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

Mechanisms of vesicle spreading on surfaces: coarse-grained simulations

Exposition of unilamellar vesicles to attractive surfaces is a frequently used way to create supported lipid bilayers. Although this approach is known to produce continuous supported bilayer coatings, the mechanism of their formation and its dependence on factors like surface interaction and roughness or membrane tension as well as the interplay between neighboring vesicles or the involvement of preadsorbed bilayer patches are not well understood. Using dissipative particle dynamics simulations, we assess different mechanisms of vesicle spreading on attractive surfaces, placing special emphasis on the orientation of the resulting bilayer. Making use of the universality of collective phenomena in lipid membranes, we employed a solvent-free coarse-grained model, enabling us to cover the relatively large system sizes and time scales required. Our results indicate that one can control the mechanism of vesicle spreading by tuning the strength and range of the interactions with the substrate as well as the surface's roughness, resulting in a switch from a predominant inside-up to an outside-up orientation of the created supported bilayer.

Monolayer curvature stabilizes nanoscale raft domains in mixed lipid bilayers

According to the lipid raft hypothesis, biological lipid membranes are laterally heterogeneous and filled with nanoscale ordered "raft" domains, which are believed to play an important role for the organization of proteins in membranes. However, the mechanisms stabilizing such small rafts are not clear, and even their existence is sometimes questioned. Here, we report the observation of raft-like structures in a coarse-grained molecular model for multicomponent lipid bilayers. On small scales, our membranes demix into a liquid ordered (lo) phase and a liquid disordered (ld) phase. On large scales, phase separation is suppressed and gives way to a microemulsion-type state that contains nanometer-sized lo domains in an ld environment. Furthermore, we introduce a mechanism that generates rafts of finite size by a coupling between monolayer curvature and local composition. We show that mismatch between the spontaneous curvatures of monolayers in the lo and ld phases induces elastic interactions, which reduce the line tension between the lo and ld phases and can stabilize raft domains with a characteristic size of the order of a few nanometers. Our findings suggest that rafts in multicomponent bilayers might be closely related to the modulated ripple phase in one-component bilayers.

Directional interactions and cooperativity between mechanosensitive membrane proteins

While modern structural biology has provided us with a rich and diverse picture of membrane proteins, the biological function of membrane proteins is often influenced by the mechanical properties of the surrounding lipid bilayer. Here we explore the relation between the shape of membrane proteins and the cooperative function of membrane proteins induced by membrane-mediated elastic interactions. For the experimental model system of mechanosensitive ion channels we find that the sign and strength of elastic interactions depend on the protein shape, yielding distinct cooperative gating curves for distinct protein orientations. Our approach predicts how directional elastic interactions affect the molecular structure, organization, and biological function of proteins in crowded membranes.

Effect of capsid confinement on the chromatin organization of the SV40 minichromosome

Using small-angle X-ray scattering, we determined the three-dimensional packing architecture of the minichromosome confined within the SV40 virus. In solution, the minichromosome, composed of closed circular dsDNA complexed in nucleosomes, was shown to be structurally similar to cellular chromatin. In contrast, we find a unique organization of the nanometrically encapsidated chromatin, whereby minichromosomal density is somewhat higher at the center of the capsid and decreases towards the walls. This organization is in excellent agreement with a coarse-grained computer model, accounting for tethered nucleosomal interactions under viral capsid confinement. With analogy to confined liquid crystals, but contrary to the solenoid structure of cellular chromatin, our simulations indicate that the nucleosomes within the capsid lack orientational order. Nucleosomes in the layer adjacent to the capsid wall, however, align with the boundary, thereby inducing a 'molten droplet' state of the chromatin. These findings indicate that nucleosomal interactions suffice to predict the genome organization in polyomavirus capsids and underscore the adaptable nature of the eukaryotic chromatin architecture to nanoscale confinement.

Multiscale molecular dynamics simulations of membrane proteins

The time and length scales accessible by biomolecular simulations continue to increase. This is in part due to improvements in algorithms and computing performance, but is also the result of the emergence of coarse-grained (CG) potentials, which complement and extend the information obtainable from fully detailed models. CG methods have already proven successful for a range of applications that benefit from the ability to rapidly simulate spontaneous self-assembly within a lipid membrane environment, including the insertion and/or oligomerization of a range of "toy models," transmembrane peptides, and single- and multi-domain proteins. While these simplified approaches sacrifice atomistic level detail, it is now straightforward to "reverse map" from CG to atomistic descriptions, providing a strategy to assemble membrane proteins within a lipid environment, prior to all-atom simulation. Moreover, recent developments have been made in "dual resolution" techniques, allowing different molecules in the system to be modeled with atomistic or CG resolution simultaneously.

