Development of Novel Statistical Potentials Describing Cation−π Interactions in Proteins and Comparison with Semiempirical and Quantum Chemistry Approaches

Novel statistical potentials derived from known protein structures are presented. They are designed to describe cation−π and amino−π interactions between a positively charged amino acid or an amino acid carrying a partially charged amino group and an aromatic moiety. These potentials are based on the propensity of residue types to be separated by a certain spatial distance or to have a given relative orientation. Several such potentials, describing different kinds of correlations between residue types, distances, and orientations, are derived and combined in a way that maximizes their information content and minimizes their redundancy. To test the ability of these potentials to describe cation−π and amino−π systems, we compare their energies with those computed with the CHARMM molecular mechanics force field and with quantum chemistry calculations at the Hartree−Fock level (HF) and at the second order of the Møller−Plesset perturbation theory (MP2). The latter calculations are performed in the gas phase and in acetone, in order to mimic the average dielectric constant of protein environments. The energies computed with the best of our statistical potentials and with gas-phase HF or MP2 show correlation coefficients up to 0.96 when considering one side-chain degree of freedom in the statistical potentials and up to 0.94 when using a totally simplified model excluding all side-chain degrees of freedom. These potentials perform as well as, or better than, the CHARMM molecular mechanics force field that uses a much more detailed protein representation. The good performance of our cation−π statistical potentials suggests their utility in protein structure and stability prediction and in protein design.