Systematic implicit solvent coarse graining of dimyristoylphosphatidylcholine lipids

We have used systematic structure‐based coarse graining to derive effective site–site potentials for a 10‐site coarse‐grained dimyristoylphosphatidylcholine (DMPC) lipid model and investigated their state point dependence. The potentials provide for the coarse‐grained model the same site–site radial distribution functions, bond and angle distributions as those computed in atomistic simulations carried out at four different lipid–water molar ratios. It was shown that there is a non‐negligible dependence of the effective potentials on the concentration at which they were generated, which is also manifested in the properties of the lipid bilayers simulated using these potentials. Thus, effective potentials computed at low lipid concentration favor to more condensed and ordered structure of the bilayer with lower average area per lipid, while potentials obtained at higher lipid concentrations provide more fluid‐like structure. The best agreement with the reference data and experiment was achieved using the set of potentials derived from atomistic simulations at 1:30 lipid:water molar ratio providing fully saturated hydration of DMPC lipids. Despite theoretical limitations of pairwise coarse‐grained potentials expressed in their state point dependence, all the resulting potentials provide a stable bilayer structure with correct partitioning of different lipid groups across the bilayer as well as acceptable values of the average lipid area, compressibility and orientational ordering. In addition to bilayer simulations, the model has proven its robustness in modeling of self‐aggregation of lipids from randomly dispersed solution to ordered bilayer structures, bicelles, and vesicles. © 2014 Wiley Periodicals, Inc.     

How Good Are Coarse‐Grained Polymer Models? A Comparison for Atactic Polystyrene

This review provides an overview of the various coarse‐grained models that have been developed in the past few years for amorphous polystyrene. Different techniques to develop the force fields and different mapping schemes lead to models that perform differently depending on the properties investigated. This review collects and compares the models to guide the reader in the choice of the best model for the application of interest. It is expected that the central features of the various coarse‐graining procedures will also apply to systems other than polystyrene and that some of the conclusions about different coarse‐graining strategies are general.     

How Much Can We Coarse‐Grain while Retaining the Chemical Specificity? A Study of Sulfonated Poly(ether ether ketone)

For mesoscale structural studies of polymers, obtaining maximum level of coarse‐graining that maintains the chemical specificity is highly desirable. Here we present a systematic coarse‐graining study of sulfonated poly(ether ether ketone), sPEEK, and show that a 71:3 coarse‐grained (CG) mapping is the maximum possible map within a CG bead‐spring model. We perform single chain atomistic simulation on the system to collect various structural distributions, against which the CG potentials are optimized using iterative Boltzmann inversion technique. The potentials thus extracted are shown to reproduce the target distributions for larger single chains as well as for multiple chains. The structure at the atomistic level is shown to be preserved when we back‐map the CG system to re‐introduce the atomistic details. By using the same CG mapping for another repeat unit sequence of sPEEK, we show that the nature of the effective interaction at the CG level depends strongly on the polymer sequence and cannot be assumed based on the nature of the corresponding atomistic unit. These CG potentials will be the key to future mesoscopic simulations to study the structure of sPEEK based polymer electrolyte membranes.

     

Coarse‐grained A‐graft‐B model of poly(lactic acid) for molecular dynamics simulations

A mesoscopic model of poly(lactic acid) is developed where the polymer is represented as an A‐graft‐B chain with monomer units consisting of two covalently connected beads. A coarse‐graining algorithm is proposed to convert an atomistic model of PLA into a coarse‐grained one. The developed model is based on atomistic simulations of oligolactides to take into account terminal groups correctly. It was used for coarse‐grained simulations of polylactide. Gyration radii and end to end distances of polymer chains as well as the density of the polymer melt are shown to be in a good agreement with those obtained from atomistic simulations. The thermal expansion coefficients of the OLA melts calculated using the coarse‐grained model are in reasonable agreement with those obtained from all‐atom molecular dynamics. The model provides a 17‐fold speedup compared with atomistic calculations. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 604–612     

