Error and efficiency of simulated tempering simulations

Abstract

We derive simple analytical expressions for the error and computational efficiency of simulated tempering ͑ST͒ simulations. The theory applies to the important case of systems whose dynamics at long times is dominated by the slow interconversion between two metastable states. An extension to the multistate case is described. We show that the relative gain in efficiency of ST simulations over regular molecular dynamics ͑MD͒ or Monte Carlo ͑MC͒ simulations is given by the ratio of their reactive fluxes, i.e., the number of transitions between the two states summed over all ST temperatures divided by the number of transitions at the single temperature of the MD or MC simulation. This relation for the efficiency is derived for the limit in which changes in the ST temperature are fast compared to the two-state transitions. In this limit, ST is most efficient. Our expression for the maximum efficiency gain of ST simulations is essentially identical to the corresponding expression derived by us for replica exchange MD and MC simulations ͓E. Rosta and G. Hummer, J. Chem. Phys. 131, 165102 ͑2009͔͒ on a different route. We find quantitative agreement between predicted and observed efficiency gains in a test against ST and replica exchange MC simulations of a two-dimensional Ising model. Based on the efficiency formula, we provide recommendations for the optimal choice of ST simulation parameters, in particular, the range and number of temperatures, and the frequency of attempted temperature changes.

Communication: Simulated tempering with fast on-the-fly weight determination

“…As seen, while the T 1 ↔ T 2 transitions took place more often because the parameter f 2 was getting better, the T 2 → T 3 transitions were also attempted but all failed. At the step 7.95 × 10 5 , another large positive energy fluctuation occurred and the attempt T 2 → T 3 was successful, and this resulted in the new update for f 3 (Fig. 2(d)).…”

“…To accelerate the sampling, there has been considerable progress in developing a new class of simulation methods, referred to as the generalized-ensemble algorithms. [1][2][3][4] One of widely used generalized-ensemble algorithms is simulated tempering (ST). 5,6 The basic idea is that by coupling low temperature simulations with high temperature ones, one hopes to transfer the improved sampling at the higher temperature to the lower temperature.…”

Generalized simulated tempering for exploring strong phase transitions

“…In more recent years, considerable attention has been paid to the application of ST to biomolecular simulations [36][37][38] due to its better scaling property with system size and superior acceptance ratio for temperature transitions. Several comparison studies [39][40][41] revealed that ST with a properly chosen temperature weight exhibits faster diffusion in temperature space and a better sampling efficiency in comparison to the tREM. Combinations of the ST and other enhanced sampling methods have further explored this synergistic advantage.…”

Peptide dimerization-dissociation rates from replica exchange molecular dynamics

“…45 A converged ST trajectory is essentially equivalent with a replica trajectory in an REMD simulation. Therefore, the following formula can be applied to the per replica data of the REMD simulations …”