The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations

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.

Coarse-grained modeling of lipids

Molecular modeling of phospholipids on many scales has progressed significantly over the last years. Here we review several membrane models on intermediate to large length scales restricting ourselves to particle based coarse-grained models with implicit and explicit solvent. We explain similarities and differences as well as their connection to experiments and fine-grained models. We neglect any field descriptions on larger scales. We discuss then a few examples where we focus on studies of lipid phase behavior as well as supported lipid bilayers as these examples can only be meaningfully studied using large-scale models to date.

Solvent-free lipid bilayer model using multiscale coarse-graining

The multiscale coarse-graining (MS-CG) approach developed in our previous work is extended here to model solvent-free lipid bilayers. The water (solvent) molecules are completely integrated out of the coarse-grained (CG) effective force field. The MS-CG potential, a sum of pairwise central terms, accurately approximates the many-body potential of mean force in the coarse-grained coordinates. It thus incorporates both energetic and entropic contributions. To improve the stability and elastic properties of the MS-CG simulated bilayer, an additional constraint was adopted: the partial virial associated with CG bilayer sites was matched to its corresponding atomistic value for each configuration of the system. The resulting solvent-free MS-CG model reproduces a liquid-state lipid bilayer with accurate structural and elastic properties. Finally, the solvent-free MS-CG model is used to simulate a very large, flat bilayer and two liposome geometries, demonstrating its greatly enhanced computational efficiency.

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 structural basis for peptide selection by the transport receptor OppA

Oligopeptide-binding protein A (OppA) from Lactococcus lactis binds peptides of an exceptionally wide range of lengths (4-35 residues), with no apparent sequence preference. Here, we present the crystal structures of OppA in the open- and closed-liganded conformations. The structures directly explain the protein's phenomenal promiscuity. A huge cavity allows binding of very long peptides, and a lack of constraints for the position of the N and C termini of the ligand is compatible with binding of peptides with varying lengths. Unexpectedly, the peptide's amino-acid composition (but not the exact sequence) appears to have a function in selection, with a preference for proline-rich peptides containing at least one isoleucine. These properties can be related to the physiology of the organism: L. lactis is auxotrophic for branched chain amino acids and favours proline-rich caseins as a source of amino acids. We propose a new mechanism for peptide selection based on amino-acid composition rather than sequence.

The interaction of C60 and its derivatives with a lipid bilayer via molecular dynamics simulations

Coarse-grained molecular dynamics simulations have been used to explore the interactions of C(60) and its derivatives with lipid bilayers. Pristine C(60) partitions into the bilayer core, whilst C(60)(OH)(20) experiences a central energetic barrier to permeation across the bilayer. For intermediate levels of derivatization, e.g. C(60)(OH)(10), this central barrier is smaller and there is an energetic well at the bilayer/water interface, thus promoting entry into cells via bilayer permeation whilst maintaining solubility in water.

Interaction of monotopic membrane enzymes with a lipid bilayer: a coarse-grained MD simulation study

Monotopic membrane proteins bind tightly to cell membranes but do not generally span the lipid bilayer. Their interactions with lipid bilayers may be studied via coarse-grained molecular dynamics (CG-MD) simulations. Understanding such interactions is important as monotopic enzymes frequently act on hydrophobic substrates, while X-ray structures rarely provide direct information about their interactions with membranes. CG-MD self-assembly simulations enable prediction of the orientation and depth of insertion into a lipid bilayer of a monotopic protein, and also of the interactions of individual protein residues with lipid molecules. The CG-MD method has been evaluated via comparison with extended (>30 ns) atomistic simulations of monoamine oxidase, revealing good agreement between the results of coarse-grained and atomistic simulations. CG-MD simulations have been applied to a set of 11 monotopic proteins for which three-dimensional structures are available. These proteins may be divided into two groups on the basis of the results of the simulations. One group consists of those proteins which are inserted into the lipid bilayer to a limited extent, interacting mainly at the phospholipid-water interface. The second group consists of those which are inserted more deeply into the bilayer. Those monotopic proteins which are inserted more deeply cause significant local perturbation of bilayer properties such as bilayer thickness. Deeper insertion seems to correlate with a greater number of basic residues in the "foot" whereby a monotopic protein interacts with the membrane.

Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

Multiscale modeling of emergent materials: biological and soft matter

In this review, we focus on four current related issues in multiscale modeling of soft and biological matter. First, we discuss how to use structural information from detailed models (or experiments) to construct coarse-grained ones in a hierarchical and systematic way. This is discussed in the context of the so-called Henderson theorem and the inverse Monte Carlo method of Lyubartsev and Laaksonen. In the second part, we take a different look at coarse graining by analyzing conformations of molecules. This is done by the application of self-organizing maps, i.e., a neural network type approach. Such an approach can be used to guide the selection of the relevant degrees of freedom. Then, we discuss technical issues related to the popular dissipative particle dynamics (DPD) method. Importantly, the potentials derived using the inverse Monte Carlo method can be used together with the DPD thermostat. In the final part we focus on solvent-free modeling which offers a different route to coarse graining by integrating out the degrees of freedom associated with solvent.

Molecular dynamics simulations of a DMPC bilayer using nonadditive interaction models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.

3D pressure field in lipid membranes and membrane-protein complexes

We calculate full 3D pressure fields for inhomogeneous nanoscale systems using molecular dynamics simulation data. The fields represent systems with increasing level of complexity, ranging from semivesicles and vesicles to membranes characterized by coexistence of two phases, including also a protein-membrane complex. We show that the 3D pressure field is distinctly different for curved and planar bilayers, the pressure field depends strongly on the phase of the membrane, and that an integral protein modulates the tension and elastic properties of the membrane.

Effect of cholesterol on the structure of a phospholipid bilayer

Cholesterol plays an important role in regulating the properties of phospholipid membranes. To obtain a detailed understanding of the lipid-cholesterol interactions, we have developed a mesoscopic water-lipid-cholesterol model. In this model, we take into account the hydrophobic-hydrophilic interactions and the structure of the molecules. We compute the phase diagram of dimyristoylphosphatidylcholine-cholesterol by using dissipative particle dynamics and show that our model predicts many of the different phases that have been observed experimentally. In quantitative agreement with experimental data our model also shows the condensation effect; upon the addition of cholesterol, the area per lipid decreases more than one would expect from ideal mixing. Our calculations show that this effect is maximal close to the main-phase transition temperature, the lowest temperature for which the membrane is in the liquid phase, and is directly related to the increase of this main-phase transition temperature upon addition of cholesterol. We demonstrate that no condensation is observed if we slightly change the structure of the cholesterol molecule by adding an extra hydrophilic head group or if we decrease the size of the hydrophobic part of cholesterol.

On using a too large integration time step in molecular dynamics simulations of coarse-grained molecular models

The use of a coarse-grained (CG) model that is widely used in molecular dynamics simulations of biomolecular systems is investigated with respect to the dependence of a variety of quantities upon the size of the used integration time step and cutoff radius. The results suggest that when using a non-bonded interaction-cutoff radius of 1.4 nm a time step of maximally 10 fs should be used, in order not to produce energy sinks or wells. Using a too-large time step, e.g. 50 fs with a cutoff of 1.2 nm, as is done in the coarse-grained model of Marrink et al. (J. Phys. Chem. B, 2004, 108, 250 and 2007, 111, 7812), induces errors due to the linear approximation of the integrators that are commonly used to integrate the equations of motion. As a spin-off of the investigation of the mentioned CG models, we found that the parameters of the CG water model place it at physiological temperatures well into the solid phase of the phase diagram.

Systematic coarse-graining of a multicomponent lipid bilayer

A solvent-free coarse-grained model for a 1:1 mixed dioleoylphosphatidylcholine (DOPC) and a dioleoylphospatidylethanolamine (DOPE) bilayer is developed using the multiscale coarse-graining (MS-CG) approach. B-spline basis functions are implemented instead of the original cubic spline basis functions in the MS-CG method. The new B-spline basis functions are able to dramatically reduce memory requirements and increase computational efficiency of the MS-CG calculation. Various structural properties from the CG simulations are compared with their corresponding all-atom counterpart in order to validate the CG model. The resulting CG structural properties agree well with atomistic results, which shows that the MS-CG force field can reasonably approximate the many-body potential of mean force in the coarse-grained coordinates. Fast lipid lateral diffusion in the CG simulations, as a result of smoother free energy landscape, makes the study of phase behavior of the binary mixture possible. Small clusters of distinct lipid composition are identified by analyzing the DOPC/DOPE lipid lateral distribution, indicating a nonuniform distribution for the mixed bilayer. The results of lipid phase behavior are compared to experimental results, and connections between the experimental and simulation conclusions are discussed.

