Simulating replica exchange simulations of protein folding with a kinetic network model

Abstract

Replica exchange (RE) is a generalized ensemble simulation method for accelerating the exploration of free-energy landscapes, which define many challenging problems in computational biophysics, including protein folding and binding. Although temperature RE (T-RE) is a parallel simulation technique whose implementation is relatively straightforward, kinetics and the approach to equilibrium in the T-RE ensemble are very complicated; there is much to learn about how to best employ T-RE to protein folding and binding problems. We have constructed a kinetic network model for RE studies of protein folding and used this reduced model to carry out ''simulations of simulations'' to analyze how the underlying temperature dependence of the conformational kinetics and the basic parameters of RE (e.g., the number of replicas, the RE rate, and the temperature spacing) all interact to affect the number of folding transitions observed. When protein folding follows anti-Arrhenius kinetics, we observe a speed limit for the number of folding transitions observed at the low temperature of interest, which depends on the maximum of the harmonic mean of the folding and unfolding transition rates at high temperature. The results shown here for the network RE model suggest ways to improve atomic-level RE simulations such as the use of ''training'' simulations to explore some aspects of the temperature dependence for folding of the atomic-level models before performing RE studies.anti-Arrhenius ͉ Markov process ͉ parallel tempering O ne of the key challenges in the computer simulation of proteins at the atomic level is the sampling of conformational space. The efficiency of many common sampling protocols, such as Monte Carlo (MC) and molecular dynamics (MD), is limited by the need to cross high free-energy barriers between conformational states and rugged energy landscapes. One class of methods for studying equilibrium properties of quasi-ergodic systems that has received a great deal of recent attention is based on the replica exchange (RE) algorithm (1, 2) (also known as parallel tempering). To accomplish barrier crossings, RE methods simulate a series of replicas over a range of temperatures. Periodically, coordinates are exchanged by using a Metropolis criterion (3) that ensures that at any given temperature a canonical distribution is realized. RE methods, particularly REMD (4), have become very popular for the study of protein biophysics, including peptide and protein folding (5, 6), aggregation (7-9), and protein-ligand interactions (10, 11). Previous studies of protein folding appear to show a significant increase in the number of reversible folding events in REMD simulations versus conventional MD (12,13). Given the wide use of REMD, a better understanding of the RE algorithm and how it can be used most effectively for the study of protein folding and binding is of considerable interest.The effectiveness of RE methods is determined by the number of temperatures (replicas) that are simulated, their range and spacing, the rate at ...

Error and efficiency of replica exchange molecular dynamics simulations

“…In our model, REMD is described by a rate matrix for 2 N states, where N is the number of replicas. This kinetic framework is similar to the one presented recently by Zheng et al, 9 but is simplified by not keeping track of the temperature at which a certain replica started ͑which substantially reduces the number of states from N !2 N to 2 N ͒. Our kinetic framework is also related to the master-equation description of replica exchange introduced by Nadler and Hansmann.…”

“…[8][9][10][11][12][13][14][15][16][17][18][19] An important result obtained by Sindhikara et al 8 is that exchange attempts are best chosen as frequently as possible. Similar conclusions were obtained by Abraham and Gready 17 based on analyzing the autocorrelation function of the potential energy.…”

Efficiency of Adaptive Temperature-Based Replica Exchange for Sampling Large-Scale Protein Conformational Transitions

“…-11 -Theoretical studies based on two-state model systems have predicted that REMD cannot drive transitions faster than the maximal rates at all the temperatures sampled (which should occur at slightly above T m for actual proteins) 13 . Indeed, the average time per conformational transition, τ TS , is ~30 μs or more in all REMD simulations, which over twice longer than τ TS of ~14.3 μs observed in regular MD at T m (see Table 1).…”

“…The key parameters of REMD of protein simulations has been a subject of substantial research interest in recent years, examined both based on theoretical considerations [11][12][13][14][15][16] and through actual simulations of small peptides 8,[17][18][19] . These studies generally confirm that RE can enhance the conformational sampling as long as the activation enthalpies are positive.…”

“…These studies generally confirm that RE can enhance the conformational sampling as long as the activation enthalpies are positive. In particular, recent theoretical analysis 14 and kinetic network models 13,16 of RE for two-state systems have emphasized the importance of choosing a maximum temperature slightly above the temperature where the folding rate is maximal because of the anti-Arrhenius behavior of protein folding at high temperatures. Once the maximum temperature is chosen, other REMD parameters can be set to achieve effective diffusion of replicas across the temperature ladder, arguably with the smallest possible number of replicas.…”