A generic force field for protein coarse-grained molecular dynamics simulation

Coarse-grained (CG) force fields have become promising tools for studies of protein behavior, but the balance of speed and accuracy is still a challenge in the research of protein coarse graining methodology. In this work, 20 CG beads have been designed based on the structures of amino acid residues, with which an amino acid can be represented by one or two beads, and a CG solvent model with five water molecules was adopted to ensure the consistence with the protein CG beads. The internal interactions in protein were classified according to the types of the interacting CG beads, and adequate potential functions were chosen and systematically parameterized to fit the energy distributions. The proposed CG force field has been tested on eight proteins, and each protein was simulated for 1000 ns. Even without any extra structure knowledge of the simulated proteins, the Cα root mean square deviations (RMSDs) with respect to their experimental structures are close to those of relatively short time all atom molecular dynamics simulations. However, our coarse grained force field will require further refinement to improve agreement with and persistence of native-like structures. In addition, the root mean square fluctuations (RMSFs) relative to the average structures derived from the simulations show that the conformational fluctuations of the proteins can be sampled.

Bilayer elasticity at the nanoscale: the need for new terms

Continuum elastic models that account for membrane thickness variations are especially useful in the description of nanoscale deformations due to the presence of membrane proteins with hydrophobic mismatch. We show that terms involving the gradient and the Laplacian of the area per lipid are significant and must be retained in the effective Hamiltonian of the membrane. We reanalyze recent numerical data, as well as experimental data on gramicidin channels, in light of our model. This analysis yields consistent results for the term stemming from the gradient of the area per molecule. The order of magnitude we find for the associated amplitude, namely 13-60 mN/m, is in good agreement with the 25 mN/m contribution of the interfacial tension between water and the hydrophobic part of the membrane. The presence of this term explains a systematic variation in previously published numerical data.

Thermal fluctuations in shape, thickness, and molecular orientation in lipid bilayers

We present a unified continuum-level model for bilayer energetics that includes the effects of bending, compression, lipid orientation (tilting relative to the monolayer surface normal), and microscopic noise (protrusions). Expressions for thermal fluctuation amplitudes of several physical quantities are derived. These predictions are shown to be in good agreement with molecular simulations.

Hierarchical Order Parameters for Macromolecular Assembly Simulations I: Construction and Dynamical Properties of Order Parameters

Macromolecular assemblies often display a hierarchical organization of macromolecules or their sub-assemblies. To model this, we have formulated a space warping method that enables capturing overall macromolecular structure and dynamics via a set of coarse-grained order parameters (OPs). This article is the first of two describing the construction and computational implementation of an additional class of OPs that has built into them the hierarchical architecture of macromolecular assemblies. To accomplish this, first, the system is divided into subsystems, each of which is described via a representative set of OPs. Then, a global set of variables is constructed from these subsystem-centered OPs to capture overall system organization. Dynamical properties of the resulting OPs are compared to those of our previous nonhierarchical ones, and implied conceptual and computational advantages are discussed for a 100ns, 2 million atom solvated Human Papillomavirus-like particle simulation. In the second article, the hierarchical OPs are shown to enable a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Langevin equations of stochastic OP dynamics. The latter is demonstrated via a force-field based simulation algorithm that probes key structural transition pathways, simultaneously accounting for all-atom details and overall structure.

Quantitative modeling of membrane deformations by multihelical membrane proteins: application to G-protein coupled receptors

The interpretation of experimental observations of the dependence of membrane protein function on the properties of the lipid membrane environment calls for a consideration of the energy cost of protein-bilayer interactions, including the protein-bilayer hydrophobic mismatch. We present a novel (to our knowledge) multiscale computational approach for quantifying the hydrophobic mismatch-driven remodeling of membrane bilayers by multihelical membrane proteins. The method accounts for both the membrane remodeling energy and the energy contribution from any partial (incomplete) alleviation of the hydrophobic mismatch by membrane remodeling. Overcoming previous limitations, it allows for radially asymmetric bilayer deformations produced by multihelical proteins, and takes into account the irregular membrane-protein boundaries. The approach is illustrated by application to two G-protein coupled receptors: rhodopsin in bilayers of different thickness, and the serotonin 5-HT(2A) receptor bound to pharmacologically different ligands. Analysis of the results identifies the residual exposure that is not alleviated by bilayer adaptation, and its quantification at specific transmembrane segments is shown to predict favorable contact interfaces in oligomeric arrays. In addition, our results suggest how distinct ligand-induced conformations of G-protein coupled receptors may elicit different functional responses through differential effects on the membrane environment.

