Calculating Free-Energy Differences Using an Average Force: A Tutorial for Adaptive Biasing Force Simulations

The purpose of this tutorial is to get the reader familiarized
with the calculation of a free-energy change along a reaction-coordinate
(RC) model through a number of applications of variants of the importance-sampling
adaptive biasing force algorithm. The reversible sodium-chloride ion
pairing in aqueous solution serves as an introductory example, wherein
the RC model is defined as the distance separating the ions. For the
reversible folding of the short peptide deca-alanine, alternative
collective variables are considered to map the conformational free-energy
landscape. The importance-sampling algorithm is then applied to the
transfer of an ethanol molecule across the water liquid–vapor
interface to estimate its hydration free energy. The results are compared
to those of an alchemical transformation using free-energy perturbation
calculations. In the final application, the Ramachandran free-energy
surface underlying the conformational equilibrium of N-methyl-N′-acetylalanylamide is determined
in two dimensions, comparing single- and multiple-walker strategies.