Multiscale computer simulation of the immature HIV-1 virion.

Multiscale computer simulations, employing a combination of experimental data and coarse-graining methods, are used to explore the structure of the immature HIV-1 virion. A coarse-grained (CG) representation is developed for the virion membrane shell and Gag polypeptides using molecular level information. Building on the results from electron cryotomography experiments, the simulations under certain conditions reveal the existence of an incomplete p6 hexameric lattice formed from hexameric bundles of the Gag CA domains. In particular, the formation and stability of the immature Gag lattice at the CG level requires enhanced interfacial interactions of the CA protein C-terminal domains (CTDs). An exact mapping of the CG representation back to the molecular level then allows for detailed atomistic molecular dynamics studies to confirm the existence of these enhanced CA(CTD) interactions and to probe their possible origin. The multiscale simulations further provide insight into potential CA(CTD) mutations that may disrupt or modify the Gag immature lattice assembly process in the immature HIV-1 virion.

Hierarchical coarse-graining strategy for protein-membrane systems to access mesoscopic scales.

An overall multiscale simulation strategy for large scale coarse-grain simulations of membrane protein systems is presented. The protein is modeled as a heterogeneous elastic network, while the lipids are modeled using the hybrid analytic-systematic (HAS) methodology, where in both cases atomistic level information obtained from molecular dynamics simulation is used to parameterize the model. A feature of this approach is that from the outset liposome length scales are employed in the simulation (i.e., on the order of 1/2 a million lipids plus protein). A route to develop highly coarse-grained models from molecular-scale information is proposed and results for N-BAR domain protein remodeling of a liposome are presented.

Role of protein interactions in defining HIV-1 viral capsid shape and stability: a coarse-grained analysis.

Coarse-grained models of the HIV-1 CA dimer are constructed based on all-atom molecular dynamics simulations. Coarse-grained representations of the capsid shell, which is composed of approximately 1500 copies of CA proteins, are constructed and their stability is examined. A key interaction between carboxyl and hexameric amino terminal domains is shown to generate the curvature of the capsid shell. It is demonstrated that variation of the strength of this interaction for different subunits in the lattice can cause formation of asymmetric, conical-shaped closed capsid shells, and it is proposed that variations, in the structure of the additional carboxyl-amino terminal binding interface during self-assembly, are important aspects of capsid cone formation. These results are in agreement with recent structural studies of the capsid hexamer subunit, which suggest that variability in the binding interface is a cause of the differences in subunit environments that exist in a conical structure.

Multiscale simulation of protein mediated membrane remodeling.

Proteins interacting with membranes can result in substantial membrane deformations and curvatures. This effect is known in its broadest terms as membrane remodeling. This review article will survey current multiscale simulation methodologies that have been employed to examine protein mediated membrane remodeling.

Membrane binding by the endophilin N-BAR domain.

The structure of the endophilin N-terminal amphipathic helix Bin/Amphiphysin/Rvs-homology (N-BAR) domain is unique because of an additional insert helix under the arch of the N-BAR dimer. The structure of this additional helix has not been fully resolved in crystallographic studies, and thus presents a challenge to molecular-level analysis. Large-scale molecular-dynamics simulations were therefore employed to investigate the interaction of a single endophilin N-BAR with a lipid bilayer. Various possible configurations of the additional insert helix under the top of the arch of the endophilin N-BAR were modeled to examine their effect on membrane bending. A residue-residue and residue-lipid headgroup distance analysis, similar to that performed with electron paramagnetic resonance spectroscopy, revealed that the insert helix remains perpendicular to the long axis of the N-BAR over the duration of the simulations. It was also found that the degree of membrane bending is directly related to the orientation of the additional insert helix, and that the perpendicular configuration generates the largest curvature consistent with mutation experiments. In addition, the angle formed between the two N-BAR monomers at the top of the arch is sensitive to the orientation of the insert helices. A membrane sensing-binding-bending mechanism is proposed to describe the process of an endophilin N-BAR interaction with a membrane.

New insights into BAR domain-induced membrane remodeling.

Mesoscopic simulations and electron microscopy of N-BAR domain-induced liposome remodeling are used to characterize the process of liposome tubulation and vesiculation. The overall process of membrane remodeling is found to involve complex couplings among the N-BAR protein density, the degree of N-BAR oligomerization, and the membrane density. A comparison of complex remodeled liposome structures from mesoscopic simulations with those measured by electron microscopy experiments suggests that the process of membrane remodeling can be described via an appropriate mesoscopic free energy framework. Liposome remodeling more representative of F-BAR domains is also presented within the mesoscopic simulation framework.

Systematic multiscale simulation of membrane protein systems.

