Coarse-grained Beads Research Articles

On the Effect of Mapping in the Coarse Graining of Elastic Networks

Elastic Networks (ENs) are a subset of coarse-grained (CG) models that have proven useful when studying the fluctuations of proteins. All CG models involve two aspects: (1) the mapping of the high resolution particles to low resolution particles and (2) the new interaction between the low resolution particles. The most common choice of mapping is to simply map all the particles of an amino acid to a CG bead at the position of the Cα atom (or to CG beads at both the Cα and Cβ atoms). Clearly, the interactions between the CG degrees of freedom affect the ability of the EN model to reproduce the fluctuations of the actual protein, but what about the choice of mapping? In this project, we use a method for the systematic creation of a low resolution EN from a high resolution model to investigate how the mapping can affect the ability of the EN to emulate the high resolution model. We show that the mapping has a large effect on the final accuracy and that it is possible to efficiently search for superior mappings. To this end, we present an easily calculated metric that correlates with the validity of the EN, and discuss a couple of optimization techniques that have shown success.

Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane.

Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. The DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.

Calculation of Enzyme Fluctuograms from All-Atom Molecular Dynamics Simulation.

In this work, a computational framework is presented to compute the time evolution of force constants for a coarse grained (CG) elastic network model along an all-atom molecular dynamics trajectory of a protein system. Obtained via matching distance fluctuations, these force constants represent strengths of mechanical coupling between CG beads. Variation of coupling strengths with time is hence termed the fluctuogram of protein dynamics. In addition to the schematic procedure and implementation considerations, several ways of combining force constants and data analysis are presented to illustrate the potential application of protein fluctuograms. The unique angle provided by the fluctuogram expands the scope of atomistic simulations and is expected to impact upon fundamental understanding of protein dynamics as well as protein engineering technologies.

A dynamical coarse-grained model to disclose allosteric control of misfolding β2-microglobulin

Development of a novel Coarse-Grained (CG) model to study β2-microglobulin dynamical features related to fibrillation: our one CG bead model is able to indicate propensities in the deformation behavior of the protein via investigation of the protein motion correlations.

Flexible Boundaries for Multiresolution Solvation: An Algorithm for Spatial Multiscaling in Molecular Dynamics Simulations.

An algorithm is proposed for performing molecular dynamics (MD) simulations of a biomolecular solute represented at atomistic resolution surrounded by a surface layer of atomistic fine-grained (FG) solvent molecules within a bulk represented by coarse-grained (CG) solvent beads. The method, called flexible boundaries for multiresolution solvation (FBMS), is based on: (i) a three-region layering of the solvent around the solute, involving an FG layer surrounded by a mixed FG-CG buffer layer, itself surrounded by a bulk CG region; (ii) a definition of the layer boundary that relies on an effective distance to the solute surface and is thus adapted to the shape of the solute as well as adjusts to its conformational changes. The effective surface distance is defined by inverse-nth power averaging over the distances to all non-hydrogen solute atoms, and the layering is enforced by means of half-harmonic distance restraints, attractive for the FG molecules and repulsive for the CG beads. A restraint-free region at intermediate distances enables the formation of the buffer layer, where the FG and CG solvents can mix freely. The algorithm is tested and validated using the GROMOS force field and the associated FG (SPC) and CG (polarizable CGW) water models. The test systems include pure-water systems, where one FG molecule plays the role of a solute, and a deca-alanine peptide with two widely different solute shapes considered, α-helical and fully extended. In particular, as the peptide unfolds, the number of FG molecules required to fill its close-range solvation layer increases, with the additional molecules being provided by the buffer layer. Further validation involves simulations of four proteins in multiresolution FG/CG mixtures. The resulting structural, energetic, and solvation properties are found to be similar to those observed in corresponding pure FG simulations.

A simple and transferable all-atom/coarse-grained hybrid model to study membrane processes.

We present an efficient all-atom/coarse-grained hybrid model and apply it to membrane processes. This model is an extension of the all-atom/ELBA model applied previously to processes in water. Here, we improve the efficiency of the model by implementing a multiple-time step integrator that allows the atoms and the coarse-grained beads to be propagated at different timesteps. Furthermore, we fine-tune the interaction between the atoms and the coarse-grained beads by computing the potential of mean force of amino acid side chain analogs along the membrane normal and comparing to atomistic simulations. The model was independently validated on the calculation of small-molecule partition coefficients. Finally, we apply the model to membrane peptides. We studied the tilt angle of the Walp23 and Kalp23 helices in two different model membranes and the stability of the glycophorin A dimer. The model is efficient, accurate, and straightforward to use, as it does not require any extra interaction particles, layers of atomistic solvent molecules or tabulated potentials, thus offering a novel, simple approach to study membrane processes.

