Tunable coarse graining for Monte Carlo simulations of proteins via smoothed energy tables: Direct and exchange simulations

Many commonly used coarse-grained models for proteins are based on simplified interaction sites and consequently may suffer from significant limitations, such as the inability to properly model protein secondary structure without the addition of restraints. Recent work on a benzene fluid (Lettieri, S.; Zuckerman, D. M. J. Comput. Chem. 2012, 33, 268-275) suggested an alternative strategy of tabulating and smoothing fully atomistic orientation-dependent interactions among rigid molecules or fragments. Here we report our initial efforts to apply this approach to the polar and covalent interactions intrinsic to polypeptides. We divide proteins into nearly rigid fragments, construct distance and orientation-dependent tables of the atomistic interaction energies between those fragments, and apply potential energy smoothing techniques to those tables. The amount of smoothing can be adjusted to give coarse-grained models that range from the underlying atomistic force field all the way to a bead-like coarse-grained model. For a moderate amount of smoothing, the method is able to preserve about 70-90% of the α-helical structure while providing a factor of 3-10 improvement in sampling per unit computation time (depending on how sampling is measured). For a greater amount of smoothing, multiple folding-unfolding transitions of the peptide were observed, along with a factor of 10-100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations. For a β hairpin, secondary structure is also preserved, albeit for a narrower range of the smoothing parameter and, consequently, for a more modest improvement in sampling. We have also applied the new method in a "resolution exchange" setting, in which each replica runs a Monte Carlo simulation with a different degree of smoothing. We obtain exchange rates that compare favorably to our previous efforts at resolution exchange (Lyman, E.; Zuckerman, D. M. J. Chem. Theory Comput. 2006, 2, 656-666).