Positional dependence, cliques, and predictive motifs in the bHLH protein domain

Quantitative analyses were carried out on a large number of proteins that contain the highly conserved basic helix-loop-helix domain. Measures derived from information theory were used to examine the extent of conservation at amino acid sites within the bHLH domain as well as the extent of mutual information among sites within the domain. Using the Boltzmann entropy measure, we described the extent of amino acid conservation throughout the bHLH domain. We used position association (pa) statistics that reflect the joint probability of occurrence of events to estimate the "mutual information content" among distinct amino acid sites. Further, we used pa statistics to estimate the extent of association in amino acid composition at each site in the domain and between amino acid composition and variables reflecting clade and group membership, loop length, and the presence of a leucine zipper. The pa values were also used to describe groups of amino acid sites called "cliques" that were highly associated with each other. Finally, a predictive motif was constructed that accurately identifies bHLH domain-containing proteins that belong to Groups A and B.