Branched–linear polyion complexes at variable charge densities

Structural behavior of complexes formed by a charged and branched copolymer and an oppositely charged and linear polyion was examined by Monte Carlo simulations employing a coarse-grained bead–spring model. The fractional bead charge and the branching density were systematically varied; the former between 0e and 1e and the latter such that both the comb-polymer and the bottle-brush limits were included. The number of beads of the main chain of the branched copolymer and of the linear polyion was always kept constant and equal, and a single side-chain length was used. Our analysis involved characterization of the complex as well as investigation of size, shape, and flexibility of the charged moieties. An interplay between Coulomb interaction and side-chain repulsion governed the structure of the polyion complex. At strong Coulomb interaction, the complexes underwent a gradual transition from a globular structure at low branching density to an extended one at high branching density. As the electrostatic coupling was decreased, the transition was smoothened and shifted to lower branching density, and, eventually, a behavior similar to that found for neutral branched polymer was observed. Structural analogies and dissimilarities with uncharged branched polymers in poor solutions are discussed.

Martini Coarse-Grained Force Field: Extension to DNA.

We systematically parameterized a coarse-grained (CG) model for DNA that is compatible with the Martini force field. The model maps each nucleotide into six to seven CG beads and is parameterized following the Martini philosophy. The CG nonbonded interactions are based on partitioning of the nucleobases between polar and nonpolar solvents as well as base-base potential of mean force calculations. The bonded interactions are fit to single-stranded DNA (ssDNA) atomistic simulations and an elastic network is used to retain double-stranded DNA (dsDNA) and other specific DNA conformations. We present the implementation of the Martini DNA model and demonstrate the properties of individual bases, ssDNA as well as dsDNA, and DNA-protein complexes. The model opens up large-scale simulations of DNA interacting with a wide range of other (bio)molecules that are available within the Martini framework.

Supra-Atomic Coarse-Grained GROMOS Force Field for Aliphatic Hydrocarbons in the Liquid Phase

A supra-atomic coarse-grained (CG) force field for liquid n-alkanes is presented. The model was calibrated using experimental thermodynamic data and structural as well as energetic properties for 14 n-alkanes as obtained from atomistic fine-grained (FG) simulations of the corresponding hydrocarbons using the GROMOS 45A3 biomolecular force field. A variation of the nonbonded force-field parameters obtained from mapping the FG interactions onto the CG degrees of freedom to fit the density and heat of vaporization to experimental values turned out to be mandatory for a correct reproduction of these data by the CG model, while the bonded force-field parameters for the CG model could be obtained from a Boltzmann-weighted fit with some variations with respect to the corresponding properties from the FG simulations mapped onto the CG degrees of freedom. The model presents 6 different CG bead types, for bead sizes from 2 to 4 distinguishing between terminal and nonterminal beads within an alkane chain (end or middle). It contains different nonbonded Lennard-Jones parameters for the interaction of CG alkanes with CG water. The CG alkane model was further tested by comparing predictions of the excess free energy, the self-diffusion constant, surface tension, isothermal compressibility, heat capacity, thermal expansion coefficient, and shear viscosity for n-alkanes to experimental values. The CG model offers a thermodynamically calibrated basis for the development of CG models of lipids.

Polarizable coarse-grained models for molecular dynamics simulation of liquid cyclohexane.

Force field parameters for polarizable coarse-grained (CG) supra-atomic models of liquid cyclohexane are proposed. Two different bead sizes were investigated, one representing two fine-grained (FG) CH(2)r united atoms of the cyclohexane ring, and one representing three FG CH(2)r united atoms. Electronic polarizability is represented by a massless charge-on-spring particle connected to each CG bead. The model parameters were calibrated against the experimental density and heat of vaporization of liquid cyclohexane, and the free energy of cyclohexane hydration. Both models show good agreement with thermodynamic properties of cyclohexane, yet overestimate the self-diffusion. The dielectric properties of the polarizable models agree very well with experiment.

