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Several methods are available for the detection of covarying positions from amultiple sequence alignment (MSA). If the MSA contains a large number ofsequences, information about the proximities between residues derived fromcovariation maps can be sufficient to predict a protein fold. If the structureis already known, information on the covarying positions can be valuable tounderstand the protein mechanism.  In this study we have sought to determine whether a multivariate extension oftraditional mutual information (MI) can be an additional tool to studycovariation. The performance of two multidimensional MI (mdMI) methods,designed to remove the effect of ternary/quaternary interdependencies, wastested with a set of 9 MSAs each containing <400 sequences, and was shown to becomparable to that of methods based on maximum entropy/pseudolikelyhoodstatistical models of protein sequences. However, while all the methods testeddetected a similar number of covarying pairs among the residues separated by <8 {\AA} 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 ondifferent principles.  We have also attempted to identify whether the difference in performanceamong methods is due to different efficiency in removing covariationoriginating from chains of structural contacts. We found that the reason whymethods that derive partial correlation between the columns of a MSA provide abetter recognition of close contacts is not because they remove chainingeffects, but because they filter out the correlation between distant residuesthat originates from general fitness constraints. In contrast we found thattrue chaining effects are expression of real physical perturbations thatpropagate inside proteins, and therefore are not removed by the derivation ofpartial correlation between variables.

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