Coarse grained model of entangled polymer melts

A coarse graining procedure aimed at reproducing both the chain structure and dynamics in melts of linear monodisperse polymers is presented. The reference system is a bead-spring-type representation of the melt. The level of coarse graining is selected equal to the number of beads in the entanglement segment, Ne. The coarse model is still discrete and contains blobs each representing Ne consecutive beads in the fine scale model. The mapping is defined by the following conditions: the probability of given state of the coarse system is equal to that of all fine system states compatible with the respective coarse state, the dissipation per coarse grained object is similar in the two systems, constraints to the motion of a representative chain exist in the fine phase space, and the coarse phase space is adjusted such to represent them. Specifically, the chain inner blobs are constrained to move along the backbone of the coarse grained chain, while the end blobs move in the three-dimensional embedding space. The end blobs continuously redefine the diffusion path for the inner blobs. The input parameters governing the dynamics of the coarse grained system are calibrated based on the fine scale model behavior. Although the coarse model cannot reproduce the whole thermodynamics of the fine system, it ensures that the pair and end-to-end distribution functions, the rate of relaxation of segmental and end-to-end vectors, the Rouse modes, and the diffusion dynamics are properly represented.     

Diffusive dynamics of DNA unzipping in a nanopore

When an electric field is applied to an insulating membrane, movement of charged particles through a nanopore is induced. The measured ionic current reports on biomolecules passing through the nanopore. In this work, we explored the kinetics of DNA unzipping in a nanopore using our coarse‐grained model (Stachiewicz and Molski, J. Comput. Chem. 2015, 36, 947). Coarse graining allowed a more detailed analysis for a wider range of parameters than all‐atom simulations. Dependence of the translocation mode (unzipping or distortion) on the pore diameter was examined, and the threshold voltages were estimated. We determined the potential of mean force, position‐dependent diffusion coefficient, and position‐dependent effective charge for the DNA unzipping. The three molecular profiles were correlated with the ionic current and molecular events. On the unzipping/translocation force profile, two energy maxima were found, one of them corresponding to the unzipping, and the other to the translocation barriers. The unzipping kinetics were further explored using Brownian dynamics. © 2015 Wiley Periodicals, Inc.     

Time versus temperature rescaling for coarse grain molecular dynamics simulations

Coarse graining procedures are intended to well reproduce the structure of a material while increasing the simulations efficiency. However, the dynamics usually accelerates with coarse graining and a scaling procedure has to be used for dynamical data calculations. Most often a simple time-scaling coefficient is used for this purpose. However, for low temperature liquids this simple scaling procedure is questionable. Because supercooled liquids in their approach to the glass transition temperature do not follow a simple dynamics. In order to test if this scaling procedure is still pertinent at low temperature, we use molecular dynamics simulations of a coarse grain model of the methylmethacrylate molecule compared to simulations with the All atom model. We compare two different rescaling procedures, a time rescale and a temperature rescale procedure. Using these two procedures we compare the behaviors of the mean square displacements, the incoherent scattering functions, the self and distinct part of the Van Hove correlation functions and the non-Gaussian parameters. Results show that the temperature rescaling procedure reproduces well the All atom dynamical data at low temperatures, while the time rescaling procedure is correct only in the Brownian regime. We also find that the melting and the glass-transition temperatures are relatively well reproduced with the temperature rescaling procedure.     

Comparing normal modes across different models and scales: Hessian reduction versus coarse‐graining

Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse‐graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the “implosion” of the all‐atom (AA) Hessian to a coarse‐grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass‐weighting. The dimension‐dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension‐independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Gō‐like model, a canonical elastic network model, and a network model with intentionally unphysical force constants. Published 2012 Wiley Periodicals, Inc.     