The structural dynamics of macromolecular processes

Dynamic processes involving macromolecular complexes are essential to cell function. These processes take place over a wide variety of length scales from nanometers to micrometers, and over time scales from nanoseconds to minutes. As a result, information from a variety of different experimental and computational approaches is required. We review the relevant sources of information and introduce a framework for integrating the data to produce representations of dynamic processes.

Carbon nanotube self-assembly with lipids and detergent: a molecular dynamics study

The dispersion of carbon nanotubes (CNTs) in aqueous media is of potential importance in a number of biomedical applications. CNT solubilization has been achieved via the non-covalent adsorption of lipids and detergent onto the tube surface. We use coarse-grained molecular dynamics to study the self-assembly of CNTs with various amphiphiles, namely a bilayer-forming lipid, dipalmitoylphosphatidylcholine (DPPC), and two species of detergent, dihexanoylphosphatidylcholine (DHPC) and lysophosphatidylcholine (LPC). We find that for a low amphiphile/CNT ratio, DPPC, DHPC and LPC all wrap around the CNT. Upon increasing the number of amphiphiles, a transition in adsorption is observed: DPPC encapsulates the CNT within a cylindrical micelle, whilst both DHPC and LPC adsorb onto CNTs in hemimicelles. This study highlights differences in adsorption mechanism of bilayer-forming lipids and detergents on CNTs which may in the future be exploitable to enable enhancement of CNT solubilization whilst minimizing perturbation of cell membrane integrity.

Multiscale modeling of dendrimers and their interactions with bilayers and polyelectrolytes

Recent advances in molecular dynamics simulation methodologies and computational power have allowed accurate predictions of dendrimer size, shape, and interactions with bilayers and polyelectrolytes with modest computational effort. Atomistic and coarse-grained (CG) models show strong interactions of cationic dendrimers with lipid bilayers. The CG simulations with explicit lipid and water capture bilayer penetration and pore formation, showing that pore formation is enhanced at high dendrimer concentration, but suppressed at low temperature and high salt concentration, in agreement with experiments. Cationic linear polymers have also been simulated, but do not perforate membranes, evidently because by deforming into a pancake, the charges on a linear polymer achieve intimate contact with a single bilayer leaflet. The relatively rigid dendrimers, on the other hand, penetrate the bilayer, because only by interacting with both leaflets can they achieve a similar degree of contact between charged groups. Also, a "dendrimer-filled vesicle" structure for the dendrimer-membrane interaction is predicted by mesoscale thermodynamic simulations, in agreement with a picture derived from experimental observations. In simulations of complexes of dendrimer and polyelectrolyte, anionic linear chains wrap around the cationic dendrimer and penetrate inside it. Overall, these new results indicate that simulations can now provide predictions in excellent agreement with experimental observations, and provide atomic-scale insights into dendrimer structure and dynamics.

Visualization of complex processes in lipid systems using computer simulations and molecular graphics

Computer simulation has become an increasingly popular tool in the study of lipid membranes, complementing experimental techniques by providing information on structure and dynamics at high spatial and temporal resolution. Molecular visualization is the most powerful way to represent the results of molecular simulations, and can be used to illustrate complex transformations of lipid aggregates more easily and more effectively than written text. In this chapter, we review some basic aspects of simulation methodologies commonly employed in the study of lipid membranes and we describe a few examples of complex phenomena that have been recently investigated using molecular simulations. We then explain how molecular visualization provides added value to computational work in the field of biological membranes, and we conclude by listing a few molecular graphics packages widely used in scientific publications.

Membrane-protein interactions in a generic coarse-grained model for lipid bilayers

We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: direct interactions; lipid-induced depletion interactions; lipid bridging; lipid packing; and a smooth long-range contribution. The mechanisms leading to hydrophobic mismatch interactions are critically analyzed.

