A continuum method for determining membrane protein insertion energies and the problem of charged residues

Membrane curvature sensing and symmetry breaking of the M2 proton channel from Influenza A

The M2 proton channel aids in the exit of mature influenza viral particles from the host plasma membrane through its ability to stabilize regions of high negative Gaussian curvature (NGC) that occur at the neck of budding virions. The channels are homo-tetramers that contain a cytoplasm-facing amphipathic helix (AH) that is necessary and sufficient for NGC generation; however, constructs containing the transmembrane spanning helix, which facilitates tetramerization, exhibit enhanced curvature generation. Here, we used all-atom molecular dynamics (MD) simulations to explore the conformational dynamics of M2 channels in lipid bilayers revealing that the AH is dynamic, quickly breaking the fourfold symmetry observed in most structures. Next, we carried out MD simulations with the protein restrained in four- and twofold symmetric conformations to determine the impact on the membrane shape. While each pattern was distinct, all configurations induced pronounced curvature in the outer leaflet, while conversely, the inner leaflets showed minimal curvature and significant lipid tilt around the AHs. The MD-generated profiles at the protein-membrane interface were then extracted and used as boundary conditions in a continuum elastic membrane model to calculate the membrane-bending energy of each conformation embedded in different membrane surfaces characteristic of a budding virus. The calculations show that all three M2 conformations are stabilized in inward-budding, concave spherical caps and destabilized in outward-budding, convex spherical caps, the latter reminiscent of a budding virus. One of the C2-broken symmetry conformations is stabilized by 4 kT in NGC surfaces with the minimum energy conformation occurring at a curvature corresponding to 33 nm radii. In total, our work provides atomistic insight into the curvature sensing capabilities of M2 channels and how enrichment in the nascent viral particle depends on protein shape and membrane geometry.

Correction Schemes for Absolute Binding Free Energies Involving Lipid Bilayers

Absolute binding free-energy (ABFE) calculations are playing an increasing role in drug design, especially as they can be performed on a range of disparate compounds and direct comparisons between them can be made. It is, however, especially important to ensure that they are as accurate as possible, as unlike relative binding free-energy (RBFE) calculations, one does not benefit as much from a cancellation of errors during the calculations. In most modern implementations of ABFE calculations, a particle mesh Ewald scheme is typically used to treat the electrostatic contribution to the free energy. A central requirement of such schemes is that the box preserves neutrality throughout the calculation. There are many ways to deal with this problem that have been discussed over the years ranging from a neutralizing plasma with a post hoc correction term through to a simple co-alchemical ion within the same box. The post hoc correction approach is the most widespread. However, the vast majority of these studies have been applied to a soluble protein in a homogeneous solvent (water or salt solution). In this work, we explore which of the more common approaches would be the most suitable for a simulation box with a lipid bilayer within it. We further develop the idea of the so-called Rocklin correction for lipid-bilayer systems and show how such a correction could work. However, we also show that it will be difficult to make this generalizable in a practical way and thus we conclude that the use of a “co-alchemical ion” is the most useful approach for simulations involving lipid membrane systems.

Spiers Memorial Lecture: Analysis and de novo design of membrane-interactive peptides

Membrane-peptide interactions play critical roles in many cellular and organismic functions, including protection from infection, remodeling of membranes, signaling, and ion transport. Peptides interact with membranes in a variety of ways: some associate with membrane surfaces in either intrinsically disordered conformations or well-defined secondary structures. Peptides with sufficient hydrophobicity can also insert vertically as transmembrane monomers, and many associate further into membrane-spanning helical bundles. Indeed, some peptides progress through each of these stages in the process of forming oligomeric bundles. In each case, the structure of the peptide and the membrane represent a delicate balance between peptide-membrane and peptide-peptide interactions. We will review this literature from the perspective of several biologically important systems, including antimicrobial peptides and their mimics, α-synuclein, receptor tyrosine kinases, and ion channels. We also discuss the use of de novo design to construct models to test our understanding of the underlying principles and to provide useful leads for pharmaceutical intervention of diseases.

Free Energy Analyses of Cell-Penetrating Peptides Using the Weighted Ensemble Method

Cell-penetrating peptides (CPPs) have been widely used for drug-delivery agents; however, it has not been fully understood how they translocate across cell membranes. The Weighted Ensemble (WE) method, one of the most powerful and flexible path sampling techniques, can be helpful to reveal translocation paths and free energy barriers along those paths. Within the WE approach we show how Arg9 (nona-arginine) and Tat interact with a DOPC/DOPG(4:1) model membrane, and we present free energy (or potential mean of forces, PMFs) profiles of penetration, although a translocation across the membrane has not been observed in the current simulations. Two different compositions of lipid molecules were also tried and compared. Our approach can be applied to any CPPs interacting with various model membranes, and it will provide useful information regarding the transport mechanisms of CPPs.

Principles and Methods in Computational Membrane Protein Design

After decades of progress in computational protein design, the design of proteins folding and functioning in lipid membranes appears today as the next frontier. Some notable successes in the de novo design of simplified model membrane protein systems have helped articulate fundamental principles of protein folding, architecture and interaction in the hydrophobic lipid environment. These principles are reviewed here, together with the computational methods and approaches that were used to identify them. We provide an overview of the methodological innovations in the generation of new protein structures and functions and in the development of membrane-specific energy functions. We highlight the opportunities offered by new machine learning approaches applied to protein design, and by new experimental characterization techniques applied to membrane proteins. Although membrane protein design is in its infancy, it appears more reachable than previously thought.

