Systematic coarse-graining of nanoparticle interactions in molecular dynamics simulation

A recently developed multiscale coarse-graining procedure [Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469] is extended to derive coarse-grained models for nanoparticles. The methodology is applied to C(60) and to carbonaceous nanoparticles produced in combustion environments. The coarse-graining of the interparticle force field is accomplished applying a force-matching procedure to data obtained from trajectories and forces from all-atom MD simulations. The CG models are shown to reproduce accurately the structural properties of the nanoparticle systems studied, while allowing for MD simulations of much larger self-assembled nanoparticle systems.     

Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel

The recently developed multiscale coarse-graining (MS-CG) method (Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469; J. Chem. Phys. 2005, 123, 134105) is used to build a mixed all-atom and coarse-grained (AA-CG) model of the gramicidin A (gA) ion channel embedded in a dimyristoylphosphatidylcholine (DMPC) lipid bilayer and water environment. In this model, the gA peptide was described in full atomistic detail, while the lipid and water molecules were described using coarse-grained representations. The atom-CG and CG-CG interactions in the mixed AA-CG model were determined using the MS-CG method. Molecular dynamics (MD) simulations were performed using the resulting AA-CG model. The results from simulations of the AA-CG model compare very favorably to those from all-atom MD simulations of the entire system. Since the MS-CG method employs a general and systematic approach to obtain effective interactions from the underlying all-atom models, the present approach to rigorously develop mixed AA-CG models has the potential to be extended to many other systems.     

Multiscale coarse-graining of ionic liquids

A recently developed multiscale coarse-graining (MS-CG) approach for obtaining coarse-grained force fields from fully atomistic molecular dynamics simulation is applied to the challenging case of the EMIM+NO3- ionic liquid. The force-matching in the MS-CG methodology is accomplished with an explicit separation of bonded and nonbonded forces. While the nonbonded forces are adopted from this force-matching approach, the bonded forces are obtained from fitting the statistical configurational data from the atomistic simulations. The many-body electronic polarizability is also successfully broken into effective pair interactions. With a virial constraint fixing the system pressure, the MS-CG models rebuild satisfactory structural and thermodynamic properties for different temperatures. The MS-CG model developed from a modest atomistic simulation is therefore suitable for simulating much larger systems, because the coarse-grained models show significant time integration efficiency. This approach is expected to be general for coarse-graining other ionic liquids, as well as many other liquid-state systems. The limitations of the present coarse-graining procedure are also discussed.     

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.     

Ab initio analysis of the structural properties of alkyl-substituted polyhedral oligomeric silsesquioxanes

Ab initio quantum mechanical calculations have been performed to establish the potentials for alkyl-substituted polyhedral oligomeric silsesquioxane (POSS) monomers RxH8-x(SiO1.5)8. More specifically, we have examined the unsubstituted POSS (SiO1.5H)8 cage as well as linear and cyclic alkyl-substituted cages where one of the terminating hydrogen atoms is replaced by a hydrocarbon group, that is, R1H7(SiO1.5)8. The results for the minimum-energy configurations indicate that the presence of the linear hydrocarbon chains and cyclic intermediates have very little effect on the structure of the POSS cage. Although the POSS monomeric cage does influence the partial charges of the first few carbon atoms covalently bound to the POSS monomer, its effect on the structural properties of the alkyl chain is small. Differences arise, however, for cyclic alkyl substitutents bound to the POSS cage due to the repulsive interactions between the POSS cage and bulkier cyclic intermediates that result upon rotation of the Si-C-C-C dihedral angles. The interatomic potentials for these rotational, or torsional, terms need to be modified slightly in order to appropriately simulate sterically hindered substitutents on the cage. Our results suggest that combining an atomistic force field independently developed to describe silsesquioxanes with an independent atomistic model developed to describe hydrocarbon chains can be used in classical molecular simulation studies of most alkyl-silsesquioxanes. This avoids the need to develop specific force fields for each substituted POSS cage studied and opens up the possibility of using molecular simulation to probe the thermodynamic and structural properties of these unique nanoscale building blocks.     

Coarse-grained force field for the nucleosome from self-consistent multiscaling

A coarse-grained simulation model for the nucleosome is developed, using a methodology modified from previous work on the ribosome. Protein residues and DNA nucleotides are represented as beads, interacting through harmonic (for neighboring) or Morse (for nonbonded) potentials. Force-field parameters were estimated by Boltzmann inversion of the corresponding radial distribution functions obtained from a 5-ns all-atom molecular dynamics (MD) simulation, and were refined to produce agreement with the all-atom MD simulation. This self-consistent multiscale approach yields a coarse-grained model that is capable of reproducing equilibrium structural properties calculated from a 50-ns all-atom MD simulation. This coarse-grained model speeds up nucleosome simulations by a factor of 10(3) and is expected to be useful in examining biologically relevant dynamical nucleosome phenomena on the microsecond timescale and beyond.     

