November 3 - 7, 2008
We apply random acceleration molecular dynamics (RAMD) simulation to identify potential escape routes of phenol from hydrophobic cavities in the hexameric insulin-phenol complex. We find three major pathways which provide new insights into (un)binding mechanisms for phenol. We identify several residues directly participating in escape events that serve to resolve ambiguities from recent NMR experiments. Reaction coordinates (RC) for dissociation of phenol are developed based on these exit pathways. Potentials of mean force (PMFs) along the RC for each pathway are resolved using multiple independent steered molecular dynamics (SMD) simulations with second order cumulant expansion of Jarzynski's equality. Our results for ΔF agree reasonably well within the range of known experimental and previous simulation magnitudes of this quantity. Based on structural analysis and energetic barriers for each pathway, we suggest a plausible preferred mechanism of phenolic exchange that differs from previous mechanisms. Several weakly-bound metastable states are also observed for the first time in the phenol dissociation reaction.
Charge mobilities of several derivatives of discotic liquid crystals have been determined by combining three methods into one scheme: (i) quantum chemical methods for the calculation of molecular electronic structures and reorganization energies (ii) molecular dynamics for simulation of the relative positions and orientations of molecules in a columnar mesophase, and (iii) kinetic Monte Carlo simulations and Master Equation approach to simulate charge transport. We reproduce the trends and magnitudes of mobilities as measured by pulse-radiolysis time-resolved microwave conductivity (PR-TRMC) and connect mobility directly to the microscopic morphology of the columns. Our study also shows that it is possible to understand and reproduce experimental charge transport parameters, and, in some cases, accurately predict them.
We shall discuss a multiscale modeling and simulation formalism for soft matter materials taking into account hydrodynamic interactions and thermal fluctuations. A specific motivation is the study of lipid bilayer membranes and polymer fluids taking into account microstructure degrees of freedom. The approach is based on the immersed boundary method, where hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses. The microstructures (lipid molecules / polymers) are represented by Lagrangian degrees of freedom which are coupled to an Eulerian representation of the fluid, treated at the level of continuum mechanics. Thermal fluctuations are incorporated in the formalism by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The
theoretical formalism presents a number of numerical challenges for temporal integration and spatial resolution which we shall address. This includes a time integrator for
the stiff stochastic dynamics and methods
to handle adaptive spatial discretizations of the underlying stochastic partial differential equations. We shall discuss specific applications of the approach, including
the study of lipid flow in bilayer membranes, the shear viscosity of polymer fluids, and the diffusivity of particles in complex fluids.
Asymptotic variational methods are aimed at describing the overall properties of an increasingly complicated system by computing an effective limit energy where some parameters are averaged out or greatly simplified. Such methods include Gamma-convergence and variational expansions. An extremely interesting field of application is that of discrete (lattice) systems, where the determination of the relevant parameters in the limit theory is part of the problem.
I will present an overview of the Gamma-convergence methods and a few examples that range from nonlinear discrete homogenization to expansions in fracture mechanics to size effects in thin films to variational percolation problems.
Simulation of biomembranes over length and time scales relevant
to cellular biology is not currently feasible with Molecular
Dynamics including full atomic detail. Barring an unforeseen
revolution in the computer industry, this situation will not
change for many decades. We present two coarse grained
simulation models for biomembranes that treat water implicitly
(i.e. no water molecules appear in our simulations. The
hydrophobic effect, hydrodynamics and related properties are
approximately included without simulation of solvent). These
models enable the study of systems and phenomena previously
intractable to simulation.
Concurrent multiscale methods are a powerful tool to solve with a low computational cost the local phenomena that occur at a small scale (atomic for example). Such methods are commonly used to study for example crack propagation, dislocations or nanoindentations. Even for small domain sizes, like the volume of a hundred nanometer cube, 3D atomistic simulations can lead to several hundred of millions atoms, and high performance parallel computation is naturally required. These simulations couple different parallel codes such as molecular dynamic code and elasticity code. The performance of the coupled code depends on how the data are well distributed on the processors.
