Satoru G. Itoh

pH replica-exchange method based on discrete protonation states†

We propose a new algorithm for obtaining proton titration curves of ionizable residues. The algorithm is a pH replica‐exchange method (PHREM), which is based on the constant pH algorithm of Mongan et al. (J Comput Chem 2004;25:2038–2048). In the original replica‐exchange method, simulations of different replicas are performed at different temperatures, and the temperatures are exchanged between the replicas. In our PHREM, simulations of different replicas are performed at different pH values, and the pHs are exchanged between the replicas. The PHREM was applied to a blocked amino acid and to two protein systems (snake cardiotoxin and turkey ovomucoid third domain), in conjunction with a generalized Born implicit solvent. The performance and accuracy of this algorithm and the original constant pH method (PHMD) were compared. For a single set of simulations at different pHs, the use of PHREM yields more accurate Hill coefficients of titratable residues. By performing multiple sets of constant pH simulations started with different initial states, the accuracy of predicted pKa values and Hill coefficients obtained with PHREM and PHMD methods becomes comparable. However, the PHREM algorithm exhibits better samplings of the protonation states of titratable residues and less scatter of the titration points and thus better precision of measured pKa values and Hill coefficients. In addition, PHREM exhibits faster convergence of individual simulations than the original constant pH algorithm. Proteins 2011;

Explicit symplectic integrators of molecular dynamics algorithms for rigid-body molecules in the canonical, isobaric-isothermal, and related ensembles.

The authors propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isobaric-isothermal ensembles. They also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, they can perform a MD simulation more stably than by conventional nonsymplectic algorithms. They applied this algorithm to a TIP3P pure water system at 300 K and compared the time evolution of the Hamiltonian with those by the nonsymplectic algorithms. They found that the Hamiltonian was conserved well by the symplectic algorithm even for a time step of 4 fs. This time step is longer than typical values of 0.5-2 fs which are used by the conventional nonsymplectic algorithms.

Replica-exchange method in van der Waals radius space: overcoming steric restrictions for biomolecules.

We present a new type of the Hamiltonian replica-exchange method, where the van der Waals radius parameter and not the temperature is exchanged. By decreasing the van der Waals radii, which control spatial sizes of atoms, this Hamiltonian replica-exchange method overcomes the steric restrictions and energy barriers. Furthermore, the simulation based on this method escapes from the local-minimum free-energy states and realizes effective sampling in the conformational space. We applied this method to an alanine dipeptide in aqueous solution and showed the effectiveness of the method by comparing the results with those obtained from the conventional canonical and replica-exchange methods.

Amyloid-β(29−42) Dimer Formations Studied by a Multicanonical−Multioverlap Molecular Dynamics Simulation

Amyloid-beta peptides are known to form amyloid fibrils and are considered to play an important role in Alzheimers disease. Amyloid-beta(29-42) is a fragment of the amyloid-beta peptide and also has a tendency to form amyloid fibrils. In order to study the mechanism of amyloidogenesis of this fragment, we applied one of the generalized-ensemble algorithms, the multicanonical-multioverlap algorithm, to amyloid-beta(29-42) dimer in aqueous solution. We obtained a detailed free-energy landscape of the dimer system. From the detailed free-energy landscape, we examined monomer and dimer formations of amyloid-beta(29-42) and deduced dimerization processes, which correspond to seeding processes in the amyloidogenesis of amyloid-beta(29-42).

Theoretical studies of transition states by the multioverlap molecular dynamics methods.

The multioverlap molecular dynamics method gives a flat probability distribution in the multidimensional dihedral-angle-distance space, where the dihedral-angle distance of a configuration with respect to a reference state gives a measure for structural similarity. Hence, this method realizes a random walk among specific configurations in the multidimensional dihedral-angle-distance space at a constant temperature and explores widely in the configurational space. We applied the multioverlap molecular dynamics method to a pentapeptide, Met-enkephalin, in gas phase as a test system. Comparing the results of this method with those of the conventional canonical and multicanonical algorithms, we demonstrate its effectiveness. Furthermore, from the detailed free-energy landscape obtained from the results of the multioverlap molecular dynamics simulation, we obtain the transition state between two specific reference configurations of Met-enkephalin. We also deduce the transition pathway between the two specific reference configurations.