Supramolecular polymerization: a coarse grained molecular dynamics study.

A coarse-grained (CG) force field to model the self-assembly of benzene-1,3,5-tricarboxamide (BTA) class of compounds in nonpolar solvents has been developed. The model includes an intrinsic point dipole embedded on one of the CG beads so as to impart a macrodipole moment to the oligomer, one of its characteristic feature. Chemical specificity has been preserved by benchmarking against results, including dimerization and solvation free energies, obtained from an all-atom representation. Starting from a well-dispersed configuration in n-nonane, BTA molecules self-assemble to form one-dimensional stacks. Free energy (FE) changes for the various manner in which short oligomers can exchange between the assembled and the dispersed states have been calculated. These calculations show BTA to self-assemble via a downhill cooperative mechanism with a nucleus size of three.

SAFT-γ force field for the simulation of molecular fluids: 4. A single-site coarse-grained model of water applicable over a wide temperature range

In this work, we develop coarse-grained (CG) force fields for water, where the effective CG intermolecular interactions between particles are estimated from an accurate description of the macroscopic experimental vapour–liquid equilibria data by means of a molecular-based equation of state. The statistical associating fluid theory for Mie (generalised Lennard-Jones) potentials of variable range (SAFT-VR Mie) is used to parameterise spherically symmetrical (isotropic) force fields for water. The resulting SAFT-γ CG models are based on the Mie (8-6) form with size and energy parameters that are temperature dependent; the latter dependence is a consequence of the angle averaging of the directional polar interactions present in water. At the simplest level of CG where a water molecule is represented as a single bead, it is well known that an isotropic potential cannot be used to accurately reproduce all of the thermodynamic properties of water simultaneously. In order to address this deficiency, we propose two CG potential models of water based on a faithful description of different target properties over a wide range of temperatures: our CGW1-vle model is parameterised to match the saturated-liquid density and vapour pressure; our other CGW1-ift model is parameterised to match the saturated-liquid density and vapour–liquid interfacial tension. A higher level of CG corresponding to two water molecules per CG bead is also considered: the corresponding CGW2-bio model is developed to reproduce the saturated-liquid density and vapour–liquid interfacial tension in the physiological temperature range, and is particularly suitable for the large-scale simulation of bio-molecular systems. A critical comparison of the phase equilibrium and transport properties of the proposed force fields is made with the more traditional atomistic models.

Mucin aggregation from a rod-like meso-scale model

Dissipative particle dynamics, a meso–scale particle-based model, was used to study the aggregation of mucins in aqueous solutions. Concentration, strength of the mucin–water interactions, as well as the effects of size, shape, and composition of the model molecules were studied. Model proteins were represented as rod-like objects formed by coarse-grained beads. In the first model, only one type of beads formed the mucin. It was found that all the surfaces were available to form aggregates and the conformation of the aggregates was a function of the strength of the mucin–water interaction. With this model, the number of aggregates was unaffected by the initial position of the mucins in the simulation box, except for the lowest mucin concentration. In a more refined mucin model, two kinds of beads were used in the molecule in order to represent the existence of cysteine-like terminal groups in the actual molecule. With this new scheme, aggregation took place by the interaction of the terminal groups between model molecules. The kinetic analysis of the evolution of the number of aggregates with time was also studied for both mucin models.

PSII-LHCII supercomplex organizations in photosynthetic membrane by coarse-grained simulation.

Green plant photosystem II (PSII) and light-harvesting complex II (LHCII) in the stacked grana regions of thylakoid membranes can self-organize into various PSII-LHCII supercomplexes with crystalline or fluid-like supramolecular structures to adjust themselves with external stimuli such as high/low light and temperatures, rendering tunable solar light absorption spectrum and photosynthesis efficiencies. However, the mechanisms controlling the PSII-LHCII supercomplex organizations remain elusive. In this work, we constructed a coarse-grained (CG) model of the thylakoid membrane including lipid molecules and a PSII-LHCII supercomplex considering association/dissociation of moderately bound-LHCIIs. The CG interaction between CG beads were constructed based on electron microscope (EM) experimental results, and we were able to simulate the PSII-LHCII supramolecular organization of a 500 × 500 nm(2) thylakoid membrane, which is compatible with experiments. Our CGMD simulations can successfully reproduce order structures of PSII-LHCII supercomplexes under various protein packing fractions, free-LHCII:PSII ratios, and temperatures, thereby providing insights into mechanisms leading to PSII-LHCII supercomplex organizations in photosynthetic membranes.

