Convergence of folding free energy landscapes via application of enhanced sampling methods in a distributed computing environment

Abstract

We have implemented the serial replica exchange method ͑SREM͒ and simulated tempering ͑ST͒ enhanced sampling algorithms in a global distributed computing environment. Here we examine the helix-coil transition of a 21 residue ␣-helical peptide in explicit solvent. For ST, we demonstrate the efficacy of a new method for determining initial weights allowing the system to perform a random walk in temperature space based on short trial simulations. These weights are updated throughout the production simulation by an adaptive weighting method. We give a detailed comparison of SREM, ST, as well as standard MD and find that SREM and ST give equivalent results in reasonable agreement with experimental data. In addition, we find that both enhanced sampling methods are much more efficient than standard MD simulations. The melting temperature of the Fs peptide with the AMBER99 potential was calculated to be about 310 K, which is in reasonable agreement with the experimental value of 334 K. We also discuss other temperature dependent properties of the helix-coil transition. Although ST has certain advantages over SREM, both SREM and ST are shown to be powerful methods via distributed computing and will be applied extensively in future studies of complex bimolecular systems.

Error and efficiency of simulated tempering simulations

“…This makes ST particularly useful for distributed computing. 15 Our analytical result for the efficiency gain in ST simulations has practical implications in the setup of ST simulations as follows.…”

“…ST and REMD have been proven particularly useful to enhance the sampling of biomolecular systems. 5,6,[11][12][13][14][15] Key questions in ST, REMD, REMC, or other extended ensemble simulations are as follows: ͑1͒ How large is the possible gain in computational efficiency, ͑2͒ for which simulation parameters can this maximum gain be realized, and ͑3͒ how do the different methods compare with respect to their efficiency gains? We have previously developed a simple analytical formula for the efficiency gain in REMD and REMC simulations 16 for the important case that the slow dynamics of the system of interest can be described by twostate transitions.…”

Rapid equilibrium sampling initiated from nonequilibrium data

“…At high temperatures, energetic barriers may be crossed easily; at low temperatures, the system is generally constrained to local minima. However, recent studies have shown that GE simulations do not yield converged equilibrium sampling much faster than standard constant temperature MD if the phenomena of interest are non-Arrhenius (11,12,(15)(16)(17)(18)(19)(20).…”

“…At high temperatures, energetic barriers may be crossed easily; at low temperatures, the system is generally constrained to local minima. However, recent studies have shown that GE simulations do not yield converged equilibrium sampling much faster than standard constant temperature MD if the phenomena of interest are non-Arrhenius (11,12,(15)(16)(17)(18)(19)(20).For example, Zuckerman and Lyman (17) used the Arrhenius equation to argue that the maximum efficiency gain of GE simulations is no more than an order of magnitude at physiological temperatures, and Zheng et al (18,19) used a kinetic network model to show that there is an optimal temperature for non-Arrhenius folding kinetics, and any time spent above this temperature will decrease the efficiency of GE simulations. This lack of improvement is the result of the interplay between energy and entropy.…”

“…Generalized ensemble (GE) algorithms, such as the replica exchange method (REM), or parallel tempering (1,2) and simulated tempering (ST) (3,4), are popular approaches for studying biomolecular folding (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15). They attempt to overcome the sampling problem by inducing a random walk in temperature space while maintaining canonical sampling at each temperature.…”