Here we focus on the parallel aspects of the Bridging Method introduced by T. Belytschko and Xiao [1]. This method assumes that an atomistic model and a continuum model are coupled through an overlap zone. We present our parallel multiscale environment called LibMultiscale [2], which is based on a coupling involving a legacy parallel code for molecular dynamics (Lammps) and a parallel finite element code for continuum mechanics (LibMesh). Data redistribution and atom migration issues are discussed. Moreover 2D and 3D waves propagation simulations and a 2D penny shape crack propagation simulation are shown.
References:
[1] Coupling Methods for continuum model with molecular model. T. Belytschko, S.P. Xio. International Journal for Multiscale Computational Engineering, 11 (2003).
[2] LibMultiscale:
http://libmultiscale.gforge.inria.fr/
The final goal of multiscale methods based on domain decomposition, is
to retain full atomistic
detail only where needed (within a region of interest), while using
a coarse-grained model to introduce the essential information about the
surroundings dynamics. Importantly, the atomistic region becomes an open
sub-system
which exchanges mass, momentum and energy with the exterior. The
hydrodynamics of flux exchange can be
solved using an hybrid molecular-continuum description (hybrid MD)
[1,2]. However, molecule exchange across the hybrid interface becomes
a complicated task as one deals with more complicated molecules,
essentially owing to larger steric hindrance. A way to solve this
bottleneck is to combine hybrid MD with adaptive coarse-graining. The
set-up is like the layers of an onion [3]: the atomistic model lies at
the core, surrounded by a thermodynamically compatible coarse-grained
model, which interfaces with a continuum description of the liquid
(maybe also including hydrodynamic fluctuations). Finally, open
boundary conditions for the continuum description [4] allow evacuation
of (shear, heat or sound) waves out of the whole system, and let it
behave in a grand-canonical way, in contact with the prescribed
outer thermodynamic state.
[1] G. De Fabritiis, R. Delgado-Buscalioni and P. Coveney, Phys. Rev.
Lett.97, 134501 (2006)
[2] R .Delgado-Buscalioni and G. De Fabritiis, Phys. Rev. E 76, 036709
(2007)
[3] R. Delgado-Buscalioni, K. Kremer and M. Praprotnik, J. Chem. Phys.
128, 114110 (2008)
[4] R. Delgado-Buscalioni, A. Dejoan, Phys. Rev. E, in press, (2008)
We propose a method to evaluate the approximation of separation of variables (ASV) in Molecular Dynamics (MD) and related fields. It is based on a point-by-point evaluation of the difference between the true potential and the corresponding potential where the separation of variables is applied. The major advantage of such an approach is the fact that it requires only the analytical form of the potential as provided in most of the MD codes. We provide an application of this criterion for alkane (aliphatic) chain and compare the efficiency for two different Mapping Schemes (MS).
For the study of complex synthetic and biological molecular systems by computer
simulations one is still restricted to simple model systems or to, by far too
small, time scales. To overcome this problem multiscale techniques are being
developed. However in almost all cases, the regions treated at different level of
resolution are kept fixed and the free exchange of particles among these regions
is not allowed. I here present a robust computational method and its basic theoretical framework for an efficient and flexible coupling of the different regimes. The key feature of the method is
that it allows for a dynamical change of the number of molecular degrees of freedom during the course of the MD simulation by an on-the-fly switching between the atomistic and coarse-grained levels of detail. Thermodynamic equilibrium is preserved by interpreting the concept
of changing resolution in terms of "geometrically induced phase transition."
This leads to the introduction of a "latent heat" of switching and to the extension of the equipartition theorem to fractional (switching) degrees of freedom. The efficiency of the presented approach is illustrated in the application to several systems.
Lipid membranes exhibit a large spectrum of fascinating physical
behavior, spanning many orders of magnitude both in length- and time
scales. To cover this wide range, models of different resolution have
been developed, from atomistically resolved lipid representations to
triangulated fluid-elastic surfaces. In the intermediate regime of
about 100 nanometer length scale and micro- to millisecond time scale
mesoscopic coarse-grained models have recently covered much ground.
