A canonical replica exchange molecular dynamics implementation with normal pressure in each replica

Use of multistate Bennett acceptance ratio method for free-energy calculations from enhanced sampling and free-energy perturbation

Multistate Bennett acceptance ratio (MBAR) works as a method to analyze molecular dynamics (MD) simulation data after the simulations have been finished. It is widely used to estimate free-energy changes between different states and averaged properties at the states of interest. MBAR allows us to treat a wide range of states from those at different temperature/pressure to those with different model parameters. Due to the broad applicability, the MBAR equations are rather difficult to apply for free-energy calculations using different types of MD simulations including enhanced conformational sampling methods and free-energy perturbation. In this review, we first summarize the basic theory of the MBAR equations and categorize the representative usages into the following four: (i) perturbation, (ii) scaling, (iii) accumulation, and (iv) full potential energy. For each, we explain how to prepare input data using MD simulation trajectories for solving the MBAR equations. MBAR is also useful to estimate reliable free-energy differences using MD trajectories based on a semi-empirical quantum mechanics/molecular mechanics (QM/MM) model and ab initio QM/MM energy calculations on the MD snapshots. We also explain how to use the MBAR software in the GENESIS package, which we call mbar_analysis, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.

Temporally Coarse-Grained All-Atom Molecular Dynamics Achieved via Stochastic Padé Approximants

A Padé approximant scheme for realizing the discrete-time evolution of the state of a many-atom system is introduced. This temporal coarse-graining scheme accounts for the underlying Newtonian physics and avoids the need for construction of spatially coarse-grained variables. Newtonian physics is incorporated through short molecular dynamics simulations at the beginning of each of the large coarse-grained timesteps. The balance between stochastic and coherent dynamics expressed by many-atom systems is captured via incorporation of the Ito formula into a Padé approximant for the time dependence of individual atom positions over large timesteps. Since the time for a many-atom system to express a characteristic ensemble of atomic velocity fluctuations is typically short relative to the characteristic time of large-scale atomic displacements, a computationally efficient and accurate temporal coarse-graining of the atom-resolved Newtonian dynamics is formulated, denoted all-atom Padé-Ito molecular dynamics (APIMD). Evolution of the system over a time step much longer than that required for standard molecular dynamics (MD) is achieved via incorporation of information from the short MD simulations into a Padé approximant extrapolation in time. The extrapolated atomic configuration is subjected to energy minimization and, when needed, thermal equilibration so as to avoid occasional unphysical close encounters deriving from the Padé approximant extrapolation and to represent configurations appropriate for the temperature of interest. APIMD is implemented and tested via comparison with traditional MD simulations of five phenomena: (1) pertussis toxin subunit deformation, (2) structural transition in a T = 1 capsid-like structure of HPV16 L1 protein, (3) coalescence of argon nanodroplets, and structural transitions in dialanine in (4) vacuum, and (5) water. Accuracy of APIMD is demonstrated using semimicroscopic descriptors (rmsd, radius of gyration, residue-residue contact maps, and densities) and the free energy. Significant computational acceleration relative to traditional molecular dynamics is illustrated.

Gas phase dynamics, conformational transitions and spectroscopy of charged saccharides: the oxocarbenium ion, protonated anhydrogalactose and protonated methyl galactopyranoside

Protonated intermediates are postulated to be involved in the rate determining step of many sugar reactions. This paper presents a study of protonated sugar species, isolated in the gas phase, using a combination of infrared multiple photon dissociation (IRMPD) spectroscopy, classical ab initio molecular dynamics (AIMD) and quantum mechanical vibrational self-consistent field (VSCF) calculations. It provides a likely identification of the reactive intermediate oxocarbenium ion structure in a d-galactosyl system as well as the saccharide pyrolysis product anhydrogalactose (that suggests oxocarbenium ion stabilization), along with the spectrum of the protonated parent species: methyl d-galactopyranoside-H+. Its vibrational fingerprint indicates intramolecular proton sharing. Classical AIMD simulations for galactosyl oxocarbenium ions, conducted in the temperature range ∼300-350 K (using B3LYP potentials on-the-fly) reveal efficient transitions on the picosecond timescale. Multiple conformers are likely to exist under the experimental conditions and along with static VSCF calculations, they have facilitated the identification of the individual structural motifs of the galactosyl oxocarbenium ion and protonated anhydrogalactose ion conformers that contribute to the observed experimental spectra. These results demonstrate the power of experimental IRMPD spectroscopy combined with dynamics simulations and with computational spectroscopy at the anharmonic level to unravel conformer structures of protonated saccharides, and to provide information on their lifetimes.