Chapter 10: Free Energy Analysis Algorithms along Transition Paths and Transmembrane Ion Permeation

Umbrella sampling is one of the most popular free energy methods to compute the potential of mean force (PMF), which is routinely combined with the weighted histogram analysis method (WHAM). For multiple reaction coordinates (RCs), multidimensional umbrella sampling is generally required to compute the PMF surface under the framework of WHAM, which is inconvenient and computationally expensive in real applications. In this chapter, a new free energy analysis method, weighted least squares analysis method (WELSAM) is introduced, and a free energy calculation framework along the transition path is proposed. Using this method, the sampling cost can be greatly reduced, and the accuracy and precision of the PMF curves can also be improved. The method has been successfully applied to the study of transmembrane ion permeation mechanisms and, based on this, the effect of membrane thickness and ion type on the selection of membrane permeation mechanisms are explored.