Identification of a pattern in protein structure based on energetic and statistical considerations

We carry out a statistical analysis of the nonbonded interactions in 10 high-resolution nonhomologous protein structures, using original algorithms. We observe a tendency of nonbonded interactions which contribute significantly (i.e., with an energy lower than the average value, referred to as "strong") to protein stability, to be concentrated in clusters of residues that are strongly sequence correlated. We characterize this sequence correlation and subsequently define a "system" as the pattern that describes these clusters. In order to study the distribution of the systems in the proteins we build a matrix for each protein and for each term of the empirical potential function used to compute the nonbonded interactions; each ij element is the number of common residues between the systems i and j. The analysis of the matrices shows the presence of compact blocks that define units in the protein structure which concentrate strong and weak interactions inside the unit itself and display relative independence with respect to the rest of the protein. Comparing the blocks defined by the three nonbonded energy components (electrostatic, hydrogen bonds, and van der Waals interactions) we observe a one-to-one correspondence between the blocks of different energy components with an average overlap of 90% of the residues forming each block.