Electron density based analysis of N-H center dot center dot center dot O=C hydrogen bonds and electrostatic interaction energies in high-resolution secondary protein structures: insights from quantum crystallographic approaches

In proteins, the main-chain N-H center dot center dot center dot O=C hydrogen bonds (HBs) play a crucial role in the formation of alpha-helices and beta-sheets. Accurate analysis of such hydrogen bonds and their electrostatic interaction energies is essential for studying binding interactions and for better understanding of the energetics involved in protein folding. Here, we studied 22 high-resolution (0.87 angstrom to 0.48 angstrom) secondary protein structures (4.7 kDa to 54.5 kDa) from the RCSB PDB and performed topological analyses of 1443 N-H center dot center dot center dot O=C HBs (750 in alpha-helices and 693 in beta-sheets) using the multipole analysis based experimental electron densities as transferred from the ELMAM2 database. This is the first study of its kind involving by far the largest number of high-resolution protein structures and HBs from both alpha-helices and beta-sheets. Further, based on the accurate estimation of the electrostatic interaction energies, the excellent correlations with various topological parameters have been demonstrated. The excellent correlations have also been observed between the topological parameters. Thereby, we identified the limiting values of the topological parameters and the electrostatic interaction energies to establish the presence of the true N-H center dot center dot center dot O=C HBs in protein main-chains via quantitative and qualitative analyses of electron densities using quantum crystallographic approaches - the quantum theory of atoms in molecules (QTAIM) and the noncovalent interaction (NCI) index.