Unusual mode of dimerization of retinitis pigmentosa-associated F220C rhodopsin

Mutations in the G protein-coupled receptor (GPCR) rhodopsin are a common cause of autosomal dominant retinitis pigmentosa, a blinding disease. Rhodopsin self-associates in the membrane, and the purified monomeric apo-protein opsin dimerizes in vitro as it transitions from detergent micelles to reconstitute into a lipid bilayer. We previously reported that the retinitis pigmentosa-linked F220C opsin mutant fails to dimerize in vitro, reconstituting as a monomer. Using fluorescence-based assays and molecular dynamics simulations we now report that whereas wild-type and F220C opsin display distinct dimerization propensities in vitro as previously shown, they both dimerize in the plasma membrane of HEK293 cells. Unexpectedly, molecular dynamics simulations show that F220C opsin forms an energetically favored dimer in the membrane when compared with the wild-type protein. The conformation of the F220C dimer is unique, with transmembrane helices 5 and 6 splayed apart, promoting widening of the intracellular vestibule of each protomer and influx of water into the protein interior. FRET experiments with SNAP-tagged wild-type and F220C opsin expressed in HEK293 cells are consistent with this conformational difference. We speculate that the unusual mode of dimerization of F220C opsin in the membrane may have physiological consequences.

Molecular Dynamics Simulations Based on Polarizable Models Show that Ion Permeation Interconverts between Different Mechanisms as a Function of Membrane Thickness

Different mechanisms have been proposed to explain the permeation of charged compounds through lipid membranes. Overall, it is expected that an ion-induced defect permeation mechanism, where substantial membrane deformations accompany ion movement, should be dominant in thin membranes but that a solubility-diffusion mechanism, where ions partition into the membrane core with large associated dehydration energy costs, becomes dominant in thicker membranes. However, while this physical picture is intuitively reasonable, capturing the interconversion between these two permeation mechanisms in molecular dynamics (MD) simulations based on atomic models is challenging. In particular, simulations relying on nonpolarizable force fields are artificially unfavorable to the solubility-diffusion mechanism, as induced polarization of the nonpolar hydrocarbon is ignored, causing overestimated free energy costs for charged molecules to enter into this region of the membrane. In this study, all-atom MD simulations based on nonpolarizable and polarizable force fields are used to quantitatively characterize the permeation process for the arginine side chain analog methyl-guanidinium through bilayer membranes of mono-unsaturated phosphatidylcholine lipids with and without cholesterol, resulting in thicknesses spanning from ∼24 to ∼42 Å. With simulations based on a nonpolarizable force field, ion translocation can take place solely through an ion-induced defect mechanism, with free energy barriers increasing linearly from 14 to 40 kcal/mol, depending on the thickness. However, with simulations based on a polarizable force field, ion translocation is predominantly dominated by an ion-induced defect mechanism in thin membranes, which progressively converts to a solubility-diffusion mechanism as the membranes get thicker. The transition between the two mechanisms occurs at a thickness of ∼29 Å, with lipid tails of 22 or more carbon atoms. This situation appears to represent the upper limit for ion-induced defect permeation within the current polarizable models. Beyond this thickness, it becomes energetically preferable for the ion to dehydrate and partition into the membrane core-a phenomenon that cannot be captured using the nonpolarizable models. Induced electronic polarizability therefore leads not just to a shift in permeation energetics but to an interconversion between two strikingly different physical mechanisms. The result highlights the importance of induced polarizability in modeling lipid membranes.

A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface

Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces.

Symmetry of membrane protein polyhedra with heterogeneous protein size

In experiments on membrane protein polyhedral nanoparticles (MPPNs) [Basta et al., Proc. Natl. Acad. Sci. USA 111, 670 (2014)PNASA60027-842410.1073/pnas.1321936111], it has been observed that membrane proteins and lipids can self-assemble into closed lipid bilayer vesicles with a polyhedral arrangement of membrane proteins. In particular, MPPNs formed from the mechanosensitive channel of small conductance (MscS) were found to have the symmetry of the snub cube-a chiral, Archimedean solid-with one MscS protein located at each one of the 24 vertices of the snub cube. It is currently unknown whether MPPNs with heterogeneous protein composition maintain a high degree of symmetry. Inspired by previous work on viral capsid symmetry, we employ here computational modeling to study the symmetry of MPPNs with heterogeneous protein size. We focus on MPPNs formed from MscS proteins, which can exist in closed or open conformational states with distinct sizes. We find that, as an increasing number of closed-state MscS proteins transitions to the open conformational state of MscS, the minimum-energy MscS arrangement in MPPNs follows a strikingly regular pattern, with the dominant MPPN symmetry always being provided by the snub cube. Our results suggest that MPPNs with heterogeneous protein size can be highly symmetric, with a well-defined polyhedral ordering of membrane proteins of different sizes.

Protein Structure Prediction and Design in a Biologically Realistic Implicit Membrane

Protein design is a powerful tool for elucidating mechanisms of function and engineering new therapeutics and nanotechnologies. Although soluble protein design has advanced, membrane protein design remains challenging because of difficulties in modeling the lipid bilayer. In this work, we developed an implicit approach that captures the anisotropic structure, shape of water-filled pores, and nanoscale dimensions of membranes with different lipid compositions. The model improves performance in computational benchmarks against experimental targets, including prediction of protein orientations in the bilayer, ΔΔG calculations, native structure discrimination, and native sequence recovery. When applied to de novo protein design, this approach designs sequences with an amino acid distribution near the native amino acid distribution in membrane proteins, overcoming a critical flaw in previous membrane models that were prone to generating leucine-rich designs. Furthermore, the proteins designed in the new membrane model exhibit native-like features including interfacial aromatic side chains, hydrophobic lengths compatible with bilayer thickness, and polar pores. Our method advances high-resolution membrane protein structure prediction and design toward tackling key biological questions and engineering challenges.

