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

The membrane protein LeuT in micellar systems: aggregation dynamics and detergent binding to the S2 site

Structural and functional properties of integral membrane proteins are often studied in detergent micellar environments (proteomicelles), but how such proteomicelles form and organize is not well understood. This makes it difficult to evaluate the relationship between the properties of the proteins measured in such a detergent-solubilized form and under native conditions. To obtain mechanistic information about this relationship for the leucine transporter (LeuT), a prokaryotic homologue of the mammalian neurotransmitter/sodium symporters (NSSs), we studied the properties of proteomicelles formed by n-dodecyl-β,D-maltopyranoside (DDM) detergent. Extensive atomistic molecular dynamics simulations of different protein/detergent/water number ratios revealed the formation of a proteomicelle characterized by a constant-sized shell of detergents surrounding LeuT protecting its transmembrane segments from unfavorable hydrophobic/hydrophilic exposure. Regardless of the DDM content in the simulated system, this shell consisted of a constant number of DDM molecules (∼120 measured at a 4 Å cutoff distance from LeuT). In contrast, the overall number of DDMs in the proteomicelle (aggregation number) was found to depend on the detergent concentration, reaching a saturation value of 226±17 DDMs in the highest concentration regime simulated. Remarkably, we found that at high detergent-to-protein ratios we observed two independent ways of DDM penetration into LeuT, both leading to a positioning of the DDM molecule in the second substrate (S2) binding site of LeuT. Consonant with several recent experimental studies demonstrating changes in functional properties of membrane proteins due to detergent, our findings highlight how the environment in which the membrane proteins are examined may affect the outcome and interpretation of their mechanistic features.

A comparison of coarse-grained and continuum models for membrane bending in lipid bilayer fusion pores

To establish the validity of continuum mechanics models quantitatively for the analysis of membrane remodeling processes, we compare the shape and energies of the membrane fusion pore predicted by coarse-grained (MARTINI) and continuum mechanics models. The results at these distinct levels of resolution give surprisingly consistent descriptions for the shape of the fusion pore, and the deviation between the continuum and coarse-grained models becomes notable only when the radius of curvature approaches the thickness of a monolayer. Although slow relaxation beyond microseconds is observed in different perturbative simulations, the key structural features (e.g., dimension and shape of the fusion pore near the pore center) are consistent among independent simulations. These observations provide solid support for the use of coarse-grained and continuum models in the analysis of membrane remodeling. The combined coarse-grained and continuum analysis confirms the recent prediction of continuum models that the fusion pore is a metastable structure and that its optimal shape is neither toroidal nor catenoidal. Moreover, our results help reveal a new, to our knowledge, bowing feature in which the bilayers close to the pore axis separate more from one another than those at greater distances from the pore axis; bowing helps reduce the curvature and therefore stabilizes the fusion pore structure. The spread of the bilayer deformations over distances of hundreds of nanometers and the substantial reduction in energy of fusion pore formation provided by this spread indicate that membrane fusion can be enhanced by allowing a larger area of membrane to participate and be deformed.

The cost of living in the membrane: a case study of hydrophobic mismatch for the multi-segment protein LeuT

