Equilibrium and Nonequilibrium Methods for Free-Energy Calculations With Molecular Dynamics

The past decades have witnessed significant progress in the field of molecular simulation, particularly in enhancing the sampling of complex biological processes. These advancements have allowed a large theoretical and computational community to address a wide range of questions, such as conformational transitions in biomolecular systems and protein-ligand reversible association, which are notoriously impossible to investigate using common brute-force computer simulations. The primary reason for this progress is the development of a diverse set of methods aimed at exploring rare events through reliable free-energy calculations. These methods have provided new ways to enhance the sampling of intricate molecular processes by overcoming the limitations of traditional simulation approaches. However, the introduction of new and often conceptually related methods has made it increasingly challenging to select the best-suited option for a given problem. In this context, it is crucial to understand the theoretical foundations of these approaches and how they can be blended together to improve performance. Here, tracing the mathematical roots of different methods, as well as the connections between them, we show how free-energy calculations have become more robust and efficient for the investigation of complex biological objects, eminently relevant to drug discovery.