2.5 Discussion
The analysis in this chapter proved that the 20x20 dimensional coupling matrices \(\wij\) contain a wealth of information that is irretrievably lost when computing the heuristic contact score in form of the Frobenius norm of the coupling matrix. For several amino acid pairs (e.g. E-R, E-E) the direction of the corresponding coupling value is a strong indicator for a contact. More quantitatively, the distribution of individual couplings reflect physico-chemical interaction preferences between amino acids. Furthermore, characteristic patterns in the coupling matrices often point at the undelrying structural constraint that is subject to evolutionary pressure. The patterns also illustrate that there are higher order dependencies between the individual coupling values that also are in accordance with physico-chemical interaction preferences between amino acids.
Coucke and collegues performed a thorough quantitative analysis of coupling matrices selected from confidently predicted residue pairs [190]. They showed that eigenmodes obtained from a spectral analysis of averaged coupling matrices are closely related to physico-chemical properties of amino acid interactions, like electrostaticity, hydrophobicity, steric interactions or disulphide bonds. By looking at specific populations of residues, like buried and exposed residues or residues from specific protein classes (small, mainly \(\alpha\), etc), the eigenmodes of corresponding coupling matrices are found to capture very characteristic interactions for each class, e.g. rare disulfide contacts within small proteins and hydrophilic contacts between exposed residues. Their study confirms the qualitative observations presented above that amino acid interactions can leave characteristic physico-chemical fingerprints in coupling matrices.
References
190. Coucke, A., Uguzzoni, G., Oteri, F., Cocco, S., Monasson, R., and Weigt, M. (2016). Direct coevolutionary couplings reflect biophysical residue interactions in proteins. J. Chem. Phys. 145, 174102., doi: 10.1063/1.4966156.