Coarse‐grained models and collective phenomena in membranes: Computer simulation of membrane fusion

We discuss the role coarse‐grained models play in investigating collective phenomena in bilayer membranes and place them in the context of alternative approaches. By reducing the degrees of freedom and applying simple effective potentials, coarse‐grained models can address the large time scales and length scales of collective phenomena in membranes. Although the mapping from a coarse‐grained model onto chemically realistic models is a challenge, such models provide a direct view on the phenomena that occur on the length scales of a few tens of nanometers. Their relevance is exemplified by the study of fusion of model membranes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1441–1450, 2003     

MOLSIM: A modular molecular simulation software

The modular software MOLSIM for all‐atom molecular and coarse‐grained simulations is presented with focus on the underlying concepts used. The software possesses four unique features: (1) it is an integrated software for molecular dynamic, Monte Carlo, and Brownian dynamics simulations; (2) simulated objects are constructed in a hierarchical fashion representing atoms, rigid molecules and colloids, flexible chains, hierarchical polymers, and cross‐linked networks; (3) long‐range interactions involving charges, dipoles and/or anisotropic dipole polarizabilities are handled either with the standard Ewald sum, the smooth particle mesh Ewald sum, or the reaction‐field technique; (4) statistical uncertainties are provided for all calculated observables. In addition, MOLSIM supports various statistical ensembles, and several types of simulation cells and boundary conditions are available. Intermolecular interactions comprise tabulated pairwise potentials for speed and uniformity and many‐body interactions involve anisotropic polarizabilities. Intramolecular interactions include bond, angle, and crosslink potentials. A very large set of analyses of static and dynamic properties is provided. The capability of MOLSIM can be extended by user‐providing routines controlling, for example, start conditions, intermolecular potentials, and analyses. An extensive set of case studies in the field of soft matter is presented covering colloids, polymers, and crosslinked networks. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Coarse‐grained molecular dynamics simulations of protein–ligand binding

Coarse‐grained molecular dynamics (CGMD) simulations with the MARTINI force field were performed to reproduce the protein–ligand binding processes. We chose two protein–ligand systems, the levansucrase–sugar (glucose or sucrose), and LinB–1,2‐dichloroethane systems, as target systems that differ in terms of the size and shape of the ligand‐binding pocket and the physicochemical properties of the pocket and the ligand. Spatial distributions of the Coarse‐grained (CG) ligand molecules revealed potential ligand‐binding sites on the protein surfaces other than the real ligand‐binding sites. The ligands bound most strongly to the real ligand‐binding sites. The binding and unbinding rate constants obtained from the CGMD simulation of the levansucrase–sucrose system were approximately 10 times greater than the experimental values; this is mainly due to faster diffusion of the CG ligand in the CG water model. We could obtain dissociation constants close to the experimental values for both systems. Analysis of the ligand fluxes demonstrated that the CG ligand molecules entered the ligand‐binding pockets through specific pathways. The ligands tended to move through grooves on the protein surface. Thus, the CGMD simulations produced reasonable results for the two different systems overall and are useful for studying the protein–ligand binding processes. © 2014 Wiley Periodicals, Inc.     

