Coarse-grained Sites Research Articles

A n-vector model for charge transport in molecular semiconductors.

We develop a lattice model utilizing coarse-grained molecular sites to study charge transport in molecular semiconducting materials. The model bridges atomistic descriptions and structureless lattice models by mapping molecular structure onto sets of spatial vectors isomorphic with spin vectors in a classical n-vector Heisenberg model. Specifically, this model incorporates molecular topology-dependent orientational and intermolecular coupling preferences, including the direct inclusion of spatially correlated transfer integrals and site energy disorder. This model contains the essential physics required to explicitly simulate the interplay of molecular topology and correlated structural disorder, and their effect on charge transport. As a demonstration of its utility, we apply this model to analyze the effects of long-range orientational correlations, molecular topology, and intermolecular interaction strength on charge motion in bulk molecular semiconductors.

A pressure-transferable coarse-grained potential for modeling the shock Hugoniot of polyethylene.

We investigate the thermomechanical response of semi-crystalline polyethylene under shock compression by performing molecular dynamics (MD) simulations using a new coarse-graining scheme inspired by the embedded atom method. The coarse-graining scheme combines the iterative Boltzmann inversion method and least squares optimization to parameterize interactions between coarse-grained sites, including a many-body potential energy designed to improve the representability of the model across a wide range of thermodynamic states. We demonstrate that a coarse-grained model of polyethylene, calibrated to match target structural and thermodynamic data generated from isothermal MD simulations at different pressures, can also accurately predict the shock Hugoniot response. Analysis of the rise in temperature along the shock Hugoniot and comparison with analytical predictions from the Mie-Grüneisen equation of state are performed to thoroughly explore the thermodynamic consistency of the model. As the coarse-graining model affords nearly two orders of magnitude reduction in simulation time compared to all-atom MD simulations, the proposed model can help identify how nanoscale structure in semi-crystalline polymers, such as polyethylene, influences mechanical behavior under extreme loading.

Development of a Coarse-Grained Model of Chitosan for Predicting Solution Behavior.

A new coarse-grained (CG) model of chitosan has been developed for predicting solution behavior as a function of degree of acetylation (DA). A multiscale modeling approach was used to derive the energetic and geometric parameters of this implicit-solvent, CG model from all-atom simulations of chitosan and chitin molecules in explicit water. The model includes representations of both protonated d-glucosamine (GlcN(+)) and N-acetyl-d-glucosamine (GlcNAc) monomers, where each monomer consists of three CG sites. Chitosan molecules of any molecular weight, DA, and monomer sequence can be built using this new CG model. Discontinuous molecular dynamics simulations of chitosan solutions show increased self-assembly in solution with increasing DA and chitosan concentration. The chitosan solutions form larger percolated networks earlier in time as DA and concentration increase, indicating "gel-like" behavior, which qualitatively matches experimental studies of chitosan gel formation. Increasing DA also results in a greater number of monomer-monomer associations, which has been predicted experimentally based on an increase in the storage modulus of chitosan gels with increasing DA. Our model also gives insight into how the monomer sequence affects self-assembly and the frequency of interaction between different pairs of monomers.

Constructing Optimal Coarse-Grained Sites of Huge Biomolecules by Fluctuation Maximization.

Coarse-grained (CG) models are valuable tools for the study of functions of large biomolecules on large length and time scales. The definition of CG representations for huge biomolecules is always a formidable challenge. In this work, we propose a new method called fluctuation maximization coarse-graining (FM-CG) to construct the CG sites of biomolecules. The defined residual in FM-CG converges to a maximal value as the number of CG sites increases, allowing an optimal CG model to be rigorously defined on the basis of the maximum. More importantly, we developed a robust algorithm called stepwise local iterative optimization (SLIO) to accelerate the process of coarse-graining large biomolecules. By means of the efficient SLIO algorithm, the computational cost of coarse-graining large biomolecules is reduced to within the time scale of seconds, which is far lower than that of conventional simulated annealing. The coarse-graining of two huge systems, chaperonin GroEL and lengsin, indicates that our new methods can coarse-grain huge biomolecular systems with up to 10,000 residues within the time scale of minutes. The further parametrization of CG sites derived from FM-CG allows us to construct the corresponding CG models for studies of the functions of huge biomolecular systems.