Current multiscale simulation approaches for membrane protein systems vary depending on their degree of connection to the underlying molecular scale interactions. Various approaches have been developed that include such information into coarse-grained models of both the membrane and the proteins. By contrast, other approaches employ parameterizations obtained from experimental data. Mesoscopic models operate at larger scales and have also been employed to examine membrane remodeling, protein inclusions, and ion channel gating. When bridged together such that molecular-level information is propagated between the different scales, a systematic multiscale methodology for membrane protein systems can be achieved.

Hybrid coarse-graining approach for lipid bilayers at large length and time scales.

A hybrid analytic-systematic (HAS) coarse-grained (CG) lipid model is developed and employed in a large-scale simulation of a liposome. The methodology is termed hybrid analytic-systematic because one component of the interaction between CG sites is variationally determined from the multiscale coarse-graining (MS-CG) methodology, whereas the remaining component utilizes an analytic potential. The systematic component models the in-plane center-of-mass interaction of the lipids as determined from an atomistic-level MD simulation of a bilayer. The analytic component is based on the well-known Gay-Berne ellipsoid-of-revolution liquid-crystal model and is designed to model the highly anisotropic interactions at a highly coarse-grained level. The HAS CG approach is the first step in an "aggressive" CG methodology designed to model multicomponent biological membranes at very large length and time scales.

The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models.

Coarse-grained (CG) models provide a computationally efficient method for rapidly investigating the long time- and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining (MS-CG) method [J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.

The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models.

The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM(+)NO(3) (-) ionic liquid are provided to illustrate the method.

Accelerated Superposition State Molecular Dynamics for Condensed Phase Systems.

An extension of superposition state molecular dynamics (SSMD) [Venkatnathan and Voth J. Chem. Theory Comput. 2005, 1, 36] is presented with the goal to accelerate timescales and enable the study of "long-time" phenomena for condensed phase systems. It does not require any a priori knowledge about final and transition state configurations, or specific topologies. The system is induced to explore new configurations by virtue of a fictitious (free-particle-like) accelerating potential. The acceleration method can be applied to all degrees of freedom in the system and can be applied to condensed phases and fluids.

Transient violations of the second law of thermodynamics in protein unfolding examined using synthetic atomic force microscopy and the fluctuation theorem.

The synthetic atomic force microscopy (AFM) method is developed to simulate a periodically replicated atomistic system subject to force and length fluctuations characteristic of an AFM experiment. This new method is used to examine the forced-extension and subsequent rupture of the alpha-helical linker connecting periodic images of a spectrin protein repeat unit. A two-dimensional potential of mean force (PMF) along the length and a reaction coordinate describing the state of the linker was calculated. This PMF reveals that the basic material properties of the spectrin repeat unit are sensitive to the state of linker, an important feature that cannot be accounted for in a one-dimensional PMF. Furthermore, nonequilibrium simulations were generated to examine the rupture event in the context of the fluctuation theorem. These atomistic simulations demonstrate that trajectories which are in apparent violation of the second law can overcome unfolding barriers at significantly reduced rupture forces.

Multiscale modeling of biomolecular systems: in serial and in parallel.

Considerable progress has been recently achieved in the multiscale modeling of complex biological processes. Multiscale models have now investigated the structure and dynamics of lipid membranes, proteins, peptides and DNA over length and time scales ranging from the atomic to the macroscopic. Serial multiscale methods that parameterize low-resolution coarse-grained models with data from high-resolution models have studied long time or length scale phenomena that cannot be investigated with atomically detailed models. Parallel multiscale methods that directly couple high- and low-resolution models have efficiently explored slow structural transitions and the importance of long-wavelength fluctuations for biological molecules. The success of such models relies upon new theories and methods for constructing accurate multiscale bridges that transfer information between models with different resolutions.

Multiscale coarse-graining and structural correlations: connections to liquid-state theory.

A statistical mechanical framework elucidates the significance of structural correlations between coarse-grained (CG) sites in the multiscale coarse-graining (MS-CG) method (Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469; J. Chem. Phys. 2005, 123, 134105). If no approximations are made, then the MS-CG method yields a many-body multidimensional potential of mean force describing the interactions between CG sites. However, numerical applications of the MS-CG method typically employ a set of pair potentials to describe nonbonded interactions. The analogy between coarse-graining and the inverse problem of liquid-state theory clarifies the general significance of three-particle correlations for the development of such CG pair potentials. It is demonstrated that the MS-CG methodology incorporates critical three-body correlation effects and that, for isotropic homogeneous systems evolving under a central pair potential, the MS-CG equations are a discretized representation of the well-known Yvon-Born-Green equation. Numerical calculations validate the theory and illustrate the role of these structural correlations in the MS-CG method.

Extending the fluctuation theorem to describe reaction coordinates.

