Resolution Exchange Simulation

We extend replica-exchange simulation in two ways and apply our approaches to biomolecules. The first generalization permits exchange simulation between models of differing resolution—i.e., between detailed and coarse-grained models. Such “resolution exchange” can be applied to molecular systems or spin systems. The second extension is to “pseudoexchange” simulations, which require little CPU usage for most levels of the exchange ladder and also substantially reduce the need for overlap between levels. Pseudoexchanges 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.

Figure 1

Coarse-grained simulation accelerates transitions in high-resolution simulation with ResEx and PsEx. (a) United-atom trajectory for dileucine, showing transitions between $\alpha$ and $\beta$ states, which is randomly reordered to create trajectory (b) with extremely rapid transitions. Via pseudoexchanges with the shuffled trajectory, ResEx generates the all-atom trajectory in (c). The time axes in (c) and (d) differ by a factor of 20.

Figure 2

ResEx produces canonical sampling despite a poor coarse-grained potential. (a) Probability densities $P(\varphi )$ for butane. Reference data from standard simulation are indicated by the solid line. The ResEx simulation with the asymmetric potential (b) is plotted with triangles, and ResEx simulation with the symmetric potential (c) is plotted with circles.

Figure 3

ResEx simulation accelerates equilibration among dileucine substates. Dashed lines show running estimates of the intersubstate $\Delta G_{\alpha \beta }$ as a function of time for 8 independent, 40 nsec trajectories, and the solid line shows the estimate of $\Delta G_{\alpha \beta }$ from 600 nsec of standard simulation. Each symbol with error bars gives the average and range of 8 independent ResEx simulations, displaced from the origin to reflect total CPU time (measured in all-atom time steps), including investment in the united-atom simulation. The efficiency gain can be estimated by the relative ranges of the $\Delta G_{\alpha \beta }$ estimates.