Transmembrane helices can induce domain formation in crowded model membranes

We studied compositionally heterogeneous multi-component model membranes comprised of saturated lipids, unsaturated lipids, cholesterol, and α-helical TM protein models using coarse-grained molecular dynamics simulations. Reducing the mismatch between the length of the saturated and unsaturated lipid tails reduced the driving force for segregation into liquid-ordered (l(o)) and liquid-disordered (l(d)) lipid domains. Cholesterol depletion had a similar effect, and binary lipid mixtures without cholesterol did not undergo large-scale phase separation under the simulation conditions. The phase-separating ternary dipalmitoyl-phosphatidylcholine (DPPC)/dilinoleoyl-PC (DLiPC)/cholesterol bilayer was found to segregate into l(o) and l(d) domains also in the presence of a high concentration of ΤΜ helices. The l(d) domain was highly crowded with TM helices (protein-to-lipid ratio ~1:5), slowing down lateral diffusion by a factor of 5-10 as compared to the dilute case, with anomalous (sub)-diffusion on the μs time scale. The membrane with the less strongly unsaturated palmitoyl-linoleoyl-PC instead of DLiPC, which in the absence of TM α-helices less strongly deviated from ideal mixing, could be brought closer to a miscibility critical point by introducing a high concentration of TM helices. Finally, the 7-TM protein bacteriorhodopsin was found to partition into the l(d) domains irrespective of hydrophobic matching. These results show that it is possible to directly study the lateral reorganization of lipids and proteins in compositionally heterogeneous and crowded model biomembranes with coarse-grained molecular dynamics simulations, a step toward simulations of realistic, compositionally complex cellular membranes. This article is part of a Special Issue entitled: Protein Folding in Membranes.

Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects

Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.

Modeling the self-assembly of lipids and nanotubes in solution: forming vesicles and bicelles with transmembrane nanotube channels

Via dissipative particle dynamics (DPD), we simulate the self-assembly of end-functionalized, amphiphilic nanotubes and lipids in a hydrophilic solvent. Each nanotube encompasses a hydrophobic stalk and two hydrophilic ends, which are functionalized with end-tethered chains. With a relatively low number of the nanotubes in solution, the components self-assemble into stable lipid-nanotube vesicles. As the number of nanotubes is increased, the system exhibits a vesicle-to-bicelle transition, resulting in stable hybrid bicelle. Moreover, our results reveal that the nanotubes cluster into distinct tripod-like structures within the vesicles and aggregate into a ring-like assembly within the bicelles. For both the vesicles and bicelles, the nanotubes assume trans-membrane orientations, with the tethered hairs extending into the surrounding solution or the encapsulated fluid. Thus, the hairs provide a means of regulating the transport of species through the self-assembled structures. Our findings provide guidelines for creating nanotube clusters with distinctive morphologies that might be difficult to achieve through more conventional means. The results also yield design rules for creating synthetic cell-like objects or microreactors that can exhibit biomimetic functionality.

Modeling the release kinetics of poorly water-soluble drug molecules from liposomal nanocarriers

Liposomes are frequently used as pharmaceutical nanocarriers to deliver poorly water-soluble drugs such as temoporfin, cyclosporine A, amphotericin B, and paclitaxel to their target site. Optimal drug delivery depends on understanding the release kinetics of the drug molecules from the host liposomes during the journey to the target site and at the target site. Transfer of drugs in model systems consisting of donor liposomes and acceptor liposomes is known from experimental work to typically exhibit a first-order kinetics with a simple exponential behavior. In some cases, a fast component in the initial transfer is present, in other cases the transfer is sigmoidal. We present and analyze a theoretical model for the transfer that accounts for two physical mechanisms, collisions between liposomes and diffusion of the drug molecules through the aqueous phase. Starting with the detailed distribution of drug molecules among the individual liposomes, we specify the conditions that lead to an apparent first-order kinetic behavior. We also discuss possible implications on the transfer kinetics of (1) high drug loading of donor liposomes, (2) attractive interactions between drug molecules within the liposomes, and (3) slow transfer of drugs between the inner and outer leaflets of the liposomes.

Clusters of proteins in biomembranes: insights into the roles of interaction potential shapes and of protein diversity

It has recently been proposed that proteins embedded in lipidic biomembranes can spontaneously self-organize into stable small clusters, or membrane nanodomains, due to the competition between short-range attractive and longer-range repulsive forces between proteins, specific to these systems. In this paper, we carry on our investigation, by Monte Carlo simulations, of different aspects of cluster phases of proteins in biomembranes. First, we compare different long-range potentials (including notably three-body terms) to demonstrate that the existence of cluster phases should be quite generic. Furthermore, a real membrane contains hundreds of different protein species that are far from being randomly distributed in these nanodomains. We take this protein diversity into account by modulating protein-protein interaction potentials both at short and longer range. We confirm theoretical predictions in terms of biological cluster specialization by deciphering how clusters recruit only a few protein species. In this respect, we highlight that cluster phases can turn out to be an advantage at the biological level, for example by enhancing the cell response to external stimuli.