Amyloid Fibril Disruption by Ultrasonic Cavitation: Nonequilibrium Molecular Dynamics Simulations

We describe the disruption of amyloid fibrils of Alzheimers amyloid-β peptides by ultrasonic cavitation. For this purpose, we performed nonequilibrium all-atom molecular dynamics simulations with sinusoidal pressure and visualized the process with movies. When the pressure is negative, a bubble is formed, usually at hydrophobic residues in the transmembrane region. Most β-strands maintain their secondary structures in the bubble. When the pressure becomes positive, the bubble collapses, and water molecules crash against the hydrophilic residues in the nontransmembrane region to disrupt the amyloid. Shorter amyloids require longer sonication times for disruption because they do not have enough hydrophobic residues to serve as a nucleus to form a bubble. These results agree with experiments in which monodispersed amyloid fibrils were obtained by ultrasonication.

Hamiltonian replica-permutation method and its applications to an alanine dipeptide and amyloid-β(29–42) peptides

We propose the Hamiltonian replica‐permutation method (RPM) (or multidimensional RPM) for molecular dynamics and Monte Carlo simulations, in which parameters in the Hamiltonian are permuted among more than two replicas with the Suwa‐Todo algorithm. We apply the Coulomb RPM, which is one of realization of the Hamiltonian RPM, to an alanine dipeptide and to two amyloid‐β(29–42) molecules. The Hamiltonian RPM realizes more efficient sampling than the Hamiltonian replica‐exchange method. We illustrate the protein misfolding funnel of amyloid‐β(29–42) and reveal its dimerization pathways.

Effective sampling in the configurational space of a small peptide by the multicanonical-multioverlap algorithm

We propose a generalized-ensemble algorithm, which we refer to as the multicanonical-multioverlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the multidimensional, energy-overlap space and explores widely in the configurational space including specific configurations, where the overlap of a configuration with respect to a reference state is a measure for structural similarity. We apply the multicanonical-multioverlap molecular dynamics method to a penta peptide, Met-enkephalin, in vacuum as a test system. We also apply the multicanonical and multioverlap molecular dynamics methods to this system for the purpose of comparisons. We see that the multicanonical-multioverlap molecular dynamics method realizes effective sampling in the configurational space including specific configurations more than the other two methods. Furthermore, from the results of the multicanonical-multioverlap molecular dynamics simulation, we obtain a local-minimum state of the Met-enkephalin system.

Generalized-ensemble algorithms for molecular dynamics simulations

In complex systems with many degrees of freedom such as biomolecular systems, conventional Monte Carlo and molecular dynamics simulations in canonical ensemble or isobaric–isothermal ensemble suffer from the multiple-minima problem, resulting in entrapment in states of energy local minima. A simulation in generalized ensemble performs a random walk in specified variables and overcomes this difficulty. In this article we review the generalized-ensemble algorithms. Multicanonical algorithm is described first. In this method, a random walk in potential energy space is realized and the simulation can avoid the multiple-minima problem. We then present two new generalized-ensemble algorithms, namely multioverlap algorithm and multibaric–multithermal algorithm, which are multi-variable/multi-dimensional extensions of the multicanonical algorithm. In the former method, a random walk in overlap space is realized, and in the latter that in both potential energy space and volume space is obtained. Emphasis is laid in the description of the molecular dynamics versions of these algorithms.

Dimerization process of amyloid-β(29-42) studied by the Hamiltonian replica-permutation molecular dynamics simulations.

The amyloid-β peptides form amyloid fibrils which are associated with Alzheimers disease. Amyloid-β(29-42) is its C-terminal fragment and a critical determinant of the amyloid formation rate. This fragment forms the amyloid fibril by itself. However, the fragment conformation in the fibril has yet to be determined. The oligomerization process including the dimerization process is also still unknown. The dimerization process corresponds to an early process of the amyloidogenesis. In order to investigate the dimerization process and conformations, we applied the Hamiltonian replica-permutation method, which is a better alternative to the Hamiltonian replica-exchange method, to two amyloid-β(29-42) molecules in explicit water solvent. At the first step of the dimerization process, two amyloid-β(29-42) molecules came close to each other and had intermolecular side chain contacts. When two molecules had the intermolecular side chain contacts, the amyloid-β(29-42) tended to have intramolecular secondary structures, especially β-hairpin structures. The two molecules had intermolecular β-bridge structures by coming much closer at the second step of the dimerization process. Formation of these intermolecular β-bridge structures was induced by the β-hairpin structures. The intermolecular β-sheet structures elongated at the final step. Structures of the amyloid-β(29-42) in the monomer and dimer states are also shown with the free-energy landscapes, which were obtained by performing efficient sampling in the conformational space in our simulations.