Multiscale coupling of mesoscopic- and atomistic-level lipid bilayer simulations

A multiscale method is presented to bridge between the atomistic and mesoscopic membrane systems. The atomistic model in this case is the united atom dimyristoylphosphatidylcholine membrane system, although the method is completely general. Atomistic molecular dynamics provides the expansion modulus which is used to parametrize a mesoscopic elastic membrane model. The resulting elastic membrane model, including explicit mesoscopic solvent, shows appropriate static and dynamic undulation behaviors. Large membranes of approximately 100 nm in length can then be easily simulated using the mesoscopic membrane system. The critical feedback from the mesoscopic system back down to the atomistic-scale system is accomplished by bridging the stress (or surface tension) of a small region in the mesoscopic membrane to the corresponding atomistic membrane system. Because of long length-scale modes of membranes such as undulation and buckling, the local tension responds differently from the frame tension, when subjected to external perturbations. The effect of these membrane modes is shown for the stress response of a local membrane region and therefore the atomistic membrane system. In addition, certain equilibrium static and dynamic properties of stand-alone and multiscale coupled systems are presented for several different membrane sizes. Although static properties such as two-dimensional pair-correlation function and order parameters show no noticeable discrepancy for the different systems, lipid self-diffusion and the rotational relaxation of lipid dipoles have a strong dependence on the membrane size (or long-wavelength membrane motions), which is properly modeled by the present multiscale method.     

Multiscale modeling of solvent extraction and the choice of reference state: Mesoscopic modeling as a bridge between nanoscale and chemical engineering

This article highlights current paradigms and challenges in modeling of lanthanides and actinides solvent extraction by lipophilic extractants. Within the multiscale approach, complex phenomena that occur in solvent systems can be rationalized at different length scales. Strengths and drawbacks of quantum and classical simulations, as well as mesoscopic modeling, are presented. In the multiscale modeling, the definition of standard states is of paramount importance because it dictates the amount of collective effects included within calculations. Mesoscopic modeling of the transfer and the aggregation free energies can be used to successfully predict properties of extraction systems at phenomenological scale and to assist chemical engineering of separation industry.     

Simulations of self-assembling systems

The previous focus on the thermodynamics of self-assembly of surfactants in solution through simulations is now being expanded to include phenomena in the fluid dynamic regime. This expansion implies that a formal edifice must be built to link molecular dynamics smoothly to mesoscopic and macroscopic length and time scales. We summarize and comment on recent trends in this area along with new results based on classical approaches. The latter include molecular dynamics as well as off-lattice Monte Carlo simulations and lattice-based Guggenheim-type models.     

Length scales in heterogeneous polymers from solid state NMR

New methods for probing structure and dynamics of heterogeneous polymers by multidimensional nuclear magnetic resonance (NMR) are described. On the molecular level high resolution multiple quantum spectroscopy of solids probes connectivities of different functional groups on length scales below 1 nm. On a mesoscopic scale NMR spin diffusion techniques probe phase separation and interfacial effects in polymer blends and block copolymers. On a macroscopic scale NMR imaging techniques allow to spatially resolve differences in order and mobility in the necking region or in shearbands of deformed polymers. The techniques are illustrated with amorphous polymers, elastomers, and core-shell systems.     

Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules

While lattice kinetic Monte Carlo (KMC) methods provide insight into numerous complex physical systems governed by interatomic interactions, they are limited to relatively short length and time scales. Recently introduced coarse-grained Monte Carlo (CGMC) simulations can reach much larger length and time scales at considerably lower computational cost. In this paper we extend the CGMC methods to spatially adaptive meshes for the case of surface diffusion (canonical ensemble). We introduce a systematic methodology to derive the transition probabilities for the coarse-grained diffusion process that ensure the correct dynamics and noise, give the correct continuum mesoscopic equations, and satisfy detailed balance. Substantial savings in CPU time are demonstrated compared to microscopic KMC while retaining high accuracy.     

Multiscale modelling of mesoscopic phenomena triggered by quantum events: light-driven azo-materials and beyond

The macroscopic functionality of soft (bio-)materials is often triggered by quantum-mechanical events which are highly local in space and time. In order to arrive at the resulting macroscopically observable phenomena, many orders of magnitude need to be bridged on both the time and the length scale. In the present paper, we first introduce a range of simulation methods at different scales as well as theoretical approaches to form bridges between them. We then outline a strategy to develop an adaptive multiscale simulation approach which connects the quantum to the mesoscopic level by bringing together ab initio molecular dynamics (QM), classical (force field) molecular dynamics (MM), and coarse grained (CG) simulation techniques. With a multitude of photoactive materials in mind, we apply our methodology to a prototypical test case-light-induced phase transitions in a liquid crystal containing the azobenzene photoswitch.     