Many observations of the role of the membrane in the function and organization of transmembrane (TM) proteins have been explained in terms of hydrophobic mismatch between the membrane and the inserted protein. For a quantitative investigation of this mechanism in the lipid-protein interactions of functionally relevant conformations adopted by a multi-TM segment protein, the bacterial leucine transporter (LeuT), we employed a novel method, Continuum-Molecular Dynamics (CTMD), that quantifies the energetics of hydrophobic mismatch by combining the elastic continuum theory of membrane deformations with an atomistic level description of the radially asymmetric membrane-protein interface from MD simulations. LeuT has been serving as a model for structure-function studies of the mammalian neurotransmitter:sodium symporters (NSSs), such as the dopamine and serotonin transporters, which are the subject of intense research in the field of neurotransmission. The membrane models in which LeuT was embedded for these studies were composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid, or 3:1 mixture of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG) lipids. The results show that deformation of the host membrane alone is not sufficient to alleviate the hydrophobic mismatch at specific residues of LeuT. The calculations reveal significant membrane thinning and water penetration due to the specific local polar environment produced by the charged K288 of TM7 in LeuT, that is membrane-facing deep inside the hydrophobic milieu of the membrane. This significant perturbation is shown to result in unfavorable polar-hydrophobic interactions at neighboring hydrophobic residues in TM1a and TM7. We show that all the effects attributed to the K288 residue (membrane thinning, water penetration, and the unfavorable polar-hydrophobic interactions at TM1a and TM7), are abolished in calculations with the K288A mutant. The involvement of hydrophobic mismatch is somewhat different in the functionally distinct conformations (outward-open, occluded, inward-open) of LeuT, and the differences are shown to connect to structural elements (e.g., TM1a) known to play key roles in transport. This finding suggests a mechanistic hypothesis for the enhanced transport activity observed for the K288A mutant, suggesting that the unfavorable hydrophobic-hydrophilic interactions hinder the motion of TM1a in the functionally relevant conformational transition to the inward-open state. Various extents of such unfavorable interactions, involving exposure to the lipid environment of adjacent hydrophobic and polar residues, are common in multi-segment transmembrane proteins, and must be considered to affect functionally relevant conformational transitions.

Membrane sculpting by F-BAR domains studied by molecular dynamics simulations

Interplay between cellular membranes and their peripheral proteins drives many processes in eukaryotic cells. Proteins of the Bin/Amphiphysin/Rvs (BAR) domain family, in particular, play a role in cellular morphogenesis, for example curving planar membranes into tubular membranes. However, it is still unclear how F-BAR domain proteins act on membranes. Electron microscopy revealed that, in vitro, F-BAR proteins form regular lattices on cylindrically deformed membrane surfaces. Using all-atom and coarse-grained (CG) molecular dynamics simulations, we show that such lattices, indeed, induce tubes of observed radii. A 250 ns all-atom simulation reveals that F-BAR domain curves membranes via the so-called scaffolding mechanism. Plasticity of the F-BAR domain permits conformational change in response to membrane interaction, via partial unwinding of the domains 3-helix bundle structure. A CG simulation covering more than 350 µs provides a dynamic picture of membrane tubulation by lattices of F-BAR domains. A series of CG simulations identified the optimal lattice type for membrane sculpting, which matches closely the lattices seen through cryo-electron microscopy.

To generate organelles, eukaryotic cells sculpt their membranes into compartments, often employing proteins as chaperones, for example, F-BAR domains. The latter induce formation of tubular and vesicular membranes. Functional and structural studies suggest that F-BAR domains sculpt membranes through electrostatic interactions, driving the membrane to match the concave surface of the protein's banana-like shape. Cryo-electron microscopy (cryo-EM) studies provide an average static picture of how F-BAR domains form lattices on the surface of membranes to induce tube formation. Complementing the cryo-EM images, molecular dynamics simulations reported here offer a detailed, dynamic picture of membrane tubulation by a lattice of F-BAR domains and identified lattice types optimally attuned to producing high membrane curvature. The simulations reproduced also a process lasting 350 µs in which lattices of F-BAR domains form a complete tube out of an initially flat membrane. The molecular dynamics study offers, thereby, both a large-scale picture of membrane sculpting by F-BAR domain lattices as well as atomic-level dynamic information about the involvement of the individual F-BAR domain and its interactions with partner F-BAR domains and membrane in the sculpting process.

