Replica exchange with solute tempering: A method for sampling biological systems in explicit water

Abstract

An innovative replica exchange (parallel tempering) method called replica exchange with solute tempering (REST) for the efficient sampling of aqueous protein solutions is presented here. The method bypasses the poor scaling with system size of standard replica exchange and thus reduces the number of replicas (parallel processes) that must be used. 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, REST is compared with standard replica exchange for an alanine dipeptide molecule in water. The comparisons confirm that REST greatly reduces the number of CPUs required by regular replica exchange and increases the sampling efficiency. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water. molecular dynamics ͉ Monte Carlo ͉ parallel tempering ͉ protein solutions ͉ rough energy landscapes S ampling the conformation space of complex systems, such as proteins, is a notoriously difficult problem in structural biology and theoretical chemistry. The difficulty arises from the infrequent crossings of high-energy barriers between local energy minima, leading to local trapping for long times and concomitant quasi-ergodicity in the sampling. Many methods have been devised to overcome the problem of quasi-ergodicity. These methods include the multicanonical ensemble method (1-3), the simulated tempering method (4-6), and the parallel tempering or replica exchange method (REM) (7-9).The first two methods require a non-Boltzmann weight factor arrived at by iteration. For systems with rough energy landscapes, such as proteins dissolved in explicit water, obtaining the weight factor is not a trivial process. Thus, the REM has been attracting more and more attention because the standard Boltzmann weight factor can be used. By using high-temperature replicas to overcome the energy barrier, the REM has proven to be a useful method for sampling phase space (10, 11).For the standard REM, the number of replicas needed increases as O(f 1/2 ), where f is the solution's total number of degrees of freedom (12). Even for a relatively small biomolecular system consisting of one ␤-hairpin protein molecule dissolved in water (4,342 atoms in all), 64 replicas were needed to cover the temperature range between 270 and 695 K with a nonvanishing acceptance ratio for replica exchange (13). This requirement severely restricts the applicability of REM to reasonably small systems, unless one has access to a massively parallel computer.The main reason that a large number of replicas are required is that the overall Hamiltonian grows with system size. The acceptance probability for the exchange of configurations between two replicas at different temperatures is exp(⌬␤⌬E), a quantity that depends exponentially on the change in energy. For a larger system, o...

Replica Exchange with Solute Tempering: Efficiency in Large Scale Systems

“…The advantage of this approach is that the neighbor list of water molecules is static. Hence, it may compare favorably with our earlier suggestion 8 to include the first few solvation shells of water around the protein in the central group. Which of the two approaches will prevail remains to be seen.…”

“…8 However, this implementation of REST is very inefficient on two larger systems, a solvated β-hairpin and a solvated TrpCage. We attribute the poor performance of this implementation of REST to the removal of the full water self-interaction energy from the replica exchange acceptance criterion.…”

“…This is relevant for systems where the average structural energies of folded (F) and unfolded (U) protein conformations are vastly different at neighboring temperatures, that is, Δβ|〈E pp + E pw 〉 U,n − 〈E pp + E pw 〉 F,m | ≫ 1. While E ww may reduce Δ nm somewhat, as described above, it is often the fluctuations in the water self-interaction energy that make exchanges between energetically disparate conformations possible, that is, (3) To counter the poor scaling of the REM with system size, we recently introduced a new version 8 of the REM, called REST. In this more general Hamiltonian replica exchange method, 7 we modified the potential energy surface according to (4) where p denotes the central group, w the bath, and β m = 1/(kT m ).…”

Conformational flexibility of N-glycans in solution studied by REMD simulations

“…The application of the REMD method to larger protein-glycan systems requires a large number of replicas. There have been several attempts to reduce the number of replicas, such as using REMD with a hybrid explicit/implicit solvation model (Okur et al 2006), solute tempering (Liu et al 2005), and REMD coupled to a high-temperature structure reservoir (Okur et al 2007). Such methods and further methodological developments could lead to accurate free-energy calculations of protein-glycan binding, and help explore the relationship between the flexibility of glycans and their specific recognition.…”

ORAC: A molecular dynamics simulation program to explore free energy surfaces in biomolecular systems at the atomistic level

“…Unlike standard implementation of the solute tempering techniques, 27 the "solute" can be any portion of the system. The solute can be freely defined as the portion of the system that is strongly coupled to the relevant coordinates for the process under study, minimizing the number of degrees of freedom involved in the replica exchanges.…”