The molecular face of lipid rafts in model membranes

Cell membranes contain a large number of different lipid species. Such a multicomponent mixture exhibits a complex phase behavior with regions of structural and compositional heterogeneity. Especially domains formed in ternary mixtures, composed of saturated and unsaturated lipids together with cholesterol, have received a lot of attention as they may resemble raft formation in real cells. Here we apply a simulation model to assess the molecular nature of these domains at the nanoscale, information that has thus far eluded experimental determination. We are able to show the spontaneous separation of a saturated phosphatidylcholine (PC)/unsaturated PC/cholesterol mixture into a liquid-ordered and a liquid-disordered phase with structural and dynamic properties closely matching experimental data. The near-atomic resolution of the simulations reveals remarkable features of both domains and the boundary domain interface. Furthermore, we predict the existence of a small surface tension between the monolayer leaflets that drives registration of the domains. At the level of molecular detail, raft-like lipid mixtures show a surprising face with possible implications for many cell membrane processes.

Synthetic ion channels via self-assembly: a route for embedding porous polyoxometalate nanocapsules in lipid bilayer membranes

Porous polyoxometalate nanocapsules of Keplerate type are known to exhibit the functionality of biological ion channels; however, their use as an artificial ion channel is tempered by the high negative charge of the capsules, which renders their spontaneous incorporation into a lipid bilayer membrane unlikely. In this Letter we report coarse-grained molecular dynamics simulations that demonstrate a route for embedding negatively charged nanocapsules into lipid bilayer membranes via self-assembly. A homogeneous mixture of water, cationic detergent, and phospholipid was observed to spontaneously self-assemble around the nanocapsule into a layered, liposome-like structure, where the nanocapsule was enveloped by a layer of cationic detergent followed by a layer of phospholipid. Fusion of such a layered liposome with a lipid bilayer membrane was observed to embed the nanocapsule into the lipid bilayer. The resulting assembly was found to remain stable even after the surface of the capsule was exposed to electrolyte. In the latter conformation, water was observed to flow into and out of the capsule as Na(+) cations entered, suggesting that a polyoxometalate nanocapsule can form a functional synthetic ion channel in a lipid bilayer membrane.

Coarse-grained molecular dynamics simulations of the energetics of helix insertion into a lipid bilayer

Experimental and computational studies have indicated that hydrophobicity plays a key role in driving the insertion of transmembrane alpha-helices into lipid bilayers. Molecular dynamics simulations allow exploration of the nature of the interactions of transmembrane alpha-helices with their lipid bilayer environment. In particular, coarse-grained simulations have considerable potential for studying many aspects of membrane proteins, ranging from their self-assembly to the relation between their structure and function. However, there is a need to evaluate the accuracy of coarse-grained estimates of the energetics of transmembrane helix insertion. Here, three levels of complexity of model system have been explored to enable such an evaluation. First, calculated free energies of partitioning of amino acid side chains between water and alkane yielded an excellent correlation with experiment. Second, free energy profiles for transfer of amino acid side chains along the normal to a phosphatidylcholine bilayer were in good agreement with experimental and atomistic simulation studies. Third, estimation of the free energy profile for transfer of an arginine residue, embedded within a hydrophobic alpha-helix, to the center of a lipid bilayer gave a barrier of approximately 15 kT. Hence, there is a substantial barrier to membrane insertion for charged amino acids, but the coarse-grained model still underestimates the corresponding free energy estimate (approximately 29 kT) from atomistic simulations (Dorairaj, S., and Allen, T. W. (2007) Proc. Natl. Acad. Sci. U.S.A. 104, 4943-4948). Coarse-grained simulations were then used to predict the free energy profile for transfer of a simple model transmembrane alpha-helix (WALP23) across a lipid bilayer. The results indicated that a transmembrane orientation was favored by about -70 kT.

Lipids on the move: simulations of membrane pores, domains, stalks and curves

In this review we describe the state-of-the-art of computer simulation studies of lipid membranes. We focus on collective lipid-lipid and lipid-protein interactions that trigger deformations of the natural lamellar membrane state, showing that many important biological processes including self-aggregation of membrane components into domains, the formation of non-lamellar phases, and membrane poration and curving, are now amenable to detailed simulation studies.

