New Method To Determine The Effect Of Dimerization On Protein Flexibility From Molecular Dynamics Simulation Using Structural Hierarchy

Macromolecular binding involves two major terms: enthalpy and entropy. Most efforts are focused on evaluating the enthalpy component because it can be computed simply from the atomic positions, which makes it convenient to compute interactions among binding partners or with the solvent phase. Nonetheless, for numerous cases, the entropy component can be equally or even more important than the enthalpy. However, computing entropy for large biomolecular systems is not trivial because the large number of atoms involved can make it very time-intensive. In this work, we present a simple and fast method to compute the entropy of solvated protein-dimer systems directly from molecular dynamics simulations which builds on an existing theory of entropy of liquids and isolated, flexible molecules. The total entropy is split into two terms: vibrational and topographical. The vibrational term quantifies the population of energy states accessible in a single multi-dimensional energy well in phase space and the topographical term depicts the effective number of these energy wells. The vibrational term is derived using a hierarchical approach whereby covariance matrices of forces and torques are evaluated at different length-scales associated with the macromolecular structure - whole-molecule, residue and united-atom levels. The topographical term is derived hierarchically from the distribution of dihedrals and molecular contacts to account for the conformations of side chains and orientations of the residues in the complex. In totality, the theory is scalable across the hierarchical levels and, therefore, averts the need to deal with large number of atoms simultaneously. The theory is tested on a large library of proteins to demonstrate its application in computing the entropic changes that occur due binding and is benchmarked against the conventional Quasiharmonic method.