They can approach phenomena in which cooperativity between several
proteins are crucial, while still preserving the essence of many lipid
degrees of freedom (area density, order, tilt, composition, etc.),
whose coupling is deemed relevant in many biological situations,
notably the "raft question". I will describe in more detail a
particular solvent-free coarse-grained model recently developed by us
and illustrate its applicability to a wide variety of phenomena, among
them pore-formation by amphipathic peptides, protein aggregation on
critically mixed bilayers, and membrane vesiculation driven by
curvature-imprinting proteins.
A brief introduction into the lattice Boltzmann method is given. For
soft-matter applications, it is necessary to include thermal
fluctuations by introducing stochastic collision rules. This can be
done consistently based upon the concept of detailed balance.
Brownian particles are coupled to the lattice Boltzmann solvent
via a Stokes friction and interpolation. The Langevin equations
of the overall system satisfy both momentum conservation and
the fluctuation-dissipation theorem. The long-time mobility of the
particles differs from the input Stokes value by a contribution
from the surrounding flow. The usefulness of this method is
demonstrated by examples from polymer physics (hydrodynamic
screening of semidilute polymer solutions) and colloid physics
(electrophoresis of charge-stabilized colloidal dispersions).
I will discuss the mathematical and numerical problems involved
in coupling atomistic and continuum models as well as coupling
electronic and atomistic models,
with examples from materials and fluids.
An advantage with the framework of the heterogeneous multiscale method is that the full knowledge of an effective or macroscale equation is not required for the numerical approximation of a homogenized or averaged solution. A higher fidelity microscale model is used to supply the missing data. The efficiency is gained by only applying the microscale model in sub domains. The structure of the macroscale equation must however be known. Often it is well known from the setting of the original problem, but if it is not, new techniques are required to find the form of a relevant effective or macroscale equation.
A rich variety of spatiotemporal pattern formation and reaction front propagation has been observed
in simple reactions on metal surfaces. Modeling has typically applied mean-field reaction-diffusion
equations - ignoring the impact of reactant ordering or islanding on the reaction kinetics, and
oversimplifying the treatment of surface diffusion in mixed reactant adlayers. In 1995, we introduced
an equation-free HCLG simulation approach [Tammaro et al. J. Chem. Phys. 103 (1995) 10277]
which performs parallel KMC simulations of an atomistic lattice-gas reaction model at spatial
locations distributed across the surface, and suitably couples these to describe the effects of
macroscopic surface diffusion. Recently, we have applied this approach to realistic models for
CO-oxidation on Pd(100) and Rh(100) surfaces [Liu & Evans, Phys. Rev. B 70 (2004) 193408;
Surf. Sci. - Ertl Nobel Issue 2008]. This requires a precise treatment of the collective and "tensorial"
nature of the rapid diffusion of CO through a disordered environment of relatively immobile oxygen
[Liu & Evans, J. Chem. Phys. 125 (2006) 054709].
Polystyrene is a very abundant and industrially important polymer. We are modeling its dynamical behavior on multiple length scales and different environments. We start with pure PS where we develop a mesoscale polystyrene model based on atomistic simulations. The non-bonded effective potential is optimized against the atomistic simulation until the radial distribution function generated from the mesoscale model is consistent with the atomistic simulation. The mesoscale model allows understanding the polymer dynamics of long chains in reasonable computer time. Both models are investigated in the melt, the blend and in confined geometries. The dynamics of polystyrene melts are investigated at various chain lengths ranging from 15 to 240 monomers and the crossover to entangled dynamics is observed. As computer simulations cannot only address average properties of the system under study but also the distribution over any observable of interest we are study mixtures of polystyrene and polyisoprene by atomistic molecular dynamics and calculate correlation times for all segments in the system. We then identify fast and slow segments and can correlate the segment speed with the local neighborhood and obtain that fast segments have a surplus of the faster component in their neighborhood and vice versa. Finally we present a coarse grained model for the blend which is capable of showing phase separation.
