Coupling of replica exchange simulations to a non-Boltzmann structure reservoir

Abstract

Computing converged ensemble properties remains challenging for large biomolecules. Replica exchange molecular dynamics (REMD) can significantly increase the efficiency of conformational sampling by using high temperatures to escape kinetic traps. Several groups, including ours, introduced the idea of coupling replica exchange to a pre-converged, Boltzmann-populated reservoir, usually at a temperature higher than that of the highest temperature replica. This procedure reduces computational cost because the long simulation times needed for extensive sampling are only carried out for a single temperature. However, a weakness of the approach is that the Boltzmann-weighted reservoir can still be difficult to generate. We now present the idea of employing a non-Boltzmann reservoir, whose structures can be generated through more efficient conformational sampling methods. We demonstrate that the approach is rigorous and derive a correct statistical mechanical exchange criterion between the reservoir and the replicas that drives Boltzmann-weighted probabilities for the replicas. We test this approach on the trpzip2 peptide and demonstrate that the resulting thermal stability profile is essentially indistinguishable from that obtained using very long (>100 ns) standard REMD simulations. The convergence of this reservoir-aided REMD is significantly faster than for regular REMD. Furthermore, we demonstrate that modification of the exchange criterion is essential; REMD simulations using a standard exchange function with the non-Boltzmann reservoir produced incorrect results.

Figure 1

The trpzip2 model peptide, in the native β-hairpin conformation. Backbone atoms are shown colored by element; for clarity, side chain heavy atoms are only shown for Trp residues (orange).

Figure 2

Thermal stability profiles for trpzip2 obtained from REMD simulations. Black: standard REMD (150ns); red: REMD with non-Boltzmann reservoir and standard (eq. 3) exchange probability (20ns); blue: REMD with non-Boltzmann reservoir and modified (eq. 4) exchange probability (25ns). Error bars indicate lower bounds to uncertainty, obtained from the difference between data calculated from first and last half of the ensemble.

Figure 3

Fraction of native hairpin conformation as a function of time at 350K for four REMD simulations. Black: standard REMD; red: REMD with non-Boltzmann reservoir and standard exchange probability (eq. 3); blue: REMD with non-Boltzmann reservoir and modified exchange probability (eq. 4); green: REMD with Boltzmann reservoir and standard exchange probability (eq. 3). It is apparent that the simulations employing the reservoir reach a plateau value much more rapidly than standard REMD and that the non-Boltzmann reservoir requires modified exchange probability.