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 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 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.     

Anisotropic elastic network modeling of entire microtubules

Microtubules are supramolecular structures that make up the cytoskeleton and strongly affect the mechanical properties of the cell. Within the cytoskeleton filaments, the microtubule (MT) exhibits by far the highest bending stiffness. Bending stiffness depends on the mechanical properties and intermolecular interactions of the tubulin dimers (the MT building blocks). Computational molecular modeling has the potential for obtaining quantitative insights into this area. However, to our knowledge, standard molecular modeling techniques, such as molecular dynamics (MD) and normal mode analysis (NMA), are not yet able to simulate large molecular structures like the MTs; in fact, their possibilities are normally limited to much smaller protein complexes. In this work, we developed a multiscale approach by merging the modeling contribution from MD and NMA. In particular, MD simulations were used to refine the molecular conformation and arrangement of the tubulin dimers inside the MT lattice. Subsequently, NMA was used to investigate the vibrational properties of MTs modeled as an elastic network. The coarse-grain model here developed can describe systems of hundreds of interacting tubulin monomers (corresponding to up to 1,000,000 atoms). In particular, we were able to simulate coarse-grain models of entire MTs, with lengths up to 350 nm. A quantitative mechanical investigation was performed; from the bending and stretching modes, we estimated MT macroscopic properties such as bending stiffness, Young modulus, and persistence length, thus allowing a direct comparison with experimental data.     

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.     

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.     

Mechanical Properties of the Icosahedral Shell of Southern Bean Mosaic Virus: A Molecular Dynamics Study

The mechanical properties of viral shells are crucial for viral assembly and infection. To study their distribution and heterogeneity on the viral surface, we performed atomistic force-probe molecular dynamics simulations of the complete shell of southern bean mosaic virus, a prototypical T = 3 virus, in explicit solvent. The simulation system comprised more than 4,500,000 atoms. To facilitate direct comparison with atomic-force microscopy (AFM) measurements, a Lennard-Jones sphere was used as a model of the AFM tip, and was pushed with different velocities toward the capsid protein at 19 different positions on the viral surface. A detailed picture of the spatial distribution of elastic constants and yielding forces was obtained that can explain corresponding heterogeneities observed in previous AFM experiments. Our simulations reveal three different deformation regimes: a prelinear regime of outer surface atom rearrangements, a linear regime of elastic capsid deformation, and a rearrangement regime that describes irreversible structural changes and the transition from elastic to plastic deformation. For both yielding forces and elastic constants, a logarithmic velocity dependency is evident over nearly two decades, the explanation for which requires including nonequilibrium effects within the established theory of enforced barrier crossing.     

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.     

Primary Changes of the Mechanical Properties of Southern Bean Mosaic Virus upon Calcium Removal

The mechanical properties of viral shells are crucial determinates for the pathway and mechanism by which the genetic material leaves the capsid during infection and have therefore been studied by atomic force microscopy as well as by atomistic simulations. The mechanical response to forces from inside the capsid are found to be relevant, especially after ion removal from the shell structure, which is generally assumed to be essential during viral infection; however, atomic force microscopy measurements are restricted to probing the capsids from outside, and the primary effect of ion removal is still inaccessible. To bridge this gap, we performed atomistic force-probe molecular dynamics simulations of the complete solvated icosahedral shell of Southern Bean Mosaic Virus and compared the distribution of elastic constants and yielding forces on the icosahedral shell for probing from inside with the distribution of outside mechanical properties obtained previously. Further, the primary effect of calcium removal on the mechanical properties on both sides, as well as on their spatial distribution, is quantified. Marked differences are seen particularly at the pentamer centers, although only small structural changes occur on the short timescales of the simulation. This unexpected primary effect, hence, precedes subsequent effects due to capsid swelling. In particular, assuming that genome release is preceded by an opening of capsomers instead of a complete capsid bursting, our observed weakening along the fivefold symmetry axes let us suggest pentamers as possible exit ports for RNA release.     

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.     

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.     

A multiscale coarse-grained model of the SARS-CoV-2 virion

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the COVID-19 pandemic. Computer simulations of complete viral particles can provide theoretical insights into large-scale viral processes including assembly, budding, egress, entry, and fusion. Detailed atomistic simulations are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and ongoing development of a largely “bottom-up” coarse-grained (CG) model of the SARS-CoV-2 virion. Data from a combination of cryo-electron microscopy (cryo-EM), x-ray crystallography, and computational predictions were used to build molecular models of structural SARS-CoV-2 proteins, which were then assembled into a complete virion model. We describe how CG molecular interactions can be derived from all-atom simulations, how viral behavior difficult to capture in atomistic simulations can be incorporated into the CG models, and how the CG models can be iteratively improved as new data become publicly available. Our initial CG model and the detailed methods presented are intended to serve as a resource for researchers working on COVID-19 who are interested in performing multiscale simulations of the SARS-CoV-2 virion.     