The study of lipid structure and phase behavior at the nano scale length is of importance due to implications in understanding the role of the lipids in biochemical membrane processes. We performed a variety of simulations in homogeneous and heterogeneous membrane systems to elucidate such behaviors. Our simulations demonstrate that various coarse grained simulation models can predict different aspects of lipid phase separation and describe the change of the system under the influences of hydrophilic and hydrophobic support. The simulations are performed using models at different length scales ranging from the all atom scale to a scale where lipids are modeled by only three interaction sites. We are able to follow transformations, such as lipids phase transitions. These phase transitions are determined by analyzing parameters like area per lipid head group, the deuterium order parameter and dynamic properties. Phase diagrams of mixtures are reproduced consistent with experiments. We study the influence of a support on the systems on different length scales. We discuss the changes of the system phase behavior as well as differences between the two leaflets as induced by the support.
We present a coarse grained model for polystyrene, which is only based on properties of single chains and of systems consisting of two short oligomers. We do not need any fitting to atomistic melt simulations. The model keeps the information about the tacticity of the chains and reproduces the local distributions for bond length, angles and dihedral angles. Furthermore it is modeling statical properties of atomistic melts, e.g. radial distribution functions and internal distances.
We are interested in the rigorous justification of the passage from quantum to classical molecular dynamics in the heavy nuclei limit, i.e., when the mass ratio of elecronic to nucleonic mass tends to zero.
For positive mass ratio the (non-relativistic) quantum dynamics is described by the time-dependent linear Schroedinger equation, where the potential U is the ground state Born-Oppenheimer potential energy surface obtained by minimization over electronic states.
The classical dynamics is governed by the Liouville equation for an (appropriately defined)
time-dependent Wigner measure W, obtained as the limit (for mass ratio tending to zero)
of the Wigner functions corresponding to the wavefunctions solving the Schroedinger equation.
Since the physically correct potential U possesses Coulomb singularities due to nuclei repulsion and can have kink type singularities if eigenvalue crossings are present, its level of smoothness is far lower than that required in previous rigorous approaches and renders the justification of the Liouville equation quite difficult.
In the poster we present our results mainly concerning the case of potentials U with only Coulomb singularities and no crossings.
I will describe two coarse-grained models and a multiscale
model relevant in the context of molecular or langevin dynamics
of bulk liquids and macromolecules. We have recently achieved a
fundamental result in deriving an analytical solution for
computing the screened electrostatic interaction between
arbitrary numbers of proteins of arbitrarily complex charge
distributions, assuming they are well described by spherical
low dielectric cavities in a higher dielectric salty medium
[1]. Ultimately, smooth and systematic increase or decrease in
spatial resolution back and forth between simple dielectric
cavities and atomic level descriptions will be the centerpiece
of a multiscale scheme [2]. I will also describe a
coarse-grained model of water to investigate
thermodynamic-dynamic relationships [3] as well as a
coarse-grained protein model relevant for lengthscales and
timescales relevant for disease aggregation [4, 5].
[1] I. Lotan & T. Head-Gordon (2006). An analytical
electrostatic model for salt screened interactions between
multiple proteins J. Comp. Theo. Chem. 2, 541-555.
[2] E.-H. Yap & T.Head-Gordon (2008). In progress
[3] M.E. Johnson and T. Head-Gordon (2008). Thermodynamic
theories of liquid dynamics. submitted.
[4] E.-H. Yap, N. Lux Fawzi & T. Head-Gordon (2008). A
coarse-grained a-carbon protein model with anisotropic
hydrogen-bonding. Proteins, Struct. Func.. Bioinf. 70, 626-638.
[5] N. Lux Fawzi, E.-H. Yap, Y. Okabe, K. Kohlstedt, S. P.
Brown & T. Head-Gordon (2008). Contrasting disease and
non-disease protein aggregation. Acc. Chem. Research 41,
1037-1047.
We employ the inverse Boltzmann method to coarse-grain three commonly used three site water models (TIP3P, SPC and SPC/E) where one molecule is replaced by one coarse-grained particle with two body interactions only. The shape of the coarse-grained potentials is dominated by the ratio two lengths, which can be rationalized by the geometric constraints of the water clusters. It is shown that for simple two body potentials either the radial distribution function or the geometrical packing can be optimized. In a similar way, as needed for multiscale methods, either the pressure or the compressibility can be fitted to the all atom liquid. In total, a speedup of a factor of about 50 in computation time can be reached by this coarse-gaining procedure.