Assessing smectic liquid-crystal continuum models for elastic bilayer deformations

For four decades, since W. Helfrich's pioneering study of smectic A liquid crystals in 1973, continuum elastic models (CEMs) have been employed as tools to understand the energetics of protein-induced lipid bilayer deformations. Among the assumptions underlying this use is that all relevant protein-lipid interactions can be included in the continuum representation of the protein-bilayer interactions through the physical parameters determined for protein-free bilayers and the choice of boundary conditions at the protein/bilayer interface. To better understand this assumption, we review the general structure of CEMs, examine how different choices of boundary conditions and physical moduli profiles alter the predicted bilayer thickness profiles around gramicidin A (gA) and mitochondrial voltage-dependent anion channels (VDAC), respectively, and compare these profiles with those obtained from all-atom molecular dynamics simulations. We find that the profiles differ qualitatively in the first lipid shell around the channels, indicating that the CEMs do not capture accurately the consequences of the protein-induced local changes in lipid bilayer dynamics. Therefore, one needs to be careful when interpreting the results of CEM-based analyses of lipid bilayer-membrane protein interactions.

Membrane-mediated protein-protein interactions and connection to elastic models: a coarse-grained simulation analysis of gramicidin A association

To further foster the connection between particle based and continuum mechanics models for membrane mediated biological processes, we carried out coarse-grained (CG) simulations of gramicidin A (gA) dimer association and analyzed the results based on the combination of potential of mean force (PMF) and stress field calculations. Similar to previous studies, we observe that the association of gA dimers depends critically on the degree of hydrophobic mismatch, with the estimated binding free energy of >10 kcal/mol in a distearoylphosphatidylcholine bilayer. Qualitative trends in the computed PMF can be understood based on the stress field distributions near a single gA dimer and between a pair of gA dimers. For example, the small PMF barrier, which is ∼1 kcal/mol independent of lipid type, can be captured nearly quantitatively by considering membrane deformation energy associated with the region confined by two gA dimers. However, the PMF well depth is reproduced poorly by a simple continuum model that only considers membrane deformation energy beyond the annular lipids. Analysis of lipid orientation, configuration entropy, and stress distribution suggests that the annular lipids make a significant contribution to the association of two gA dimers. These results highlight the importance of explicitly considering contributions from annular lipids when constructing approximate models to study processes that involve a significant reorganization of lipids near proteins, such as protein-protein association and protein insertion into biomembranes. Finally, large-scale CG simulations indicate that multiple gA dimers also form clusters, although the preferred topology depends on the protein concentration. Even at high protein concentrations, every gA dimer requires contact to lipid hydrocarbons to some degree, and at most three to four proteins are in contact with each gA dimer; this observation highlights another aspect of the importance of interactions between proteins and annular lipids.

Three-dimensional stress field around a membrane protein: atomistic and coarse-grained simulation analysis of gramicidin A

Using both atomistic and coarse-grained (CG) models, we compute the three-dimensional stress field around a gramicidin A (gA) dimer in lipid bilayers that feature different degrees of negative hydrophobic mismatch. The general trends in the computed stress field are similar at the atomistic and CG levels, supporting the use of the CG model for analyzing the mechanical features of protein/lipid/water interfaces. The calculations reveal that the stress field near the protein-lipid interface exhibits a layered structure with both significant repulsive and attractive regions, with the magnitude of the stress reaching 1000 bar in certain regions. Analysis of density profiles and stress field distributions helps highlight the Trp residues at the protein/membrane/water interface as mechanical anchors, suggesting that similar analysis is useful for identifying tension sensors in other membrane proteins, especially membrane proteins involved in mechanosensation. This work fosters a connection between microscopic and continuum mechanics models for proteins in complex environments and makes it possible to test the validity of assumptions commonly made in continuum mechanics models for membrane mediated processes. For example, using the calculated stress field, we estimate the free energy of membrane deformation induced by the hydrophobic mismatch, and the results for regions beyond the annular lipids are in general consistent with relevant experimental data and previous theoretical estimates using elasticity theory. On the other hand, the assumptions of homogeneous material properties for the membrane and a bilayer thickness at the protein/lipid interface being independent of lipid type (e.g., tail length) appear to be oversimplified, highlighting the importance of annular lipids of membrane proteins. Finally, the stress field analysis makes it clear that the effect of even rather severe hydrophobic mismatch propagates to only about two to three lipid layers, thus putting a limit on the range of cooperativity between membrane proteins in crowded cellular membranes.