Modeling Solution X-Ray Scattering with Knowledge-Based Coarse-Grained form Factors

In molecular simulation, the atomic interaction sites of a biomolecule are often grouped into a fewer number of coarse-grained sites for higher computational efficiency. Coarse-grained protein models are also widely used in computing solution X-ray scattering intensities. Traditionally, coarse-grained scattering form factors are constructed based on the Debye formula, which assumes free rotation of each coarse-grained site, such as an amino acid residue. Nevertheless, this approach results in significant discrepancy between all-atom and coarse-grained scattering profiles, due to the structure correlations between different parts of a protein.We implemented a bioinformatics approach to tackle this problem, and a set of coarse-grained form factors were developed on the basis of a protein structure database. In our numerical approach, the form factor parameterization is converted to a linear least square problem, which can efficiently construct form factors with arbitrary coarse-grained mapping. We systematically compared the scattering intensities of various proteins from atomic form factors, Debye formula-based coarse-grained form factors and our developed form factors. The results show that the chi-square values from our developed form factors are substantially improved, using intensities from all-atom models as the standard. Moreover, we computed the hydration effect using an explicit water model for a few proteins with experimental small angle X-ray scattering data, and fitted the simulated scattering profiles to the experimental counterparts. We found that the intensities modeled using our coarse-grained form factors can fit the experimental intensities with small chi-square values, indicating the capability of our form factors in modeling experimental data. The developed form factors have potential usage in scattering-guided biomacromolecule structure optimization and high throughput scattering modeling, where computational efficiency plays an important role.

A new algorithm for construction of coarse-grained sites of large biomolecules

The development of coarse-grained (CG) models for large biomolecules remains a challenge in multiscale simulations, including a rigorous definition of CG representations for them. In this work, we proposed a new stepwise optimization imposed with the boundary-constraint (SOBC) algorithm to construct the CG sites of large biomolecules, based on the s cheme of essential dynamics CG. By means of SOBC, we can rigorously derive the CG representations of biomolecules with less computational cost. The SOBC is particularly efficient for the CG definition of large systems with thousands of residues. The resulted CG sites can be parameterized as a CG model using the normal mode analysis based fluctuation matching method. Through normal mode analysis, the obtained modes of CG model can accurately reflect the functionally related slow motions of biomolecules. The SOBC algorithm can be used for the construction of CG sites of large biomolecules such as F-actin and for the study of mechanical properties of biomaterials.

The multiscale coarse-graining method. XI. Accurate interactions based on the centers of charge of coarse-grained sites.

It is essential to be able to systematically construct coarse-grained (CG) models that can efficiently and accurately reproduce key properties of higher-resolution models such as all-atom. To fulfill this goal, a mapping operator is needed to transform the higher-resolution configuration to a CG configuration. Certain mapping operators, however, may lose information related to the underlying electrostatic properties. In this paper, a new mapping operator based on the centers of charge of CG sites is proposed to address this issue. Four example systems are chosen to demonstrate this concept. Within the multiscale coarse-graining framework, CG models that use this mapping operator are found to better reproduce the structural correlations of atomistic models. The present work also demonstrates the flexibility of the mapping operator and the robustness of the force matching method. For instance, important functional groups can be isolated and emphasized in the CG model.

Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach

In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficient orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test different choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.

Conformational Properties of Sodium Polystyrenesulfonate in Water: Insights from a Coarse-Grained Model with Explicit Solvent.

Polymer solutions present a significant computational challenge because chemical realism on small length scales can be important, but the polymer molecules are very large. In polyelectrolyte solutions, there is often the additional complexity that the molecules consist of hydrophobic and charged groups, which makes an accurate treatment of the solvent, water, crucial. One route to achieve this balance is through coarse-grained models where several atoms on a monomer are grouped into one interaction site. In this work, we develop a coarse grained (CG) model for sodium polystyrenesulfonate (NaPSS) in water using a methodology consistent with the MARTINI coarse-graining philosophy, where four heavy atoms are grouped into one CG site. We consider two models for water: polarizable MARTINI (POL) and big multipole water (BMW). In each case, interaction parameters for the polymer sites are obtained by matching the potential of mean force between two monomers to results of atomistic simulations. The force field based on the POL water provides a more reasonable description of polymer properties than that based on the BMW water. We study the properties of single chains using the POL force field. Fully sulfonated chains are rodlike (i.e., the root-mean-square radius of gyration, Rg, scales linearly with degree of polymerization, N). When the fraction of sulfonation, f, is 0.25 or less, the chain collapses into a cylindrical globule. For f = 0.5, pearl-necklace conformations are observed when every second monomer is sulfonated. The lifetime of a counterion around a polymer is on the order of 100 ps, suggesting that there is no counterion condensation. The model is computationally feasible and should allow one to study the effect of local chemistry on the properties of polymers in aqueous solution.

