Protein contacts contain important information for protein structure and functional study, but contact prediction is very challengingespecially for protein families without many sequence homologs. Recently evolutionary coupling (EC) analysis , which predicts contactsby analyzing residue co-evolution in a single target family, has made good progress due to better statistical and optimization techniques . Different from these single-family EC methods that focus on only a single protein family, this paper presents a joint multi-family EC analysis method that predicts contacts of one target family by jointly modeling residue co-evolution in itself and also (distantly) related familieswith divergent sequences but similar folds , and enforcing their co-evolution pattern consistency based upon their evolutionary distance . To implement this multi-family EC analysisstrategy, this paper presents a novel joint graphical lasso method to model a set of related protein families . In particular, we model a set of related families using a set of correlated multivariate Gaussian distributions, the inverse covariance matrix (or precision matrix) of each distribution encoding the contact pattern of one family. Then we co-estimate the precision matrices by maximizing the occurring probability of all the involved sequences , subject to the constraint that the  matrices shall share similar patterns . Finally we solve this optimization problem using Alternating Direction Method of Multipliers (ADMM). Experiments show that joint multi-family EC analysis can reveal many more native contacts than single-family analysis even for a target family with 4000-5000 non-redundant sequence homologs, which makes many more protein families amenable to co-evolution-based structure and function prediction .
Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence remains very challenging. Both evolutionary coupling (EC) analysis and supervised machine learning methods are developed to predict contacts, making use of different types of information, respectively. This paper presents a group graphical lasso (GGL) method for contact prediction that integrates joint multi-family EC analysis and supervised learning . Different from existing single-family EC analysis that uses residue co-evolution information in only the target protein family, our joint EC analysis uses residue co-evolution in both the target family and its related families, which may have divergent sequences but similar folds . To implement joint EC analysis, we model a set of related protein families using Gaussian graphical models (GGM) and then co-estimate their precision matrices by maximum-likelihood , subject to the constraint that the precision matrices shall share similar residue co-evolution patterns. To further improve the accuracy of the estimated precision matrices, we employ a supervised learning method to predict contact probability from a variety of evolutionary and non-evolutionary information and then incorporate the predicted probability as prior into our GGL framework . Experiments show that our method can predict contacts much more accurately than existing methods, and that our method performs better on both conserved and family-specific contacts .
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