One for All, All for One: A Unified Framework for Free-Energy Calculations

ConspectusEnhanced-sampling techniques
employed in free-energy calculations
overcome the limitations of brute-force molecular dynamics (MD) and
are widely used to interrogate complex biological and chemical systems
at atomic resolution. Depending on the nature of the problem at hand,
different strategies are utilized to estimate the underlying free-energy
change. In geometrical transformations, sampling is accelerated along
a defined set of collective variables (CVs) to reconstruct the associated
free-energy landscape. Conversely, in alchemical transformations,
the free-energy difference between the two end states is determined
by tracing a nonphysical pathway. Generalized-ensemble techniques
accelerate sampling through rapid exchanges between low and high temperatures,
and the resulting trajectories are then reweighted to recover the
free energy. This methodological diversitypaired with distinct
schools of thought promoting incompatible or competing procedurescan
often breed confusion and jeopardize the reproducibility of results.
To alleviate this problem, we have recently expanded the theoretical
foundation of the adaptive biasing force (ABF) frameworkoriginally
classified as an importance-sampling methodand have extended
its application to geometrical, alchemical, and generalized-ensemble
free-energy calculations. In this Account, we review these developments
and introduce a unified strategy: Well-tempered metadynamics-xABF (WTM-xABF). WTM-xABF accommodates geometrical, alchemical, generalized-ensemble, and
hybrid schemes with minimal parameter tuning, making it a robust and
accessible platform for a wide range of applications. Its geometrical
and alchemical variants are demonstrably more efficient than, or at
least competitive with, leading state-of-the-art algorithms. To illustrate
its versatility, we demonstrate the use of WTM-xABF
in (1) disentangling coupled motions in complex biochemical systems
by combining human-designed and machine-learning CVs, (2) performing
extensive protein–ligand binding free-energy calculations for
substrates of greater size and flexibility than traditional drug-like
molecules, and (3) conducting fully blind folding simulations of fast-folding
proteins. With its sound theoretical foundation, computational efficiency,
and broad applicability, WTM-xABF is poised to become
a powerful method for MD across physical chemistry, biophysics, and
drug discovery.