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.     

Hydrophobic mismatch and lipid sorting near OmpA in mixed bilayers: atomistic and coarse-grained simulations

To understand the effects of lipid composition on membrane protein function in a mixture as complex as a biomembrane, one must know whether the lipid composition local to the protein differs from the mean lipid composition. In this study, we simulated the transmembrane domain of a β-barrel protein, OmpA, in mixtures of lipids of different tail lengths under conditions of negative hydrophobic mismatch, i.e., local bilayer thinning. We modeled the influence of OmpA on the local lipid composition both at a coarse-grained (CG) resolution using conventional molecular dynamics, and at an atomistic resolution within the semi-grand canonical ensemble using mutation moves to rapidly approach an equilibrium lateral distribution of lipids. Moderate enrichment of the shorter tail component (either DDPC in DDPC/DMPC mixtures or DMPC in DMPC/DSPC mixtures) extending 2-3 nm away from the protein surface was observed with both the atomistic and CG models. The similarity in trends suggests that the more computationally economical CG models capture the essential features of lipid sorting induced by hydrophobic mismatch.     

Coarse-Graining Provides Insights on the Essential Nature of Heterogeneity in Actin Filaments

Experiments have shown that actin is structurally polymorphic, but knowledge of the details of molecular level heterogeneity in both the dynamics of a single subunit and the interactions between subunits is still lacking. Here, using atomistic molecular dynamics simulations of the actin filament, we identify domains of atoms that move in a correlated fashion, quantify interactions between these domains using coarse-grained (CG) analysis methods, and perform CG simulations to explore the importance of filament heterogeneity. The persistence length and torsional stiffness calculated from molecular dynamics simulation data agree with experimental values. We additionally observe that distinct actin conformations coexist in actin filaments. The filaments also exhibit random twist angles that are broadly distributed. CG analysis reveals that interactions between equivalent CG pairs vary from one subunit to another. To explore the importance of heterogeneity on filament dynamics, we perform CG simulations using different methods of parameterization to show that only by including heterogeneous interactions can we reproduce the twist angles and related properties. Free energy calculations further suggest that in general the actin filament is best represented as a set of subunits with differing CG sites and interactions, and the incorporating heterogeneity into the CG interactions is more important than including that in the CG sites. Our work therefore presents a systematic method to explore molecular level detail in this large and complex biopolymer.     

Molecular dynamics simulation of intrinsically disordered proteins

Intrinsically disordered proteins are biomolecules that do not have a definite 3D structure; therefore, their dynamical simulation cannot start from a known list of atomistic positions, such as a Protein Data Bank file. We describe a method to start a computer simulation of these proteins. The first step of the procedure is the creation of a multi-rod configuration of the molecule, derived from its primary sequence. This structure is dynamically evolved in vacuo until its gyration radius reaches the experimental average value; at this point solvent molecules, in explicit or implicit implementation, are added to the protein and a regular molecular dynamics simulation follows. We have applied this procedure to the simulation of tau, one of the largest totally disordered proteins.     

Refinement of a coarse-grained model of poly(2,6-dimethyl-1,4-phenylene ether) and its application to blends of PPE and PS

A coarse-grained (CG) molecular simulation model has been refined for poly(2,6-dimethyl-1,4-phenylene ether) (PPE). This was successfully validated against atomistic simulation and experimental data. Particularly, the glass transition temperature (T_g) of PPE was studied using both atomistic and CG models and compared favourably to experimental data. In addition, we used the CG model together with an existing Martini CG model of polystyrene (PS) to study the blending behaviour of these two polymers. We solved the problem to mix the different potentials and molecular dynamics of high-molecular-weight blends of PPE/PS was performed in detail.     

