AbstractCoevolution-based contact prediction, either directly by coevolutionary couplings resulting from global statistical sequence models or using structural supervision and deep learning, has found widespread application in protein-structure prediction from sequence. However, one of the basic assumptions in global statistical modeling is that sequences form an at least approximately independent sample of an unknown probability distribution, which is to be learned from data. In the case of protein families, this assumption is obviously violated by phylogenetic relations between protein sequences. It has turned out to be notoriously difficult to take phylogenetic correlations into account in coevolutionary model learning. Here, we propose a complementary approach: we develop two strategies to randomize or resample sequence data, such that conservation patterns and phylogenetic relations are preserved, while intrinsic (i.e. structure- or function-based) coevolutionary couplings are removed. An analysis of these data shows that the strongest coevolutionary couplings, i.e. those used by Direct Coupling Analysis to predict contacts, are only weakly influenced by phylogeny. However, phylogeny-induced spurious couplings are of similar size to the bulk of coevolutionary couplings, and dissecting functional from phylogeny-induced couplings might lead to more accurate contact predictions in the range of intermediate-size couplings.The code is available at https://github.com/ed-rodh/Null_models_I_and_II.Author summaryMany homologous protein families contain thousands of highly diverged amino-acid sequences, which fold in close-to-identical three-dimensional structures and fulfill almost identical biological tasks. Global coevolutionary models, like those inferred by the Direct Coupling Analysis (DCA), assume that families can be considered as samples of some unknown statistical model, and that the parameters of these models represent evolutionary constraints acting on protein sequences. To learn these models from data, DCA and related approaches have to also assume that the distinct sequences in a protein family are close to independent, while in reality they are characterized by involved hierarchical phylogenetic relationships. Here we propose Null models for sequence alignments, which maintain patterns of amino-acid conservation and phylogeny contained in the data, but destroy any coevolutionary couplings, frequently used in protein structure prediction. We find that phylogeny actually induces spurious non-zero couplings. These are, however, significantly smaller that the largest couplings derived from natural sequences, and therefore have only little influence on the first predicted contacts. However, in the range of intermediate couplings, they may lead to statistically significant effects. Dissecting phylogenetic from functional couplings might therefore extend the range of accurately predicted structural contacts down to smaller coupling strengths than those currently used.
Fast pseudolikelihood maximization for direct-coupling analysis of protein structure from many homologous amino-acid sequences