M2 amphipathic helices facilitate pH-dependent conformational transition in influenza A virus

The matrix-2 (M2) protein from influenza A virus is a tetrameric, integral transmembrane (TM) protein that plays a vital role in viral replication by proton flux into the virus. The His37 tetrad is a pH sensor in the center of the M2 TM helix that activates the channel in response to the low endosomal pH. M2 consists of different regions that are believed to be involved in membrane targeting, packaging, nucleocapsid binding, and proton transport. Although M2 has been the target of many experimental and theoretical studies that have led to significant insights into its structure and function under differing conditions, the main mechanism of proton transport, its conformational dynamics, and the role of the amphipathic helices (AHs) on proton conductance remain elusive. To this end, we have applied explicit solvent constant pH molecular dynamics using the multisite λ-dynamics approach (CpHMD^MSλD) to investigate the buried ionizable residues comprehensively and to elucidate their effect on the conformational transition. Our model recapitulates the pH-dependent conformational transition of M2 from closed to open state when the AH domain is included in the M2 construct, revealing the role of the amphipathic helices on this transition and shedding light on the proton-transport mechanism. This work demonstrates the importance of including the amphipathic helices in future experimental and theoretical studies of ion channels. Finally, our work shows that explicit solvent CpHMD^MSλD provides a realistic pH-dependent model for membrane proteins.

Molecular Modeling of Surfactant Micellization Using Solvent-Accessible Surface Area

We report a new implicit solvent simulation model for studying the self-assembly of surfactants, where the hydrophobic interactions were captured by calculating the relative changes of the solvent-accessible surface area (SASA) of the hydrophobic domains. Using histogram-reweighting grand canonical Monte Carlo simulations, we demonstrate that this approach allows us to match both the experimental critical micelle concentrations (cmc) and micellar aggregation numbers simultaneously with a single phenomenological surface tension γ_SASA for the poly(oxyethylene) monoalkyl ether (C _mE _n) surfactants in aqueous solutions. Excellent transferability is observed: the same model can accurately predict the experimental cmc and aggregation numbers for the C _mE _n surfactants with the alkyl lengths m between 6 and 12 and the poly(oxyethylene) lengths n between 1 and 9. The SASA-based implicit solvent model put forward in this work is general and may be applied to study more complex amphiphilic systems such as surfactants with branched alkyl chains or surfactant-hydrocarbon mixtures.

An engineered opsin monomer scrambles phospholipids

The G protein-coupled receptor opsin is a phospholipid scramblase that facilitates rapid transbilayer phospholipid exchange in liposomes. The mechanism by which opsin scrambles lipids is unknown. It has been proposed that lipid translocation may occur at protein-protein interfaces of opsin dimers. To test this possibility, we rationally engineered QUAD opsin by tryptophan substitution of four lipid-facing residues in transmembrane helix 4 (TM4) that is known to be important for dimerization. Atomistic molecular dynamics simulations of wild type and QUAD opsins combined with continuum modeling revealed that the tryptophan substitutions lower the energetically unfavorable residual hydrophobic mismatch between TM4 and the membrane, reducing the drive of QUAD opsin to dimerize. We purified thermostable wild type and QUAD opsins, with or without a SNAP tag for fluorescence labeling. Single molecule fluorescence measurements of purified SNAP-tagged constructs revealed that both proteins are monomers. Fluorescence-based activity assays indicated that QUAD opsin is a fully functional scramblase. However, unlike wild type opsin which dimerizes en route to insertion into phospholipid vesicles, QUAD opsin reconstitutes as a monomer. We conclude that an engineered opsin monomer can scramble phospholipids, and that the lipid-exposed face of TM4 is unlikely to contribute to transbilayer phospholipid exchange.

New Continuum Approaches for Determining Protein-Induced Membrane Deformations

The influence of the membrane on transmembrane proteins is central to a number of biological phenomena, notably the gating of stretch activated ion channels. Conversely, membrane proteins can influence the bilayer, leading to the stabilization of particular membrane shapes, topological changes that occur during vesicle fission and fusion, and shape-dependent protein aggregation. Continuum elastic models of the membrane have been widely used to study protein-membrane interactions. These mathematical approaches produce physically interpretable membrane shapes, energy estimates for the cost of deformation, and a snapshot of the equilibrium configuration. Moreover, elastic models are much less computationally demanding than fully atomistic and coarse-grained simulation methodologies; however, it has been argued that continuum models cannot reproduce the distortions observed in fully atomistic molecular dynamics simulations. We suggest that this failure can be overcome by using chemically and geometrically accurate representations of the protein. Here, we present a fast and reliable hybrid continuum-atomistic model that couples the protein to the membrane. We show that the model is in excellent agreement with fully atomistic simulations of the ion channel gramicidin embedded in a POPC membrane. Our continuum calculations not only reproduce the membrane distortions produced by the channel but also accurately determine the channel's orientation. Finally, we use our method to investigate the role of membrane bending around the charged voltage sensors of the transient receptor potential cation channel TRPV1. We find that membrane deformation significantly stabilizes the energy of insertion of TRPV1 by exposing charged residues on the S4 segment to solution.

Transmembrane helix hydrophobicity is an energetic barrier during the retrotranslocation of integral membrane ERAD substrates

Integral membrane proteins fold inefficiently and are susceptible to turnover via the endoplasmic reticulum-associated degradation (ERAD) pathway. During ERAD, misfolded proteins are recognized by molecular chaperones, polyubiquitinated, and retrotranslocated to the cytoplasm for proteasomal degradation. Although many aspects of this pathway are defined, how transmembrane helices (TMHs) are removed from the membrane and into the cytoplasm before degradation is poorly understood. In this study, we asked whether the hydrophobic character of a TMH acts as an energetic barrier to retrotranslocation. To this end, we designed a dual-pass model ERAD substrate, Chimera A*, which contains the cytoplasmic misfolded domain from a characterized ERAD substrate, Sterile 6* (Ste6p*). We found that the degradation requirements for Chimera A* and Ste6p* are similar, but Chimera A* was retrotranslocated more efficiently than Ste6p* in an in vitro assay in which retrotranslocation can be quantified. We then constructed a series of Chimera A* variants containing synthetic TMHs with a range of ΔG values for membrane insertion. TMH hydrophobicity correlated inversely with retrotranslocation efficiency, and in all cases, retrotranslocation remained Cdc48p dependent. These findings provide insight into the energetic restrictions on the retrotranslocation reaction, as well as a new computational approach to predict retrotranslocation efficiency.