High-Resolution Coarse-Grained Modeling Using Oriented Coarse-Grained Sites.

We introduce a method to bring nearly atomistic resolution to coarse-grained models, and we apply the method to proteins. Using a small number of coarse-grained sites (about one per eight atoms) but assigning an independent three-dimensional orientation to each site, we preferentially integrate out stiff degrees of freedom (bond lengths and angles, as well as dihedral angles in rings) that are accurately approximated by their average values, while retaining soft degrees of freedom (unconstrained dihedral angles) mostly responsible for conformational variability. We demonstrate that our scheme retains nearly atomistic resolution by mapping all experimental protein configurations in the Protein Data Bank onto coarse-grained configurations and then analytically backmapping those configurations back to all-atom configurations. This roundtrip mapping throws away all information associated with the eliminated (stiff) degrees of freedom except for their average values, which we use to construct optimal backmapping functions. Despite the 4:1 reduction in the number of degrees of freedom, we find that heavy atoms move only 0.051 Å on average during the roundtrip mapping, while hydrogens move 0.179 Å on average, an unprecedented combination of efficiency and accuracy among coarse-grained protein models. We discuss the advantages of such a high-resolution model for parametrizing effective interactions and accurately calculating observables through direct or multiscale simulations.

Phase separation behavior of mixed lipid systems at neutral and low pH: coarse-grained simulations with DMD/LIME.

We extend LIME, an intermediate resolution, implicit solvent model for phospholipids previously used in discontinuous molecular dynamics simulations of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) bilayer formation at 325 K, to the description of the geometry and energetics of 1,2-distearoyl-sn-glycero-3-phospho-l-serine (DSPS) and 1,2-dihenarachidoyl-sn-glycero-3-phosphocholine (21PC) and mixtures thereof at both neutral and low pH at 310 K. A multiscale modeling approach is used to calculate the LIME parameters from atomistic simulation data on a mixed DPPC/DSPS system at different pH values. In the model, 17 coarse-grained sites represent DSPS and 18 coarse-grained sites represent 21PC. Each of these coarse-grained sites is classified as 1 of 9 types. LIME/DMD simulations of equimolar bilayers show the following: (1) 21PC/DSPS bilayers with and without surface area restrictions separate faster at low pH than at neutral pH, (2) 21PC/DSPS systems separate at approximately the same rate regardless of whether they are subjected to surface area restrictions, and (3) bilayers with a molar ratio of 9:1 (21PC:DSPS) phase separate to form heterogeneous domains faster at low pH than at neutral pH. Our results are consistent with experimental findings of Sofou and co-workers (Bandekar et al. Mol. Pharmaceutics, 2013, 10, 152–160; Karve et al. Biomaterials, 2010, 31, 4409–4416) that more doxorubicin is released from 21PC/DSPS liposomes at low pH than at neutral pH, presumably because greater phase separation is achieved at low pH than at neutral pH. These are the first molecular-level simulations of the phase separation in mixed lipid bilayers induced by a change in pH.

The Theory of Ultra-Coarse-Graining. 2. Numerical Implementation.

The increasing interest in the modeling of complex macromolecular systems in recent years has spurred the development of numerous coarse-graining (CG) techniques. However, many of the CG models are constructed assuming that all details beneath the resolution of CG degrees of freedom are fast and average out, which sets limits on the resolution of feasible coarse-grainings and on the range of applications of the CG models. Ultra-coarse-graining (UCG) makes it possible to construct models at any desired resolution while accounting for discrete conformational or chemical changes within the CG sites that can modulate the interactions between them. Here, we discuss the UCG methodology and its numerical implementation. We pay particular attention to the numerical mechanism for including state transitions between different conformations within CG sites because this has not been discussed previously. Using a simple example of 1,2-dichloroethane, we demonstrate the ability of the UCG model to reproduce the multiconfigurational behavior of this molecular liquid, even when each molecule is modeled with only one CG site. The methodology can also be applied to other molecular liquids and macromolecular systems with time scale separation between conformational transitions and other intramolecular motions and rotations.