Mesoscale model of polymer melt structure: self-consistent mapping of molecular correlations to coarse-grained potentials

Development and application of coarse-graining methods to condensed phases of macromolecules is an active area of research. Multiscale modeling of polymeric systems using coarse-graining methods presents unique challenges. Here we apply a coarse-graining method that self-consistently maps structural correlations from detailed molecular dynamics (MD) simulations of alkane oligomers onto coarse-grained potentials using a combination of MD and inverse Monte Carlo methods. Once derived, the coarse-grained potentials allow computationally efficient sampling of ensemble of conformations of significantly longer polyethylene chains. Conformational properties derived from coarse-grained simulations are in excellent agreement with experiments. The level of coarse graining provides a control over the balance of computational efficiency and retention of chemical identity of the underlying polymeric system. Challenges to extension and application of this and similar structure-based coarse-graining methods to model dynamics and phase behavior in polymeric systems are briefly discussed.     

Coarse-grained potential models for structural prediction of carbon dioxide (CO2) in confined environments

In this paper, we propose coarse-grained single-site (CGSS), wall-CO(2), and CO(2)-CO(2) interaction potential models to study the structure of carbon dioxide under confinement. The CGSS potentials are used in an empirical potential based quasi-continuum theory, EQT, to compute the center-of-mass density and potential profiles of CO(2) confined inside different size graphite slit pores. Results obtained from EQT are compared with those obtained from all-atom molecular dynamics (AA-MD) simulations, and are found to be in good agreement with each other. Though these CGSS interaction potentials are primarily developed and parameterized for EQT, they are also used to perform coarse-grained molecular dynamics (CG-MD) simulations. The results obtained from CG-MD simulations are also found to be in reasonable agreement with AA-MD simulation results.     

Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers lambda per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time tau, and the chain center of mass self-diffusion D(CM), are computed for different chain lengths at different coarse-graining factor lambda. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties.     

On Coarse-Graining by the Inverse Monte Carlo Method: Dissipative Particle Dynamics Simulations Made to a Precise Tool in Soft Matter Modeling

We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD) simulations, which are then used in coarse-grained dissipative particle dynamics (DPD) simulations. Here, the effective potentials were obtained by applying the inverse Monte Carlo method [Lyubartsev and Laaksonen, Phys. Rev. E. 52, 3730 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. In our first application of the method, the effective potentials were used in DPD simulations of aqueous NaCl solutions. With the same computational effort we were able to simulate systems of one order of magnitude larger than the MD simulations. The results from the MD and DPD simulations are in excellent agreement.     

Deriving effective mesoscale potentials from atomistic simulations

We demonstrate how an iterative method for potential inversion from distribution functions developed for simple liquid systems can be generalized to polymer systems. It uses the differences in the potentials of mean force between the distribution functions generated from a guessed potential and the true distribution functions to improve the effective potential successively. The optimization algorithm is very powerful: convergence is reached for every trial function in few iterations. As an extensive test case we coarse-grained an atomistic all-atom model of polyisoprene (PI) using a 13:1 reduction of the degrees of freedom. This procedure was performed for PI solutions as well as for a PI melt. Comparisons of the obtained force fields are drawn. They prove that it is not possible to use a single force field for different concentration regimes.     

Coarse grained protein-lipid model with application to lipoprotein particles

A coarse-grained model for molecular dynamics simulations is extended from lipids to proteins. In the framework of such models pioneered by Klein, atoms are described group-wise by beads, with the interactions between beads governed by effective potentials. The extension developed here is based on a coarse-grained lipid model developed previously by Marrink et al., although future versions will reconcile the approach taken with the systematic approach of Klein and other authors. Each amino acid of the protein is represented by two coarse-grained beads, one for the backbone (identical for all residues) and one for the side-chain (which differs depending on the residue type). The coarse-graining reduces the system size about 10-fold and allows integration time steps of 25-50 fs. The model is applied to simulations of discoidal high-density lipoprotein particles involving water, lipids, and two primarily helical proteins. These particles are an ideal test system for the extension of coarse-grained models. Our model proved to be reliable in maintaining the shape of preassembled particles and in reproducing the overall structural features of high-density lipoproteins accurately. Microsecond simulations of lipoprotein assembly revealed the formation of a protein-lipid complex in which two proteins are attached to either side of a discoidal lipid bilayer.     