The fluctuation theorem describes the distribution of work done on small systems which have been pushed out of equilibrium in response to an external field. The theorem has recently been a subject of much interest for describing single-molecule experiments and simulations. In this communication, it is shown how the fluctuation theorem can be extended to describe fluctuations not only in the work done on a system, but also in a reaction coordinate. The extension explored in this work allows for a generalized derivation of Hummer and Szabo's expression (G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. 98, 3658 (2001)) for reconstructing the potential of mean force from nonequilibrium trajectories. The derivation demonstrates how implementation of this expression can be more easily facilitated. Atomistic simulations of a biomolecular system are presented which support these results.

Membrane remodeling from N-BAR domain interactions: insights from multi-scale simulation.

Liposome remodeling processes (e.g., vesiculation and tubulation) due to N-BAR domain interactions with the lipid bilayer are explored with a multi-scale simulation approach. Results from atomistic-level molecular dynamics simulations of membrane binding to the concave face of N-BAR domains are used along with discretized mesoscopic field-theoretic simulations to examine how the spontaneous curvature fields generated by N-BAR domains result in membrane remodeling. It is found that tubulation can be generated by anisotropic N-BAR spontaneous curvature fields, whereas vesiculation is only observed with isotropic N-BAR spontaneous curvature fields at high density. The results of the multi-scale simulations provide insight into recent experimental observations.

Multiscale simulation of transmembrane proteins.

Multiscale simulation is employed to examine changes in atomistic-level protein structure due to long wavelength membrane undulations and plane stress fields. An ensemble of atomistic-level simulations of a model of a transmembrane influenza A virus M2 proton channel in a dimyristoylphosphatidylcholine (DMPC) bilayer is coupled to a corresponding mesoscopic model of a DMPC bilayer in an explicit mesoscopic solvent. Structural variations in the key proton gating His37 residues of the M2 channel are examined. Small, but distinct variations in the structure of the His37 residues are observed in both the open and closed states of the channel as a result of the coupling to mesoscopic-level membrane motions.

Atomistic and coarse-grained analysis of double spectrin repeat units: the molecular origins of flexibility.

Spectrin is an ubiquitous protein in metazoan cells, and its flexibility is one of the keys to maintaining cellular structure and organization. Both alpha-spectrin and beta-spectrin polypeptides consist primarily of triple coiled-coil modular repeat units, and two important factors that determine spectrin flexibility are the bending flexibility between two consecutive repeat units and the conformational flexibility of individual repeat units. Atomistic molecular dynamics (MD) simulations are used here to study double spectrin repeat units (DSRUs) from the human erythrocyte beta-spectrin (HEbeta89) and the chicken brain alpha-spectrin (CBalpha1617). From the results of MD simulations, a highly conserved Trp residue in the A-helix of most repeat units that has been suggested to be important in conferring stability to the coiled-coil structures is found not to have a significant effect on the conformational flexibility of individual repeat units. Characterization of the bending flexibility for two consecutive repeats of spectrin via atomistic simulations and coarse-grained (CG) modeling indicate that the bending flexibility is governed by the interactions between the AB-loop of the first repeat unit, the BC-loop of the second repeat unit and the linker region. Specifically, interactions between residues in these regions can lead to a strong directionality in the bending behavior of two repeat units. The biological implications of these finding are discussed.

Mesoscopic modeling of bacterial flagellar microhydrodynamics.

A particle-based hybrid method of elastic network model and smooth-particle hydrodynamics has been employed to describe the propulsion of bacterial flagella in a viscous hydrodynamic environment. The method explicitly models the two aspects of bacterial propulsion that involve flagellar flexibility and long-range hydrodynamic interaction of low-Reynolds-number flow. The model further incorporates the molecular organization of the flagellar filament at a coarse-grained level in terms of the 11 protofilaments. Each of these protofilaments is represented by a collection of material points that represent the flagellin proteins. A computational model of a single flexible helical segment representing the filament of a bacterial flagellum is presented. The propulsive dynamics and the flow fields generated by the motion of the model filament are examined. The nature of flagellar deformation and the influence of hydrodynamics in determining the shape of deformations are examined based on the helical filament.

A second generation mesoscopic lipid bilayer model: connections to field-theory descriptions of membranes and nonlocal hydrodynamics.

A new mesoscopic membrane model is developed in order to examine long-wavelength structural and dynamical membrane phenomena. Two different explicit mesoscopic solvent models are employed. The first mesoscopic solvent is denoted the big liquid oscillating blob system, which is parametrized to model water at a coarse-grained level and is motivated by a Langevin-like approach; the resulting membrane dynamics predict a solvent viscosity dependence consistent with the known viscosity of water. The second mesoscopic solvent is a Weeks-Chandler-Anderson model. Here, it is found that the correct mesoscopic hydrodynamic scaling of the membrane undulation dynamics is still preserved, although accelerated. When the behavior of the two membranes in close proximity to one another is examined, very little correlated motion is observed. However, the theoretically predicted scaling of the entropic undulation energy is confirmed, demonstrating that the entropic interaction between two membranes becomes increasingly repulsive with decreasing separation.