CopulaNet: Learning residue co-evolution directly from multiple sequence alignment for protein structure prediction

Protein functions are largely determined by the final details of their tertiary structures, and the structures could be accurately reconstructed based on inter-residue distances. Residue co-evolution has become the primary principle for estimating inter-residue distances since the residues in close spatial proximity tend to co-evolve. The widely-used approaches infer residue co-evolution using an indirect strategy, i.e., they first extract from the multiple sequence alignment (MSA) of query protein some handcrafted features, say, co-variance matrix, and then infer residue co-evolution using these features rather than the raw information carried by MSA. This indirect strategy always leads to considerable information loss and inaccurate estimation of inter-residue distances. Here, we report a deep neural network framework (called CopulaNet) to learn residue co-evolution directly from MSA without any handcrafted features. The CopulaNet consists of two key elements: i) an encoder to model context-specific mutation for each residue, and ii) an aggregator to model correlations among residues and thereafter infer residue co-evolutions. Using the CASP13 (the 13th Critical Assessment of Protein Structure Prediction) target proteins as representatives, we demonstrated the successful application of CopulaNet for estimating inter-residue distances and further predicting protein tertiary structure with improved accuracy and efficiency. Head-to-head comparison suggested that for 24 out of the 31 free modeling CASP13 domains, ProFOLD outperformed AlphaFold, one of the state-of-the-art prediction approaches.