Implementation of residue-level coarse-grained models in GENESIS for large-scale molecular dynamics simulations

Residue-level coarse-grained (CG) models have become one of the most popular tools in biomolecular simulations in the trade-off between modeling accuracy and computational efficiency. To investigate large-scale biological phenomena in molecular dynamics (MD) simulations with CG models, unified treatments of proteins and nucleic acids, as well as efficient parallel computations, are indispensable. In the GENESIS MD software, we implement several residue-level CG models, covering structure-based and context-based potentials for both well-folded biomolecules and intrinsically disordered regions. An amino acid residue in protein is represented as a single CG particle centered at the Cα atom position, while a nucleotide in RNA or DNA is modeled with three beads. Then, a single CG particle represents around ten heavy atoms in both proteins and nucleic acids. The input data in CG MD simulations are treated as GROMACS-style input files generated from a newly developed toolbox, GENESIS-CG-tool. To optimize the performance in CG MD simulations, we utilize multiple neighbor lists, each of which is attached to a different nonbonded interaction potential in the cell-linked list method. We found that random number generations for Gaussian distributions in the Langevin thermostat are one of the bottlenecks in CG MD simulations. Therefore, we parallelize the computations with message-passing-interface (MPI) to improve the performance on PC clusters or supercomputers. We simulate Herpes simplex virus (HSV) type 2 B-capsid and chromatin models containing more than 1,000 nucleosomes in GENESIS as examples of large-scale biomolecular simulations with residue-level CG models. This framework extends accessible spatial and temporal scales by multi-scale simulations to study biologically relevant phenomena, such as genome-scale chromatin folding or phase-separated membrane-less condensations.     

RedMDStream: Parameterization and Simulation Toolbox for Coarse-Grained Molecular Dynamics Models

Coarse-grained (CG) models in molecular dynamics (MD) are powerful tools to simulate the dynamics of large biomolecular systems on micro- to millisecond timescales. However, the CG model, potential energy terms, and parameters are typically not transferable between different molecules and problems. So parameterizing CG force fields, which is both tedious and time-consuming, is often necessary. We present RedMDStream, a software for developing, testing, and simulating biomolecules with CG MD models. Development includes an automatic procedure for the optimization of potential energy parameters based on metaheuristic methods. As an example we describe the parameterization of a simple CG MD model of an RNA hairpin.     

Defining Coarse-Grained Representations of Large Biomolecules and Biomolecular Complexes from Elastic Network Models

Coarse-grained (CG) models of large biomolecular complexes enable simulations of these systems over long timescales that are not accessible for atomistic molecular dynamics (MD) simulations. A systematic methodology, called essential dynamics coarse-graining (ED-CG), has been developed for defining coarse-grained sites in a large biomolecule. The method variationally determines the CG sites so that key dynamic domains in the protein are preserved in the CG representation. The original ED-CG method relies on a principal component analysis (PCA) of a MD trajectory. However, for many large proteins and multi-protein complexes such an analysis may not converge or even be possible. This work develops a new ED-CG scheme using an elastic network model (ENM) of the protein structure. In this procedure, the low-frequency normal modes obtained by ENM are used to define dynamic domains and to define the CG representation accordingly. The method is then applied to several proteins, such as the HIV-1 CA protein dimer, ATP-bound G-actin, and the Arp2/3 complex. Numerical results show that ED-CG with ENM (ENM-ED-CG) is much faster than ED-CG with PCA because no MD is necessary. The ENM-ED-CG models also capture functional essential dynamics of the proteins almost as well as those using full MD with PCA. Therefore, the ENM-ED-CG method may be better suited to coarse-grain a very large biomolecule or biomolecular complex that is too computationally expensive to be simulated by conventional MD, or when a high resolution atomic structure is not even available.     

A Coarse Grained Model for a Lipid Membrane with Physiological Composition and Leaflet Asymmetry

The resemblance of lipid membrane models to physiological membranes determines how well molecular dynamics (MD) simulations imitate the dynamic behavior of cell membranes and membrane proteins. Physiological lipid membranes are composed of multiple types of phospholipids, and the leaflet compositions are generally asymmetric. Here we describe an approach for self-assembly of a Coarse-Grained (CG) membrane model with physiological composition and leaflet asymmetry using the MARTINI force field. An initial set-up of two boxes with different types of lipids according to the leaflet asymmetry of mammalian cell membranes stacked with 0.5 nm overlap, reliably resulted in the self-assembly of bilayer membranes with leaflet asymmetry resembling that of physiological mammalian cell membranes. Self-assembly in the presence of a fragment of the plasma membrane protein syntaxin 1A led to spontaneous specific positioning of phosphatidylionositol(4,5)bisphosphate at a positively charged stretch of syntaxin consistent with experimental data. An analogous approach choosing an initial set-up with two concentric shells filled with different lipid types results in successful assembly of a spherical vesicle with asymmetric leaflet composition. Self-assembly of the vesicle in the presence of the synaptic vesicle protein synaptobrevin 2 revealed the correct position of the synaptobrevin transmembrane domain. This is the first CG MD method to form a membrane with physiological lipid composition as well as leaflet asymmetry by self-assembly and will enable unbiased studies of the incorporation and dynamics of membrane proteins in more realistic CG membrane models.     