Molecular simulation of the effect of cholesterol on lipid-mediated protein-protein interactions

Experiments and molecular simulations have shown that the hydrophobic mismatch between proteins and membranes contributes significantly to lipid-mediated protein-protein interactions. In this article, we discuss the effect of cholesterol on lipid-mediated protein-protein interactions as function of hydrophobic mismatch, protein diameter and protein cluster size, lipid tail length, and temperature. To do so, we study a mesoscopic model of a hydrated bilayer containing lipids and cholesterol in which proteins are embedded, with a hybrid dissipative particle dynamics-Monte Carlo method. We propose a mechanism by which cholesterol affects protein interactions: protein-induced, cholesterol-enriched, or cholesterol-depleted lipid shells surrounding the proteins affect the lipid-mediated protein-protein interactions. Our calculations of the potential of mean force between proteins and protein clusters show that the addition of cholesterol dramatically reduces repulsive lipid-mediated interactions between proteins (protein clusters) with positive mismatch, but does not affect attractive interactions between proteins with negative mismatch. Cholesterol has only a modest effect on the repulsive interactions between proteins with different mismatch.

Coarse-grained simulations of membranes under tension

We investigate the properties of membranes under tension by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers. We give a comprising overview of the behavior of several membrane characteristics, such as the area per lipid, the monolayer overlap, the nematic order, and pressure profiles. Both the low-temperature regime, where the membranes are in a gel L(beta(')) phase, and the high-temperature regime, where they are in the fluid L(alpha) phase, are considered. In the L(beta(')) state, the membrane is hardly influenced by tension. In the fluid state, high tensions lead to structural changes in the membrane, which result in different compressibility regimes. The ripple state P(beta(')), which is found at tension zero in the transition regime between L(alpha) and L(beta(')), disappears under tension and gives way to an interdigitated phase. We also study the membrane fluctuations in the fluid phase. In the low-tension regime the data can be fitted nicely to a suitably extended elastic theory. At higher tensions the elastic fit consistently underestimates the strength of long-wavelength fluctuations. Finally, we investigate the influence of tension on the effective interaction between simple transmembrane inclusions and show that tension can be used to tune the hydrophobic mismatch interaction between membrane proteins.

Lipid membranes with transmembrane proteins in shear flow

The effects of embedded proteins on the dynamical properties of lipid bilayer membranes are studied in shear flow. Coarse-grained molecular simulations are employed, in which lipids are modeled as short polymers consisting of hydrophilic head groups and hydrophobic tail monomers; similarly, transmembrane proteins are modeled as connected hydrophobic double- or triple-chain molecules with hydrophilic groups at both ends. In thermal equilibrium, rigid proteinlike molecules aggregate in a membrane of flexible lipids, while flexible proteins do not aggregate. In shear flow parallel to the membrane, the monolayers of lipid bilayer slide over each other. The presence of transmembrane proteins enhances the intermonolayer friction. The friction coefficient depends on the chain lengths of lipids, the membrane tension, the length of the protein, and the cluster size. It is found to increase with protein length (with positive mismatch, i.e., proteins which are longer than the membrane thickness) and protein cluster size. In flow, proteins get oriented in the flow direction to reduce friction, with large fluctuations of the orientation angle.

Molecular modeling of proteinlike inclusions in lipid bilayers: lipid-mediated interactions

We investigated the insertion of transmembrane structures in a lipid bilayer and their interactions using self-consistent field theory. The lipids are coarse-grained on a united-atom level and consist of a phosphatidylcholinelike headgroup and two hydrophobic tails. The inclusions, acting as simple models for proteins that span biological membranes, are rigid rods (radius R ) with a hydrophobic surface and hydrophilic end caps. The insertion free energy Omega of an individual rod is strongly regulated by the affinity between its hydrophobic surface and the lipid tails. This affinity also controls the best match of the hydrophobic length of the rod with that of the bilayer. The line tension tau(=Omega/2piR) is practically independent of R . The perturbations in the bilayer as a function of distance from the inclusion, have the shape of a damped oscillation. The wavelength and decay length are related to the elastic properties of the bilayer and do not depend on R . These results are used to analyze how the lipid matrix affects the interaction between transmembrane objects, for computational reasons considering the limit of R-->infinity . Contributions on different length scales can be distinguished: (i) a long-range elastic interaction, which is an exponentially decaying oscillation; (ii) an exponentially decaying repulsion on an intermediate length scale, resulting from the loss of conformational entropy of the lipid tails; and (iii) a short-range interaction due to the finite compressibility of the lipid tails, which manifests either as a depletion attraction if there is no affinity between the tails and the inclusions' surface or, otherwise, as an oscillatory structural force.

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.

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.