Inferring Contacting Residues within and between Proteins: What Do the Probabilities Mean?

Although correlations between residues occurring at different positions within multiple protein alignments have long been used to infer directly interacting residues, most of these methods suffer from the frequent occurrence of indirectly correlated residues. Recently, a number of methods have been proposed that incorporate the entire set of observed frequencies of amino acid pairs for all pairs of positions into rigorous probabilistic models; these models have been shown to strongly improve the prediction of directly interacting residues by successfully distinguishing direct from indirect correlations. Some of these methods make use of the maximum entropy principle, originating in statistical physics. It has recently been argued that there is no reason to assume that protein sequences should follow maximum entropy distributions and that it is therefore puzzling that the max-ent formalism is successful for predicting interacting residues in proteins. In this brief review I will argue that such apparent puzzles result from a misconception of the meaning of the max-ent formalism and, more generally, on the meaning of probabilities.