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

Enhanced-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.