Multidimensional mutual information methods for the analysis of covariation in multiple sequence alignments

Background: Several methods are available for the detection of covarying positions from a multiple sequence alignment (MSA). If the MSA contains a large number of sequences, information about the proximities between residues derived from covariation maps can be sufficient to predict a protein fold. However, in many cases the structure is already known, and information on the covarying positions can be valuable to understand the protein mechanism and dynamic properties. Results: In this study we have sought to determine whether a multivariate (multidimensional) extension of traditional mutual information (MI) can be an additional tool to study covariation. The performance of two multidimensional MI (mdMI) methods, designed to remove the effect of ternary/quaternary interdependencies, was tested with a set of 9 MSAs each containing <400 sequences, and was shown to be comparable to that of the newest methods based on maximum entropy/pseudolikelyhood statistical models of protein sequences. However, while all the methods tested detected a similar number of covarying pairs among the residues separated by < 8 angstrom in the reference X-ray structures, there was on average less than 65% overlap between the top scoring pairs detected by methods that are based on different principles. Conclusions: Given the large variety of structure and evolutionary history of different proteins it is possible that a single best method to detect covariation in all proteins does not exist, and that for each protein family the best information can be derived by merging/comparing results obtained with different methods. This approach may be particularly valuable in those cases in which the size of the MSA is small or the quality of the alignment is low, leading to significant differences in the pairs detected by different methods.