New Continuum Approaches for Determining Protein-Induced Membrane Deformations

TRPV1-dependent NKCC1 activation in mouse lens involves integrin and the tubulin cytoskeleton

Previously we showed hyperosmotic solution caused TRPV1-dependent NKCC1 activation in the lens by a mechanism that involved ERK1/2 signaling. In various tissues, integrins and the cytoskeletal network play a role in responses to osmotic stress. Here, we examined the association between integrins and TRPV1-dependent activation of NKCC1 in mouse lens epithelium. Wild-type (WT) lenses exposed to the integrin agonist leukadherin-1 (LA-1) for 10 min displayed a ~33% increase in the bumetanide-sensitive rate of Rb uptake indicating NKCC activation. Paclitaxel, a microtubule stabilizing agent, abolished the Rb uptake response. In primary cultured lens epithelium LA-1 caused a robust ERK1/2 activation response that was almost fully suppressed by paclitaxel. The TRPV1 agonist capsaicin caused a similar ERK1/2 activation response. Consistent with an association between integrins and TRPV1, the TRPV1 antagonist A889425 prevented the Rb uptake response to LA-1 as did the ERK inhibitor U0126. LA-1 did not increase Rb uptake by lenses from TRPV1 knockout mice. In cells exposed to a hyperosmotic stimulus, both the ERK1/2 activation and Rb uptake responses were prevented by paclitaxel. Taken together, the findings suggest TRPV1 activation is associated with integrins and the tubulin cytoskeleton. This aligned with the observation that LA-1 elicited a robust cytoplasmic calcium rise in cells from WT lenses but failed to increase calcium in cells from TRPV1 knockout lenses. The results are consistent with the notion that integrin activation by LA-1, or a hyperosmotic stimulus, causes TRPV1 channel opening and the consequent downstream activation of the ERK1/2 and NKCC1 responses.

Bilayer tension-induced clustering of the UPR sensor IRE1

The endoplasmic reticulum acts as a protein quality control center where a range of chaperones and foldases facilitates protein folding. IRE1 is a sensory transmembrane protein that transduces signals of proteotoxic stress by forming clusters and activating a cellular program called the unfolded protein response (UPR). Recently, membrane thickness variation due to membrane compositional changes have been shown to drive IRE1 cluster formation, activating the UPR even in the absence of proteotoxic stress. Here, we demonstrate a direct relationship between bilayer tension and UPR activation based on IRE1 dimer stability. The stability of the IRE1 dimer in a (50%DOPC-50%POPC) membrane at different applied bilayer tensions was analyzed via molecular dynamics simulations. The potential of mean force for IRE1 dimerization predicts a higher concentration of IRE1 dimers for both tensed and compressed ER membranes. This study shows that IRE1 may be a mechanosensitive membrane protein and establishes a direct biophysical relationship between bilayer tension and UPR activation.

Membrane free-energy landscapes derived from atomistic dynamics explain nonuniversal cholesterol-induced stiffening

All lipid membranes have inherent morphological preferences and resist deformation. Yet adaptations in membrane shape can and do occur at multiple length scales. While this plasticity is crucial for cellular physiology, the factors controlling the morphological energetics of lipid bilayers and the dominant mechanisms of membrane remodeling remain to be fully understood. An ongoing debate regarding the universality of the stiffening effect of cholesterol underscores the challenges facing this field, both experimentally and theoretically, even for simple lipid mixtures. On the computational side, we have argued that enhanced-sampling all-atom molecular dynamics simulations are uniquely suited for the quantification of membrane conformational energetics, as they minimize a priori assumptions and permit analysis of bilayers in deformed states. To showcase this approach, we examine reported inconsistencies between alternative experimental measurements of bending moduli for cholesterol-enriched membranes. Specifically, we analyze lipid bilayers with different chain saturation and compute free-energy landscapes for curvature deformations distributed over areas from ∼5 to ∼60 nm2 . These enhanced simulations, totaling over 100 μs of sampling time, enable us to directly quantify both bending and tilt moduli and to dissect the contributing factors and molecular mechanisms of curvature generation at each length scale. Our results show that the effects of cholesterol on bending rigidity are lipid-specific and suggest that this specificity arises from differences in the torsional dynamics of the acyl chains. In summary, we demonstrate that quantitative relationships can now be established between lipid structure and bending energetics, paving the way for addressing open fundamental questions in cell membrane mechanics.

