CORRELATION BETWEEN INTERMOLECULAR INTERACTION ENERGY AND ELECTRONIC ORBITAL SHARING IN BIOMOLECULAR COMPLEXES

Intermolecular interactions play a central role in biological systems and are essential for the occurrence of life. These are fundamental for protein folding, protein function, lipid bilayer formation, molecular recognition, among others. In particular, molecular recognition is the basis for cell signaling, metabolism, DNA replication, RNA translation into proteins and enzymatic reactions. From the point of view of Quantum Mechanics, the wave function completely describes the physical system to which it is associated, providing information about covalent bond, ionization energy, absorption and emission of light, among others. In the same vein, the wave function is expected to provide information about intermolecular interactions, consistent with empirical observations, however there are still few descriptions for this, especially in biological systems. In this sense, it is known that a radial and angular wave function can be distributed in several molecules and in the intermolecular space, a phenomenon observed by Atomic Force Microscopy (ZHANG; CHEN; YUAN; JI; CHENG; QIU, 2013). Then, our goal is verify the correlation between interaction energy and molecular orbital sharing, we used (a) 48 Beta-Secretase I complexes taken from PDBbind; (b) 53 complexes sampled from the refined-set dataset; and (c) the S66 database of small molecules relevant for interaction with biomolecules. Proteins were protonated at pH 7.4 using the PDB2PQR Webserver (UNNI, et al., 2011). The geometry of the protonated complexes was optimized using semi-empirical method PM7, with MOPAC2016 (STEWART, 2016). Then, hybrid Quantum Mechanics Molecular Mechanics (QMMM) calculations were performed, using B3LYP 6-31G* and HF-3c, with Orca 5 software (NEESE, 2022); and the CHARMM36 force field (HUANG et al., 2017), for QM and MM region, respectively. Finally, based on the QM data, the shared electron density interaction between non-covalently bound molecules was calculated using equations formulated here, based on Mulliken populations (1955, 1935). We obtained for the S66 bank molecules a correlation with R of -0.53 (p=2.9x10-3), and removing outliers we obtained R = -0.81 (p=2.3x10-7). Also, separately correlating the molecules that interact by π-π and by hydrogen bonds interactions, we obtained R = -0.97 (p= 2.1x10-4) and R = -0.86 (p=6.4x10-7), respectively. Observing distinct behavior between the two interactions, being more pronounced the sharing of molecular orbitals in the π-π interactions. When analyzing the Beta-Secretase I complexes, a strong correlation was observed between the sharing of protein orbitals with the ligand and the experimental ∆G values, with R less than or equal to -0.76 (p=1.1x10-9). The sampled PDBbind complexes showed R values equal or lower than -0.43 (p=6.3x10-3). Finally, we formulate a descriptor that correlates the wave function with molecular interactions, whereby the higher the sharing, the lower the interaction ∆E or ∆G, id est the higher the shared electron density between non-covalently bonded molecules, the higher the interaction between the molecules.