Estimating Boltzmann Statistical Energy for Proteins from 3D Structure Using Pairwise Amino Acid Energy Matrix - GEM-X2120-N871

A pairwise amino acid energy matrix: GEM-X2120-N871 is developed for evaluating the Boltzmann statistical energy (BSE) for proteins of known 3D structure. The matrix was derived from a dataset of representative protein crystal structures and NMR structures selected from the Protein Data Bank (PDB). The pairwise amino acid contacts separated by distance [≤] 3.2 [A] in protein 3D structures was used to evaluate probabilities and propensities against background and the Boltzmann equation P(x) = e-(E(x)/KT) that links the probability of observing an event x with energy E(x) at a given temperature T was used to evaluate the BSE for proteins defined in Millielectron Volts (MeV) units. The BSE for a protein is obtained by summing up corresponding values for amino acid pairs from the matrix that satisfy the distance criterion in protein 3D structure. The landscape of BSE values for representative proteins based on propensities ranged between -890.99 MeV to 711.57 MeV among crystal structures and between -717.64 MeV to 234.78 MeV among NMR structures. Whereas, the landscape of BSE values based on probability alone was comparatively much narrower and ranged between 36.88 MeV to 131.28 MeV for the crystal structures and between 34.30 MeV to 102.23 MeV for the 871 NMR structures. Therefore, BSEs based on propensity with a broader range of values is suggested as being useful to discriminate individual proteins. The evaluation of BSE for proteins can be used to estimate relative gain or loss in energy between proteins that has applications in identifying low-energy conformations among an ensemble of protein conformations, or changes in energy due to drug/inhibitor/small molecule binding to the protein. The method was applied to evaluate changes in BSE for certain cancer drugs bound to protein targets and to analyse trends in predictions based on BSE with experimental observations on drug/inhibitor binding effectiveness as reported in literature.