Coarse-grained biomolecular simulation with REACH: realistic extension algorithm via covariance Hessian

Coarse-graining of protein interactions provides a means of simulating large biological systems. Here, a coarse-graining method, REACH, is introduced, 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. In test calculations, the C(alpha)-atoms variance-covariance matrices are calculated from the ensembles of 1-ns atomistic MD trajectories in monomeric and dimeric myoglobin, and used to derive coarse-grained force constants for the local and nonbonded interactions. Construction of analytical model functions of the distance-dependence of the interresidue force constants allows rapid calculation of the REACH normal modes. The model force constants from monomeric and dimeric myoglobin are found to be similar in magnitude to each other. The MD intra- and intermolecular mean-square fluctuations and the vibrational density of states are well reproduced by the residue-scale REACH normal modes without requiring rescaling of the force constant parameters. The temperature-dependence of the myoglobin REACH force constants reveals that the dynamical transition in protein internal fluctuations arises principally from softening of the elasticity in the nonlocal interactions. The REACH method is found to be a reliable way of determining spatiotemporal protein motion without the need for expensive computations of long atomistic MD simulations.     

REACH Coarse-Grained Simulation of a Cellulose Fiber

A molecular level understanding of the structure, dynamics and mechanics of cellulose fibers can aid in understanding the recalcitrance of biomass to hydrolysis in cellulosic biofuel production. Here, a residue-scale REACH (Realistic Extension Algorithm via Covariance Hessian) coarse-grained force field was derived from all-atom molecular dynamics (MD) simulations of the crystalline Iβ cellulose fibril. REACH maps the atomistic covariance matrix onto coarse-grained elastic force constants. The REACH force field was found to reproduce the positional fluctuations and low-frequency vibrational spectra from the all-atom model, allowing elastic properties of the cellulose fibril to be characterized using the coarse-grained force field with a speedup of >20 relative to atomistic MD on systems of the same size. The calculated longitudinal/transversal Young's modulus and the velocity of sound are in agreement with experiment. The persistence length of a 36-chain cellulose microcrystal was estimated to be ～380 μm. Finally, the normal-mode analysis with the REACH force field suggests that intrinsic dynamics might facilitate the deconstruction of the cellulose fibril from the hydrophobic surface.     

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.     

Systematic multiscale parameterization of heterogeneous elastic network models of proteins

We present a method to parameterize heterogeneous elastic network models (heteroENMs) of proteins to reproduce the fluctuations observed in atomistic simulations. Because it is based on atomistic simulation, our method allows the development of elastic coarse-grained models of proteins under different conditions or in different environments. The method is simple and applicable to models at any level of coarse-graining. We validated the method in three systems. First, we computed the persistence length of ADP-bound F-actin, using a heteroENM model. The value of 6.1 ± 1.6 μm is consistent with the experimentally measured value of 9.0 ± 0.5 μm. We then compared our method to a uniform elastic network model and a realistic extension algorithm via covariance Hessian (REACH) model of carboxy myoglobin, and found that the heteroENM method more accurately predicted mean-square fluctuations of α-carbon atoms. Finally, we showed that the method captures critical differences in effective harmonic interactions for coarse-grained models of the N-terminal Bin/amphiphysin/Rvs (N-BAR) domain of amphiphysin, by building models of N-BAR both bound to a membrane and free in solution.     

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.     

Reconstruction and Stability of Secondary Structure Elements in the Context of Protein Structure Prediction

Efficient and accurate reconstruction of secondary structure elements in the context of protein structure prediction is the major focus of this work. We present a novel approach capable of reconstructing α-helices and β-sheets in atomic detail. The method is based on Metropolis Monte Carlo simulations in a force field of empirical potentials that are designed to stabilize secondary structure elements in room-temperature simulations. Particular attention is paid to lateral side-chain interactions in β-sheets and between the turns of α-helices, as well as backbone hydrogen bonding. The force constants are optimized using contrastive divergence, a novel machine learning technique, from a data set of known structures. Using this approach, we demonstrate the applicability of the framework to the problem of reconstructing the overall protein fold for a number of commonly studied small proteins, based on only predicted secondary structure and contact map. For protein G and chymotrypsin inhibitor 2, we are able to reconstruct the secondary structure elements in atomic detail and the overall protein folds with a root mean-square deviation of <10 Å. For cold-shock protein and the SH3 domain, we accurately reproduce the secondary structure elements and the topology of the 5-stranded β-sheets, but not the barrel structure. The importance of high-quality secondary structure and contact map prediction is discussed.     

