Standard Free Energy of Binding from a One-Dimensional Potential of Mean Force

A practical approach that enables one to calculate the standard free energy of binding from a one-dimensional potential of mean force (PMF) is proposed. Umbrella sampling and the weighted histogram analysis method are used to generate a PMF along the reaction coordinate of binding. At each point, a restraint is applied orthogonal to the reaction coordinate to make possible the determination of the volume sampled by the ligand. The free energy of binding from an arbitrary unbound volume to the restrained bound form is calculated from the ratio of the PMF integrated over the bound region to that of the unbound. Adding the free energy changes from the standard-state volume to the unbound volume and from the restrained to the unrestrained bound state gives the standard free energy of binding. Exploration of the best choice of binding paths is also made. This approach is first demonstrated on a model binding system and then tested on the benzamidine-trypsin system for which reasonable agreement with experiment is found. A comparison is made with other methods to obtain the standard free energy of binding from the PMF.