A Complete Multiscale Modelling Approach for Polymer–Clay Nanocomposites

We present an innovative, multiscale computational approach to probe the behaviour of polymer–clay nanocomposites (PCNs). Our modeling recipe is based on 1) quantum/force‐field‐based atomistic simulation to derive interaction energies among all system components; 2) mapping of these values onto mesoscopic bead–field (MBF) hybrid‐method parameters; 3) mesoscopic simulations to determine system density distributions and morphologies (i.e., intercalated versus exfoliated); and 4) simulations at finite‐element levels to calculate the relative macroscopic properties. The entire computational procedure has been applied to two well‐known PCN systems, namely Nylon 6/Cloisite 20A and Nylon 6/Cloisite 30B, as test materials, and their mechanical properties were predicted in excellent agreement with the available experimental data. Importantly, our methodology is a truly bottom‐up approach, and no “learning from experiment” was needed in any step of the entire procedure.     

Kinetic theory of binary nucleation based on a first passage time analysis

The binary classical nucleation theory (BCNT) is based on the Gibbsian thermodynamics and applies the macroscopic concept of surface tension to nanosize clusters. This leads to severe inconsistencies and large discrepancies between theoretical predictions and experimental results regarding the nucleation rate. We present an alternative approach to the kinetics of binary nucleation which avoids the use of classical thermodynamics for clusters. The new approach is an extension to binary mixtures of the kinetic theory previously developed by Narsimhan and Ruckenstein and Ruckenstein and Nowakowski [J. Colloid Interface Sci. 128, 549 (1989); 137, 583 (1990)] for unary nucleation which is based on molecular interactions and in which the rate of emission of molecules from a cluster is determined via a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution of a "surface" molecule moving in a potential field created by the cluster. The starting master equation is a Fokker-Planck equation for the probability distribution of a surface molecule with respect to its phase coordinates. Owing to the hierarchy of characteristic time scales in the evolution of the molecule, this equation can be reduced to the Smoluchowski equation for the distribution function involving only the spatial coordinates. The new theory is combined with density functional theory methods to determine the density profiles. This is essential for nucleation in binary systems particularly when one of the components is surface active. Knowing these profiles, one can determine the potential fields created by the cluster, its rate of emission of molecules, and the nucleation rate more accurately than by using the uniform density approximation. The new theory is illustrated by numerical calculations for a model binary mixture of Lennard-Jones monomers and rigidly bonded dimers of Lennard-Jones atoms. The amphiphilic character of the dimer component (i.e., its surface activity) is induced by the asymmetry in the interaction between a monomer and the two different sites of a dimer. The inconsistencies of the BCNT are avoided in the new theory.     

Fluctuating hydrodynamics for multiscale modeling and simulation: Energy and heat transfer in molecular fluids

This work illustrates that fluctuating hydrodynamics (FHD) simulations can be used to capture the thermodynamic and hydrodynamic responses of molecular fluids at the nanoscale, including those associated with energy and heat transfer. Using all-atom molecular dynamics (MD) trajectories as the reference data, the atomistic coordinates of each snapshot are mapped onto mass, momentum, and energy density fields on Eulerian grids to generate a corresponding field trajectory. The molecular length-scale associated with finite molecule size is explicitly imposed during this coarse-graining by requiring that the variances of density fields scale inversely with the grid volume. From the fluctuations of field variables, the response functions and transport coefficients encoded in the all-atom MD trajectory are computed. By using the extracted fluid properties in FHD simulations, we show that the fluctuations and relaxation of hydrodynamic fields quantitatively match with those observed in the reference all-atom MD trajectory, hence establishing compatibility between the atomistic and field representations. We also show that inclusion of energy transfer in the FHD equations can more accurately capture the thermodynamic and hydrodynamic responses of molecular fluids. The results indicate that the proposed MD-to-FHD mapping with explicit consideration of finite molecule size provides a robust framework for coarse-graining the solution phase of complex molecular systems.     

