Multipolar electrostatics for proteins: atom-atom electrostatic energies in crambin

Accurate electrostatics necessitates the use of multipole moments centered on nuclei or extra point charges centered away from the nuclei. Here, we follow the former alternative and investigate the convergence behavior of atom-atom electrostatic interactions in the pilot protein crambin. Amino acids are cut out from a Protein Data Bank structure of crambin, as single amino acids, di, or tripeptides, and are then capped with a peptide bond at each side. The atoms in the amino acids are defined through Quantum Chemical Topology (QCT) as finite volume electron density fragments. Atom-atom electrostatic energies are computed by means of a multipole expansion with regular spherical harmonics, up to a total interaction rank of L = ℓA+ ℓB + 1 = 10. The minimum internuclear distance in the convergent region of all the 15 possible types of atom-atom interactions in crambin that were calculated based on single amino acids are close to the values calculated from di and tripeptides. Values obtained at B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels are only slightly larger than those calculated at HF/6-31G(d,p) level. This convergence behavior is transferable to the well-known amyloid beta polypeptide Aβ1-42. Moreover, for a selected central atom, the influence of its neighbors on its multipole moments is investigated, and how far away this influence can be ignored is also determined. Finally, the convergence behavior of AMBER becomes closer to that of QCT with increasing internuclear distance.