# Perturbation Potentials to Overcome Order/Disorder Transitions in Alchemical Binding Free Energy Calculations

## TL;DR

This paper explores how order/disorder transitions affect alchemical free energy calculations in protein-ligand systems, proposing analytical models and strategies to improve sampling efficiency and accuracy.

## Contribution

It introduces an analytical model combined with existing formalism to analyze and mitigate order/disorder transition effects in alchemical binding free energy simulations.

## Key findings

- Order/disorder transitions hinder sampling efficiency.
- Analytical models can predict and analyze these transitions.
- Strategies to design better alchemical schedules are proposed.

## Abstract

We investigate the role of order/disorder transitions in alchemical simulations of protein-ligand absolute binding free energies. We show, in the context of a potential of mean force description, that for a benchmarking system (the complex between the L99A mutant of T4 lysozyme and 3-iodotoluene) and for a more challenging system relevant for medicinal applications (the complex of the farnesoid X receptor and inhibitor 26 from a recent D3R challenge) that order/disorder transitions can significantly hamper Hamiltonian replica exchange sampling efficiency and slow down the rate of equilibration of binding free energy estimates. We further show that our analytical model of alchemical binding combined with the formalism developed by Straub et al. for the treatment of order/disorder transitions of molecular systems can be successfully employed to analyze the transitions and help design alchemical schedules and soft-core functions that avoid or reduce the adverse effects of rare binding/unbinding transitions. The results of this work pave the way for the application of these techniques to the alchemical estimation with explicit solvation of hydration free energies and absolute binding free energies of systems undergoing order/disorder transitions.