Scale-Hopping in Computer Simulations of Polymers

Polymer simulations can be performed at many different length scales by using techniques ranging from quantum chemistry to finite element via a hierarchy of coarser and coarser particle or field-based methods. Recent years have seen many efforts to connect simulations at different levels to 1) indirectly predict large-scale properties starting from fundamental models and 2) to accelerate the equilibration at more fundamental levels via the detour of coarse-grained levels. It is the purpose of the present synopsis to review some of the recent methodological advances concerning the systematic and, where available, automatic bridging between different levels of polymer simulation.     

Constant-pressure simulations with dissipative particle dynamics

Dissipative particle dynamics (DPD) is a mesoscopic simulation method for studying hydrodynamic behavior of complex fluids. Ideally, a mesoscopic model should correctly represent the thermodynamic and hydrodynamic properties of a real system beyond certain length and time scales. Traditionally defined DPD quite successfully mimics hydrodynamics but is not flexible enough to accurately describe the thermodynamics of a real system. The so-called multibody DPD (MDPD) is a pragmatic extension of the classical DPD that allows one to prescribe the thermodynamic behavior of a system with only a small performance impact. In an earlier paper [S. Y. Trofimov, E. L. F. Nies, and M. A. J. Michels, J. Chem. Phys. 117, 9383 (2002)] we much improved the accuracy of the MDPD model for strongly nonideal systems, which are of most practical interest. The ability to correctly reproduce the equation of state of realistic systems in turn makes simulations at constant pressure sensible and useful. This situation of constant-pressure conditions is very common in experimental studies of (soft) condensed matter but has so far remained unexplored with the traditional DPD. Here, as a proof of concept, we integrate a modified version of the Andersen barostat into our improved MDPD model and make an evaluation of the performance of the new model on a set of single- and multicomponent systems. The modification of the barostat suppresses the "unphysical" volume oscillations after a sudden pressure change and simplifies the equilibration of the system.     

Nematic phase transition and texture dynamics

ABSTRACT

Research advances over the past decade in the areas of nematic phase transition and texture dynamics are reviewed. Research studies applying theoretical techniques able to resolve the length and time scales inherent to liquid crystal (LC) dynamics are focused on: coarse-grained molecular dynamics and continuum mechanics. The focus on LC dynamics is due to their importance in both fundamental and technological processes involving complex LC textures and texture transitions. Meta-stable textures frequently occur in soft matter systems, thus knowledge of LC textures that result in free energy minima for a specific system is not sufficient to characterise its behaviour. Resolution of dynamics enables researchers to predict with more accuracy observable LC textures and texture transitions. As is reflected in the reviewed research, LC dynamics simulations have enabled both validation of simulations with existing experimental observations and predictive results, which augment direct experimentation. While the outlook is positive as a result of this, several key challenges stymie further progress: (i) the availability of validated open-source software implementing nematic dynamics simulation methods, (ii) development of suitable visualisation and characterisation methods for transient three-dimensional LC textures, and (iii) inclusion of thermal fluctuations in nematic dynamics models.     

Inhomogeneous multiscale dynamics in harmonic lattices

We use projection operators to address the coarse-grained multiscale problem in harmonic systems. Stochastic equations of motion for the coarse-grained variables, with an inhomogeneous level of coarse graining in both time and space, are presented. In contrast to previous approaches that typically start with thermodynamic averages, the key element of our approach is the use of a projection matrix chosen both for its physical appeal in analogy to mechanical stability theory and for its algebraic properties. We show that thermodynamic equilibrium can be recovered and obtain the fluctuation dissipation theorem a posteriori. All system-specific information can be computed from a series of feasible molecular dynamics simulations. We recover previous results in the literature and show how this approach can be used to extend the quasicontinuum approach and comment on implications for dissipative particle dynamics type of methods. Contrary to what is assumed in the latter models, the stochastic process of all coarse-grained variables is not necessarily Markovian, even though the variables are slow. Our approach is applicable to any system in which the coarse-grained regions are linear. As an example, we apply it to the dynamics of a single mesoscopic particle in the infinite one-dimensional harmonic chain.     

On the study of nonlinear dynamics of complex chemical reaction systems

When driven far from equilibrium,nonlinear chemical reactions often show a variety of self-organization behavior,including chemical oscillations,waves,chaos and patterns[1].Recently,the study of such nonlinear phenomena in‘complex’systems,such as the li…     

A Bayesian method for construction of Markov models to describe dynamics on various time-scales

The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time-scales.     

Multiscale modeling of proteins interaction with functionalized nanoparticles

Understanding protein interactions with inorganic nanoparticle is central to the rational design of new tools in biomaterial sciences, nanobiotechnology, and nanomedicine. Theoretical modeling and simulations provide complementary approaches for experimental studies and are applied for exploring protein–particle surface-binding mechanisms, the determinants of binding specificity toward different surfaces, and the thermodynamics and kinetics of adsorption. The use of multiscale approaches is inevitable because the adsorption events extend over a wide range of time and length scales, which require the system to be addressed at different resolution levels. Here, we review the latest advances in coarse-grained treatment of these systems, usually addressed using residue-level resolution for proteins and mesoscale for the nanoparticle. We illustrate the parameterization strategies, focusing on those combining experimental and atomistic simulation data, within the theoretical framework of multiscale approaches.     