Membrane free-energy landscapes derived from atomistic dynamics explain nonuniversal cholesterol-induced stiffening

All lipid membranes have inherent morphological preferences and resist deformation. Yet adaptations in membrane shape can and do occur at multiple length scales. While this plasticity is crucial for cellular physiology, the factors controlling the morphological energetics of lipid bilayers and the dominant mechanisms of membrane remodeling remain unclear. An ongoing debate regarding the universality of the stiffening effect of cholesterol underscores the challenges facing this field, both experimentally and theoretically, even for simple lipid mixtures. On the computational side, we have argued that enhanced- sampling all-atom molecular dynamics simulations are uniquely suited for quantification of membrane conformational energetics, not only because they minimize a-priori assumptions, but also because they permit analysis of bilayers in deformed states. To showcase this approach, we examine reported inconsistencies between alternative experimental measurements of bending moduli for cholesterol-enriched membranes. Specifically, we analyze lipid bilayers with different chain saturation, and compute free-energy landscapes for curvature deformations distributed over areas from ∼5 to ∼60 nm 2 . These enhanced simulations, totaling over 100 microseconds of sampling time, enable us to directly quantify both bending and tilt moduli, and to dissect the contributing factors and molecular mechanisms of curvature generation at each length scale. Our results show that cholesterol effects are lipid-specific, in agreement with giantvesicle measurements, and explain why experiments probing nanometer scale lipid dynamics diverge. In summary, we demonstrate that quantitative structure-mechanics relationships can now be established for heterogenous membranes, paving the way for addressing open fundamental questions in cell membrane mechanics.

Significance

Elucidating the energetics and mechanisms of membrane remodeling is an essential step towards understanding cell physiology. This problem is challenging, however, because membrane bending involves both large-scale and atomic-level dynamics, which are difficult to measure simultaneously. A recent controversy regarding the stiffening effect of cholesterol, which is ubiquitous in animal cells, illustrates this challenge. We show how enhanced molecular-dynamics simulations can bridge this length-scale gap and reconcile seemingly incongruent observations. This approach facilitates a conceptual connection between lipid chemistry and membrane mechanics, thereby providing a solid basis for future research on remodeling phenomena, such as in membrane trafficking or viral infection.

Dependence of protein-induced lipid bilayer deformations on protein shape

Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. While analytic solutions of protein-induced elastic bilayer deformations are most easily developed for proteins with approximately circular cross sections, structural biology has shown that membrane proteins come in a variety of distinct shapes, with often considerable deviations from a circular cross section. We develop here a boundary value method (BVM) that permits the construction of analytic solutions of protein-induced elastic bilayer deformations for protein shapes with arbitrarily large deviations from a circular cross section, for constant as well as variable boundary conditions along the bilayer-protein interface. We apply this BVM to protein-induced lipid bilayer thickness deformations. Our BVM reproduces available analytic solutions for proteins with circular cross section and yields, for proteins with noncircular cross section, excellent agreement with numerical, finite element solutions. On this basis, we formulate a simple analytic approximation of the bilayer thickness deformation energy associated with general protein shapes and show that, for modest deviations from rotational symmetry, this analytic approximation is in good agreement with BVM solutions. Using the BVM, we survey the dependence of protein-induced elastic bilayer thickness deformations on protein shape, and thus explore how the coupling of protein shape and bilayer thickness deformations affects protein oligomerization and transitions in protein conformational state.

Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

Mechanochemical coupling of lipid organization and protein function through membrane thickness deformations

Cell membranes are composed of a great variety of protein and lipid species with distinct unperturbed hydrophobic thicknesses. To achieve hydrophobic matching, the lipid bilayer tends to deform around membrane proteins so as to match the protein hydrophobic thickness at bilayer-protein interfaces. Such protein-induced distortions of the lipid bilayer hydrophobic thickness incur a substantial energy cost that depends critically on the bilayer-protein hydrophobic mismatch, while distinct conformational states of membrane proteins often show distinct hydrophobic thicknesses. As a result, hydrophobic interactions between membrane proteins and lipids can yield a rich interplay of lipid-protein organization and transitions in protein conformational state. We combine here the membrane elasticity theory of protein-induced lipid bilayer thickness deformations with the Landau-Ginzburg theory of lipid domain formation to systematically explore the coupling between local lipid organization, lipid and protein hydrophobic thickness, and protein-induced lipid bilayer thickness deformations in membranes with heterogeneous lipid composition. We allow for a purely mechanical coupling of lipid and protein composition through the energetics of protein-induced lipid bilayer thickness deformations as well as a chemical coupling driven by preferential interactions between particular lipid and protein species. We find that the resulting lipid-protein organization can endow membrane proteins with diverse and controlled mechanical environments that, via protein-induced lipid bilayer thickness deformations, can strongly influence protein function. The theoretical approach employed here provides a general framework for the quantitative prediction of how membrane thickness deformations influence the joint organization and function of lipids and proteins in cell membranes.