Atomistic insight into lipid translocation by a TMEM16 scramblase

The transmembrane protein 16 (TMEM16) family of membrane proteins includes both lipid scramblases and ion channels involved in olfaction, nociception, and blood coagulation. The crystal structure of the fungal Nectria haematococca TMEM16 (nhTMEM16) scramblase suggested a putative mechanism of lipid transport, whereby polar and charged lipid headgroups move through the low-dielectric environment of the membrane by traversing a hydrophilic groove on the membrane-spanning surface of the protein. Here, we use computational methods to explore the membrane-protein interactions involved in lipid scrambling. Fast, continuum membrane-bending calculations reveal a global pattern of charged and hydrophobic surface residues that bends the membrane in a large-amplitude sinusoidal wave, resulting in bilayer thinning across the hydrophilic groove. Atomic simulations uncover two lipid headgroup-interaction sites flanking the groove. The cytoplasmic site nucleates headgroup-dipole stacking interactions that form a chain of lipid molecules that penetrate into the groove. In two instances, a cytoplasmic lipid interdigitates into this chain, crosses the bilayer, and enters the extracellular leaflet, and the reverse process happens twice as well. Continuum membrane-bending analysis carried out on homology models of mammalian homologs shows that these family members also bend the membrane-even those that lack scramblase activity. Sequence alignments show that the lipid-interaction sites are conserved in many family members but less so in those with reduced scrambling ability. Our analysis provides insight into how large-scale membrane bending and protein chemistry facilitate lipid permeation in the TMEM16 family, and we hypothesize that membrane interactions also affect ion permeation.

Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S.A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein arrangement and characteristic size. We develop a model of MPPN self-assembly in which the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects. With all model parameters determined directly from experiments, our model correctly predicts the observed symmetry and size of MPPNs. Our model suggests how key lipid and protein properties can be modified to produce a range of MPPN symmetries and sizes in experiments.

Continuum descriptions of membranes and their interaction with proteins: Towards chemically accurate models

Biological membranes deform in response to resident proteins leading to a coupling between membrane shape and protein localization. Additionally, the membrane influences the function of membrane proteins. Here we review contributions to this field from continuum elastic membrane models focusing on the class of models that couple the protein to the membrane. While it has been argued that continuum models cannot reproduce the distortions observed in fully-atomistic molecular dynamics simulations, we suggest that this failure can be overcome by using chemically accurate representations of the protein. We outline our recent advances along these lines with our hybrid continuum-atomistic model, and we show the model is in excellent agreement with fully-atomistic simulations of the nhTMEM16 lipid scramblase. We believe that the speed and accuracy of continuum-atomistic methodologies will make it possible to simulate large scale, slow biological processes, such as membrane morphological changes, that are currently beyond the scope of other computational approaches. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Synaptobrevin transmembrane domain influences exocytosis by perturbing vesicle membrane curvature

Membrane fusion requires that nearly flat lipid bilayers deform into shapes with very high curvature. This makes membrane bending a critical force in determining fusion mechanisms. A lipid bilayer will bend spontaneously when material is distributed asymmetrically between its two monolayers, and its spontaneous curvature (C0) will influence the stability of curved fusion intermediates. Prior work on Ca(2+)-triggered exocytosis revealed that fusion pore lifetime (τ) varies with vesicle content (Q), and showed that this relation reflects membrane bending energetics. Lipids that alter C0 change the dependence of τ on Q. These results suggested that the greater stability of an initial exocytotic fusion pore associated with larger vesicles reflects the need to bend more membrane during fusion pore dilation. In this study, we explored the possibility of manipulating C0 by mutating the transmembrane domain (TMD) of the vesicle membrane protein synaptobrevin 2 (syb2). Amperometric measurements of exocytosis in mouse chromaffin cells revealed that syb2 TMD mutations altered the relation between τ and Q. The effects of these mutations showed a striking periodicity, changing sign as the structural perturbation moved through the inner and outer leaflets. Some glycine and charge mutations also influenced the dependence of τ on Q in a manner consistent with expected changes in C0. These results suggest that side chains in the syb2 TMD influence the kinetics of exocytosis by perturbing the packing of the surrounding lipids. The present results support the view that membrane bending occurs during fusion pore expansion rather than during fusion pore formation. This supports the view of an initial fusion pore through two relatively flat membranes formed by protein.

Solid-State NMR-Restrained Ensemble Dynamics of a Membrane Protein in Explicit Membranes

Solid-state NMR has been used to determine the structures of membrane proteins in native-like lipid bilayer environments. Most structure calculations based on solid-state NMR observables are performed using simulated annealing with restrained molecular dynamics and an energy function, where all nonbonded interactions are represented by a single, purely repulsive term with no contributions from van der Waals attractive, electrostatic, or solvation energy. To our knowledge, this is the first application of an ensemble dynamics technique performed in explicit membranes that uses experimental solid-state NMR observables to obtain the refined structure of a membrane protein together with information about its dynamics and its interactions with lipids. Using the membrane-bound form of the fd coat protein as a model membrane protein and its experimental solid-state NMR data, we performed restrained ensemble dynamics simulations with different ensemble sizes in explicit membranes. For comparison, a molecular dynamics simulation of fd coat protein was also performed without any restraints. The average orientation of each protein helix is similar to a structure determined by traditional single-conformer approaches. However, their variations are limited in the resulting ensemble of structures with one or two replicas, as they are under the strong influence of solid-state NMR restraints. Although highly consistent with all solid-state NMR observables, the ensembles of more than two replicas show larger orientational variations similar to those observed in the molecular dynamics simulation without restraints. In particular, in these explicit membrane simulations, Lys(40), residing at the C-terminal side of the transmembrane helix, is observed to cause local membrane curvature. Therefore, compared to traditional single-conformer approaches in implicit environments, solid-state NMR restrained ensemble simulations in explicit membranes readily characterize not only protein dynamics but also protein-lipid interactions in detail.