Lipid bilayer curvature and pore formation induced by charged linear polymers and dendrimers: the effect of molecular shape

We performed molecular dynamics (MD) simulations of multiple copies of poly- l-lysine (PLL) and charged polyamidoamine (PAMAM) dendrimers in dimyristoylphosphatidylcholine (DMPC) bilayers with explicit water using the coarse-grained model developed by Marrink et al. ( J. Chem. Theory Comput. 2008, 4, 819 ). Membrane disruption is enhanced at higher concentrations and charge densities of both spheroidally shaped dendrimers and linear PLL polymers, in qualitatively agreement with experimental studies by Hong et al. (Bioconjugate Chem. 2006, 17, 728 ). However, larger molecular size enhances membrane disruption and pore formation only for dendrimers and not for the linear PLL. Despite more intimate electrostatic interactions of linear molecules than are possible for spheroidal dendrimers, only the dendrimers were found to perforate membranes, apparently because they cannot spread onto a single leaflet, and so must penetrate the bilayer to get favorable electrostatic interactions with head groups on the opposite leaflet. These results indicate that a relatively rigid spheroidal shape is more efficient than a flexible linear shape in increasing membrane permeability. These results compare favorably with experimental findings.

Multiscale methods for macromolecular simulations

In this article we review the key modeling tools available for simulating biomolecular systems. We consider recent developments and representative applications of mixed quantum mechanics/molecular mechanics (QM/MM), elastic network models (ENMs), coarse-grained molecular dynamics, and grid-based tools for calculating interactions between essentially rigid protein assemblies. We consider how the different length scales can be coupled, both in a sequential fashion (e.g. a coarse-grained or grid model using parameterization from MD simulations), and via concurrent approaches, where the calculations are performed together and together control the progression of the simulation. We suggest how the concurrent coupling approach familiar in the context of QM/MM calculations can be generalized, and describe how this has been done in the CHARMM macromolecular simulation package.

Coarse-grained simulations of the membrane-active antimicrobial Peptide maculatin 1.1

Maculatin 1.1 (M1.1) is a membrane-active antimicrobial peptide (AMP) from an Australian tree frog that forms a kinked amphipathic alpha-helix in the presence of a lipid bilayer or bilayer-mimetic environment. To help elucidate its mechanism of membrane-lytic activity, we performed a total of approximately 8 micros of coarse-grained molecular dynamics (CG-MD) simulations of M1.1 in the presence of zwitterionic phospholipid membranes. Several systems were simulated in which the peptide/lipid ratio was varied. At a low peptide/lipid ratio, M1.1 adopted a kinked, membrane-interfacial location, consistent with experiment. At higher peptide/lipid ratios, we observed spontaneous, cooperative membrane insertion of M1.1 peptide aggregates. The minimum size for formation of a transmembrane (TM) aggregate was just four peptides. The absence of a simple and well-defined central channel, along with the exclusion of lipid headgroups from the aggregates, suggests that a pore-like model is an unlikely explanation for the mechanism of membrane lysis by M1.1. We also performed an extended 1.25 micros simulation of the permeabilization of a complete liposome by multiple peptides. Consistent with the simpler bilayer simulations, formation of monomeric interfacial peptides and TM peptide clusters was observed. In contrast, major structural changes were observed in the vesicle membrane, implicating induced membrane curvature in the mechanism of active antimicrobial peptide lysis. This contrasted with the behavior of the nonpore-forming model peptide WALP23, which inserted into the vesicle to form extended clusters of TM alpha-helices with relatively little perturbation of bilayer properties.

Self-assembly of a simple membrane protein: coarse-grained molecular dynamics simulations of the influenza M2 channel

The transmembrane (TM) domain of the M2 channel protein from influenza A is a homotetrameric bundle of alpha-helices and provides a model system for computational approaches to self-assembly of membrane proteins. Coarse-grained molecular dynamics (CG-MD) simulations have been used to explore partitioning into a membrane of M2 TM helices during bilayer self-assembly from lipids. CG-MD is also used to explore tetramerization of preinserted M2 TM helices. The M2 helix monomer adopts a membrane spanning orientation in a lipid (DPPC) bilayer. Multiple extended CG-MD simulations (5 x 5 micros) were used to study the tetramerization of inserted M2 helices. The resultant tetramers were evaluated in terms of the most populated conformations and the dynamics of their interconversion. This analysis reveals that the M2 tetramer has 2x rotationally symmetrical packing of the helices. The helices form a left-handed bundle, with a helix tilt angle of approximately 16 degrees. The M2 helix bundle generated by CG-MD was converted to an atomistic model. Simulations of this model reveal that the bundle's stability depends on the assumed protonation state of the H37 side chains. These simulations alongside comparison with recent x-ray (3BKD) and NMR (2RLF) structures of the M2 bundle suggest that the model yielded by CG-MD may correspond to a closed state of the channel.