Interpretation of H-NMR Experiments on the Orientation of the Transmembrane Helix WALP23 by Computer Simulations

Orientation, dynamics, and packing of transmembrane helical peptides are important determinants of membrane protein structure, dynamics, and function. Because it is difficult to investigate these aspects by studying real membrane proteins, model transmembrane helical peptides are widely used. NMR experiments provide information on both orientation and dynamics of peptides, but they require that motional models be interpreted. Different motional models yield different interpretations of quadrupolar splittings (QS) in terms of helix orientation and dynamics. Here, we use coarse-grained (CG) molecular dynamics (MD) simulations to investigate the behavior of a well-known model transmembrane peptide, WALP23, under different hydrophobic matching/mismatching conditions. We compare experimental ²H-NMR QS (directly measured in experiments), as well as helix tilt angle and azimuthal rotation (not directly measured), with CG MD simulation results. For QS, the agreement is significantly better than previously obtained with atomistic simulations, indicating that equilibrium sampling is more important than atomistic details for reproducing experimental QS. Calculations of helix orientation confirm that the interpretation of QS depends on the motional model used. Our simulations suggest that WALP23 can form dimers, which are more stable in an antiparallel arrangement. The origin of the preference for the antiparallel orientation lies not only in electrostatic interactions but also in better surface complementarity. In most cases, a mixture of monomers and antiparallel dimers provides better agreement with NMR data compared to the monomer and the parallel dimer. CG MD simulations allow predictions of helix orientation and dynamics and interpretation of QS data without requiring any assumption about the motional model.     

Coarse-grained molecular dynamics of tetrameric transmembrane peptide bundles within a lipid bilayer

The conformations of model transmembrane peptides are studied to understand the structural and dynamical aspects of tetrameric bundles using a series of coarse grain (CG) molecular dynamics (MD) simulations since membrane proteins play a crucial role in cell function. In this work, two different amphipathic models have been constructed using similar hydrophobic/hydrophilic characteristics with two structurally distinct morphologies to evaluate the effect of roughness and hydrophilic topology on the structure of tetrameric bundles, one class that forms an ion-channel and one class that does not. Free energy calculations of typical amphipathic peptide topologies show that using a relatively smooth surface morphology allows for a stable conformation of the tetramer bundle in a diamond formation. However, the model with side chains attached to the core in order to roughen the surface has a stable square tetramer bundle which is consistent with experimental data and all-atom (AA) MD simulations. Comparisons of the CG simulations with AA MD simulations are in reasonable agreement with the formation of tetrameric homo-oligomers, partitioning within the lipid bilayer and tilt angle with respect to the bilayer normal. We concluded that a square or diamond shape tetrameric homo-oligomers could be stabilized by rational design of the peptide morphology and topology of the surface, thus allowing us to tune the permeability of the bundle or channel.     

Membrane Binding and Self-Association of the Epsin N-Terminal Homology Domain

Epsin possesses a conserved epsin N-terminal homology (ENTH) domain that acts as a phosphatidylinositol 4,5-bisphosphate‐lipid‐targeting and membrane‐curvature‐generating element. Upon binding phosphatidylinositol 4,5‐bisphosphate, the N-terminal helix (H₀) of the ENTH domain becomes structured and aids in the aggregation of ENTH domains, which results in extensive membrane remodeling. In this article, atomistic and coarse-grained (CG) molecular dynamics (MD) simulations are used to investigate the structure and the stability of ENTH domain aggregates on lipid bilayers. EPR experiments are also reported for systems composed of different ENTH-bound membrane morphologies, including membrane vesicles as well as preformed membrane tubules. The EPR data are used to help develop a molecular model of ENTH domain aggregates on preformed lipid tubules that are then studied by CG MD simulation. The combined computational and experimental approach suggests that ENTH domains exist predominantly as monomers on vesiculated structures, while ENTH domains self-associate into dimeric structures and even higher‐order oligomers on the membrane tubes. The results emphasize that the arrangement of ENTH domain aggregates depends strongly on whether the local membrane curvature is isotropic or anisotropic. The molecular mechanism of ENTH‐domain-induced membrane vesiculation and tubulation and the implications of the epsin's role in clathrin-mediated endocytosis resulting from the interplay between ENTH domain membrane binding and ENTH domain self-association are also discussed.     

