Binding Free Energy Calculations Based on the Path Collective Variable along a String Pathway

Calculating the binding free energy of small drug-like molecules to a macromolecular receptor is one of the most important applications of molecular dynamics simulations. One computational approach (the "geometrical route") seeks to determine the binding free energy of a ligand by calculating the potential of mean force along a physical path corresponding to the dissociation of the ligand from its receptor. We show here that it is possible to rigorously map the entire ligand-receptor separation process onto a curvilinear separation pathway constructed from the string method and then sample the longitudinal and orthogonal order parameters defined from the Path Collective Variable (PCV) along this pathway to calculate the binding free energy. The theory is illustrated by computing the absolute binding free energy of a glycogen synthase kinase-3 beta (GSK-3β) inhibitor, and the results are compared with the result from a calculation based on the standard alchemical double decoupling approach.