Modeling the dynamics of complex molecular systems is difficult
since physically relevant distance and time scales are
often very long. Consequently, a variety of different coarse-grained
molecular dynamics methods, which attempt to bridge gap between short
and long scales, has been developed. The talk will focus one
such method, multiparticle colision dynamics, for the computation of
the mesoscopic dynamics of molecular systems.
In particular, polymer and biopolymer dynamics in crowded molecular
environments, such as those encountered in the interior of the cell,
and the motion of self-propelled nanoparticles in solution will be considered.
The mesoscopic simulations were carried out by combining
a molecular dynamics description of the molecular with a coarse grained
description of the solvent using multiparticle collision dynamics.
I will discuss multiscale modeling of biological
membranes. The approach is based on the so-called
Inverse Monte Carlo (IMC) method and the Henderson theorem.
The specific examples [1] will include single and multicomponent
bilayers using different levels of coarse-graining, and the
improvent of accuracy of the coarse-grained models by
using a thermodynamic constraint. The motivation for
including a constraint is that the basic IMC does not
yield physically meaningful area compressibility or
surface tension in coarse-grained bilayers.
The results using cholesterol containing systems show formation of
denser transient regions, resembling lipid rafts, which is in accord with
observations from microscopic models. Finally, I will
discuss some of the advantages and disadvantages of
this approach.
References:
[1] T. Murtola, E. Falck, M. Patra, M. Karttunen, I. Vattulainen,
J. Chem. Phys. 121:9156-9165
We present the results of our recent developments of
multiscale modelling on dynamics of phase separation and
phase transition in multiphase dense polymeric systems.
Our modeling is based on density functional theories of
polymeric systems, such as the self-consistent field (SCF)
theory and the Ginzburg-Landau (GL) theory.
We combine these theories with flow dynamics, diffusion
dynamics, and the effects of external fields such as
a flow field, electric field, and confinements.
The last several years have seen a number of successful applications of continuum elasticity theory to the study of virus mechanics. Continuum modeling has been particularly effective in connection with atomic force microscopy nanoindentation experiment for understanding and predicting material properties of viral shells (capsids), and may hold promise for illuminating the physics of capsid assembly as well. I will consider the question of the limitations of continuum modeling of capsids, and discuss some examples of how conventional continuum theory is being extended or "stretched" to study multiscale features linked to the inherently discrete character of these molecular assemblies.
As revealed by techniques of structural biology and single-molecule experimentation, the capsids of viruses are some of nature's best examples of highly symmetric multiscale self-assembled structures with impressive mechanical properties of strength and elasticity. We present a novel method for creating three-dimensional finite element meshes of viral capsids from both atomic data from PDB files and electron density data from EM files. The meshes capture heterogeneous geometric features and are used in conjunction with three-dimensional continuum elasticity to simulate nanoindentation experiments as performed using atomic force microscopy. Meshes and nanoindentation simulations are presented for several viruses: Hepatitis B, CCMV, HK97, and Phi 29.
We present a possible approach for the computation of free
energies and
ensemble averages of one-dimensional coarse-grained
models in materials science. The approach is based upon a thermodynamic
limit process, and makes use of ergodic theorems and large
deviations theory. In addition to providing a possible efficient
computational strategy for ensemble averages, the approach allows for
assessing the accuracy of approximations commonly used in practice.
This is joint work with X. Blanc (University Paris 6), F. Legoll
(ENPC-INRIA) and C. Patz (Weierstrass-Institut, Berlin), submitted to
journal of nonlinear science, preprint available at
http://hal.inria.fr/inria-00282107/en/.
We consider a system described by its position X_{t}, that
evolves
according to the overdamped Langevin equation. At equilibrium,
the
statistics of X are given by the Boltzmann-Gibbs measure.