Coarse-Grained Molecular Models of Water: A Review

Coarse-grained (CG) models have proven to be very effective tools in the study of phenomena or systems that involve large time- and length-scales. By decreasing the degrees of freedom in the system and using softer interactions than seen in atomistic models, larger timesteps can be used and much longer simulation times can be studied. CG simulations are widely used to study systems of biological importance that are beyond the reach of atomistic simulation, necessitating a computationally efficient and accurate CG model for water. In this review, we discuss the methods used for developing CG water models and the relative advantages and disadvantages of the resulting models. In general, CG water models differ with regards to how many waters each CG group or bead represents, whether analytical or tabular potentials have been used to describe the interactions, and how the model incorporates electrostatic interactions. Finally, how the models are parameterized depends on their application, so, while some are fitted to experimental properties such as surface tension and density, others are fitted to radial distribution functions extracted from atomistic simulations.     

Characterisation of the hydrophobic collapse of polystyrene in water using free energy techniques

We characterise the hydrophobic collapse of single polystyrene chains in water using molecular dynamics simulations. Specifically, we calculate the potential of mean force for the collapse of a single polystyrene chain in water using metadynamics, comparing the results between all atomistic with coarse-grained (CG) molecular simulation. We next explore the scaling behaviour of the collapsed globular shape at the minimum energy configuration, characterised by the radius of gyration, as a function of chain length. The exponent is close to one third, consistent with that predicted for a polymer chain in bad solvent. We also explore the scaling behaviour of the solvent accessible surface area (SASA) as a function of chain length, finding a similar exponent for both all atomistic and CG simulations. Furthermore, calculation of the local water density as a function of chain length near the minimum energy configuration suggests that intermediate chain lengths are more likely to form dewetted states, as compared to shorter or longer chain lengths.     

Study of the Alzheimer's Aβ40 peptide in SDS micelles using molecular dynamics simulations

The interaction of the Alzheimer's amyloid beta peptide, Aβ40, with sodium dodecyl sulfate (SDS) micelles, together with the self-assembly of SDS molecules around the peptide from an initial random distribution were studied using atomistic and coarse-grained (CG) molecular dynamics simulations. In atomistic simulations, the peptide structure in the micelle was characterized by two helical regions connected through a short hinge. The initial structure of the system was shown to affect the simulation results. The atomistic self-assembly of SDS molecules resulted in a 38-molecule micelle around the peptide, along with some globules and individual molecules. Coarse-grained simulation results, however, did not show such a difference, and at the end of all CG simulations, a complete 60-molecule micelle was obtained, with the peptide located at the interface of the micelle with water. The obtained CG radial density profiles and SDS micelle size and shape properties were identical for all CG simulations.     

Brownian dynamics simulations of ion atmospheres around polyalanine and B-DNA: effects of biomolecular dielectric

We have extended an earlier Brownian dynamics simulation algorithm for simulating the structural dynamics of ions around biomolecules to accommodate dielectric inhomogeneity. The electrostatic environment of a biomolecule immersed in water was obtained by numerically solving the Poisson equation with the biomolecule treated as a low dielectric region and the solvent treated as a high dielectric region. Instead of using the mean-field type approximations of ion interactions as in the Poisson-Boltzmann model, the ions were treated explicitly by allowing them to evolve dynamically under the electrostatic field of the biomolecule. This model thus accounts for ion-ion correlations and the finite-size effects of the ions. For a 13-residue alpha-helical polyalanine and a 12-base-pair bp B-form DNA, we found that the choice of the dielectric constant of the biomolecule has much larger effects on the mean ionic structure around the biomolecule than on the fluctuational and dynamical properties of the ions surrounding the biomolecule.     

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.     

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.     

