Resolution Exchange Simulation

Abstract

We extend replica exchange simulation in two ways, and apply our approaches to biomolecules. The first generalization permits exchange simulation between models of differing resolutioni.e., between detailed and coarse-grained models. Such "resolution exchange" can be applied to molecular systems or spin systems. The second extension is to "pseudo-exchange" simulations, which require little CPU usage for most levels of the exchange ladder and also substantially reduces the need for overlap between levels. Pseudo exchanges can be used in either replica or resolution exchange simulations. We perform efficient, converged simulations of a 50-atom peptide to illustrate the new approaches.Accepted for publication in physical review letters. PACS numbers:The simulation of biomolecules with 10 4 − 10 5 degrees of freedom has become routine, thanks to the accessibility of powerful computing resources, the development of reliable simulation software, and standardized empirical potential energy functions. For many biological applications, such as binding free energy estimation, it is desirable to generate an equilibrated ensemble of conformations. In principle, standard Monte Carlo (MC) and molecular dynamics (MD) algorithms are perfectly ergodic, and therefore will eventually generate such ensembles. In practice, the µ sec − sec timescale, which describes biologically relevant fluctuations, is not within reach of computation even for small proteins.Two broad strategies have been developed to address this problem. In one approach, dating to the earliest computational studies of proteins[1, 2], coarse-grained protein representations are adopted. This strategy continues to be popular [3,4].A second class of strategies attempts directly to enhance sampling of atomic-resolution models, including multiple time step methods [5,6], replica exchange [7]/parallel tempering [8,9,10], and other generalized ensemble techniques [11]. Parallel tempering (PT), which employs a ladder of replicas simulated at increasing temperatures, is widely used for state-of-the-art molecular dynamics simulations, but presently is limited to small proteins [12], as the resources required increase rapidly with the system size.This Letter presents two new tools for biomolecular simulation, by extending the PT approach and exploiting the speed of coarse-grained models. The first extension is a "resolution exchange" (res-ex) algorithm whichinstead of using high-temperature simulation to increase sampling, as does PT -uses inexpensive coarse-grained * elyman@ccbb.pitt.edu † dmz@ccbb.pitt.edu models to cross barriers. Boltzmann-weighted ensembles are produced. The algorithm is implemented in close analogy to PT, and can also be applied to magnetic systems (e.g., the Ising model). The res-ex approach is natural for proteins, and indeed the kernel of the idea was suggested in the early days of protein simulation [1]. More recently, the approach has been implemented in an ad hoc way, without proper statistical weighting [3]. A rigorous method to calculate free en...

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