Nonbonded force field parameters derived from Atom-In-Molecules methods reproduce interactions in proteins from first--principles

Non-covalent interactions govern many chemical and biological phenomena and are crucial in protein-protein interactions, enzyme catalysis, and DNA folding. The size of these macromolecules and their various conformations demand computational inexpensive force fields that can accurately mimic the quantum chemical nature of the atomic non-covalent interactions. Accurate force fields, coupled with increasingly longer molecular dynamics (MD) simulations, may empower us to predict conformational changes associated with the biochemical function of proteins. Here, we aim to derive nonbonded protein force field parameters from the partitioned electron density of amino acids - the fundamental units of proteins - via the atoms-in-molecules (AIM) approach. The AIM parameters are validated using a database of charged, aromatic and hyrdrophilic side chain interactions in 610 conformations, primarily involving pi-pi interactions, as recently reported by one of us. Electrostatic and van der Waals interaction energies calculated with nonbonded force field parameters from different AIM methodologies were compared to first principle interaction energies from absolute localized molecular orbital - energy decomposition analysis (ALMO-EDA) at the wB97XV/def2TZVPD level. Our findings show that electrostatic interactions between side chains are accurately reproduced by atomic charges from the minimal basis iterative stockholder (MBIS) scheme with mean absolute errors of 4-7 kJ/mol. Meanwhile, C6 coefficients from the MBIS AIM method effectively predicts dispersion interactions with a mean error of -2 kJ/mol and a maximal error or -5 kJ/mol. As an outlook to use AIM methods in the development of protein force fields we present the constrained AIM method that allows to fix backbone parameters during the optimization of side chain interactions. Backbone dihedral parameters have been optimized to reproduce secondary structure elements in proteins and not altering them maintains compatibility with conventional protein force fields while improving the description of side chain interactions. Our validated AIM methods allow for the depiction of non-covalent, long-range interactions in proteins using cost-effective force fields that achieve chemical precision.