Elastic properties of polyunsaturated phosphatidylethanolamines influence rhodopsin function

Membranes with a high content of polyunsaturated phosphatidylethanolamines (PE) facilitate formation of metarhodopsin-II (M(II)), the photointermediate of bovine rhodopsin that activates the G protein transducin. We determined whether M(II)-formation is quantitatively linked to the elastic properties of PEs. Curvature elasticity of monolayers of the polyunsaturated lipids 18 : 0-22 : 6(n - 3)PE, 18 : 0-22 : 5(n)- 6PE and the model lipid 18 : 1(n - 9)-18 : 1,(n- 9)PE were investigated in the inverse hexagonal phase. All three lipids form lipid monolayers with rather low spontaneous radii of curvature of 26-28 angstroms. In membranes, all three PEs generate high negative curvature elastic stress that shifts the equilibrium of MI(I)/M(II) photointermediates of rhodopsin towards M(II) formation.

Structure-based molecular modeling approaches to GPCR oligomerization

Classical structure-based drug design techniques using G-protein-coupled receptors (GPCRs) as targets focus nearly exclusively on binding at the orthosteric site of a single receptor. Dimerization and oligomerization of GPCRs, proposed almost 30 years ago, have, however, crucial relevance for drug design. Targeting these complexes selectively or designing small molecules that affect receptor-receptor interactions might provide new opportunities for novel drug discovery. In order to study the mechanisms and dynamics that rule GPCRs oligomerization, it is essential to understand the dynamic process of receptor-receptor association and to identify regions that are suitable for selective drug binding, which may be determined with experimental methods such as Förster resonance energy transfer (FRET) or Bioluminescence resonance energy transfer (BRET) and computational sequence- and structure-based approaches. The aim of this chapter is to provide a comprehensive description of the structure-based molecular modeling methods for studying GPCR dimerization, that is, protein-protein docking, molecular dynamics, normal mode analysis, and electrostatics studies.

Rhodopsin-lipid interactions studied by NMR

The biophysical properties of the lipid matrix are known to influence function of integral membrane proteins. We report on a sample preparation method for reconstitution of membrane proteins which uses porous anodic aluminum oxide (AAO) filters with 200-nm-wide pores of high density. The substrate permits formation of tubular, single membranes that line the inner surface of pores. One square centimeter of filter with a thickness of 60μm yields on the order of 500cm(2) of solid-supported single bilayer surface, sufficient for NMR studies. The tubular bilayers are free of detergent, fully hydrated, and accessible for ligands from one side of the membrane. The use of AAO filters greatly improves reproducibility of the reconstitution process such that the influence of protein on lipid order parameters can be studied with high resolution. As an example, results for the G protein-coupled receptor of class A, bovine rhodopsin, are shown. By (2)H NMR order parameter measurements, it is detected that rhodopsin insertion elastically deforms membranes near the protein. Furthermore, by (1)H saturation-transfer NMR under conditions of magic angle spinning, we demonstrate detection of preferences in interactions of rhodopsin with particular lipid species. It is assumed that function of integral membrane proteins depends on both protein-induced elastic deformations of the lipid matrix and preferences for interaction of the protein with particular lipid species in the first layer of lipids surrounding the protein.

Curvature forces in membrane lipid-protein interactions

Membrane biochemists are becoming increasingly aware of the role of lipid-protein interactions in diverse cellular functions. This review describes how conformational changes in membrane proteins, involving folding, stability, and membrane shape transitions, potentially involve elastic remodeling of the lipid bilayer. Evidence suggests that membrane lipids affect proteins through interactions of a relatively long-range nature, extending beyond a single annulus of next-neighbor boundary lipids. It is assumed the distance scale of the forces is large compared to the molecular range of action. Application of the theory of elasticity to flexible soft surfaces derives from classical physics and explains the polymorphism of both detergents and membrane phospholipids. A flexible surface model (FSM) describes the balance of curvature and hydrophobic forces in lipid-protein interactions. Chemically nonspecific properties of the lipid bilayer modulate the conformational energetics of membrane proteins. The new biomembrane model challenges the standard model (the fluid mosaic model) found in biochemistry texts. The idea of a curvature force field based on data first introduced for rhodopsin gives a bridge between theory and experiment. Influences of bilayer thickness, nonlamellar-forming lipids, detergents, and osmotic stress are all explained by the FSM. An increased awareness of curvature forces suggests that research will accelerate as structural biology becomes more closely entwined with the physical chemistry of lipids in explaining membrane structure and function.

