Configurational space discretization and free energy calculation in complex molecular systems

TL;DR

This paper proposes a new free energy calculation method for complex molecular systems that uses configurational space discretization into explicit conformers with invariant statistical weight distribution, bypassing the need for dynamical trajectories.

Contribution

It introduces a scheme to construct explicit conformers with invariant statistical weight distribution for efficient free energy estimation in complex molecules.

Findings

Implicit conformers have invariant statistical weight distribution.

Change in free energy correlates with conformational entropy change.

The method leverages entropy enthalpy compensation for accuracy.

Abstract

Trajectories provide dynamical information that is discarded in free energy calculations, for which we sought to design a scheme with the hope of saving cost for generating dynamical information. We first demonstrated that snapshots in a converged trajectory set are associated with implicit conformers that have invariant statistical weight distribution (ISWD). Based on the thought that infinite number of sets of implicit conformers with ISWD may be created through independent converged trajectory sets, we hypothesized that explicit conformers with ISWD may be constructed for complex molecular systems through systematic increase of conformer fineness, and tested the hypothesis in lipid molecule palmitoyloleoylphosphatidylcholine (POPC). Furthermore, when explicit conformers with ISWD were utilized as basic states to define conformational entropy, change of which between two given macrostates was found to be equivalent to change of free energy except a mere difference of a negative temperature factor, and change of enthalpy essentially cancels corresponding change of average intra-conformer entropy. These findings suggest that entropy enthalpy compensation is inherently a local phenomenon in configurational space. By implicitly taking advantage of entropy enthalpy compensation and forgoing all dynamical information, constructing explicit conformers with ISWD and counting thermally accessible number of which for interested end macrostates is likely to be an efficient and reliable alternative end point free energy calculation strategy.