Effect of periodic box size on aqueous molecular dynamics simulation of a DNA dodecamer with particle-mesh Ewald method

The particle-mesh Ewald (PME) method is considered to be both efficient and accurate for the evaluation of long-range electrostatic interactions in large macromolecular systems being studied by molecular dynamics simulations. This method assumes "infinite" periodic boundary conditions resembling the symmetry of a crystal environment. Can such a "solid-state" method accurately portray a macromolecular solute such as DNA in solution? To address this issue, we have performed three 1500-ps PME molecular dynamics (MD) simulations, each with a different box size, on the d(CGCGA6CG)-(CGT6CGCG) DNA dodecamer. The smallest box had the DNA solvated by a layer of water molecules of at least 5 A along each orthogonal direction. The intermediate size box and the largest box had the DNA solvated by a layer of water molecules of at least 10 A and 15 A, respectively, along each orthogonal direction. The intermediate size box in the present study is similar to the box size currently chosen by most workers in the field. Based on a comparison of RMSDs and curvature for this single DNA dodecamer sequence, the larger two box sizes do not appear to afford any extra benefit over the smallest box. The implications of this finding are briefly discussed.     

Coarse-grained modeling of the actin filament derived from atomistic-scale simulations

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.     

Coarse-grained modeling study of nonpeptide RGD ligand density and PEG molecular weight on the conformation of poly(γ-glutamyl-glutamate) paclitaxel conjugates

Molecular shape, flexibility, and surface hydrophilicity are thought to influence the ability of nanoparticles to cross biological barriers during drug delivery. In this study, coarse-grained (CG) molecular dynamics (MD) simulations were used to study these properties of a polymer-drug construct in potential clinical development: poly(γ-glutamyl-glutamate)-paclitaxel-poly(ethylene glycol) nonpeptide RGD (PGG-PTX-PEG-npRGD), a linear glutamyl-glutamate polymer with paclitaxel and poly(ethylene glycol)-nonpeptide RGD side groups. It was hypothesized that the PEG molecular weight (MW) (500 Da; 1,000 Da; and 2,000 Da) and nonpeptide RGD ligand density (4, 8, 12, and 16 per molecule), respectively, may have advantageous effects on the shape, flexibility, and surface hydrophilicity of PGG-PTX-PEG-npRGD. Circular dichroism spectroscopy was used to suggest initial structures for the all-atom (AA) models of PGG-PTX-PEG-npRGD, which were further converted to CG models using a commercially available mapping algorithm. Due to its semi-flexibility, PGG-PTX-PEG-npRGD is not limited to one specific conformation. Thus, CG MD simulations were run until statistical equilibrium, at which PGG-PTX-PEG-npRGD is represented as an ensemble of statistically similar conformations. The size of a PGG-PTX-PEG-npRGD molecule is not affected by the PEG MW or the nonpeptide RGD density, but higher PEG MW results in increased surface density of a PGG-PTX-PEG-npRGD molecule. Most PGG-PTX-PEG-npRGD shapes are globular, although filamentous shapes were also observed in the PEG500 and PEG1000 molecules. PEG500 and PEG1000 molecules are more flexible than PEG2000 systems. A higher presence of npRGD ligands results in decrease surface hydrophilicity of PGG-PTX-PEG-npRGD. These results indicate that the PGG-PTX-PEG1000-npRGD₄ and PGG-PTX-PEG1000-npRGD₈ molecules are the most efficacious candidates and are further recommended for experimental preclinical studies.     

REACH coarse-grained biomolecular simulation: transferability between different protein structural classes

Coarse graining of protein interactions provides a means of simulating large biological systems. The REACH (Realistic Extension Algorithm via Covariance Hessian) coarse-graining method, in which the force constants of a residue-scale elastic network model are calculated from the variance-covariance matrix obtained from atomistic molecular dynamics (MD) simulation, involves direct mapping between scales without the need for iterative optimization. Here, the transferability of the REACH force field is examined between protein molecules of different structural classes. As test cases, myoglobin (all α), plastocyanin (all β), and dihydrofolate reductase (α/β) are taken. The force constants derived are found to be closely similar in all three proteins. An MD version of REACH is presented, and low-temperature coarse-grained (CG) REACH MD simulations of the three proteins are compared with atomistic MD results. The mean-square fluctuations of the atomistic MD are well reproduced by the CGMD. Model functions for the CG interactions, derived by averaging over the three proteins, are also shown to produce fluctuations in good agreement with the atomistic MD. The results indicate that, similarly to the use of atomistic force fields, it is now possible to use a single, generic REACH force field for all protein studies, without having first to derive parameters from atomistic MD simulation for each individual system studied. The REACH method is thus likely to be a reliable way of determining spatiotemporal motion of a variety of proteins without the need for expensive computation of long atomistic MD simulations.     

