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Residue-residue interactions that fold a protein into a unique three-dimensional structure and make it play a specific function impose structural and functional constraints on each residue site. Selective constraints on residue sites are recorded in amino acid orders in homologous sequences and also in the evolutionary trace of amino acid substitutions. A challenge is to extract direct dependences between residue sites by removing indirect dependences through other residues within a protein or even through other molecules. Recent attempts of disentangling direct from indirect dependences of amino acid types between residue positions in multiple sequence alignments have revealed that the strength of inferred residue pair couplings is an excellent predictor of residue-residue proximity in folded structures. Here, we report an alternative attempt of inferring co-evolving site pairs from concurrent and compensatory substitutions between sites in each branch of a phylogenetic tree. First, branch lengths of a phylogenetic tree inferred by the neighbor-joining method are optimized as well as other parameters by maximizing a likelihood of the tree in a mechanistic codon substitution model. Mean changes of quantities, which are characteristic of concurrent and compensatory substitutions, accompanied by substitutions at each site in each branch of the tree are estimated with the likelihood of each substitution. Partial correlation coefficients of the characteristic changes along branches between sites are calculated and used to rank co-evolving site pairs. Accuracy of contact prediction based on the present co-evolution score is comparable to that achieved by a maximum entropy model of protein sequences for 15 protein families taken from the Pfam release 26.0. Besides, this excellent accuracy indicates that compensatory substitutions are significant in protein evolution.
The outcome of an epidemic is closely related to the network of interactions between the individuals. Likewise, protein functions depend on the 3D arrangement of their residues and on the underlying energetic interaction network. Borrowing ideas from
The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important becau
We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the contact pair is
We introduce a new geometric structure on differentiable manifolds. A textit{Contact} textit{Pair}on a manifold $M$ is a pair $(alpha,eta) $ of Pfaffian forms of constant classes $2k+1$ and $2h+1$ respectively such that $alphawedge dalpha^{k}wedgeeta
Consistently predicting biopolymer structure at atomic resolution from sequence alone remains a difficult problem, even for small sub-segments of large proteins. Such loop prediction challenges, which arise frequently in comparative modeling and prot