Suppose that we are only interested in some given
low-dimensional function
ξ(X) of the complete variable (the so-called reaction
coordinate). The statistics of ξ are
completely determined by the free energy associated to this
reaction coordinate. In this work, we try and design an
effective dynamics on ξ, that is
a low-dimensional dynamics which is a good approximation of
ξ(X_{t}). Using conditional expectations, we build an
original
dynamics, and discuss how it is related to the free energy
itself. Using an entropy-based approach, we are also able to
derive error estimates.
Numerical simulations will illustrate the accuracy of the
proposed dynamics.
Joint work with T. Lelievre (ENPC and INRIA).
Joint work with Victor Rühle and Denis Andrienko
(Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany).
We are working on a detailed comparison of two coarse-graining methods, force matching [1] and iterative inverse Boltzmann [2]. Force matching is generalized for coarse-graining of angle and dihedral potentials, in addition to standard bond stretching and non-bonded interactions. Some initial steps are made in order to develop solvent-free coarsegraining models for polymers in solutions for systems of a particular importance for organic electronics (soluble conjugated polymers).
1. S. Izvekov, G. Voth „Multiscale coarse graining of liquid-state systems“, J. Chem. Phys. 123, 134105 (2005)
2. W. Tschoep, K. Kremer, J. Batoulis, T. Buerger and O. Hahn, Acta Polym 49, 61 (1998)
The development of predictive and efficient atomistic-to-continuum
computational methods requires both an analysis of the
error and efficiency of its many components (coupling method,
model and mesh adaptivity, solution methods) as well as its integration
into an efficient code capable of solving problems of technological interest.
There are many choices available for the interaction between the
representative atoms of the quasicontinuum method, especially between those in the atomistic
and continuum regions, which has led to the development of a
variety of quasicontinuum approximations.
We will present criteria for determining a good choice of quasicontinuum approximation that considers trade-offs between accuracy and
algorithmic efficiency. Our criteria are based on
the effect of the coupling error on the goal of
the computation, on the
integration of the quasicontinuum approximation with model and mesh adaptivity, and
on the development of efficient iterative solution methods.
Joint Work with Marcel Arndt, Matthew Dobson, Ron Miller, Christoph Ortner, and Ellad Tadmor.
Joint work with B. Janssen and B. Wade.
Stabilized Runge-Kutta
methods (or Chebyshev-Runge-Kutta methods) are explicit methods with
extended stability domains, usually along the negative real axis. They are
easy to use (they do not require algebra routines) and they are especially
suited for MOL discretizations of two and three dimensional parabolic
partial differential equations. However, existing codes have some
difficulties in cases when the eigenvalues are very large. We have
developed a new procedure to build this kind of algorithm and derive
second-order methods with up to 320 stages, all with good stability
properties. These methods are efficient numerical integrators of very
large stiff ordinary differential equations. Applications to the numerical
solution of reaction-diffusion problems will be presented.
The topological state of entangled polymers has been analyzed
recently in terms of primitive paths which allowed obtaining reliable
predictions for the static (statistical) properties of the underlying
entanglement network for many polymeric systems. Through a systematic
methodology that first maps atomistic molecular dynamics trajectories onto
time trajectories of primitive paths and then documents primitive path
motion in terms of a one-dimensional curvilinear diffusion in a tube-like
region around the coarse-grained chain contour, we further extend these
static approaches by computing the most fundamental function of the
reptation theory, namely the probability that a segment s of the
primitive chain remains inside the initial tube after time t. Linear
viscoelastic properties, such as the zero shear rate viscosity and the
spectra of storage and loss moduli, obtained on the basis of the obtained
curves, for three different polymer melts (polyethylene,
cis-1,4-polybutadiene and trans-1,4-polybutadiene) agree remarkably well
with experimental rheological data. The new methodology is general and can
be routinely applied to analyze primitive path dynamics and chain
reptation in atomistic trajectories (accumulated through computer
simulations) of other model polymers or polymeric systems (e.g.,
bidisperse, branched, grafted, etc); it is thus believed to be
particularly useful in future theoretical developments of more accurate
tube theories for entangled systems.
