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 <i>N</i>-methyl-<i>N</i>'-acetylalanylamide is determined in two dimensions, comparing single- and multiple-walker strategies.