Coarse Grained Molecular Dynamics Simulation of Nanoconfined Water

A coarse‐grained (CG) model for the simulation of nanoconfined water between graphene surfaces is developed. For this purpose, mixed‐grained simulations are done, in which the two‐site water model of Riniker and van Gunsteren [S. Riniker, W. F. van Gunsteren, J. Chem. Phys. 2011 , 134, 084110] is simulated between atomistically resolved graphene surfaces. In the developed pure CG model, the two interaction sites of water and a combination of eight carbon atoms in the graphene surface are grouped together to construct water and surface CG beads. The pure CG potentials are constructed by iteratively matching the radial distribution functions and the density profiles of water beads in the pore with the corresponding mixed‐grained distributions. The constructed potentials are shown to be pore‐size transferable, capable of predicting structural properties of confined water over the whole range of pore sizes, ranging from extremely narrow pores to bulk water. The model is used to simulate a number of nanoconfined systems of a variety of pore sizes at constant temperature, constant parallel component of pressure, and constant surface area of the confining surfaces. The model is shown to predict the layering of water in contact with the surfaces, and the solvation force is in complete agreement with the mixed‐grained model. It is shown that water molecules in the pore have smaller parallel diffusion coefficients compared to bulk water. Well‐organized layers beside the surfaces are shown to have lower diffusion coefficients than diffuse layers. More information on the dynamics of water in the pore is obtained by calculating the rate of water exchange between slabs parallel to the surfaces. The time scale to achieve equilibrium for this process, depending on the pore width and on the degree of layering of water beside the surfaces, is a few nanoseconds in nanometric pores.     

GALAMOST: GPU‐accelerated large‐scale molecular simulation toolkit

GALAMOST [graphics processing unit (GPU)‐accelerated large‐scale molecular simulation toolkit] is a molecular simulation package designed to utilize the computational power of GPUs. Besides the common features of molecular dynamics (MD) packages, it is developed specially for the studies of self‐assembly, phase transition, and other properties of polymeric systems at mesoscopic scale by using some lately developed simulation techniques. To accelerate the simulations, GALAMOST contains a hybrid particle‐field MD technique where particle–particle interactions are replaced by interactions of particles with density fields. Moreover, the numerical potential obtained by bottom‐up coarse‐graining methods can be implemented in simulations with GALAMOST. By combining these force fields and particle‐density coupling method in GALAMOST, the simulations for polymers can be performed with very large system sizes over long simulation time. In addition, GALAMOST encompasses two specific models, that is, a soft anisotropic particle model and a chain‐growth polymerization model, by which the hierarchical self‐assembly of soft anisotropic particles and the problems related to polymerization can be studied, respectively. The optimized algorithms implemented on the GPU, package characteristics, and benchmarks of GALAMOST are reported in detail. © 2013 Wiley Periodicals, Inc.     

Some mechanisms for subtle influences of stereochemical composition on the physical properties of macromolecules

Coarse‐grained chains can be designed so that they successfully capture subtle effects arising from the local covalent structure of real chains. Constraining the conformations of the coarse‐grained chains with an appropriate rotational isomeric state model can achieve this objective. This claim has been documented by simulations of the dependence of the mixing behavior of polypropylene melts on the stereochemical composition of the chains; atactic polypropylene and isotactic polypropylene are miscible, but the replacement of either component with syndiotactic polypropylene can lead to immiscibility. This has also been documented by a comparison of simulations and infrared–visible sum frequency generation spectroscopy studies of the surface structures of atactic polystyrene and random copolymers of ethylene and propylene. The success of this method when the stereochemical composition is defined by side chains as small as CH₃ suggests that it should also be applicable to other problems in which the influence of the stereochemical composition is less subtle because the stereochemistry is defined by larger side chains. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1271‐1282, 2005     

Generalized coarse-grained model based on point multipole and Gay-Berne potentials

This paper presents a general coarse-grained molecular mechanics model based on electric point multipole expansion and Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] potential. Coarse graining of van der Waals potential is achieved by treating molecules as soft uniaxial ellipsoids interacting via a generalized anisotropic Gay-Berne function. The charge distribution is represented by point multipole expansion, including point charge, dipole, and quadrupole moments placed at the center of mass. The Gay-Berne and point multipole potentials are combined in the local reference frame defined by the inertial frame of the all-atom counterpart. The coarse-grained model has been applied to rigid-body molecular dynamics simulations of molecular liquids including benzene and methanol. The computational efficiency is improved by several orders of magnitude, while the results are in reasonable agreement with all-atom models and experimental data. We also discuss the implications of using point multipole for polar molecules capable of hydrogen bonding and the applicability of this model to a broad range of molecular systems including highly charged biopolymers.