Recipes for free energy calculations in biomolecular systems

During the last decade, several methods for sampling phase space and calculating various free energies in biomolecular systems have been devised or refined for molecular dynamics (MD) simulations. Thus, state-of-the-art methodology and the ever increasing computer power allow calculations that were forbidden a decade ago. These calculations, however, are not trivial as they require knowledge of the methods, insight into the system under study, and, quite often, an artful combination of different methodologies in order to avoid the various traps inherent in an unknown free energy landscape. In this chapter, we illustrate some of these concepts with two relatively simple systems, a sugar ring and proline oligopeptides, whose free energy landscapes still offer considerable challenges. In order to explore the configurational space of these systems, and to surmount the various free energy barriers, we combine three complementary methods: a nonequilibrium umbrella sampling method (adaptively biased MD, or ABMD), replica-exchange molecular dynamics (REMD), and steered molecular dynamics (SMD). In particular, ABMD is used to compute the free energy surface of a set of collective variables; REMD is used to improve the performance of ABMD, to carry out sampling in space complementary to the collective variables, and to sample equilibrium configurations directly; and SMD is used to study different transition mechanisms.