Free Energy Calculations for the Peripheral Binding of Proteins/Peptides to an Anionic Membrane. 1. Implicit Membrane Models

The binding of peptides and proteins to the surface of complex lipid membranes is important in many biological processes such as cell signaling and membrane remodeling. Computational studies can aid experiments by identifying physical interactions and structural motifs that determine the binding affinity and specificity. However, previous studies focused on either qualitative behaviors of protein/membrane interactions or the binding affinity of small peptides. Motivated by this observation, we set out to develop computational protocols for bimolecular binding to charged membranes that are applicable to both peptides and large proteins. In this work, we explore a method based on an implicit membrane/solvent model (generalized Born with a simple switching in combination with the Gouy-Chapman-Stern model for a charged interface), which we expect to lead to useful results when the binding does not implicate significant membrane deformation and local demixing of lipids. We show that the binding free energy can be efficiently computed following a thermodynamic cycle similar to protein-ligand binding calculations, especially when a Bennett acceptance ratio based protocol is used to consider both the membrane bound and solution conformational ensembles. Test calculations on a series of peptides show that our computational approach leads to binding affinities in encouraging agreement with experimental data, including for the challenging example of the bringing of flexible MARCKS-ED peptides to membranes. The calculations highlight that for a membrane with a significant fraction of anionic lipids, it is essential to include the effect of ion adsorption using the Stern model, which significantly modifies the effective surface charge. This implicit membrane model based computational protocol helps lay the groundwork for more systematic analysis of protein/peptide binding to membranes of complex shape and composition.

Refining the treatment of membrane proteins by coarse-grained models

Obtaining a quantitative description of the membrane proteins stability is crucial for understanding many biological processes. However the advance in this direction has remained a major challenge for both experimental studies and molecular modeling. One of the possible directions is the use of coarse-grained models but such models must be carefully calibrated and validated. Here we use a recent progress in benchmark studies on the energetics of amino acid residue and peptide membrane insertion and membrane protein stability in refining our previously developed coarse-grained model (Vicatos et al., Proteins 2014;82:1168). Our refined model parameters were fitted and/or tested to reproduce water/membrane partitioning energetics of amino acid side chains and a couple of model peptides. This new model provides a reasonable agreement with experiment for absolute folding free energies of several β-barrel membrane proteins as well as effects of point mutations on a relative stability for one of those proteins, OmpLA. The consideration and ranking of different rotameric states for a mutated residue was found to be essential to achieve satisfactory agreement with the reference data.

Investigating Hydrophilic Pores in Model Lipid Bilayers Using Molecular Simulations: Correlating Bilayer Properties with Pore-Formation Thermodynamics

Cell-penetrating and antimicrobial peptides show a remarkable ability to translocate across physiological membranes. Along with factors such as electric-potential-induced perturbations of membrane structure and surface tension effects, experiments invoke porelike membrane configurations during the solute transfer process into vesicles and cells. The initiation and formation of pores are associated with a nontrivial free-energy cost, thus necessitating a consideration of the factors associated with pore formation and the attendant free energies. Because of experimental and modeling challenges related to the long time scales of the translocation process, we use umbrella sampling molecular dynamics simulations with a lipid-density-based order parameter to investigate membrane-pore-formation free energy employing Martini coarse-grained models. We investigate structure and thermodynamic features of the pore in 18 lipids spanning a range of headgroups, charge states, acyl chain lengths, and saturation. We probe the dependence of pore-formation barriers on the area per lipid, lipid bilayer thickness, and membrane bending rigidities in three different lipid classes. The pore-formation free energy in pure bilayers and peptide translocating scenarios are significantly coupled with bilayer thickness. Thicker bilayers require more reversible work to create pores. The pore-formation free energy is higher in peptide-lipid systems than in peptide-free lipid systems due to penalties to maintain the solvation of charged hydrophilic solutes within the membrane environment.

Membrane environment modulates the pKa values of transmembrane helices

In this work, we apply the recently developed constant pH molecular dynamics technique to study protonation equilibria of titratable side chains in the context of simple transmembrane (TM) helices and explore the effect of pH on their configurations in membrane bilayers. We observe that, despite a significant shift toward neutral states, considerable population of different side chains stay in the charged state that give rise to pK_a values around 9.6 for Asp and Glu and 4.5 to 6 for His and Lys side chains, respectively. These charged states are highly stabilized by favorable interactions between head groups, water molecules, and the charged side chains that are facilitated by substantial changes in the configuration of the peptides. The pH dependent configurations and the measured pK_a values are in good agreement with relatively recent solid state NMR measurements. Our results presented here demonstrate that all-atom constant pH molecular dynamics can be applied to membrane proteins and peptides to obtain reliable pK_a values and pH dependent behavior for these systems.

Interactions of amino acid side-chain analogs within membrane environments

The interactions among four amino acid analog pairs (Asn, Ser, Phe, and Val) within the membrane environment were investigated using umbrella sampling molecular dynamics simulations. The results confirm generally expected qualitative trends of preferential association of polar compounds inside the membrane vs preferential interaction of hydrophobic compounds outside the membrane. Furthermore, correlations between amino acid interactions, membrane insertion, and membrane deformations are discussed and a detailed analysis of pair interaction energies is presented. A comparison of the energetics obtained from explicit lipid simulations with those from implicit membrane models reveals significant deviations and an improved parametrization of the heterogeneous dielectric generalized Born implicit model is provided that partially corrects for deficiencies in the implicit membrane model when compared with the new reference data from this study.