Regulation of Antimicrobial Peptide Activity via Tuning Deformation Fields by Membrane-Deforming Inclusions

Antimicrobial peptides (AMPs) are considered prospective antibiotics. Some AMPs fight bacteria via cooperative formation of pores in their plasma membranes. Most AMPs at their working concentrations can induce lysis of eukaryotic cells as well. Gramicidin A (gA) is a peptide, the transmembrane dimers of which form cation-selective channels in membranes. It is highly toxic for mammalians as being majorly hydrophobic gA incorporates and induces leakage of both bacterial and eukaryotic cell membranes. Both pore-forming AMPs and gA deform the membrane. Here we suggest a possible way to reduce the working concentrations of AMPs at the expense of application of highly-selective amplifiers of AMP activity in target membranes. The amplifiers should alter the deformation fields in the membrane in a way favoring the membrane-permeabilizing states. We developed the statistical model that allows describing the effect of membrane-deforming inclusions on the equilibrium between AMP monomers and cooperative membrane-permeabilizing structures. On the example of gA monomer-dimer equilibrium, the model predicts that amphipathic peptides and short transmembrane peptides playing the role of the membrane-deforming inclusions, even in low concentration can substantially increase the lifetime and average number of gA channels.

Membrane-Mediated Interactions Between Protein Inclusions

Integral or peripheral membrane proteins, or protein oligomers often get close to each other on cell membranes and carry out biological tasks in a collective manner. In addition to electrostatic and van der Waals interactions, those proteins also experience membrane-mediated interactions, which may be necessary for their functionality. The membrane-mediated interactions originate from perturbation of lipid membranes by the presence of protein inclusions, and have been the subject of intensive research in membrane biophysics. Here we review both theoretical and numerical studies of such interactions for membrane proteins and for nanoparticles bound to lipid membranes.

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.

Value of models for membrane budding

The budding of membranes and curvature generation is common to many forms of trafficking in cells. Clathrin-mediated endocytosis, as a prototypical example of trafficking, has been studied in great detail using a variety of experimental systems and methods. Recently, advances in experimental methods have led to great strides in insights on the molecular mechanisms and the spatiotemporal dynamics of the protein machinery associated with membrane curvature generation. These advances have been ably supported by computational models, which have given us insights into the underlying mechanical principles of clathrin-mediated endocytosis. On the other hand, targeted experimental perturbation of membranes has lagged behind that of proteins in cells. In this area, modeling is especially critical to interpret experimental measurements in a mechanistic context. Here, we discuss the contributions made by these models to our understanding of endocytosis and identify opportunities to strengthen the connections between models and experiments.

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.

Fibronectin-based nanomechanical biosensors to map 3D surface strains in live cells and tissue

Mechanical forces are integral to cellular migration, differentiation and tissue morphogenesis; however, it has proved challenging to directly measure strain at high spatial resolution with minimal perturbation in living sytems. Here, we fabricate, calibrate, and test a fibronectin (FN)-based nanomechanical biosensor (NMBS) that can be applied to the surface of cells and tissues to measure the magnitude, direction, and strain dynamics from subcellular to tissue length-scales. The NMBS is a fluorescently-labeled, ultra-thin FN lattice-mesh with spatial resolution tailored by adjusting the width and spacing of the lattice from 2-100 µm. Time-lapse 3D confocal imaging of the NMBS demonstrates 2D and 3D surface strain tracking during mechanical deformation of known materials and is validated with finite element modeling. Analysis of the NMBS applied to single cells, cell monolayers, and Drosophila ovarioles highlights the NMBS's ability to dynamically track microscopic tensile and compressive strains across diverse biological systems where forces guide structure and function.

TRPV1 activation stimulates NKCC1 and increases hydrostatic pressure in the mouse lens

