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A many-body term improves the accuracy of effective potentials based on protein coevolutionary data

The study of correlated mutations in alignments of homologous proteins proved to be succesful not only in the prediction of their native conformation, but also in the developement of a two-body effective potential between pairs of amino acids. In the present work we extend the effective potential, introducing a many--body term based on the same theoretical framework, making use of a principle of maximum entropy. The extended potential performs better than the two--body one in predicting the energetic effect of 308 mutations in 14 proteins (including membrane proteins). The average value of the parameters of the many-body term correlates with the degree of hydrophobicity of the corresponding residues, suggesting that this term partly reflects the effect of the solvent.