Multiscale coarse graining of liquid-state systems

A methodology is described to systematically derive coarse-grained (CG) force fields for molecular liquids from the underlying atomistic-scale forces. The coarse graining of an interparticle force field is accomplished by the application of a force-matching method to the trajectories and forces obtained from the atomistic trajectory and force data for the CG sites of the targeted system. The CG sites can be associated with the centers of mass of atomic groups because of the simplicity in the evaluation of forces acting on these sites from the atomistic data. The resulting system is called a multiscale coarse-grained (MS-CG) representation. The MS-CG method for liquids is applied here to water and methanol. For both liquids one-site and two-site CG representations without an explicit treatment of the long-ranged electrostatics have been derived. In addition, for water a two-site model having the explicit long-ranged electrostatics has been developed. To improve the thermodynamic properties (e.g., pressure and density) for the MS-CG models, the constraint for the instantaneous virial was included into the force-match procedure. The performance of the resulting models was evaluated against the underlying atomistic simulations and experiment. In contrast with existing approaches for coarse graining of liquid systems, the MS-CG approach is general, relies only on the interatomic interactions in the reference atomistic system.     

Characterization and quantification of the role of coherence in ultrafast quantum biological experiments using quantum master equations,atomistic simulations,and quantum process tomography

Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.     

Collision of a long DNA molecule with an isolated nanowire

We provide an experimental test of the universal behavior arising in simulations of the electrophoretic collision of a long DNA molecule with an isolated, thin post. Our experiments take advantage of a robust protocol to embed matrices of circa 100 nm radius ZnO nanowires in a microfluidic channel. The density and height of the nanowires are easily controlled by the seeding and growth conditions. Single-molecule videomicroscopy of λ-DNA electrophoresis in a sparse nanowire array shows that the average holdup time decays exponentially with the impact parameter, in agreement with simulations. Only at the largest electric field studied here does the hooking probability approach that for an infinitesimally thin post.     

Strategies for multiscale modeling and simulation of organic materials: polymers and biopolymers

Advances in theory and methods are making it practical to consider fully first principles (de novo) predictions of structures, properties and processes for organic materials. However, despite the progress there remains an enormous challenge in bridging the vast range of distances and time scales between de novo atomistic simulations and the quantitative continuum models for the macroscopic systems essential in industrial design and operations. Recent advances relevant to such developments include: quantum chemistry including continuum solvation and force field embedding, de novo force fields to describe phase transitions, molecular dynamics (MD) including continuum solvent, non equilibrium MD for rheology and thermal conductivity and mesoscale simulations. To provide some flavor for the opportunities we will illustrate some of the progress and challenges by summarizing some recent developments in methods and their applications to polymers and biopolymers. Four different topics will be covered: (1) hierarchical modeling approach applied to modeling olfactory receptors, (2) stabilization of leucine zipper coils by introduction of trifluoroleucine, (3) modeling response of polymers sensors for electronic nose, and (4) diffusion of gases in amorphous polymers.     

A multiscale coarse-graining method for biomolecular systems

A new approach is presented for obtaining coarse-grained (CG) force fields from fully atomistic molecular dynamics (MD) trajectories. The method is demonstrated by applying it to derive a CG model for the dimyristoylphosphatidylcholine (DMPC) lipid bilayer. The coarse-graining of the interparticle force field is accomplished by an application of a force-matching procedure to the force data obtained from an explicit atomistic MD simulation of the biomolecular system of interest. Hence, the method is termed a "multiscale" CG (MS-CG) approach in which explicit atomistic-level forces are propagated upward in scale to the coarse-grained level. The CG sites in the lipid bilayer application were associated with the centers-of-mass of atomic groups because of the simplicity in the evaluation of the forces acting on them from the atomistic data. The resulting CG lipid bilayer model is shown to accurately reproduce the structural properties of the phospholipid bilayer.     

