Free-energy landscapes of proteins in solution by generalized-ensemble simulations

Free-energy landscapes of proteins in solution are essential for understanding molecular mechanism of protein folding, stability, and dynamics. Because of the multiple-minima problem (or quasi-ergodicity problem), the conventional molecular dynamics or Monte Carlo methods cannot provide the landscapes accurately at low temperatures. By contrast, the simulations based on the generalized-ensemble algorithms can sample wider conformational spaces than the conventional approaches, thereby providing better free-energy landscapes of proteins at low temperatures. In this article, we review two well-known generalized-ensemble algorithms, namely, multicanonical algorithm and replica-exchange method, and then introduce further extensions of the above two methods, which are applicable to larger systems with rugged energy landscapes. These simulation methods have been applied to the protein folding simulations of the C-peptide in ribonuclease A with explicit solvent. We also demonstrate how the methods and the free-energy landscapes of proteins are useful for the biological research, by showing the simulation results on the phospholamban, a reversible regulator of sarco(end)plasmic reticulum Ca2+-pump.