Multiscale modeling of cellular actin filaments: from atomistic molecular to coarse-grained dynamics

In this article, we present a computational multiscale model for the characterization of subcellular proteins. The model is encoded inside a simulation tool that builds coarse-grained (CG) force fields from atomistic simulations. Equilibrium molecular dynamics simulations on an all-atom model of the actin filament are performed. Then, using the statistical distribution of the distances between pairs of selected groups of atoms at the output of the MD simulations, the force field is parameterized using the Boltzmann inversion approach. This CG force field is further used to characterize the dynamics of the protein via Brownian dynamics simulations. This combination of methods into a single computational tool flow enables the simulation of actin filaments with length up to 400 nm, extending the time and length scales compared to state-of-the-art approaches. Moreover, the proposed multiscale modeling approach allows to investigate the relationship between atomistic structure and changes on the overall dynamics and mechanics of the filament and can be easily (i) extended to the characterization of other subcellular structures and (ii) used to investigate the cellular effects of molecular alterations due to pathological conditions.     

On the interpretation and prediction of X-ray scattering profiles of biomolecules in solution

If solution scattering curves can be accurately predicted from structural models, measurements can provide useful tests of predictions of secondary and tertiary structure. We have developed a computational technique for the prediction and interpretation of x-ray scattering profiles of biomolecules in solution. The method employs a Monte Carlo procedure for the generation of length distribution functions and provides predictions to moderate resolution (～5 Å). In addition to facilitating the assignment and interpretation of features in a solution scattering profile, the method also allows the elucidation of the role of protein motion in shaping the final scattering curve. The effect of protein motion on a scattering profile is investigated by generating scattering curves from several consecutive 0.147 ps atomic coordinate frames from a molecular dynamics simulation of the motion of bovine pancreatic trypsin inhibitor (BPTI) [McCammon, J. A. & Karplus, M. (1980) Annu. Rev. Phys. Chem. 31 , 29–45]. The theoretical approach is applied to chicken egg white lysozyme and BPTI, and the overall features in the resulting theoretical scattering profiles match well with the experimental solution scattering curves recorded on film. It is apparent from this study that the scattering profile prediction technique in conjunction with other experimental methods may have value in testing ideas of conformational change based on crystallographic studies; investigations of this type would include a comparison of predicted scattering curves generated from a variety of crystallographic models with an actual scattering profile of the biomolecule in solution.     

Multiple Time Step Brownian Dynamics for Long Time Simulation of Biomolecules

We report a multiple time step algorithm applied to an atomistic Brownian dynamics simulation for simulating the long time scale dynamics of biomolecules. The algorithm was based on the original multiple time step method; a short time step was used to keep faster motions in local equilibrium. When applied to a 28-mer # # ! folded peptide, the simulation gave stable trajectories and the computation time was reduced by a factor of 160 compared to a conventional molecular dynamics simulation using explicit water molecules. We applied it for the folding simulation of a 13-mer ! -helical peptide, giving a successful folding simulation. These results indicate that the Brownian dynamics with the multiple time step algorithm is useful for studies of biomolecular motions by long time simulation.     

Reconstruction of low-resolution molecular structures from simulated atomic force microscopy images

BackgroundAtomic Force Microscopy (AFM) is an experimental technique to study structure-function relationship of biomolecules. AFM provides images of biomolecules at nanometer resolution. High-speed AFM experiments produce a series of images following dynamics of biomolecules. To further understand biomolecular functions, information on three-dimensional (3D) structures is beneficial.MethodWe aim to recover 3D information from an AFM image by computational modeling. The AFM image includes only low-resolution representation of a molecule; therefore we represent the structures by a coarse grained model (Gaussian mixture model). Using Monte-Carlo sampling, candidate models are generated to increase similarity between AFM images simulated from the models and target AFM image.ResultsThe algorithm was tested on two proteins to model their conformational transitions. Using a simulated AFM image as reference, the algorithm can produce a low-resolution 3D model of the target molecule. Effect of molecular orientations captured in AFM images on the 3D modeling performance was also examined and it is shown that similar accuracy can be obtained for many orientations.ConclusionsThe proposed algorithm can generate 3D low-resolution protein models, from which conformational transitions observed in AFM images can be interpreted in more detail.General significanceHigh-speed AFM experiments allow us to directly observe biomolecules in action, which provides insights on biomolecular function through dynamics. However, as only partial structural information can be obtained from AFM data, this new AFM based hybrid modeling method would be useful to retrieve 3D information of the entire biomolecule.     