Coarse-grained simulation of cellulose Iβ with application to long fibrils

Cellulose microfibrils are recalcitrant toward dissolution, thus it is difficult to extract and characterize them without modifying their native state. To study the molecular level behavior of microfibrils over 100 sugar residues, we construct a coarse-grained model of solvated cellulose Iβ microfibril using one bead per sugar residue. We derive the coarse-grained force field from atomistic simulation of a 36 chain, 40-residue microfibril by requiring consistency between the chain configuration, intermolecular packing and hydrogen bonding of the two levels of modeling. Coarse-grained force sites are placed at the geometric center of each glucose ring. Intermolecular van der Waals and hydrogen bonding interactions are added sequentially until the microfibril crystal structure in the atomistic simulation is achieved. This requires hydrogen bond potentials for pairs that hydrogen bond in cellulose Iβ, as well as those that can hydrogen bond in other structures, but not in cellulose Iβ. Microfibrils longer than 100 nm form kinks along their longitudinal direction, with an average periodicity of 70 nm. The behavior of kinked regions is similar with a bending angle of approximately 20°. These kinked regions might be linked to observations of periodic disorder from small angle neutron scattering and acid hydrolysis.

Solvent-Free, Highly Coarse-Grained Models for Charged Lipid Systems.

We present a methodology to develop coarse-grained lipid models such that electrostatic interactions between the coarse-grained sites can be derived accurately from an all-atom molecular dynamics trajectory and expressed as an effective pairwise electrostatic potential with appropriate screening functions. The reference nonbonded forces from the all-atom trajectory are decomposed into separate electrostatic and van der Waals (vdW) forces, based on the multiscale coarse-graining method. The coarse-grained electrostatic potential is assumed to be a general function of unknown variables and the final site–site interactions are obtained variationally, where the residual of the electrostatic forces from the assumed field is minimized. The resulting electrostatic interactions are fitted to screened electrostatics functions, with a special treatment for distance-dependent dielectrics and screened dipole–dipole interactions. The vdW interactions are derived separately. The resulting charged hybrid coarse-graining method is applied to various solvent-free three-site models of anionic lipid systems.

New Insights into Lipid Monolayers from Coarse-Grained Simulation Techniques

New Insights into Lipid Monolayers from Coarse-Grained Simulation Techniques

Web-based computational chemistry education with CHARMMing II: Coarse-grained protein folding.

A lesson utilizing a coarse-grained (CG) G-like model has been implemented into the CHARMM INterface and Graphics (CHARMMing) web portal (www.charmming.org) to the Chemistry at HARvard Macromolecular Mechanics (CHARMM) molecular simulation package. While widely used to model various biophysical processes, such as protein folding and aggregation, CG models can also serve as an educational tool because they can provide qualitative descriptions of complex biophysical phenomena for a relatively cheap computational cost. As a proof of concept, this lesson demonstrates the construction of a CG model of a small globular protein, its simulation via Langevin dynamics, and the analysis of the resulting data. This lesson makes connections between modern molecular simulation techniques and topics commonly presented in an advanced undergraduate lecture on physical chemistry. It culminates in a straightforward analysis of a short dynamics trajectory of a small fast folding globular protein; we briefly describe the thermodynamic properties that can be calculated from this analysis. The assumptions inherent in the model and the data analysis are laid out in a clear, concise manner, and the techniques used are consistent with those employed by specialists in the field of CG modeling. One of the major tasks in building the G-like model is determining the relative strength of the nonbonded interactions between coarse-grained sites. New functionality has been added to CHARMMing to facilitate this process. The implementation of these features into CHARMMing helps automate many of the tedious aspects of constructing a CG G model. The CG model builder and its accompanying lesson should be a valuable tool to chemistry students, teachers, and modelers in the field.