Dimer formation enhances structural differences between amyloid β-protein (1-40) and (1-42): an explicit-solvent molecular dynamics study

Amyloid β-protein (Aβ) is central to the pathology of Alzheimer's disease. A 5% difference in the primary structure of the two predominant alloforms, Aβ(1-40) and Aβ(1-42), results in distinct assembly pathways and toxicity properties. Discrete molecular dynamics (DMD) studies of Aβ(1-40) and Aβ(1-42) assembly resulted in alloform-specific oligomer size distributions consistent with experimental findings. Here, a large ensemble of DMD-derived Aβ(1-40) and Aβ(1-42) monomers and dimers was subjected to fully atomistic molecular dynamics (MD) simulations using the OPLS-AA force field combined with two water models, SPCE and TIP3P. The resulting all-atom conformations were slightly larger, less compact, had similar turn and lower β-strand propensities than those predicted by DMD. Fully atomistic Aβ(1-40) and Aβ(1-42) monomers populated qualitatively similar free energy landscapes. In contrast, the free energy landscape of Aβ(1-42) dimers indicated a larger conformational variability in comparison to that of Aβ(1-40) dimers. Aβ(1-42) dimers were characterized by an increased flexibility in the N-terminal region D1-R5 and a larger solvent exposure of charged amino acids relative to Aβ(1-40) dimers. Of the three positively charged amino acids, R5 was the most and K16 the least involved in salt bridge formation. This result was independent of the water model, alloform, and assembly state. Overall, salt bridge propensities increased upon dimer formation. An exception was the salt bridge propensity of K28, which decreased upon formation of Aβ(1-42) dimers and was significantly lower than in Aβ(1-40) dimers. The potential relevance of the three positively charged amino acids in mediating the Aβ oligomer toxicity is discussed in the light of available experimental data.     

How to predict diffusion of medium-sized molecules in polymer matrices. From atomistic to coarse grain simulations

The normal diffusion regime of many small and medium-sized molecules occurs on a time scale that is too long to be studied by atomistic simulations. Coarse-grained (CG) molecular simulations allow to investigate length and time scales that are orders of magnitude larger compared to classical molecular dynamics simulations, hence providing a valuable approach to span time and length scales where normal diffusion occurs. Here we develop a novel multi-scale method for the prediction of diffusivity in polymer matrices which combines classical and CG molecular simulations. We applied an atomistic-based method in order to parameterize the CG MARTINI force field, providing an extension for the study of diffusion behavior of penetrant molecules in polymer matrices. As a case study, we found the parameters for benzene (as medium sized penetrant molecule whose diffusivity cannot be determined through atomistic models) and Poly (vinyl alcohol) (PVA) as polymer matrix. We validated our extended MARTINI force field determining the self diffusion coefficient of benzene (2.27·10⁻⁹ m² s⁻¹) and the diffusion coefficient of benzene in PVA (0.263·10⁻¹² m² s⁻¹). The obtained diffusion coefficients are in remarkable agreement with experimental data (2.20·10⁻⁹ m² s⁻¹ and 0.25·10⁻¹² m² s⁻¹, respectively). We believe that this method can extend the application range of computational modeling, providing modeling tools to study the diffusion of larger molecules and complex polymeric materials.     

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.     

Conformational flexibility of the leucine binding protein examined by protein domain coarse-grained molecular dynamics

Periplasmic binding proteins are the initial receptors for the transport of various substrates over the inner membrane of gram-negative bacteria. The binding proteins are composed of two domains, and the substrate is entrapped between these domains. For several of the binding proteins it has been established that a closed-up conformation exists even without substrate present, suggesting a highly flexible apo-structure which would compete with the ligand-bound protein for the transporter interaction. For the leucine binding protein (LBP), structures of both open and closed conformations are known, but no closed-up structure without substrate has been reported. Here we present molecular dynamics simulations exploring the conformational flexibility of LBP. Coarse grained models based on the MARTINI force field are used to access the microsecond timescale. We show that a standard MARTINI model cannot maintain the structural stability of the protein whereas the ELNEDIN extension to MARTINI enables simulations showing a stable protein structure and nanosecond dynamics comparable to atomistic simulations, but does not allow the simulation of conformational flexibility. A modification to the MARTINI-ELNEDIN setup, referred to as domELNEDIN, is therefore presented. The domELNEDIN setup allows the protein domains to move independently and thus allows for the simulation of conformational changes. Microsecond domELNEDIN simulations starting from either the open or the closed conformations consistently show that also for LBP, the apo-structure is flexible and can exist in a closed form.

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

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.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.