Supplementary data are available at Bioinformatics online.

Residue co-evolution has become the primary principle for estimating inter-residue distances of a protein, which are crucially important for predicting protein structure. Most existing approaches adopt an indirect strategy, i.e., inferring residue co-evolution based on some hand-crafted features, say, a covariance matrix, calculated from multiple sequence alignment (MSA) of target protein. This indirect strategy, however, cannot fully exploit the information carried by MSA. Here, we report an end-to-end deep neural network, CopulaNet, to estimate residue co-evolution directly from MSA. The key elements of CopulaNet include: (i) an encoder to model context-specific mutation for each residue; (ii) an aggregator to model residue co-evolution, and thereafter estimate inter-residue distances. Using CASP13 (the 13th Critical Assessment of Protein Structure Prediction) target proteins as representatives, we demonstrate that CopulaNet can predict protein structure with improved accuracy and efficiency. This study represents a step toward improved end-to-end prediction of inter-residue distances and protein tertiary structures.

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.

Protein structure prediction is an interdisciplinary research topic that has attracted researchers from multiple fields, including biochemistry, medicine, physics, mathematics, and computer science. These researchers adopt various research paradigms to attack the same structure prediction problem: biochemists and physicists attempt to reveal the principles governing protein folding; mathematicians, especially statisticians, usually start from assuming a probability distribution of protein structures given a target sequence and then find the most likely structure, while computer scientists formulate protein structure prediction as an optimization problem — finding the structural conformation with the lowest energy or minimizing the difference between predicted structure and native structure. These research paradigms fall into the two statistical modeling cultures proposed by Leo Breiman, namely, data modeling and algorithmic modeling. Recently, we have also witnessed the great success of deep learning in protein structure prediction. In this review, we present a survey of the efforts for protein structure prediction. We compare the research paradigms adopted by researchers from different fields, with an emphasis on the shift of research paradigms in the era of deep learning. In short, the algorithmic modeling techniques, especially deep neural networks, have considerably improved the accuracy of protein structure prediction; however, theories interpreting the neural networks and knowledge on protein folding are still highly desired.