Does Hamiltonian Replica Exchange via Lambda-Hopping Enhance the Sampling in Alchemical Free Energy Calculations?

In the context of computational drug design, we examine the effectiveness of the enhanced sampling techniques in state-of-the-art free energy calculations based on alchemical molecular dynamics simulations. In a paradigmatic molecule with competition between conformationally restrained E and Z isomers whose probability ratio is strongly affected by the coupling with the environment, we compare the so-called λ-hopping technique to the Hamiltonian replica exchange methods assessing their convergence behavior as a function of the enhanced sampling protocols (number of replicas, scaling factors, simulation times). We found that the pure λ-hopping, commonly used in solvation and binding free energy calculations via alchemical free energy perturbation techniques, is ineffective in enhancing the sampling of the isomeric states, exhibiting a pathological dependence on the initial conditions. Correct sampling can be restored in λ-hopping simulation by the addition of a "hot-zone" scaling factor to the λ-stratification (FEP⁺ approach), provided that the additive hot-zone scaling factors are tuned and optimized using preliminary ordinary replica-exchange simulation of the end-states.