  Accurate prediction of inter-residue contacts of a protein is important to
calcu- lating its tertiary structure. Analysis of co-evolutionary events among
residues has been proved effective to inferring inter-residue contacts. The
Markov ran- dom field (MRF) technique, although being widely used for contact
prediction, suffers from the following dilemma: the actual likelihood function
of MRF is accurate but time-consuming to calculate, in contrast, approximations
to the actual likelihood, say pseudo-likelihood, are efficient to calculate but
inaccu- rate. Thus, how to achieve both accuracy and efficiency simultaneously
remains a challenge. In this study, we present such an approach (called clmDCA)
for contact prediction. Unlike plmDCA using pseudo-likelihood, i.e., the
product of conditional probability of individual residues, our approach uses
composite- likelihood, i.e., the product of conditional probability of all
residue pairs. Com- posite likelihood has been theoretically proved as a better
approximation to the actual likelihood function than pseudo-likelihood.
Meanwhile, composite likelihood is still efficient to maximize, thus ensuring
the efficiency of clmDCA. We present comprehensive experiments on popular
benchmark datasets, includ- ing PSICOV dataset and CASP-11 dataset, to show
that: i) clmDCA alone outperforms the existing MRF-based approaches in
prediction accuracy. ii) When equipped with deep learning technique for
refinement, the prediction ac- curacy of clmDCA was further significantly
improved, suggesting the suitability of clmDCA for subsequent refinement
procedure. We further present successful application of the predicted contacts
to accurately build tertiary structures for proteins in the PSICOV dataset.
  Accessibility: The software clmDCA and a server are publicly accessible
through http://protein.ict.ac.cn/clmDCA/.
