Gary S. Ayton

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.

Bridging microscopic and mesoscopic simulations of lipid bilayers.

A lipid bilayer is modeled using a mesoscopic model designed to bridge atomistic bilayer simulations with macro-scale continuum-level simulation. Key material properties obtained from detailed atomistic-level simulations are used to parameterize the meso-scale model. The fundamental length and time scale of the meso-scale simulation are at least an order of magnitude beyond that used at the atomistic level. Dissipative particle dynamics cast in a new membrane formulation provides the simulation methodology. A meso-scale representation of a dimyristoylphosphatidylcholine membrane is examined in the high and low surface tension regimes. At high surface tensions, the calculated modulus is found to be slightly less than the atomistically determined value. This result agrees with the theoretical prediction that high-strain thermal undulations still persist, which have the effect of reducing the value of the atomistically determined modulus. Zero surface tension simulations indicate the presence of strong thermal undulatory modes, whereas the undulation spectrum and the calculated bending modulus are in excellent agreement with theoretical predictions and experiment.

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.

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.

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.

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.

Emerging methods for multiscale simulation of biomolecular systems

Three multiscale computational methodologies for biomolecular systems are described: the force-matching method for developing coarse-grained models directly from atomistic simulations; the quasi-particle approach of simulating field theory representations at the mesoscopic scale; and the multiscale-coupling method for direct information transfer between mesoscopic and atomistic scales on the fly. The statistical mechanical background for each of the methods is described in a comprehensive manner in order to highlight their theoretical foundations. Examples of various applications of these methods to model different biophysical processes are given. Combining with atomistic-level MD simulations, these three methods compose a powerful tool for bridging and spanning the multiple spatial and temporal domains that are present in many biological assemblies. Future directions of the methodology developments are also discussed.

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.

Multiscale coupling of mesoscopic- and atomistic-level lipid bilayer simulations

A multiscale method is presented to bridge between the atomistic and mesoscopic membrane systems. The atomistic model in this case is the united atom dimyristoylphosphatidylcholine membrane system, although the method is completely general. Atomistic molecular dynamics provides the expansion modulus which is used to parametrize a mesoscopic elastic membrane model. The resulting elastic membrane model, including explicit mesoscopic solvent, shows appropriate static and dynamic undulation behaviors. Large membranes of approximately 100 nm in length can then be easily simulated using the mesoscopic membrane system. The critical feedback from the mesoscopic system back down to the atomistic-scale system is accomplished by bridging the stress (or surface tension) of a small region in the mesoscopic membrane to the corresponding atomistic membrane system. Because of long length-scale modes of membranes such as undulation and buckling, the local tension responds differently from the frame tension, when subjected to external perturbations. The effect of these membrane modes is shown for the stress response of a local membrane region and therefore the atomistic membrane system. In addition, certain equilibrium static and dynamic properties of stand-alone and multiscale coupled systems are presented for several different membrane sizes. Although static properties such as two-dimensional pair-correlation function and order parameters show no noticeable discrepancy for the different systems, lipid self-diffusion and the rotational relaxation of lipid dipoles have a strong dependence on the membrane size (or long-wavelength membrane motions), which is properly modeled by the present multiscale method.

Interfacing continuum and molecular dynamics: An application to lipid bilayers

A new methodology is presented for interfacing atomistic molecular dynamics simulations with continuum dynamics, and the approach is then applied to a model lipid bilayer system. The technique relies on a closed feedback loop in which atomistic level simulations are coupled with continuum level modeling. This approach allows for the examination of the trans-temporal and trans-spatial phenomena that occur in many biological systems, and nonequilibrium molecular dynamics are used to calculate the relevant transport coefficients that are required at the continuum level. It is found that for the membrane system there is significant information transfer across disparate spatial and temporal regimes, resulting in significant nonlinear behavior.