Energy Matrix of Structurally Important Side-Chain/Side-Chain Interactions in Proteins

The interactions between amino acid side chains in proteins are generally considered to be the most important stabilizing factor controlling the precise arrangement of the polypeptide chain into a well-defined spatial structure. We used the RI-DFT-D method to calculate the full 20 x 20 matrix of interaction energies between all pairs of amino acid side chains. For each pair, we used a representative 3D conformation extracted from an analysis of known protein structures from Protein Data Bank (PDB). The representative comes from the largest cluster of relative orientations of the two side chains. We find that all of the calculated interaction energies between selected pairs of amino acids are attractive in the gas phase with the exception of side chain pairs having the same total charge. We compared these data with those calculated by the parm03 and OPLS-AA/L force fields to investigate the reliability of simple methods in modeling biomolecules and their behavior. The force fields yield good overall interaction energies for our set but have problems in evaluation of some particular interactions which could be of principal importance for protein stability. We then looked in detail at the 20 side chain interactions involving tryptophan. The histograms of interaction energies showed that the distributions of the interaction energies are neither normal nor Boltzmann-like and that our representative geometries correspond mostly to the minimum energy geometry which is rather poorly populated in the whole pairwise energy distribution. We concluded that cluster representatives obtained by the clusterization algorithm based on geometry criteria cannot be considered as a typical interaction for the whole side chain/side chain interaction distribution. They seem to epitomize the strongest interactions in a protein and are often functionally or structurally important.