Modeling the dynamics of the solvated SL1 domain of HIV-1 genomic RNA

A mode-coupling solution of the Smoluchowski diffusion equation (MCD theory), designed to describe the dynamics of wobbling macromolecules in water, is applied to a macromolecular bead model including water beads in the nearest layers. The necessary statistical averages are evaluated by time averaging along a molecular dynamics (MD) trajectory where both solute and water are introduced as atomistic models. The cross peaks in (1)H nuclear Overhauser effect spectroscopy (NOESY) NMR spectra that are routinely measured to determine biological structures are here calculated for the mutated 23 nucleotides stem-loop fragment of the SL1 domain in the HIV-1(Lai) genomic RNA. The calculations are in acceptable agreement with experiments without requiring any screening of the hydrodynamic interactions. The screening of hydrodynamics was necessary in previous MCD calculations obtained by using the same full atomistic MD trajectory, but a nonsolvated frictional model.     

Genetic evidence in the mouse solidifies the calcium hypothesis of myofiber death in muscular dystrophy

Muscular dystrophy (MD) refers to a clinically and genetically heterogeneous group of degenerative muscle disorders characterized by progressive muscle wasting and often premature death. Although the primary defect underlying most forms of MD typically results from a loss of sarcolemmal integrity, the secondary molecular mechanisms leading to muscle degeneration and myofiber necrosis is debated. One hypothesis suggests that elevated or dysregulated cytosolic calcium is the common transducing event, resulting in myofiber necrosis in MD. Previous measurements of resting calcium levels in myofibers from dystrophic animal models or humans produced equivocal results. However, recent studies in genetically altered mouse models have largely solidified the calcium hypothesis of MD, such that models with artificially elevated calcium in skeletal muscle manifest fulminant dystrophic-like disease, whereas models with enhanced calcium clearance or inhibited calcium influx are resistant to myofiber death and MD. Here, we will review the field and the recent cadre of data from genetically altered mouse models, which we propose have collectively mostly proven the hypothesis that calcium is the primary effector of myofiber necrosis in MD. This new consensus on calcium should guide future selection of drugs to be evaluated in clinical trials as well as gene therapy-based approaches.     

Combining optimal control theory and molecular dynamics for protein folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the Cα atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the Cα atoms. In turn, MD simulation provides an all-atom conformation whose Cα positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the Cα atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization-MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages.     

Assessment of Global and Regional Diffusion Changes along White Matter Tracts in Parkinsonian Disorders by MR Tractography

Purpose

The aim of the study was to determine the usefulness of diffusion tensor tractography (DTT) in parkinsonian disorders using a recently developed method for normalization of diffusion data and tract size along white matter tracts. Furthermore, the use of DTT in selected white matter tracts for differential diagnosis was assessed.

Methods

We quantified global and regional diffusion parameters in major white matter tracts in patients with multiple system atrophy (MSA), progressive nuclear palsy (PSP), idiopathic Parkinson’s disease (IPD) and healthy controls). Diffusion tensor imaging data sets with whole brain coverage were acquired at 3 T using 48 diffusion encoding directions and a voxel size of 2×2×2 mm³. DTT of the corpus callosum (CC), cingulum (CG), corticospinal tract (CST) and middle cerebellar peduncles (MCP) was performed using multiple regions of interest. Regional evaluation comprised projection of fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD) and the apparent area coefficient (AAC) onto a calculated mean tract and extraction of their values along each structure.

Results

There were significant changes of global DTT parameters in the CST (MSA and PSP), CC (PSP) and CG (PSP). Consistent tract-specific variations in DTT parameters could be seen along each tract in the different patient groups and controls. Regional analysis demonstrated significant changes in the anterior CC (MD, RD and FA), CST (MD) and CG (AAC) of patients with PSP compared to controls. Increased MD in CC and CST, as well as decreased AAC in CG, was correlated with a diagnosis of PSP compared to IPD.

Conclusions

DTT can be used for demonstrating disease-specific regional white matter changes in parkinsonian disorders. The anterior portion of the CC was identified as a promising region for detection of neurodegenerative changes in patients with PSP, as well as for differential diagnosis between PSP and IPD.