Enhanced and effective conformational sampling of protein molecular systems for their free energy landscapes

Protein folding and protein-ligand docking have long persisted as important subjects in biophysics. Using multicanonical molecular dynamics (McMD) simulations with realistic expressions, i.e., all-atom protein models and an explicit solvent, free-energy landscapes have been computed for several systems, such as the folding of peptides/proteins composed of a few amino acids up to nearly 60 amino-acid residues, protein-ligand interactions, and coupled folding and binding of intrinsically disordered proteins. Recent progress in conformational sampling and its applications to biophysical systems are reviewed in this report, including descriptions of several outstanding studies. In addition, an algorithm and detailed procedures used for multicanonical sampling are presented along with the methodology of adaptive umbrella sampling. Both methods control the simulation so that low-probability regions along a reaction coordinate are sampled frequently. The reaction coordinate is the potential energy for multicanonical sampling and is a structural identifier for adaptive umbrella sampling. One might imagine that this probability control invariably enhances conformational transitions among distinct stable states, but this study examines the enhanced conformational sampling of a simple system and shows that reasonably well-controlled sampling slows the transitions. This slowing is induced by a rapid change of entropy along the reaction coordinate. We then provide a recipe to speed up the sampling by loosening the rapid change of entropy. Finally, we report all-atom McMD simulation results of various biophysical systems in an explicit solvent.