Zooming across the Alchemical Space

Alchemical transformations, whereby chemical species are modified seamlessly, represent a powerful tool in molecular simulations and free-energy calculations, with a broad range of applications. A general-extent, or alchemical parameter, λ ∈ [0,1], describes the gradual transition between the initial and final states of the transformation, and its discretization critically affects the reliability and efficiency of the free-energy calculations. For transformations involving large moieties, free-energy perturbation (FEP) and thermodynamic integration (TI) require numerous intermediates, or λ-states, to ensure appropriate overlap of the configurational ensembles and suitable convergence of the simulation, each state demanding extensive sampling, which burdens computational feasibility. To address this limitation, we combine λ-dynamics─treating λ as a dynamic variable─with the enhanced-sampling approach well-tempered metadynamics-extended adaptive biasing force (WTM-eABF), forming the basis of WTM-λABF. By handling λ as a continuously varying collective variable (CV) and applying a bin-discretized bias, WTM-λABF efficiently explores the λ-space, even when the latter is stratified in numerous intermediates. Calculations of free-energies of hydration, of protein–ligand binding, and of amino-acid mutations in proteins reveal that WTM-λABF consistently converges faster than standard FEP or λ-ABF, with its advantages becoming more pronounced as the number of intermediates rises. We find that WTM-λABF can handle alchemical transformations efficiently with as many as 1,000 intermediates, allowing transformations involving large moieties, or significant potential-energy changes, to be tackled with utmost accuracy. Additionally, its rapid exploration of the continuous λ-space accelerates sampling in the orthogonal space. We are confident that WTM-λABF has the potential to serve as a foundational method for routine applications relevant to chemistry and biophysics, ranging from drug discovery to protein engineering and design.