Reconciling structural and thermodynamic predictions using all-atom and coarse-grain force fields: the case of charged oligo-arginine translocation into DMPC bilayers

Using the translocation of short, charged cationic oligo-arginine peptides (mono-, di-, and triarginine) from bulk aqueous solution into model DMPC bilayers, we explore the question of the similarity of thermodynamic and structural predictions obtained from molecular dynamics simulations using all-atom and Martini coarse-grain force fields. Specifically, we estimate potentials of mean force associated with translocation using standard all-atom (CHARMM36 lipid) and polarizable and nonpolarizable Martini force fields, as well as a series of modified Martini-based parameter sets. We find that we are able to reproduce qualitative features of potentials of mean force of single amino acid side chain analogues into model bilayers. In particular, modifications of peptide-water and peptide-membrane interactions allow prediction of free energy minima at the bilayer-water interface as obtained with all-atom force fields. In the case of oligo-arginine peptides, the modified parameter sets predict interfacial free energy minima as well as free energy barriers in almost quantitative agreement with all-atom force field based simulations. Interfacial free energy minima predicted by a modified coarse-grained parameter set are -2.51, -4.28, and -5.42 for mono-, di-, and triarginine; corresponding values from all-atom simulations are -0.83, -3.33, and -3.29, respectively, all in units of kcal/mol. We found that a stronger interaction between oligo-arginine and the membrane components and a weaker interaction between oligo-arginine and water are crucial for producing such minima in PMFs using the polarizable CG model. The difference between bulk aqueous and bilayer center states predicted by the modified coarse-grain force field are 11.71, 14.14, and 16.53 kcal/mol, and those by the all-atom model are 6.94, 8.64, and 12.80 kcal/mol; those are of almost the same order of magnitude. Our simulations also demonstrate a remarkable similarity in the structural aspects of the ensemble of configurations generated using the all-atom and coarse-grain force fields. Both resolutions show that oligo-arginine peptides adopt preferential orientations as they translocate into the bilayer. The guiding theme centers on charged groups maintaining coordination with polar and charged bilayer components as well as local water. We also observe similar behaviors related with membrane deformations.

Simulating G protein-coupled receptors in native-like membranes: from monomers to oligomers

G protein-coupled receptors (GPCRs) are one of the most relevant superfamilies of transmembrane proteins as they participate in an important variety of biological events. Recently, the scientific community is witnessing an advent of a GPCR crystallization age along with impressive improvements achieved in the field of computer simulations during the last two decades. Computer simulation techniques such as molecular dynamics (MD) simulations are now frequent tools to study the dynamic behavior of GPCRs and, more importantly, to model the complex membrane environment where these proteins spend their lifetime. Thanks to these tools, GPCRs can be simulated not only longer but also in a more "physiological" fashion. In this scenario, scientists are taking advantage of such advances to approach certain phenomena such as GPCR oligomerization occurring only at timescales not reachable until now. Thus, despite current MD simulations having important limitations today, they have become an essential tool to study key biophysical properties of GPCRs and GPCR oligomers.

Not just an oil slick: how the energetics of protein-membrane interactions impacts the function and organization of transmembrane proteins

The membrane environment, its composition, dynamics, and remodeling, have been shown to participate in the function and organization of a wide variety of transmembrane (TM) proteins, making it necessary to study the molecular mechanisms of such proteins in the context of their membrane settings. We review some recent conceptual advances enabling such studies, and corresponding computational models and tools designed to facilitate the concerted experimental and computational investigation of protein-membrane interactions. To connect productively with the high resolution achieved by cognate experimental approaches, the computational methods must offer quantitative data at an atomistically detailed level. We show how such a quantitative method illuminated the mechanistic importance of a structural characteristic of multihelical TM proteins, that is, the likely presence of adjacent polar and hydrophobic residues at the protein-membrane interface. Such adjacency can preclude the complete alleviation of the well-known hydrophobic mismatch between TM proteins and the surrounding membrane, giving rise to an energy cost of residual hydrophobic mismatch. The energy cost and biophysical formulation of hydrophobic mismatch and residual hydrophobic mismatch are reviewed in the context of their mechanistic role in the function of prototypical members of multihelical TM protein families: 1), LeuT, a bacterial homolog of mammalian neurotransmitter sodium symporters; and 2), rhodopsin and the β1- and β2-adrenergic receptors from the G-protein coupled receptor family. The type of computational analysis provided by these examples is poised to translate the rapidly growing structural data for the many TM protein families that are of great importance to cell function into ever more incisive insights into mechanisms driven by protein-ligand and protein-protein interactions in the membrane environment.

Continuum approaches to understanding ion and peptide interactions with the membrane

Experimental and computational studies have shown that cellular membranes deform to stabilize the inclusion of transmembrane (TM) proteins harboring charge. Recent analysis suggests that membrane bending helps to expose charged and polar residues to the aqueous environment and polar head groups. We previously used elasticity theory to identify membrane distortions that minimize the insertion of charged TM peptides into the membrane. Here, we extend our work by showing that it also provides a novel, computationally efficient method for exploring the energetics of ion and small peptide penetration into membranes. First, we show that the continuum method accurately reproduces energy profiles and membrane shapes generated from molecular simulations of bare ion permeation at a fraction of the computational cost. Next, we demonstrate that the dependence of the ion insertion energy on the membrane thickness arises primarily from the elastic properties of the membrane. Moreover, the continuum model readily provides a free energy decomposition into components not easily determined from molecular dynamics. Finally, we show that the energetics of membrane deformation strongly depend on membrane patch size both for ions and peptides. This dependence is particularly strong for peptides based on simulations of a known amphipathic, membrane binding peptide from the human pathogen Toxoplasma gondii. In total, we address shortcomings and advantages that arise from using a variety of computational methods in distinct biological contexts.