Multiscale Coarse-Graining of the Protein Energy Landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.     

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.     

Coarse Grained Normal Mode Analysis vs. Refined Gaussian Network Model for Protein Residue-Level Structural Fluctuations

We investigate several approaches to coarse grained normal mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues and the forces among them. Single-atom representations using the backbone atoms C _α , C, N, and C _β are considered. Combinations of some of these atoms are also tested. The force constants between the representative atoms are extracted from the Hessian matrix of the energy function and served as the force constants between the corresponding residues. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The results are compared with all-atom normal mode analysis and the residue-level Gaussian Network Model. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, while their B-factor correlations are also higher. Their B-factor correlations are comparable with those estimated by the Gaussian Network Model and in many cases better. The extracted force constants are surveyed for different pairs of residues with different numbers of separation residues in sequence. The statistical averages are used to build a refined Gaussian Network Model, which is able to predict residue-level structural fluctuations significantly better than the conventional Gaussian Network Model in many test cases.     

Investigation of phase transitions of saturated phosphocholine lipid bilayers via molecular dynamics simulations

Lipid bilayers play an important role in biological systems as they protect cells against unwanted chemicals and provide a barrier for material inside a cell from leaking out. In this paper, nearly 30 μs of molecular dynamics (MD) simulations were performed to investigate phase transitions of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-phosphocholine (DPPC) lipid bilayers from the liquid crystalline (L_α) to the ripple (P_β) and to the gel phase (L_β). Our MD simulations accurately predict the main transition temperature for the single-component bilayers. A key focus of this work is to quantify the structure of the P_β phase for DMPC and compare with measures from x-ray experiments. The P_β major arm has similar structure to that of the L_β, while the thinner minor arm has interdigitated chains and the transition region between these two regions has large chain splay and disorder. At lower temperatures, our MD simulations predict the formation of the L_β phase with tilted fatty acid chains. The P_β and L_β phases are studied for mixtures of DMPC and DPPC and compare favorably with experiment. Overall, our MD simulations provide evidence for the relevancy of the CHARMM36 lipid force field for structures and add to our understanding of the less-defined P_β phase.     

Mechanical Resistance in Unstructured Proteins

Single-molecule pulling experiments on unstructured proteins linked to neurodegenerative diseases have measured rupture forces comparable to those for stable folded proteins. To investigate the structural mechanisms of this unexpected force resistance, we perform pulling simulations of the amyloid β-peptide (Aβ) and α-synuclein (αS), starting from simulated conformational ensembles for the free monomers. For both proteins, the simulations yield a set of rupture events that agree well with the experimental data. By analyzing the conformations occurring shortly before rupture in each event, we find that the mechanically resistant structures share a common architecture, with similarities to the folds adopted by Aβ and αS in amyloid fibrils. The disease-linked Arctic mutation of Aβ is found to increase the occurrence of highly force-resistant structures. Our study suggests that the high rupture forces observed in Aβ and αS pulling experiments are caused by structures that might have a key role in amyloid formation.     

Molecular dynamics simulations of the photoactive protein nitrile hydratase

Nitrile hydratase (NHase) is an enzyme used in the industrial biotechnological production of acrylamide. The active site, which contains nonheme iron or noncorrin cobalt, is buried in the protein core at the interface of two domains, α and β. Hydrogen bonds between βArg-56 and αCys-114 sulfenic acid (αCEA114) are important to maintain the enzymatic activity. The enzyme may be inactivated by endogenous nitric oxide (NO) and activated by absorption of photons of wavelength λ < 630 nm. To explain the photosensitivity and to propose structural determinants of catalytic activity, differences in the dynamics of light-active and dark-inactive forms of NHase were investigated using molecular dynamics (MD) modeling. To this end, a new set of force field parameters for nonstandard NHase active sites have been developed. The dynamics of the photodissociated NO ligand in the enzyme channel was analyzed using the locally enhanced sampling method, as implemented in the MOIL MD package. A series of 1 ns trajectories of NHases shows that the protonation state of the active site affects the dynamics of the catalytic water and NO ligand close to the metal center. MD simulations support the catalytic mechanism in which a water molecule bound to the metal ion directly attacks the nitrile carbon.     