Membrane bending is critical for the stability of voltage sensor segments in the membrane

The interaction between membrane proteins and the surrounding membrane is becoming increasingly appreciated for its role in regulating protein function, protein localization, and membrane morphology. In particular, recent studies have suggested that membrane deformation is needed to stably accommodate proteins harboring charged amino acids in their transmembrane (TM) region, as it is energetically prohibitive to bury charge in the hydrophobic core of the bilayer. Unfortunately, current computational methods are poorly equipped for describing such deformations, as atomistic simulations are often too short to observe large-scale membrane reorganization and most continuum approaches assume a flat membrane. Previously, we developed a method that overcomes these shortcomings by using elasticity theory to characterize equilibrium membrane distortions in the presence of a TM protein, while using traditional continuum electrostatic and nonpolar energy models to determine the energy of the protein in the membrane. Here, we linked the elastostatics, electrostatics, and nonpolar numeric solvers to permit the calculation of energies for nontrivial membrane deformations. We then coupled this procedure to a robust search algorithm that identifies optimal membrane shapes for a TM protein of arbitrary chemical composition. This advance now permits us to explore a host of biological phenomena that were beyond the scope of our original method. We show that the energy required to embed charged residues in the membrane can be highly nonadditive, and our model provides a simple mechanical explanation for this nonadditivity. Our results also predict that isolated voltage sensor segments do not insert into rigid membranes, but membrane bending dramatically stabilizes these proteins in the bilayer despite their high charge content. Additionally, we use the model to explore hydrophobic mismatch with regard to nonpolar peptides and mechanosensitive channels. Our method is in quantitative agreement with molecular dynamics simulations at a tiny fraction of the computational cost.

Why GPCRs behave differently in cubic and lamellar lipidic mesophases

Recent successes in the crystallographic determination of structures of transmembrane proteins in the G protein-coupled receptor (GPCR) family have established the lipidic cubic phase (LCP) environment as the medium of choice for growing structure-grade crystals by the method termed "in meso". The understanding of in meso crystallogenesis is currently at a descriptive level. To enable an eventual quantitative, energy-based description of the nucleation and crystallization mechanism, we have examined the properties of the lipidic cubic phase system and the dynamics of the GPCR rhodopsin reconstituted into the LCP with coarse-grained molecular dynamics simulations with the Martini force-field. Quantifying the differences in the hydrophobic/hydrophilic exposure of the GPCR to lipids in the cubic and lamellar phases, we found that the highly curved geometry of the cubic phase provides more efficient shielding of the protein from unfavorable hydrophobic exposure, which leads to a lesser hydrophobic mismatch and less unfavorable hydrophobic-hydrophilic interactions between the protein and lipid-water interface in the LCP, compared to the lamellar phase. Since hydrophobic mismatch is considered a driving force for oligomerization, the differences in exposure mismatch energies between the LCP and the lamellar structures suggest that the latter provide a more favorable setting in which GPCRs can oligomerize as a prelude to nucleation and crystal growth. These new findings lay the foundation for future investigations of in meso crystallization mechanisms related to the transition from the LCP to the lamellar phase and studies aimed at an improved rational approach for generating structure-quality crystals of membrane proteins.