Side-chain–side-chain interactions and stability of the helical state

Understanding the driving forces that lead to the stability of the secondary motifs found in proteins, namely α-helix and β-sheet, is a major goal in structural biology. The thermodynamic stability of these repetitive units is a result of a delicate balance between many factors, which in addition to the peptide chain involves also the solvent. Despite the fact that the backbones of all amino acids are the same (except of that of proline), there are large differences in the propensity of the different amino acids to promote the helical structure. In this paper, we investigate by explicit-solvent molecular dynamics simulations the role of the side chains (modeled as coarse-grained single sites) in stabilizing α helices in an aqueous solution. Our model systems include four (six-mer-nine-mer) peptide lengths in which the magnitude of the effective attraction between the side chains is systematically increased. We find that these interactions between the side chains can induce (for the nine-mer almost completely) a transition from a coil to a helical state. This transition is found to be characterized by three states in which the intermediate state is a partially folded α-helical conformation. In the absence of any interactions between the side chains the free energy change for helix formation has a small positive value indicating that favorable contributions from the side chains are necessary to stabilize the helical conformation. Thus, the helix-coil transition is controlled by the effective potentials between the side-chain residues and the magnitude of the required attraction per residue, which is on the order of the thermal energy, reduces with the length of the peptide. Surprisingly, the plots of the population of the helical state (or the change in the free energy for helix formation) as a function of the total effective interactions between the side chains in the helical state for all peptide lengths fall on the same curve.

Multiscale Simulation of Liquid Water Using a Four-to-One Mapping for Coarse-Graining.

We present a multiresolution simulation scheme for the solvent environment where four atomistic water molecules are mapped onto one coarse-grained bead. Soft restraining potentials are used to allow a resolution exchange of four water molecules into a single coarse-grained site. We first study the effect of adding restraining potentials in liquid water using full all-atom simulations. The usage of very soft restraining potentials to bundle four nearest neighbor water molecules does not disrupt the hydrogen bonding patterns in the liquid water. The structural properties of the first solvation shell around hydrophobic, hydrophilic, and ionic solutes are well preserved when soft restraining potentials are added. By modeling a bundle of four water molecules as a single molecule, a smooth transition and free exchange between coarse-grained and all-atom resolution is possible by using the adaptive resolution scheme (AdResS).

Molecular dynamics simulations of DPPC bilayers using "LIME", a new coarse-grained model.

A new intermediate resolution model for phospholipids, LIME, designed for use with discontinuous molecular dynamics (DMD) simulations is presented. The implicit-solvent model was developed using a multiscale modeling approach in which the geometric and energetic parameters are obtained by collecting data from atomistic simulations of a system composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecules and explicit water. In the model, 14 coarse-grained sites that are classified as 1 of 6 types represent DPPC. DMD simulations performed on a random solution of DPPC resulted in the formation of a defect-free bilayer in less than 4 h. The bilayer formed quantitatively reproduces the main structural properties (e.g., area per lipid, bilayer thickness, bond order parameters) that are observed experimentally. In addition, the bilayer transitions from a liquid-crystalline phase to a tilted gel phase when the temperature is reduced. Transbilayer movement of a lipid from the bottom leaflet to the top leaflet is observed when the temperature is increased.

The Theory of Ultra-Coarse-Graining. 1. General Principles.

Coarse-grained (CG) models provide a computationally efficient means to study biomolecular and other soft matter processes involving large numbers of atoms correlated over distance scales of many covalent bond lengths and long time scales. Variational methods based on information from simulations of finer-grained (e.g., all-atom) models, for example the multiscale coarse-graining (MS-CG) and relative entropy minimization methods, provide attractive tools for the systematic development of CG models. However, these methods have important drawbacks when used in the "ultra-coarse-grained" (UCG) regime, e.g., at a resolution level coarser or much coarser than one amino acid residue per effective CG particle in proteins. This is due to the possible existence of multiple metastable states "within" the CG sites for a given UCG model configuration. In this work, systematic variational UCG methods are presented that are specifically designed to CG entire protein domains and subdomains into single effective CG particles. This is accomplished by augmenting existing effective particle CG schemes to allow for discrete state transitions and configuration-dependent resolution. Additionally, certain conclusions of this work connect back to single-state force matching and open up new avenues for method development in that area. These results provide a formal statistical mechanical basis for UCG methods related to force matching and relative entropy CG methods and suggest practical algorithms for constructing optimal approximate UCG models from fine-grained simulation data.