Multi-Layer Free Energy Perturbation

Free energy perturbation (FEP) is frequently used to evaluate the free energy change of a biological process, e.g. the drug binding free energy or the ligand solvation free energy. Due to the sampling inefficiency, FEP is often employed together with computationally expensive enhanced sampling methods. Here we show that this sampling inefficiency, which stems from not accounting for the environmental reorganization, is an inherent property of the single-ensemble ansatz of FEP, and hence simply prolonging the MD simulation can hardly alleviate the problem. Instead, we propose a new, multi-ensemble ansatz – the multi-layer free energy perturbation (MLFEP), which allows environmental reorganization processes (relaxation) to occur automatically during the MD sampling. Our study paves the way toward a fast but accurate free energy calculation that can be employed in computer-aided drug design. Accurately evaluating the free energy change of a ligand binding to its receptor has a very practical use in computational drug design, i.e. determining the relative binding free energies between two drug candidates for leadoptimization. One of the most frequently employed method for this purpose is the so-called free energy perturbation (FEP) method [1], which states that the free energy change between the final target state T and the initial reference state R can be evaluated via a single ensemble average, i.e.