Replica exchange with solute scaling: a more efficient version of replica exchange with solute tempering (REST2)

Abstract

A small change in the Hamiltonian scaling in Replica Exchange with Solute Tempering (REST) is found to improve its sampling efficiency greatly, especially for the sampling of aqueous protein solutions in which there are large-scale solute conformation changes. Like the original REST (REST1), the new version (which we call REST2) also bypasses the poor scaling with system size of the standard Temperature Replica Exchange Method (TREM), reducing the number of replicas (parallel processes) from what must be used in TREM. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST2 is compared with TREM and with REST1 for the folding of the trpcage and β-hairpin in water. The comparisons confirm that REST2 greatly reduces the number of CPUs required by regular replica exchange and greatly increases the sampling efficiency over REST1. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water.

FIG. 1

Temperature trajectories of four representative replicas with the effective temperature of the protein started at 300K (a), 368K (b), 455K (c), and 572K (d) for the trpcage system starting from the native structure. It should be noted that the temperatures referred to are the effective temperatures of the protein which arrises from the scaling of the force field parameters of the protein, while the actual simulation is done at temperature T₀.

FIG. 2

Protein heavy atom RMS deviation from the native structure as a function of simulation time for replicas with different effective temperatures of the protein for the trpcage system. Inset of the figure highlights the RMSD for replica at effective temperature 300K in the first 5ns simulation.

FIG. 3

a. The temperature trajectories for three representative replicas with the effective temperature of the protein initially at low (T = 310K), intermediate (T = 419K), and high (T = 684K) temperatures for the β-hairpin system. b. The protein heavy atom RMSD versus time at each of the above temperatures when replicas visit those temperatures. (Black, T = 310K; Red, T = 419K; Green, T = 684K)

FIG. 4

The heavy atom RMSD from the native structure of the β-hairpin as a function of simulation time with the effective temperature of the protein at 600K using the scaled Hamiltonian of REST2 without attempted replica exchanges. Both RMSD > 4Å and < 4Å are sampled, by comparison in REST1 only RMSD > 4Å are sampled at high temperatures.(Fig. 4 of reference 7).

FIG. 5

Anti-correlation between the intra-molecular potential energy of the protein and the interaction energy between the protein and water for replicas with different effective temperatures of the protein for the trpcage system.

FIG. 6

a. The distribution of intra-molecular potential energy of the protein for replicas with different effective temperatures of the protein. b. The distribution of interaction energy between protein and water for replicas with different effective temperatures of the protein. c. Distribution of $(1/2)\sqrt{{\beta }_0/{\beta }_m}{E}_{pw}$ for replicas with different effective temperatures of the protein. d. Distribution of $E_{pp}+(1/2)\sqrt{{\beta }_0/{\beta }_m}{E}_{pw}$ for replicas with different effective temperatures of the protein.

FIG. 7

The distribution of intra-molecular potential energy of the protein at the lowest temperature replica using TREM and REST2 starting from an almost fully extended structure.