Mechanosensitive channels: insights from continuum-based simulations

Mechanotransduction plays an important role in regulating cell functions and it is an active topic of research in biophysics. Despite recent advances in experimental and numerical techniques, the intrinsic multiscale nature imposes tremendous challenges for revealing the working mechanisms of mechanosensitive channels. Recently, a continuum-mechanics-based hierarchical modeling and simulation framework has been established and applied to study the mechanical responses and gating behaviors of a prototypical mechanosensitive channel, the mechanosensitive channel of large conductance (MscL) in bacteria Escherichia coli (E. coli), from which several putative gating mechanisms have been tested and new insights are deduced. This article reviews these latest findings using the continuum mechanics framework and suggests possible improvements for future simulation studies. This computationally efficient and versatile continuum-mechanics-based protocol is poised to make contributions to the study of a variety of mechanobiology problems.

Peptide aggregation and pore formation in a lipid bilayer: a combined coarse-grained and all atom molecular dynamics study

We present a simulation study where different resolutions, namely coarse-grained (CG) and all-atom (AA) molecular dynamics simulations, are used sequentially to combine the long timescale reachable by CG simulations with the high resolution of AA simulations, to describe the complete processes of peptide aggregation and pore formation by alamethicin peptides in a hydrated lipid bilayer. In the 1-micros CG simulations the peptides spontaneously aggregate in the lipid bilayer and exhibit occasional transitions between the membrane-spanning and the surface-bound configurations. One of the CG systems at t = 1 micros is reverted to an AA representation and subjected to AA simulation for 50 ns, during which water molecules penetrate the lipid bilayer through interactions with the peptide aggregates, and the membrane starts leaking water. During the AA simulation significant deviations from the alpha-helical structure of the peptides are observed, however, the size and arrangement of the clusters are not affected within the studied time frame. Solid-state NMR experiments designed to match closely the setup used in the molecular dynamics simulations provide strong support for our finding that alamethicin peptides adopt a diverse set of configurations in a lipid bilayer, which is in sharp contrast to the prevailing view of alamethicin oligomers formed by perfectly aligned helical alamethicin peptides in a lipid bilayer.

The interaction of phospholipase A2 with a phospholipid bilayer: coarse-grained molecular dynamics simulations

A number of membrane-active enzymes act in a complex environment formed by the interface between a lipid bilayer and bulk water. Although x-ray diffraction studies yield structures of isolated enzyme molecules, a detailed characterization of their interactions with the interface requires a measure of how deeply such a membrane-associated protein penetrates into a lipid bilayer. Here, we apply coarse-grained (CG) molecular dynamics (MD) simulations to probe the interaction of porcine pancreatic phospholipase A2 (PLA2) with a lipid bilayer containing palmitoyl-oleoyl-phosphatidyl choline and palmitoyl-oleoyl-phosphatidyl glycerol molecules. We also used a configuration from a CG-MD trajectory to initiate two atomistic (AT) MD simulations. The results of the CG and AT simulations are evaluated by comparison with available experimental data. The membrane-binding surface of PLA2 consists of a patch of hydrophobic residues surrounded by polar and basic residues. We show this proposed footprint interacts preferentially with the anionic headgroups of the palmitoyl-oleoyl-phosphatidyl glycerol molecules. Thus, both electrostatic and hydrophobic interactions determine the location of PLA2 relative to the bilayer. From a general perspective, this study demonstrates that CG-MD simulations may be used to reveal the orientation and location of a membrane-surface-bound protein relative to a lipid bilayer, which may subsequently be refined by AT-MD simulations to probe more detailed interactions.