Dynameomics: A Consensus View of the Protein Unfolding/Folding Transition State Ensemble across a Diverse Set of Protein Folds

The Dynameomics project aims to simulate a representative sample of all globular protein metafolds under both native and unfolding conditions. We have identified protein unfolding transition state (TS) ensembles from multiple molecular dynamics simulations of high-temperature unfolding in 183 structurally distinct proteins. These data can be used to study individual proteins and individual protein metafolds and to mine for TS structural features common across all proteins. Separating the TS structures into four different fold classes (all proteins, all-α, all-β, and mixed α/β and α + β) resulted in no significant difference in the overall protein properties. The residues with the most contacts in the native state lost the most contacts in the TS ensemble. On average, residues beginning in an α-helix maintained more structure in the TS ensemble than did residues starting in β-strands or any other conformation. The metafolds studied here represent 67% of all known protein structures, and this is, to our knowledge, the largest, most comprehensive study of the protein folding/unfolding TS ensemble to date. One might have expected broad distributions in the average global properties of the TS relative to the native state, indicating variability in the amount of structure present in the TS. Instead, the average global properties converged with low standard deviations across metafolds, suggesting that there are general rules governing the structure and properties of the TS.     

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.     

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.

Glycan flexibility: insights into nanosecond dynamics from a microsecond molecular dynamics simulation explaining an unusual nuclear Overhauser effect

An atomistic all-atom molecular dynamics simulation of the trisaccharide β-d-ManpNAc-(1→4)[α-d-Glcp-(1→3)]-α-l-Rhap-OMe with explicit solvent molecules has been carried out. The trisaccharide represents a model for the branching region of the O-chain polysaccharide of a strain from Aeromonas salmonicida. The extensive MD simulations having a 1-μs duration revealed a conformational dynamics process on the nanosecond time scale, that is, a ‘time window’ not extensively investigated for carbohydrates to date. The results obtained from the MD simulation underscore the predictive power of molecular simulations in studies of biomolecular systems and also explain an unusual nuclear Overhauser effect originating from conformational exchange.     

Molecular modelling of the mass density of single proteins

Using molecular dynamics (MD) simulations, the density of single proteins and its temperature dependence was modelled starting from the experimentally determined protein structure and a generic, transferable force field, without the need of prior parameterization. Although all proteins consist of the same 20 amino acids, their density in aqueous solution varies up to 10% and the thermal expansion coefficient up to twofold. To model the protein density, systematic MD simulations were carried out for 10 proteins with a broad range of densities (1.32–1.43?g/cm³) and molecular weights (7–97?kDa). The simulated densities deviated by less than 1.4% from their experimental values that were available for four proteins. Further analyses of protein density showed that it can be essentially described as a consequence of amino acid composition. For five proteins, the density was simulated at different temperatures. The simulated thermal expansion coefficients ranged between 4.3 and 7.1?×?10^?4?K^?1 and were similar to the experimentally determined values of ribonuclease-A and lysozyme (deviations of 2.4 and 14.6%, respectively). Further analyses indicated that the thermal expansion coefficient is linked to the temperature dependence of atomic fluctuations: proteins with a high thermal expansion coefficient show a low increase in flexibility at increasing temperature. A low increase in atomic fluctuations with temperature has been previously described as a possible mechanism of thermostability. Thus, a high thermal expansion coefficient might contribute to protein thermostability.     

Binding and Cleavage of E. coli HUβ by the E. coli Lon Protease

The Escherichia coli Lon protease degrades the E. coli DNA-binding protein HUβ, but not the related protein HUα. Here we show that the Lon protease binds to both HUβ and HUα, but selectively degrades only HUβ in the presence of ATP. Mass spectrometry of HUβ peptide fragments revealed that region K18-G22 is the preferred cleavage site, followed in preference by L36-K37. The preferred cleavage site was further refined to A20-A21 by constructing and testing mutant proteins; Lon degraded HUβ-A20Q and HUβ-A20D more slowly than HUβ. We used optical tweezers to measure the rupture force between HU proteins and Lon; HUα, HUβ, and HUβ-A20D can bind to Lon, and in the presence of ATP, the rupture force between each of these proteins and Lon became weaker. Our results support a mechanism of Lon protease cleavage of HU proteins in at least three stages: binding of Lon with the HU protein (HUβ, HUα, or HUβ-A20D); hydrolysis of ATP by Lon to provide energy to loosen the binding to the HU protein and to allow an induced-fit conformational change; and specific cleavage of only HUβ.