322 research outputs found
Bayesian ensemble refinement by replica simulations and reweighting
We describe different Bayesian ensemble refinement methods, examine their
interrelation, and discuss their practical application. With ensemble
refinement, the properties of dynamic and partially disordered (bio)molecular
structures can be characterized by integrating a wide range of experimental
data, including measurements of ensemble-averaged observables. We start from a
Bayesian formulation in which the posterior is a functional that ranks
different configuration space distributions. By maximizing this posterior, we
derive an optimal Bayesian ensemble distribution. For discrete configurations,
this optimal distribution is identical to that obtained by the maximum entropy
"ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble
refinement enhances the sampling of relevant configurations by imposing
restraints on averages of observables in coupled replica molecular dynamics
simulations. We show that the strength of the restraint should scale linearly
with the number of replicas to ensure convergence to the optimal Bayesian
result in the limit of infinitely many replicas. In the "Bayesian inference of
ensembles" (BioEn) method, we combine the replica and EROS approaches to
accelerate the convergence. An adaptive algorithm can be used to sample
directly from the optimal ensemble, without replicas. We discuss the
incorporation of single-molecule measurements and dynamic observables such as
relaxation parameters. The theoretical analysis of different Bayesian ensemble
refinement approaches provides a basis for practical applications and a
starting point for further investigations.Comment: Paper submitted to The Journal of Chemical Physics (15 pages, 4
figures); updated references; expanded discussions of related formalisms,
error treatment, and ensemble refinement with and without replicas; appendi
Coarse Molecular Dynamics of a Peptide Fragment: Free Energy, Kinetics, and Long-Time Dynamics Computations
We present a ``coarse molecular dynamics'' approach and apply it to studying
the kinetics and thermodynamics of a peptide fragment dissolved in water. Short
bursts of appropriately initialized simulations are used to infer the
deterministic and stochastic components of the peptide motion parametrized by
an appropriate set of coarse variables. Techniques from traditional numerical
analysis (Newton-Raphson, coarse projective integration) are thus enabled;
these techniques help analyze important features of the free-energy landscape
(coarse transition states, eigenvalues and eigenvectors, transition rates,
etc.). Reverse integration of (irreversible) expected coarse variables backward
in time can assist escape from free energy minima and trace low-dimensional
free energy surfaces. To illustrate the ``coarse molecular dynamics'' approach,
we combine multiple short (0.5-ps) replica simulations to map the free energy
surface of the ``alanine dipeptide'' in water, and to determine the ~ 1/(1000
ps) rate of interconversion between the two stable configurational basins
corresponding to the alpha-helical and extended minima.Comment: The article has been submitted to "The Journal of Chemical Physics.
Hydrodynamics of Diffusion in Lipid Membrane Simulations
By performing molecular dynamics simulations with up to 132 million
coarse-grained particles in half-micron sized boxes, we show that hydrodynamics
quantitatively explains the finite-size effects on diffusion of lipids,
proteins, and carbon nanotubes in membranes. The resulting Oseen correction
allows us to extract infinite-system diffusion coefficients and membrane
surface viscosities from membrane simulations despite the logarithmic
divergence of apparent diffusivities with increasing box width. The
hydrodynamic theory of diffusion applies also to membranes with asymmetric
leaflets and embedded proteins, and to a complex plasma-membrane mimetic
Pair diffusion, hydrodynamic interactions, and available volume in dense fluids
We calculate the pair diffusion coefficient D(r) as a function of the
distance r between two hard-sphere particles in a dense monodisperse
suspension. The distance-dependent pair diffusion coefficient describes the
hydrodynamic interactions between particles in a fluid that are central to
theories of polymer and colloid dynamics. We determine D(r) from the
propagators (Green's functions) of particle pairs obtained from discontinuous
molecular dynamics simulations. At distances exceeding 3 molecular diameters,
the calculated pair diffusion coefficients are in excellent agreement with
predictions from exact macroscopic hydrodynamic theory for large Brownian
particles suspended in a solvent bath, as well as the Oseen approximation.
However, the asymptotic 1/r distance dependence of D(r) associated with
hydrodynamic effects emerges only after the pair distance dynamics has been
followed for relatively long times, indicating non-negligible memory effects in
the pair diffusion at short times. Deviations of the calculated D(r) from the
hydrodynamic models at short distances r reflect the underlying many-body fluid
structure, and are found to be correlated to differences in the local available
volume. The procedure used here to determine the pair diffusion coefficients
can also be used for single-particle diffusion in confinement with spherical
symmetry.Comment: 6 pages, 5 figure
Ion Pair Potentials-of-Mean-Force in Water
Recent molecular simulation and integral equation results alkali-halide ion
pair potentials-of-mean-force in water are discussed. Dielectric model
calculations are implemented to check that these models produce that
characteristic structure of contact and solvent-separated minima for oppositely
charged ions in water under physiological thermodynamic conditions. Comparison
of the dielectric model results with the most current molecular level
information indicates that the dielectric model does not, however, provide an
accurate description of these potentials-of-mean-force. We note that linear
dielectric models correspond to modelistic implementations of second-order
thermodynamic perturbation theory for the excess chemical potential of a
distinguished solute molecule. Therefore, the molecular theory corresponding to
the dielectric models is second-order thermodynamic perturbation theory for
that excess chemical potential. The second-order, or fluctuation, term raises a
technical computational issue of treatment of long-ranged interactions similar
to the one which arises in calculation of the dielectric constant of the
solvent. It is contended that the most important step for further development
of dielectric models would be a separate assessment of the first-order
perturbative term (equivalently the {\it potential at zero charge} ) which
vanishes in the dielectric models but is generally nonzero. Parameterization of
radii and molecular volumes should then be based of the second-order
perturbative term alone. Illustrative initial calculations are presented and
discussed.Comment: 37 pages and 8 figures. LA-UR-93-420
Ion Sizes and Finite-Size Corrections for Ionic-Solvation Free Energies
Free energies of ionic solvation calculated from computer simulations exhibit
a strong system size dependence. We perform a finite-size analysis based on a
dielectric-continuum model with periodic boundary conditions. That analysis
results in an estimate of the Born ion size. Remarkably, the finite-size
correction applies to systems with only eight water molecules hydrating a
sodium ion and results in an estimate of the Born radius of sodium that agrees
with the experimental value.Comment: 2 EPS figure
Systematic errors in diffusion coefficients from long-time molecular dynamics simulations at constant pressure
In molecular dynamics simulations under periodic boundary conditions,
particle positions are typically wrapped into a reference box. For diffusion
coefficient calculations using the Einstein relation, the particle positions
need to be unwrapped. Here, we show that a widely used heuristic unwrapping
scheme is not suitable for long simulations at constant pressure. Improper
accounting for box-volume fluctuations creates, at long times, unphysical
trajectories and, in turn, grossly exaggerated diffusion coefficients. We
propose an alternative unwrapping scheme that resolves this issue. At each time
step, we add the minimal displacement vector according to periodic boundary
conditions for the instantaneous box geometry. Here and in a companion paper
[J. Chem. Phys. XXX, YYYYY (2020)], we apply the new unwrapping scheme to
extensive molecular dynamics and Brownian dynamics simulation data. We provide
practitioners with a formula to assess if and by how much earlier results might
have been affected by the widely used heuristic unwrapping scheme.Comment: 6 pages, 5 figures. The following article has been accepted for
publication at The Journal of Chemical Physic
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