Implicit membrane treatment of buried charged groups: application to peptide translocation across lipid bilayers

The energetic cost of burying charged groups in the hydrophobic core of lipid bilayers has been controversial, with simulations giving higher estimates than certain experiments. Implicit membrane approaches are usually deemed too simplistic for this problem. Here we challenge this view. The free energy of transfer of amino acid side chains from water to the membrane center predicted by IMM1 is reasonably close to all-atom free energy calculations. The shape of the free energy profile, however, for the charged side chains needs to be modified to reflect the all-atom simulation findings (IMM1-LF). Membrane thinning is treated by combining simulations at different membrane widths with an estimate of membrane deformation free energy from elasticity theory. This approach is first tested on the voltage sensor and the isolated S4 helix of potassium channels. The voltage sensor is stably inserted in a transmembrane orientation for both the original and the modified model. The transmembrane orientation of the isolated S4 helix is unstable in the original model, but a stable local minimum in IMM1-LF, slightly higher in energy than the interfacial orientation. Peptide translocation is addressed by mapping the effective energy of the peptide as a function of vertical position and tilt angle, which allows identification of minimum energy pathways and transition states. The barriers computed for the S4 helix and other experimentally studied peptides are low enough for an observable rate. Thus, computational results and experimental studies on the membrane burial of peptide charged groups appear to be consistent. This article is part of a Special Issue entitled: Interfacially Active Peptides and Proteins. Guest Editors: William C. Wimley and Kalina Hristova.

Free energy change for insertion of charged, monolayer-protected nanoparticles into lipid bilayers

Charged, monolayer-protected gold nanoparticles (AuNPs) with core diameters smaller than 10 nm have recently emerged as a prominent class of nanomaterial for use in targeted drug delivery and biosensing. In particular, recent experimental studies showed that AuNPs protected by a binary mixture of purely hydrophobic and anionic, end-functionalized alkanethiol ligands were able to spontaneously penetrate through cell membranes via a non-endocytic, non-disruptive mechanism. The critical step in the penetration process is a fusion step during which the AuNPs insert into the hydrophobic core of the bilayer. This fusion step is driven by hydrophobic forces as inserted AuNPs minimize their exposed hydrophobic surface area and thereby lower their free energy compared to particles in the bulk. Here, we explore the effect of the large parameter space of composition, size, ligand length, morphology, and hydrophobicity strength on the change in the free energy upon insertion. Using a newly developed implicit bilayer, implicit solvent simulation model, our work shows that there is a size cutoff for insertion that has a strong dependence on surface composition and ligand chemistry. Our results agree well with previous experimental findings for a particular value of the hydrophobicity strength. This work provides physical insight that may be used to both understand the insertion of AuNPs into bilayers and guide the design of monolayers to either encourage or inhibit insertion.

How the dynamic properties and functional mechanisms of GPCRs are modulated by their coupling to the membrane environment

Experimental observations of the dependence of function and organization of G protein-coupled receptors (GPCRs) on their lipid environment have stimulated new quantitative studies of the coupling between the proteins and the membrane. It is important to develop such a quantitative understanding at the molecular level because the effects of the coupling are seen to be physiologically and clinically significant. Here we review findings that offer insight into how membrane-GPCR coupling is connected to the structural characteristics of the GPCR, from sequence to 3D structural detail, and how this coupling is involved in the actions of ligands on the receptor. The application of a recently developed computational approach designed for quantitative evaluation of membrane remodeling and the energetics of membrane-protein interactions brings to light the importance of the radial asymmetry of the membrane-facing surface of GPCRs in their interaction with the surrounding membrane. As the radial asymmetry creates adjacencies of hydrophobic and polar residues at specific sites of the GPCR, the ability of membrane remodeling to achieve complete hydrophobic matching is limited, and the residual mismatch carries a significant energy cost. The adjacencies are shown to be affected by ligand-induced conformational changes. Thus, functionally important organization of GPCRs in the cell membrane can depend both on ligand-determined properties and on the lipid composition of various membrane regions with different remodeling capacities. That this functionally important reorganization can be driven by oligomerization patterns that reduce the energy cost of the residual mismatch, suggests a new perspective on GPCR dimerization and ligand-GPCR interactions. The relation between the modulatory effects on GPCRs from the binding of specific cell-membrane components, e.g., cholesterol, and those produced by the non-local energetics of hydrophobic mismatch are discussed in this context.

Free energetics of arginine permeation into model DMPC lipid bilayers: coupling of effective counterion concentration and lateral bilayer dimensions

Mechanisms and underlying thermodynamic determinants of translocation of charged cationic peptides such as cell-penetrating peptides across the cellular membrane continue to receive much attention. Two widely held views include endocytotic and non-endocytotic (diffusive) processes of permeant transfer across the bilayer. Considering a purely diffusive process, we consider the free energetics of translocation of a monoarginine peptide mimic across a model DMPC bilayer. We compute potentials of mean force for the transfer of a charged monoarginine peptide unit from water to the center of a 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) model lipid bilayer. We use fully atomistic molecular dynamics simulations coupled with the adaptive biasing force (ABF) method for free energy estimation. The estimated potential of mean force difference from bulk to bilayer center is 6.94 ± 0.28 kcal/mol. The order of magnitude of this prediction is consistent with past experimental estimates of arginine partitioning into physiological bilayers in the context of translocon-based experiments, though the correlation between the bench and computer experiments is not unambiguous. Moreover, the present value is roughly one-half of previous estimates based on all-atom molecular dynamics free energy calculations. We trace the differences between the present and earlier calculations to system sizes used in the simulations and the dependence of the contributions to the free energy from various system components (water, lipids, ions, peptide) on overall system size. By varying the bilayer lateral dimensions in simulations using only sufficient numbers of counterions to maintain overall system charge neutrality, we find the possibility of an inherent convergent transfer free energy value.