Structure and Dynamics of Coarse-Grained Ionomer Melts in an External Electric Field

We perform molecular dynamics simulations on a set of ionomer melts in the presence of a static, external electric field. We employ the same coarse-grained bead–spring model from our previous simulations, which characterized the zero-field morphologies and dynamics of the isolated or percolated ionic aggregates observed in these systems. Here we investigate the electric field effects on these aggregates. In the linear response regime, the morphology of both isolated and percolated aggregates is unaltered because the force between the two ions at contact is much stronger than the force on an ion due to the external field. However, the same fields are strong enough to bias the local ion dynamics so that ions in the percolated systems, which contain a continuous ionic network, transition to the steady state drift regime. Furthermore, the field biases the motion of oppositely charged ions in opposite directions and decorrelates the ionic aggregates along the field direction. In the systems with isolated ionic...

Monte Carlo simulations of the phase separation of a copolymer blend in a thin film.

Monte Carlo simulations were carried out to study the phase separation of a copolymer blend comprising an alternating copolymer and/or block copolymer in a thin film, and a phase diagram was constructed with a series of composed recipes. The effects of composition and segregation strength on phase separation were discussed in detail. The chain conformation of the block copolymer and alternating copolymer were investigated with changes of the segregation strength. Our simulations revealed that the segment distribution along the copolymer chain and the segregation strength between coarse-grained beads are two important parameters controlling phase separation and chain conformation in thin films of a copolymer blend. A well-controlled phase separation in the copolymer blend can be used to fabricate novel nanostructures.

PITOMBA: Parameter Interface for Oligosaccharide Molecules Based on Atoms.

A novel four-bead coarse-grained (CG) model for carbohydrates denoted PITOMBA was devised using a bottom-up approach based on the atomistic GROMOS 53A6GLYC force field and on experimental thermodynamical data. The model was developed to be used in conjunction with the SPC CG water model (J. Chem. Phys. 2011, 134, 084110) and the GROMOS force field functional form. Explicit electrostatic interactions are considered by assigning point charges to each CG bead. Validation of the model is presented to a variety of structural and thermodynamic properties for mono- and oligosaccharides in solution. In addition, the model development philosophy allows for prompt extensions to include hexopyranose chains with diverse glycosidic linkages and branches.

Dissipative particle dynamics with an effective pair potential from integral equation theory of molecular liquids.

We present a method of DPD simulation based on a coarse-grained effective pair potential obtained from the DRISM-KH molecular theory of solvation. The theory is first used to calculate the radial distribution functions of all-atom solute monomers in all-atom solvent and then to invert them into an effective pair potential between coarse-grained beads such that their fluid without solvent accounts for molecular specificities and solvation effects in the all-atom system. Bonded interactions are sampled in relatively short MD of the all-atom system and modeled with best multi-Gaussian fit. Replacing the heuristically defined conservative force potential in DPD, the coarse-grained effective pair potential is free from the artificial restrictions on potential range and shape and on equal volume of solute and solvent blobs inherent in standard DPD. The procedure is flexible in specifying coarse-grained mapping and enormously increases computational efficiency by eliminating solvent. The method is validated on polystyrene chains of various length in toluene at finite concentrations for room and polystyrene glass transition temperature. It yields the chain elastic properties and diffusion coefficient in good agreement with experiment and all-atom MD simulations. DPD with coarse-grained effective pair potential is capable of predicting both structural and dynamic properties of polymer solutions and soft matter with high accuracy and computational efficiency.

New Insights into Lipid Monolayers from Coarse-Grained Simulation Techniques

New Insights into Lipid Monolayers from Coarse-Grained Simulation Techniques

Tribology of polymer brush: microscale modelling and simulation

In order to examine the tribological behaviour of the polymer brush, we constructed a mesoscale particle model of a polymer brush system, based on a Brownian dynamics scheme. The polymer model consists of coarse-grained beads connected with harmonic springs. The Lennard-Jones type interaction is assumed between beads. The flow velocity is affected by the local packing fraction of beads. With this model, we executed a series of molecular dynamics simulation to investigate the mechanical responses of brush to shear flow.