Analysis of helix-helix interactions of bacteriorhodopsin by replica-exchange simulations

Protein structure predictions by enhanced conformational sampling methods

In this Special Festschrift Issue for the celebration of Professor Nobuhiro Gō's 80th birthday, we review enhanced conformational sampling methods for protein structure predictions. We present several generalized-ensemble algorithms such as multicanonical algorithm, replica-exchange method, etc. and parallel Monte Carlo or molecular dynamics method with genetic crossover. Examples of the results of these methods applied to the predictions of protein tertiary structures are also presented.

Observation of helix associations for insertion of a retinal molecule and distortions of helix structures in bacteriorhodopsin

We applied a newly proposed prediction method for membrane protein structures to bacteriorhodopsin that has distorted transmembrane helices in the native structure. This method uses an implicit membrane model, which restricts sampling space during folding in a membrane region, and includes helix bending. Replica-exchange simulations were performed with seven transmembrane helices only without a retinal molecule. Obtained structures were classified into clusters of similar structures, which correspond to local-minimum free energy states. The two lowest free energy states corresponded to a native-like structure with the correct empty space for retinal and a structure with this empty space filled with a helix. Previous experiments of bacteriorhodopsin suggested that association of transmembrane helices enables them to make a room for insertion of a retinal. Our results are consistent with these results. Moreover, distortions of helices in the native-like structures were successfully reproduced. In the distortions, whereas the locations of kinks for all helices were similar to those of Protein Data Bank's data, the amount of bends was more similar for helices away from the retinal than for those close to the retinal in the native structure. This suggests a hypothesis that the amino-acid sequence specifies the location of kinks in transmembrane helices and that the amount of distortions depends on the interactions with the surrounding molecules such as neighboring helices, lipids, and retinal.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics

Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.

Mass-scaling replica-exchange molecular dynamics optimizes computational resources with simpler algorithm

We develop a novel method of replica-exchange molecular dynamics (REMD) simulation, mass-scaling REMD (MSREMD) method, which improves numerical stability of simulations. In addition, the MSREMD method can also simplify a replica-exchange routine by eliminating velocity scaling. As a pilot system, a Lennard-Jones fluid is simulated with the new method. The results suggest that the MSREMD method improves the numerical stability at high temperatures compared with the conventional REMD method. For the Nosé-Hoover thermostats, we analytically demonstrate that the MSREMD simulations can reproduce completely the same trajectories of the conventional REMD ones with shorter time steps at high temperatures. Accordingly, we can easily compare the computational costs of the REMD and MSREMD simulations. We conclude that the MSREMD method decreases the instability and optimizes the computational resources with simpler algorithm.

Enhanced sampling algorithms

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.

Ab initio prediction of protein-ligand binding structures by replica-exchange umbrella sampling simulations

We have developed a prediction method for the binding structures of ligands with proteins. Our method consists of three steps. First, replica-exchange umbrella sampling simulations are performed along the distance between a putative binding site of a protein and a ligand as the reaction coordinate. Second, we obtain the potential of mean force (PMF) of the unbiased system using the weighted histogram analysis method and determine the distance that corresponds to the global minimum of PMF. Third, structures that have this global-minimum distance and energy values around the average potential energy are collected and analyzed using the principal component analysis. We predict the binding structure as the global-minimum free energy state on the free energy landscapes along the two major principal component axes. As test cases, we applied our method to five protein-ligand complex systems. Starting from the configuration in which the protein and the ligand are far away from each other in each system, our method predicted the ligand binding structures in excellent agreement with the experimental data from Protein Data Bank.