In soft, coarse-grained models for dense polymer liquids, harsh
repulsive interactions (excluded volume) between segments are
replaced by soft repulsive interactions, which are sufficient to suppress
density fluctuations. These models allow to efficiently study polymer
melts with an experimentally relevant invariant degree of polymerization
by computer simulation. Two topics will be discussed:
(i) The calculation of free energies in self-assembling systems will be
illustrated by studying the interface free energy of two lamellar grains
of a symmetric diblock copolymer melt with perpendicular orientation
(T-junction).
(ii) The softness of the segmental interactions in coarse-grained models
does not guarantee non-crossability of the molecules during the course of
their motion. The effect of these topological constraints, which lead to
reptation dynamics in dense melts of long flexible molecules, can be mimicked
by slip-links and application of slip-links to the single-chain dynamics in
the disordered and lamellar phase will be discussed.
Coarse-grained (CG) models provide a promising computational tool for investigating slow complex processes that cannot be adequately studied using more detailed models. However, unless the CG model is consistent with an accurate high-resolution model, the results of CG modeling may be misleading. The present talk describes a statistical mechanical framework that provides a rigorous “multiscale bridge” connecting models with different resolution. In particular, this framework provides a formal definition of consistency and a systematic computational methodology for constructing a coarse-grained (CG) model that is consistent with a particular atomistic model. The cornerstone of this approach is a variational principle for calculating a many-body potential of mean force, which is the appropriate potential for such a consistent CG model. The multiscale coarse-graining method employs this variational principle by numerically calculating the projection of the atomistic force field onto the subspace of CG force fields spanned by a given set of basis vectors. Because typical CG force field basis vectors correspond to correlated molecular interactions, these basis vectors are not orthogonal and, consequently, many-body correlation functions must be explicitly treated. The present talk describes this development, presents numerical applications for molecular systems, and demonstrates how this framework may be employed to develop transferable CG interaction potentials.
Encoded in the strings of DNA bases that make up the genomes of living species are codes that regulate, control, and describe all sorts of biological processes. The underpinnings of these codes lie in the base sequence-dependent micromechanical properties of DNA, which determine the degree to which the long, threadlike molecule fluctuates and how it responds to the proteins that control its processing and govern its packaging. In order to understand the mechanisms by which DNA base sequence and tightly bound proteins control the biophysical properties of the long, threadlike molecule, we have developed a coarse-grained model, in which the DNA base pairs are treated as rigid bodies subject to realistic, knowledge-based energy constraints, and computational techniques to determine the minimum-energy configurations, intrinsic dynamics, and looping/cyclization propensities of these molecules. The presentation will highlight some of the unique, sequence-dependent spatial information that has been gleaned from analyses of the high-resolution structures of DNA and its complexes with other molecules and illustrate how this information can be used to gain new insights into sequence-dependent DNA polymeric behavior.
I will describe how to model the properties of non-ideal fluids using
effective, soft, many body potentials.
Although they are not derived from a microscopic systematic procedure, it is
possible to understand their properties from a systematic saddle point expansion.
Such an approach makes it possible to derive their equilibrium thermodynamic and
structural features, opening the possibility to relate the effective parameters
characterizing the soft potentials with their collective properties.
I will also describe how such many body potentials can be used to analyze the
properties of complex fluids out of equilibrium.
We have systematically developed a set of coarse-grained potentials able to describe a system of spherical monomers solved in tetrahedral molecules. The potentials are able to reproduce the basic structure and thermodynamics of the original mixture over a wide range of concentrations, and have been successfully tested in the Adaptive Resolution Scheme (AdResS), showing a symmetric behavior between the explicit and coarse-grained descriptions.
Many multiscale algorithms focus on the bulk. The rapid changes in composition and properties at interfaces between materials make them more challenging. The talk will address three strategies to incorporating interfacial behavior. The first section considers interfaces between a solid and a binary fluid mixture. Molecular simulations of binary fluid mixtures are fit to general flow boundary conditions for mesoscopic and sharp interface continuum models. Strong, counterintuitive flows are found, including plug flow with no driving pressure and Couette flow between stationary walls. The results can be described in terms of a slip velocity composed of three contributions that are proportional to the shear stress, the surface stress gradient and the concentration gradient. The second section discusses fits of fluid-fluid interface simulations to commonly used phase-field models. Fits to simulations of single phase behavior predict the interfacial tension and other properties. The surprising feature is that the prefactor of gradient squared terms in density is negative. The instability associated with this is cut off by the discreteness of atomic structure rather than higher order gradient terms. The third section of the talk describes hybrid atomistic/continuum models that retain an atomistic treatment of the interface, while using a continuum model for the bulk.