Ligand-dependent conformations and dynamics of the serotonin 5-HT(2A) receptor determine its activation and membrane-driven oligomerization properties

From computational simulations of a serotonin 2A receptor (5-HT_2AR) model complexed with pharmacologically and structurally diverse ligands we identify different conformational states and dynamics adopted by the receptor bound to the full agonist 5-HT, the partial agonist LSD, and the inverse agonist Ketanserin. The results from the unbiased all-atom molecular dynamics (MD) simulations show that the three ligands affect differently the known GPCR activation elements including the toggle switch at W6.48, the changes in the ionic lock between E6.30 and R3.50 of the DRY motif in TM3, and the dynamics of the NPxxY motif in TM7. The computational results uncover a sequence of steps connecting these experimentally-identified elements of GPCR activation. The differences among the properties of the receptor molecule interacting with the ligands correlate with their distinct pharmacological properties. Combining these results with quantitative analysis of membrane deformation obtained with our new method (Mondal et al, Biophysical Journal 2011), we show that distinct conformational rearrangements produced by the three ligands also elicit different responses in the surrounding membrane. The differential reorganization of the receptor environment is reflected in (i)-the involvement of cholesterol in the activation of the 5-HT_2AR, and (ii)-different extents and patterns of membrane deformations. These findings are discussed in the context of their likely functional consequences and a predicted mechanism of ligand-specific GPCR oligomerization.

The 5-HT_2A receptor for the neurotransmitter serotonin (5-HT) belongs to family A (rhodopsin-like) G-protein coupled receptors (GPCRs), one of the most important classes of membrane proteins that are targeted by an extensive and diverse collection of external stimuli. Recently we learned that different ligands targeting the same GPCR can elicit different biological responses, but the mechanisms remain unknown. We address this fundamental question for the serotonin 5-HT_2A receptor, because it is known to respond to the binding of structurally diverse ligands by producing similar stimuli in the cell, and to the binding of quite similar ligands with dramatically different responses. Molecular dynamics simulations of molecular models of the serotonin 5-HT_2A receptor in complex with pharmacologically distinct ligands show the dynamic rearrangements of the receptor molecule to be different for these ligands, and the nature and extents of the rearrangements reflect the known pharmacological properties of the ligands as full, partial or inverse activators of the receptor. The different rearrangements of the receptor molecule are shown to produce different rearrangements of the surrounding membrane, a remodeling of the environment that can have differential ligand-determined effects on receptor function and association in the cell's membrane.

Influence of hydrophobic mismatch on structures and dynamics of gramicidin a and lipid bilayers

Gramicidin A (gA) is a 15-amino-acid antibiotic peptide with an alternating L-D sequence, which forms (dimeric) bilayer-spanning, monovalent cation channels in biological membranes and synthetic bilayers. We performed molecular dynamics simulations of gA dimers and monomers in all-atom, explicit dilauroylphosphatidylcholine (DLPC), dimyristoylphosphatidylcholine (DMPC), dioleoylphosphatidylcholine (DOPC), and 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayers. The variation in acyl chain length among these different phospholipids provides a way to alter gA-bilayer interactions by varying the bilayer hydrophobic thickness, and to determine the influence of hydrophobic mismatch on the structure and dynamics of both gA channels (and monomeric subunits) and the host bilayers. The simulations show that the channel structure varied little with changes in hydrophobic mismatch, and that the lipid bilayer adapts to the bilayer-spanning channel to minimize the exposure of hydrophobic residues. The bilayer thickness, however, did not vary monotonically as a function of radial distance from the channel. In all simulations, there was an initial decrease in thickness within 4-5 Å from the channel, which was followed by an increase in DOPC and POPC or a further decrease in DLPC and DMPC bilayers. The bilayer thickness varied little in the monomer simulations-except one of three independent simulations for DMPC and all three DLPC simulations, where the bilayer thinned to allow a single subunit to form a bilayer-spanning water-permeable pore. The radial dependence of local lipid area and bilayer compressibility is also nonmonotonic in the first shell around gA dimers due to gA-phospholipid interactions and the hydrophobic mismatch. Order parameters, acyl chain dynamics, and diffusion constants also differ between the lipids in the first shell and the bulk. The lipid behaviors in the first shell around gA dimers are more complex than predicted from a simple mismatch model, which has implications for understanding the energetics of membrane protein-lipid interactions.