Fluctuating hydrodynamics for multiscale simulation of inhomogeneous fluids: mapping all-atom molecular dynamics to capillary waves

We introduce a multiscale framework to simulate inhomogeneous fluids by coarse-graining an all-atom molecular dynamics (MD) trajectory onto sequential snapshots of hydrodynamic fields. We show that the field representation of an atomistic trajectory is quantitatively described by a dynamic field-theoretic model that couples hydrodynamic fluctuations with a Ginzburg-Landau free energy. For liquid-vapor interfaces of argon and water, the parameters of the field model can be adjusted to reproduce the bulk compressibility and surface tension calculated from the positions and forces of atoms in an MD simulation. These optimized parameters also enable the field model to reproduce the static and dynamic capillary wave spectra calculated from atomistic coordinates at the liquid-vapor interface. In addition, we show that a density-dependent gradient coefficient in the Ginzburg-Landau free energy enables bulk and interfacial fluctuations to be controlled separately. For water, this additional degree of freedom is necessary to capture both the bulk compressibility and surface tension emergent from the atomistic trajectory. The proposed multiscale framework illustrates that bottom-up coarse-graining and top-down phenomenology can be integrated with quantitative consistency to simulate the interfacial fluctuations in nanoscale transport processes.     

Electrostatic embedding in large-scale first principles quantum mechanical calculations on biomolecules

Biomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs self-consistently during the calculation of the density. We have implemented this scheme in a linear-scaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species.     

A physical model for the longitudinal polarizabilities of polymer chains

The aim of this work is to provide a physical model to relate the polarizability per unit cell of oligomers to that of their corresponding infinite polymer chains. For this we propose an extrapolation method for the polarizability per unit cell of oligomers by fitting them to a physical model describing the dielectric properties of polymer chains. This physical model is based on the concept of a dielectric needle in which we assume a polymer chain to be well described by a cylindrically shaped nonconducting rod with a radius much smaller than its length. With this model we study in which way the polarizability per unit cell approaches the limit of the infinite chain. We show that within this model the macroscopic contribution of the induced electric field to the macroscopic electric field vanishes in the limit of an infinite polymer chain, i.e., there is no macroscopic screening. The macroscopic electric field becomes equal to the external electric field in this limit. We show that this identification leads to a relation between the polarizability per unit cell and the electric susceptibility of the infinite polymer chain. We test our dielectric needle model on the polarizability per unit cell of oligomers of the hydrogen chain and polyacetylene obtained earlier using time-dependent current-density-functional theory in the adiabatic local-density approximation and with the Vignale-Kohn functional. We also perform calculations using the same theory on truly infinite polymer chains by employing periodic boundary conditions. We show that by extrapolating the oligomer results according to our dielectric needle model we get good agreement with our results from calculations on the corresponding infinite polymer chains.     

Relaxation of internal energy and collisional energy transfer

Using the exponential model for the collisional transition probability, it is shown that relaxation of average internal energy is a measure of bulk-average energy transfer ?ΔE?. This is a macroscopic property which is a complicated function of both time and initial excitation and is only distantly related to average energy transferred per collision ?ΔE?, a microscopic property.     

Electric field inside a "Rossky cavity" in uniformly polarized water

Electric field produced inside a solute by a uniformly polarized liquid is strongly affected by dipolar polarization of the liquid at the interface. We show, by numerical simulations, that the electric "cavity" field inside a hydrated non-polar solute does not follow the predictions of standard Maxwell's electrostatics of dielectrics. Instead, the field inside the solute tends, with increasing solute size, to the limit predicted by the Lorentz virtual cavity. The standard paradigm fails because of its reliance on the surface charge density at the dielectric interface determined by the boundary conditions of the Maxwell dielectric. The interface of a polar liquid instead carries a preferential in-plane orientation of the surface dipoles thus producing virtually no surface charge. The resulting boundary conditions for electrostatic problems differ from the traditional recipes, affecting the microscopic and macroscopic fields based on them. We show that relatively small differences in cavity fields propagate into significant differences in the dielectric constant of an ideal mixture. The slope of the dielectric increment of the mixture versus the solute concentration depends strongly on which polarization scenario at the interface is realized. A much steeper slope found in the case of Lorentz interfacial polarization also implies a higher free energy penalty for polarizing such mixtures.     