A combination of methods is used to study charge transport in polypyrrole melts. First, the OPLS atomistic force field is refined using first-principles calculations. Amorphous and partially ordered melts are then generated with the help of this force-field. Finally, the charge mobility is calculated within the temperature activated hopping picture for charge transport [1].
[1] J. Kirkpatrick, V. Marcon, J. Nelson, K. Kremer, D. Andrienko, Phys. Rev. Lett. 98, 227402 (2007)
When we consider wave propagation in random media in the case when the
wave length is finite, scattering effects must be accounted for and the
effective dielectric coefficient is no longer a constant, but a spatially
dependent function. We obtain a bound on the spatial variations of the effective
permittivity that depends on the maximum volume of the inhomogeneities and the
contrast of the medium. A related optimization problem of maximizing the spatial
average of the effective dielectric coefficient with respect to the spatial
probability density function is presented. The dependence of the effective
dielectric coefficient on the contrast of the medium is also investigated and an
approximation formula is derived.
Multipronged approaches have recently gained interest for tackling structural problems related to large biological complexes. Structural dynamical information is often obtained by low-resolution experimental techniques, such as Cryo Electron Microscopy (cryo-EM), Small Angle X-ray Scattering (SAXS) and Fluorescence Resonance Energy Transfer (FRET). Each of these techniques offers different advantages and meet with different pitfalls, artifacts and limitations. Therefore a more accurate description could be obtained if all pieces of experimental data were taken together to annotate conformational states.
To achieve this goal we will present our current developments of multi-resolution/multi-scale computational tools to interpret conformational changes of biological molecules based on cryo-EM, SAXS or distance constraints. Normal Mode Analysis or Molecular Dynamics simulations are used to deform, in a physical manner, X-ray structures to fit low-resolution data. Using simulated data, we will show that such approaches are successful to predict structures in the range of 2~3 Å resolution.
Molecular Dynamics (MD) on Graphic Processing Units (GPUs) provide
spectacular advantages: an unexpensive GPU (less than 500$) provides the equivalent computer
power of a 44 core cluster. This poster will introduce HOOMD, our new General purpose MD
code, as well as describe the challenges involved in GPU programming. It will also show the very easy to use
scripting system developed directed to the end user, so that it can make full use of HOOMD without having to learn about
GPU programming. As it will become clear in the poster, HOOMD is particularly suited for coarse-grained MD.
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model immiscible binary mixtures. Excluded volume interactions between the two components are modeled by stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are conserved locally, and entropically driven phase separation occurs for high collision rates. An explicit expression for the equation of state is derived, and the concentration dependence of the bulk free energy is shown to be the same as that of the Widom-Rowlinson model. Analytic results for the phase diagram are in excellent agreement with simulation data. Results for the line tension obtained from the analysis of the capillary wave spectrum of a droplet agree with measurements based on the Laplace's equation. The dispersion relation for the capillary waves is derived and compared with the numerical measurements of the time correlations of the radial fluctuations in the damped and over-damped limits. The introduction of "amphiphilic" dimers makes it possible to model the phase behavior of ternary surfactant mixtures.
It is now known that one can use level set description to accurately capture multi-phases in computation of high frequency waves. In this paper, we develop a Bloch band based level set method for computing the semi-classical limit of Schrdinger equations in periodic media. For the underlying equation subject to a highly oscillatory initial data a hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. We evolve a level set description to capture multi-valued solutions to the band WKB system, and then evaluate total position density over a sample set of bands. A superposition of band densities is established over all bands and solution branches when away from caustic points. Numerical results with different number of bands are provided to demonstrate the good quality of the method.