicts that more polar proteins tend to evolve faster. Nevertheless, these results change if we compare proteins that evolve under different mutation biases, such as orthologous proteins in different bacterial genomes. In this case, the substitution rates are faster in genomes that evolve under mutational bias that favor hydrophobic amino acids by preferentially incorporating the nucleotide Thymine that is more frequent in hydrophobic codons. This appearingly contradictory result arises because buried sites occupied by hydrophobic amino acids are characterized by larger selective factors that largely amplify the substitution rate between hydrophobic amino acids, while the selective factors of exposed sites have a weaker effect. Thus, changes in the mutational bias produce deep effects on the biophysical properties of the protein (hydrophobicity) and on its evolutionary properties (sequence entropy and substitution rate) at the same time. The program Prot_evol that implements the two site-specific substitution processes is freely available at https://ub.cbm.uam.es/prot_fold_evol/prot_fold_evol_soft_main.php#Prot_Evol.

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          Funnels, pathways, and the energy landscape of protein folding: a synthesis.

          The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation, that is, to the energy landscape. The statistical energy landscape approach explains when and why unique behaviors, such as specific folding pathways, occur in some proteins and more generally explains the distinction between folding processes common to all sequences and those peculiar to individual sequences. This approach also gives new, quantitative insights into the interpretation of experiments and simulations of protein folding thermodynamics and kinetics. Specifically, the picture provides simple explanations for folding as a two-state first-order phase transition, for the origin of metastable collapsed unfolded states and for the curved Arrhenius plots observed in both laboratory experiments and discrete lattice simulations. The relation of these quantitative ideas to folding pathways, to uniexponential vs. multiexponential behavior in protein folding experiments and to the effect of mutations on folding is also discussed. The success of energy landscape ideas in protein structure prediction is also described. The use of the energy landscape approach for analyzing data is illustrated with a quantitative analysis of some recent simulations, and a qualitative analysis of experiments on the folding of three proteins. The work unifies several previously proposed ideas concerning the mechanism protein folding and delimits the regions of validity of these ideas under different thermodynamic conditions.
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                Author and article information

                PeerJ Inc. (San Francisco, USA )
                5 October 2018
                : 6
                : e5549
                [1 ]Bioinformatics Unit, Center for Molecular Biology Severo Ochoa, CSIC-UAM , Madrid, Spain
                [2 ]Department of Biochemistry, Genetics and Immunology, University of Vigo , Vigo, Spain
                ©2018 Jiménez-Santos et al.

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ) and either DOI or URL of the article must be cited.

                : 13 April 2018
                : 10 August 2018
                Funded by: Spanish Ministry of Economy
                Award ID: BIO2016-79043
                Award ID: BFU2012-40020
                Funded by: Ramón y Cajal
                Award ID: RYC-2015-18241
                This work was supported by the Spanish Ministry of Economy through grants BIO2016-79043 and BFU2012-40020. Miguel Arenas was supported by the Ramón y Cajal Grant RYC-2015-18241 from the Spanish Government. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Computational Biology
                Evolutionary Studies

                stability-constrained protein evolution,substitution rates,mutation bias


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