Ligand-mediated short-range attraction drives aggregation of charged monolayer-protected gold nanoparticles

Monolayer-protected gold nanoparticles (AuNPs) are a promising new class of nanomaterials with applications in drug delivery, self-assembly, and biosensing. The versatility of the AuNP platform is conferred by the properties of the protecting monolayer which can be engineered to tune the surface functionality of the nanoparticles. However, many applications are hampered by AuNP aggregation, which can inhibit functionality or induce particles to precipitate out of solution, even for water-soluble AuNPs. It is critical to understand the mechanisms of aggregation in order to optimally engineer protecting monolayers that both inhibit aggregation and maintain functionality. In this work, we use implicit solvent simulations to calculate the free energy change associated with the aggregation of two small, charged, alkanethiol monolayer-protected AuNPs under typical biological conditions. We show that aggregation is driven by the hydrophobic effect related to the amphiphilic nature of the alkanethiol ligands. The critical factor that enables aggregation is the deformation of ligands in the monolayer to shield hydrophobic surface area from water upon close association of the two particles. Our results further show that ligand deformation, and thus aggregation, is highly dependent on the size of the AuNPs, choice of ligands, and environmental conditions. This work provides insight into the key role that ligand-ligand interactions play in stabilizing AuNP aggregates and suggests guidelines for the design of protecting monolayers that inhibit aggregation under typical biological conditions.

Membrane protein native state discrimination by implicit membrane models

Four implicit membrane models [IMM1, generalized Born (GB)-surface area-implicit membrane (GBSAIM), GB with a simple switching (GBSW), and heterogeneous dielectric GB (HDGB)] were tested for their ability to discriminate the native conformation of five membrane proteins from 450 decoys generated by the Rosetta-Membrane program. The energy ranking of the native state and Z-scores were used to assess the performance of the models. The effect of membrane thickness was examined and was found to be substantial. Quite satisfactory discrimination was achieved with the all-atom IMM1 and GBSW models at 25.4 Å thickness and with the HDGB model at 28.5 Å thickness. The energy components by themselves were not discriminative. Both van der Waals and electrostatic interactions contributed to native state discrimination, to a different extent in each model. Computational efficiency of the models decreased in the order: extended-atom IMM1 > all-atom IMM1 > GBSAIM > GBSW > HDGB. These results encourage the further development and use of implicit membrane models for membrane protein structure prediction.

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.

Dynamic Heterogeneous Dielectric Generalized Born (DHDGB): An implicit membrane model with a dynamically varying bilayer thickness

An extension to the heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is presented to allow dynamic membrane deformations in response to membrane-inserted biomolecules during molecular dynamic simulations. The flexible membrane is implemented through additional degrees of freedom that represent the membrane deformation at the contact points of a membrane-inserted solute with the membrane. The extra degrees of freedom determine the dielectric and non-polar solvation free energy profiles that are used to obtain the solvation free energy in the presence of the membrane and are used to calculate membrane deformation free energies according to an elastic membrane model. With the dynamic HDGB (DHDGB) model the membrane is able to deform in response to the insertion of charged molecules thereby avoiding the overestimation of insertion free energies with static membrane models. The DHDGB model also allows the membrane to respond to the insertion of membrane-spanning solutes with hydrophobic mismatch. The model is tested with the membrane insertion of amino acid side chain analogs, arginine-containing helices, the WALP23 peptide, and the gramicidin A channel.

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.

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.

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.

The determinants of hydrophobic mismatch response for transmembrane helices

Hydrophobic mismatch arises from a difference in the hydrophobic thickness of a lipid membrane and a transmembrane protein segment, and is thought to play an important role in the folding, stability and function of membrane proteins. We have investigated the possible adaptations that lipid bilayers and transmembrane α-helices undergo in response to mismatch, using fully-atomistic molecular dynamics simulations totaling 1.4 μs. We have created 25 different tryptophan-alanine-leucine transmembrane α-helical peptide systems, each composed of a hydrophobic alanine-leucine stretch, flanked by 1-4 tryptophan side chains, as well as the β-helical peptide dimer, gramicidin A. Membrane responses to mismatch include changes in local bilayer thickness and lipid order, varying systematically with peptide length. Adding more flanking tryptophan side chains led to an increase in bilayer thinning for negatively mismatched peptides, though it was also associated with a spreading of the bilayer interface. Peptide tilting, bending and stretching were systematic, with tilting dominating the responses, with values of up to ~45° for the most positively mismatched peptides. Peptide responses were modulated by the number of tryptophan side chains due to their anchoring roles and distributions around the helices. Potential of mean force calculations for local membrane thickness changes, helix tilting, bending and stretching revealed that membrane deformation is the least energetically costly of all mismatch responses, except for positively mismatched peptides where helix tilting also contributes substantially. This comparison of energetic driving forces of mismatch responses allows for deeper insight into protein stability and conformational changes in lipid membranes.

Determination of membrane-insertion free energies by molecular dynamics simulations

The accurate prediction of membrane-insertion probability for arbitrary protein sequences is a critical challenge to identifying membrane proteins and determining their folded structures. Although algorithms based on sequence statistics have had moderate success, a complete understanding of the energetic factors that drive the insertion of membrane proteins is essential to thoroughly meeting this challenge. In the last few years, numerous attempts to define a free-energy scale for amino-acid insertion have been made, yet disagreement between most experimental and theoretical scales persists. However, for a recently resolved water-to-bilayer scale, it is found that molecular dynamics simulations that carefully mimic the conditions of the experiment can reproduce experimental free energies, even when using the same force field as previous computational studies that were cited as evidence of this disagreement. Therefore, it is suggested that experimental and simulation-based scales can both be accurate and that discrepancies stem from disparities in the microscopic processes being considered rather than methodological errors. Furthermore, these disparities make the development of a single universally applicable membrane-insertion free energy scale difficult.

A knowledge-based potential highlights unique features of membrane α-helical and β-barrel protein insertion and folding

Outer membrane β-barrel proteins differ from α-helical inner membrane proteins in lipid environment, secondary structure, and the proposed processes of folding and insertion. It is reasonable to expect that outer membrane proteins may contain primary sequence information specific for their folding and insertion behavior. In previous work, a depth-dependent insertion potential, E(z) , was derived for α-helical inner membrane proteins. We have generated an equivalent potential for TM β-barrel proteins. The similarities and differences between these two potentials provide insight into unique aspects of the folding and insertion of β-barrel membrane proteins. This potential can predict orientation within the membrane and identify functional residues involved in intermolecular interactions.