Bottom-up coarse-graining of a simple graphene model: the blob picture

The coarse-graining of a simple all-atom 2D microscopic model of graphene, in terms of "blobs" described by center of mass variables, is presented. The equations of motion of the coarse-grained variables take the form of dissipative particle dynamics (DPD). The coarse-grained conservative forces and the friction of the DPD model are obtained via a bottom-up procedure from molecular dynamics (MD) simulations. The separation of timescales for blobs of 24 and 96 carbon atoms is sufficiently pronounced for the Markovian assumption, inherent to the DPD model, to provide satisfactory results. In particular, the MD velocity autocorrelation function of the blobs is well reproduced by the DPD model, provided that the effect of friction and noise is taken into account. However, DPD cross-correlations between neighbor blobs show appreciable discrepancies with respect to the MD results. Possible extensions to mend these discrepancies are briefly outlined.     

Coarse-grained molecular dynamics simulations of nanopatterning with multivalent inks

A coarse-grained molecular dynamics (MD) model is developed to study the multivalent, or multisite, binding of small functionalized dendrimer molecules to beta-cyclodextrin-terminated self-assembled monolayers, the so-called "molecular printboards" used to print "ink" molecules on surfaces with a high degree of positional control and specificity. Some current and future bionanotechnology applications are in the creation of nanoparticle assemblies, directed protein assembly, platforms for biosensing, and cell:surface attachment. The coarse-grained model allows us to probe up to microsecond timescales and model ink diffusion, crucial for the application of the printboard in, for example, medical diagnostics. Recent all-atom MD simulations identified and quantified the molecular strain limiting the stability of nanopatterns created with small dendrimer inks, and explained the different patterns obtained experimentally with different dendrimer inks. In the present work, the all-atom simulations are "scaled up" to longer timescales via coarse graining, without incurring significant additional computational expense, and, crucially, without significant loss in atom-scale detail, the coarse-grained MD simulations yielding properties similar to those obtained from the all-atom simulations. The anchoring of the ink molecules to the monolayer is of multivalent nature and the degree of multivalency shows a sharp dependence on temperature, control of temperature thus providing a further operational "switch" for directed molecular assembly. The computational protocol developed can, in principle, be extended to model any multivalent assembly, for example, virus-cell complexation.     

Martini coarse-grained model for polyethylenimine

As a polycation with diverse applications in biomedical and environmental engineering, polyethylenimine (PEI) can be synthesized with varying degrees of branching, polymerization, and can exist in different protonation states. There have been some interests in molecular modeling of PEI at all-atom or coarse-grained (CG) levels, but present CG models are limited to linear PEIs. Here we present the methodology to systematically categorize bond lengths, bond angles and dihedral angles, which allows us to model branched PEIs. The CG model was developed under the Martini scheme based on eight ~600 Da PEIs, with four different degree of branching at two different protonation states. Comparison of the CG model with all-atom simulations shows good agreement for both local (distributions for bonded interactions) and global (end-to-end distance, radius of gyration) properties, with and without salt. Compatibility of the PEI model with other CG bio-molecules developed under the Martini scheme will allow for large-scale simulations of many PEI-enabled processes. © 2018 Wiley Periodicals, Inc.     

Organic-inorganic telechelic molecules: solution properties from simulations

We report molecular dynamics simulations for telechelic molecules composed of two polyhedral oligomeric silsesquioxane (POSS) cages connected by one hydrocarbon backbone dissolved in liquid normal hexane. Silsesquioxanes are novel hybrid organic-inorganic molecules that are useful as building blocks for the synthesis of nanostructured materials. By including POSS molecules within a polymeric material it is possible to modify mechanical properties such as resistance to heat and glass transition temperatures. Unfortunately, the molecular mechanisms responsible for these enhancements are at present not completely understood. In an effort to elucidate the molecular phenomena responsible for these effects, we have studied the conformation of telechelic POSS molecules in solution, as well as their self-diffusion coefficients, as a function of the length of the hydrocarbon backbone. We focus on molecules in which the radius of gyration of the alkane backbone is comparable to the size of the silsesquioxane cages. Our results indicate that the backbone has a significant influence on both the equilibrium and the transport properties of dissolved telechelic hybrid molecules. These observations are useful for developing strategies to direct the self-assembly of nanostructured materials.     

Thermodynamic and transport properties of polyhedral oligomeric sislesquioxanes in poly(dimethylsiloxane)

Polyhedral oligomeric silsesquioxane (POSS) molecules when functionalized appropriately and dispersed in polymers show promise as monodisperse organic-inorganic hybrid nanocomposite materials characterized by superior mechanical properties. We report here molecular-simulation results for POSS-POSS radial distribution functions, potentials of mean force, and self-diffusion coefficients for POSS monomers dissolved in poly(dimethylsiloxane) in the temperature range of 300-1000 K. Our results demonstrate that it is possible to modulate the effective POSS-POSS interaction by increasing the temperature or by substituting the hydrogen atoms in the POSS monomer with methyl groups. In addition, our results indicate that the motion of POSS monomers dissolved in poly(dimethylsiloxane) follows a hopping mechanism.