Synthetic protein alignments by CCMgen quantify noise in residue-residue contact prediction

Compensatory mutations between protein residues in physical contact can manifest themselves as statistical couplings between the corresponding columns in a multiple sequence alignment (MSA) of the protein family. Conversely, large coupling coefficients predict residue contacts. Methods for de-novo protein structure prediction based on this approach are becoming increasingly reliable. Their main limitation is the strong systematic and statistical noise in the estimation of coupling coefficients, which has so far limited their application to very large protein families. While most research has focused on improving predictions by adding external information, little progress has been made to improve the statistical procedure at the core, because our lack of understanding of the sources of noise poses a major obstacle. First, we show theoretically that the expectation value of the coupling score assuming no coupling is proportional to the product of the square roots of the column entropies, and we propose a simple entropy bias correction (EntC) that subtracts out this expectation value. Second, we show that the average product correction (APC) includes the correction of the entropy bias, partly explaining its success. Third, we have developed CCMgen, the first method for simulating protein evolution and generating realistic synthetic MSAs with pairwise statistical residue couplings. Fourth, to learn exact statistical models that reliably reproduce observed alignment statistics, we developed CCMpredPy, an implementation of the persistent contrastive divergence (PCD) method for exact inference. Fifth, we demonstrate how CCMgen and CCMpredPy can facilitate the development of contact prediction methods by analysing the systematic noise contributions from phylogeny and entropy. Using the entropy bias correction, we can disentangle both sources of noise and find that entropy contributes roughly twice as much noise as phylogeny.Author summary: Knowledge about the three-dimensional structure of proteins is key to understanding their function and role in biological processes and diseases. The experimental structure determination techniques, such as X-ray crystallography or electron cryo-microscopy, are labour intensive, time-consuming and expensive. Therefore, complementary computational methods to predict a protein’s structure have become indispensable. Over the last years, immense progress has been made in predicting protein structures from their amino acid sequence by utilizing highly accurate predictions of spatial contacts between amino acid residues as constraints in folding simulations. However, contact prediction methods require large numbers of homologous protein sequences in order to discriminate between signal and noise. A major obstacle preventing progress on the statistical methodology is our limited understanding of the different components of noise that are known to affect the predictions. We provide two tools, CCMpredPy and CCMgen, that can be used to learn highly accurate statistical models for contact prediction and to simulate protein evolution according to the statistical constraints between positions of residues as specified by these models, respectively. We showcase their usefulness by quantifying the relative contribution of noise arising from entropy and phylogeny on the predicted contacts, which will facilitate the improvement of the statistical methodology.