Structure-Based Simulations of the Translocation Mechanism of the Hepatitis C Virus NS3 Helicase along Single-Stranded Nucleic Acid

The NS3 helicase of Hepatitis C virus is an ATP-fueled molecular motor that can translocate along single-stranded (ss) nucleic acid, and unwind double-stranded nucleic acids. It makes a promising antiviral target and an important prototype system for helicase research. Despite recent progress, the detailed mechanism of NS3 helicase remains unknown. In this study, we have combined coarse-grained (CG) and atomistic simulations to probe the translocation mechanism of NS3 helicase along ssDNA. At the residue level of detail, our CG simulations have captured functionally important interdomain motions of NS3 helicase and reproduced single-base translocation of NS3 helicase along ssDNA in the 3′–5′ direction, which is in good agreement with experimental data and the inchworm model. By combining the CG simulations with residue-specific perturbations to protein-DNA interactions, we have identified a number of key residues important to the translocation machinery that agree with previous structural and mutational studies. Additionally, our atomistic simulations with targeted molecular dynamics have corroborated the findings of CG simulations and further revealed key protein-DNA hydrogen bonds that break/form during the transitions. This study offers, to our knowledge, the most detailed and realistic simulations of translocation mechanism of NS3 helicase. The simulation protocol established in this study will be useful for designing inhibitors that target the translocation machinery of NS3 helicase, and for simulations of a variety of nucleic-acid-based molecular motors.     

Coarse grain lipid-protein molecular interactions and diffusion with MsbA flippase

Coarse-grained (CG) modeling has proven effective for simulating lipid bilayer dynamics on scales of biological interest. Modeling the dynamics of flexible membrane proteins within the bilayer, on the other hand, poses a considerable challenge due to the complexity of the folding or conformational landscape. In the present work, the multiscale coarse-graining method is applied to atomistic peptide-lipid "soup" simulations to develop a general set of CG protein-lipid interaction potentials. The reduced model was constructed to be compatible with recent solvent-free CG models developed for protein-protein folding and lipid-lipid model bilayer interactions. The utility of the force field was demonstrated by molecular dynamics simulation of the MsbA ABC transporter in a mixed DOPC/DOPE bilayer. An elastic network was parameterized to restrain the MsbA dimer in its open, closed and hydrolysis intermediate conformations and its impact on domain flexibility was examined. Conformational stability enabled long-time dynamics simulation of MsbA freely diffusing in a 25 nm membrane patch. Three-dimensional density analysis revealed that a shell of weakly bound "annular lipids" solvate the membrane accessible surface of MsbA and its internal substrate-binding chamber. The annular lipid binding modes, along with local perturbations in head group structure, are a function of the orientation of grooves formed between transmembrane helices and may influence the alternating access mechanism of substrate entry and translocation.     

Comparing experimental and simulated pressure-area isotherms for DPPC

Although pressure-area isotherms are commonly measured for lipid monolayers, it is not always appreciated how much they can vary depending on experimental factors. Here, we compare experimental and simulated pressure-area isotherms for dipalmitoylphosphatidylcholine (DPPC) at temperatures ranging between 293.15 K and 323.15 K, and explore possible factors influencing the shape and position of the isotherms. Molecular dynamics simulations of DPPC monolayers using both coarse-grained (CG) and atomistic models yield results that are in rough agreement with some of the experimental isotherms, but with a steeper slope in the liquid-condensed region than seen experimentally and shifted to larger areas. The CG lipid model gives predictions that are very close to those of atomistic simulations, while greatly improving computational efficiency. There is much more variation among experimental isotherms than between isotherms obtained from CG simulations and from the most refined simulation available. Both atomistic and CG simulations yield liquid-condensed and liquid-expanded phase area compressibility moduli that are significantly larger than those typically measured experimentally, but compare well with some experimental values obtained under rapid compression.