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.