Energy transfer between polyatomic molecules. 1. Gateway modes, energy transfer quantities and energy transfer probability density functions in benzene-benzene and Ar-benzene collisions

We report collisional energy transfer, CET, quantities for polyatomic-polyatomic collisions and use excited benzene collisions with cold benzene bath, B-B, as our sample system and compare our results with the CET of excited benzene with Ar bath. We find that the gateway mode for both systems is the out-of-plane modes and that in B-B CET, vibration to vibration, V-V, is the dominant channel. Rotations play a mechanistic role in the CET but the net rotational energy transfer is small compared to V-V. The shape of the down side of the energy transfer probability density function, P(E,E'), is convex for B-B collisions and it becomes less so as the temperature increases. In Ar-B collisions, P(E,E') is concave and it becomes less so as the temperature decreases. We report average vibrational, rotational, and translational energy transferred, , as function of temperature for various initial conditions.     

Coarse-graining entropy, forces, and structures

Coarse-grained (CG) models enable highly efficient simulations of complex processes that cannot be effectively studied with more detailed models. CG models are often parameterized using either force- or structure-motivated approaches. The present work investigates parallels between these seemingly divergent approaches by examining the relative entropy and multiscale coarse-graining (MS-CG) methods. We demonstrate that both approaches can be expressed in terms of an information function that discriminates between the ensembles generated by atomistic and CG models. While it is well known that the relative entropy approach minimizes the average of this information function, the present work demonstrates that the MS-CG method minimizes the average of its gradient squared. We generalize previous results by establishing conditions for the uniqueness of structure-based potentials and identify similarities with corresponding conditions for the uniqueness of MS-CG potentials. We analyze the mapping entropy and extend the MS-CG and generalized-Yvon-Born-Green formalisms for more complex potentials. Finally, we present numerical calculations that highlight similarities and differences between structure- and force-based approaches. We demonstrate that both methods obtain identical results, not only for a complete basis set, but also for an incomplete harmonic basis set in Cartesian coordinates. However, the two methods differ when the incomplete basis set includes higher order polynomials of Cartesian coordinates or is expressed as functions of curvilinear coordinates.     

Coarse-grained computations for a micellar system

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms), and atomistic simulations of the Larson model of micelle formation. The procedure hinges on the (expected) evolution of a few slow, coarse-grained mesoscopic observables of the Monte Carlo simulation, and on (computational) time scale separation between these and the remaining "slaved," fast variables. Short bursts of appropriately initialized atomistic simulation are used to estimate the (coarse grained, deterministic) local dynamics of the evolution of the observables. These estimates are then in turn used to accelerate the evolution to computational stationarity through traditional continuum algorithms (forward Euler integration, Newton-Raphson fixed point computation). This "equation-free" framework, bypassing the derivation of explicit, closed equations for the observables (e.g., equations of state), may provide a computational bridge between direct atomistic/stochastic simulation and the analysis of its macroscopic, system-level consequences.     

Application of fluorescence polarization to enzyme assays and single nucleotide polymorphism genotyping: some recent developments

This article describes some recent developments in the field of fluorescence polarization (FP) as applied to enzyme assays and single nucleotide polymorphism (SNP) genotyping. First, we present our recent progress on the application of fluorescence polarization to high throughput screening (HTS). We show how the use of a 2-thiopyridinone-based, mixed disulfide biotinylation reagent can shorten the assay time of our recently reported kinase assay method based on thiophosphorylation and biotinylation from several hours to a few minutes. We also summarize our recent findings on a new approach for HTS of kinases, proteases and phosphatases based on the use of a cationic poly-amino acid such as polyarginine. We show how the careful selection of the polyarginine concentration and the ionic strength of the solution during the FP measurement allow one to expand the range of substrates that can be assayed. Both of these methods are valuable additions to the existing techniques for HTS. Most importantly, both of these methods can be applied to the assay of kinases without the need for any antibodies. In the area of genomics, we present some results from our studies on a new single nucleotide polymorphism typing approach based on the polymerase catalyzed extension of 3' fluorescein labeled primers. Contrary to our initial expectations, we observed that the enzymatic extension of these primers results in a significant decrease of the fluorescence polarization value. Possible explanations of this phenomenon are discussed.