Porous media: A model system for the physics of disorder

We discuss several examples of applications of soft matter and statistical physics to various problems related to porous and fractured media. The structure of porous media often displays multiple scale features which can be analysed by neutron diffraction or electron microscopy and can be approached by fractal models. Such characteristics are also observed on the surface of natural fractures.The relation between various transport parameters such as permeability or conductivity introduce characteristic microscopic length scales which can sometimes be independently determined. In some cases, if the porous medium get clogged or if the number of flow channels or fractures is low enough so that threshold effects appear which can be analysed in terms of percolation models. Disorder physics approaches are particularly useful to analyse non miscible diphasic flows in some cases in which multiscale heterogeneities of the fluid mixture composition appear. This is for instance the case for very slow non wetting invasions and of the fast injection of a low viscosity fluid : these processes can be described respectively by the “invasion percolation” and the “diffusion limited aggregation” models. Finally tracer dispersion provides an application of random walk models to disordered systems : examples of the response of this measurement in partly saturated and double porosity media are presented.     

Environmental Effects in Computational Spectroscopy: Accuracy and Interpretation

Spectroscopic techniques are valuable tools for understanding the structure and dynamics of complex systems, such as biomolecules or nanomaterials. Most of the current research is devoted to the development of new experimental techniques for improving the intrinsic resolution of different spectra. However, the subtle interplay of several different effects acting at different length and time scales still makes the interpretation and analysis of such spectra a very difficult task. In this respect, computational spectroscopy is becoming a needful and versatile tool for the assignment and interpretation of experimental spectra. It is in fact possible nowadays to model with relatively high accuracy the physical–chemical properties of complex molecules in different environments, and to link spectroscopic evidence directly to the structural and dynamical properties of optically or magnetically active solvated probes. In this Review, significant steps toward the simulation of entire spectra in condensed phases are presented together with some basic aspects of computational spectroscopy, which highlight how intramolecular and intermolecular degrees of freedom influence several spectroscopic parameters.     

A multiscale model for kinetics of formation and disintegration of spherical micelles

Dynamics of self-assembly and structural transitions in surfactant systems often involve a large span of length and time scales. A comprehensive understanding of these processes requires development of models connecting phenomena taking place on different scales. In this paper, we develop a multiscale model for formation and disintegration of spherical nonionic micelles. The study is performed under the assumption that the dominant mechanism of micelle formation (disintegration) is a stepwise addition (removal) of single monomers to (from) a surfactant aggregate. Different scales of these processes are investigated using a combination of coarse-grained molecular dynamics simulations, analytical and numerical solution of stochastic differential equations, and a numerical solution of kinetic equations. The removal of a surfactant from an aggregate is modeled by a Langevin equation for a single reaction coordinate, the distance between the centers of mass of the surfactant and the aggregate, with parameters obtained from a series of constrained molecular dynamics simulations. We demonstrate that the reverse process of addition of a surfactant molecule to an aggregate involves at least two additional degrees of freedom, orientation of the surfactant molecule and micellar microstructure. These additional degrees of freedom play an active role in the monomer addition process and neglecting their contribution leads to qualitative discrepancies in predicted surfactant addition rates. We propose a stochastic model for the monomer addition which takes the two additional degrees of freedom into account and extracts the model parameters from molecular dynamics simulations. The surfactant addition rates are determined from Brownian dynamics simulations of this model. The obtained addition and removal rates are then incorporated into the kinetic model of micellar formation and disintegration.     

G protein-coupled receptors self-assemble in dynamics simulations of model bilayers

Many integral membrane proteins assemble to form oligomeric structures in biological membranes. In particular, seven-transmembrane helical G protein-coupled receptors (GPCRs) appear to self-assemble constitutively in membranes, but the mechanism and physiological role of this assembly are unknown. We developed and employed coarse-grain molecular dynamics (CGMD) models to investigate the molecular basis of how the physicochemical properties of the phospholipid bilayer membrane affect self-assembly of visual rhodopsin, a prototypical GPCR. The CGMD method is a mesoscopic simulation technique in which groups of atoms are mapped to particles on the basis of a four-to-one rule. This systematic reduction of the degrees of freedom allows for computationally efficient calculation of the structure and dynamics of molecular assemblies for larger time and length scales than accessible to atomistic models, providing here an unprecedented view of spontaneous protein assembly in biomembranes. Systems with up to 16 rhodopsin molecules at a protein-to-lipid ratio of 1:100 were simulated for time scales of up to 8 micros. The results obtained for four different phospholipid environments showed that localized adaptation of the membrane bilayer to the presence of receptors is reproducibly most pronounced near transmembrane helices 2, 4, and 7. This local membrane deformation appears to be a key factor defining the rate, extent, and orientational preference of protein-protein association. The implications of our findings are discussed within a framework of a generalized mechanism of membrane protein self-assembly.