The molecular mechanism of lipid monolayer collapse

Lipid monolayers at an air-water interface can be compressed laterally and reach high surface density. Beyond a certain threshold, they become unstable and collapse. Lipid monolayer collapse plays an important role in the regulation of surface tension at the air-liquid interface in the lungs. Although the structures of lipid aggregates formed upon collapse can be characterized experimentally, the mechanism leading to these structures is not fully understood. We investigate the molecular mechanism of monolayer collapse using molecular dynamics simulations. Upon lateral compression, the collapse begins with buckling of the monolayer, followed by folding of the buckle into a bilayer in the water phase. Folding leads to an increase in the monolayer surface tension, which reaches the equilibrium spreading value. Immediately after their formation, the bilayer folds have a flat semielliptical shape, in agreement with theoretical predictions. The folds undergo further transformation and form either flat circular bilayers or vesicles. The transformation pathway depends on macroscopic parameters of the system: the bending modulus, the line tension at the monolayer-bilayer connection, and the line tension at the bilayer perimeter. These parameters are determined by the system composition and temperature. Coexistence of the monolayer with lipid aggregates is favorable at lower tensions of the monolayer-bilayer connection. Transformation into a vesicle reduces the energy of the fold perimeter and is facilitated for softer bilayers, e.g., those with a higher content of unsaturated lipids, or at higher temperatures.

Lipid bilayer deformation and the free energy of interaction of a Kv channel gating-modifier toxin

A number of membrane proteins act via binding at the water/lipid bilayer interface. An important example of such proteins is provided by the gating-modifier toxins that act on voltage-gated potassium (Kv) channels. They are thought to partition to the headgroup region of lipid bilayers, and so provide a good system for probing the nature of interactions of a protein with the water/bilayer interface. We used coarse-grained molecular dynamics simulations to compute the one-dimensional potential of mean force (i.e., free energy) profile that governs the interaction between a Kv channel gating-modifier toxin (VSTx1) and model phospholipid bilayers. The reaction coordinate sampled corresponds to the position of the toxin along the bilayer normal. The course-grained representation of the protein and lipids enabled us to explore extended time periods, revealing aspects of toxin/bilayer dynamics and energetics that would be difficult to observe on the timescales currently afforded by atomistic molecular dynamics simulations. In particular, we show for this model system that the bilayer deforms as it interacts with the toxin, and that such deformations perturb the free energy profile. Bilayer deformation therefore adds an additional layer of complexity to be addressed in investigations of membrane/protein systems. In particular, one should allow for local deformations that may arise due to the spatial array of charged and hydrophobic elements of an interfacially located membrane protein.

Coarse-grained molecular dynamics studies of the concentration and size dependence of fifth- and seventh-generation PAMAM dendrimers on pore formation in DMPC bilayer

We have performed molecular dynamics (MD) simulations of multiple copies of unacetylated G5 and G7 and acetylated G5 dendrimers in dimyristoylphosphatidylcholine bilayers with explicit water using the coarse-grained model developed by Marrink et al. (J. Phys. Chem. B 2007, 111, 7812) with the inclusion of long-range electrostatics. When initially clustered together near the bilayer, neutral acetylated dendrimers aggregate, whereas cationic unacetylated dendrimers do not aggregate, but separate from each other, similar to the observations from atomic force microscopy by Mecke et al. (Chem. Phys. Lipids 2004, 132, 3). The bilayers interacting with unacetylated dendrimers of higher concentration are significantly deformed and show pore formation on the positively curved portions, while acetylated dendrimers are unable to form pores. Unacetylated G7 dendrimers bring more water molecules into the pores than do unacetylated G5 dendrimers. These results agree qualitatively with experimental results showing that significant cytoplasmic-protein leakage is produced by unacetylated G7 dendrimers at concentrations as low as 10 nM, but only at a much higher concentration of 400 nM for unacetylated G5 dendrimers (Bioconjugate Chem. 2004, 15, 774). This good qualitative agreement indicates that the effect on pore formation of the concentration and size of large nanoparticles can be studied through coarse-grained MD simulations, provided that long-range electrostatic interactions are included.

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.

Computer simulation study of fullerene translocation through lipid membranes

Recent toxicology studies suggest that nanosized aggregates of fullerene molecules can enter cells and alter their functions, and also cross the blood-brain barrier. However, the mechanisms by which fullerenes penetrate and disrupt cell membranes are still poorly understood. Here we use computer simulations to explore the translocation of fullerene clusters through a model lipid membrane and the effect of high fullerene concentrations on membrane properties. The fullerene molecules rapidly aggregate in water but disaggregate after entering the membrane interior. The permeation of a solid-like fullerene aggregate into the lipid bilayer is thermodynamically favoured and occurs on the microsecond timescale. High concentrations of fullerene induce changes in the structural and elastic properties of the lipid bilayer, but these are not large enough to mechanically damage the membrane. Our results suggest that mechanical damage is an unlikely mechanism for membrane disruption and fullerene toxicity.