The porcine lens response to a hyperosmotic stimulus involves an increase in the activity of an ion cotransporter sodium-potassium/two-chloride cotransporter 1 (NKCC1). Recent studies with agonists and antagonists pointed to a mechanism that appears to depend on activation of transient receptor potential vanilloid 1 (TRPV1) ion channels. Here, we compare responses in lenses and cultured lens epithelium obtained from TRPV1^-/- and wild type (WT) mice. Hydrostatic pressure (HP) in lens surface cells was determined using a manometer-coupled microelectrode approach. The TRPV1 agonist capsaicin (100 nM) caused a transient HP increase in WT lenses that peaked after ∼30 min and then returned toward baseline. Capsaicin did not cause a detectable change of HP in TRPV1^-/- lenses. The NKCC inhibitor bumetanide prevented the HP response to capsaicin in WT lenses. Potassium transport was examined by measuring Rb⁺ uptake. Capsaicin increased Rb⁺ uptake in cultured WT lens epithelial cells but not in TRPV1^-/- cells. Bumetanide, A889425, and the Akt inhibitor Akti prevented the Rb⁺ uptake response to capsaicin. The bumetanide-sensitive (NKCC-dependent) component of Rb⁺ uptake more than doubled in response to capsaicin. Capsaicin also elicited rapid (<2 min) NKCC1 phosphorylation in WT but not TRPV1^-/- cells. HP recovery was shown to be absent in TRPV1^-/- lenses exposed to hyperosmotic solution. Bumetanide and Akti prevented HP recovery in WT lenses exposed to hyperosmotic solution. Taken together, responses to capsaicin and hyperosmotic solution point to a functional role for TRPV1 channels in mouse lens. Lack of NKCC1 phosphorylation and Rb⁺ uptake responses in TRPV1^-/- mouse epithelium reinforces the notion that a hyperosmotic challenge causes TRPV1-dependent NKCC1 activation. The results are consistent with a role for the TRPV1-activated signaling pathway leading to NKCC1 stimulation in lens osmotic homeostasis.

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.

Membrane lipids are both the substrates and a mechanistically responsive environment of TMEM16 scramblase proteins

Recent discoveries about functional mechanisms of proteins in the TMEM16 family of phospholipid scramblases have illuminated the dual role of the membrane as both the substrate and a mechanistically responsive environment in the wide range of physiological processes and genetic disorders in which they are implicated. This is highlighted in the review of recent findings from our collaborative investigations of molecular mechanisms of TMEM16 scramblases that emerged from iterative functional, structural, and computational experimentation. In the context of this review, we present new MD simulations and trajectory analyses motivated by the fact that new structural information about the TMEM16 scramblases is emerging from cryo-EM determinations in lipid nanodiscs. Because the functional environment of these proteins in in vivo and in in vitro is closer to flat membranes, we studied comparatively the responses of the membrane to the TMEM16 proteins in flat membranes and nanodiscs. We find that bilayer shapes in the nanodiscs are very different from those observed in the flat membrane systems, but the function-related slanting of the membrane observed at the nhTMEM16 boundary with the protein is similar in the nanodiscs and in the flat bilayers. This changes, however, in the bilayer composed of longer-tail lipids, which is thicker near the phospholipid translocation pathway, which may reflect an enhanced tendency of the long tails to penetrate the pathway and create, as shown previously, a nonconductive environment. These findings support the correspondence between the mechanistic involvement of the lipid environment in the flat membranes, and the nanodiscs. © 2019 Wiley Periodicals, Inc.

Large-scale state-dependent membrane remodeling by a transporter protein

That channels and transporters can influence the membrane morphology is increasingly recognized. Less appreciated is that the extent and free-energy cost of these deformations likely varies among different functional states of a protein, and thus, that they might contribute significantly to defining its mechanism. We consider the trimeric Na⁺-aspartate symporter Glt_Ph, a homolog of an important class of neurotransmitter transporters, whose mechanism entails one of the most drastic structural changes known. Molecular simulations indicate that when the protomers become inward-facing, they cause deep, long-ranged, and yet mutually-independent membrane deformations. Using a novel simulation methodology, we estimate that the free-energy cost of this membrane perturbation is in the order of 6–7 kcal/mol per protomer. Compensating free-energy contributions within the protein or its environment must thus stabilize this inward-facing conformation for the transporter to function. We discuss these striking results in the context of existing experimental observations for this and other transporters.

Quantitative Characterization of Protein-Lipid Interactions by Free Energy Simulation between Binary Bilayers

Using a recently developed binary bilayer system (BBS) consisting of two patches of laterally contacting bilayers, umbrella sampling molecular dynamics (MD) simulations were performed for quantitative characterization of protein-lipid interactions. The BBS is composed of 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) with an embedded model membrane protein, a gramicidin A (gA) channel. The calculated free energy difference for the transfer of a gA channel from DLPC (hydrophobic thickness ≈ 21.5 Å) to DMPC (hydrophobic thickness ≈ 25.5 Å) bilayers, ΔG(DLPC → DMPC), is -2.2 ± 0.7 kcal/mol. This value appears at odds with the traditional view that the hydrophobic length of the gA channel is ∼22 Å. To understand this discrepancy, we first note that recent MD simulations by different groups have shown that lipid bilayer thickness profiles in the vicinity of a gA channel differ qualitatively from the deformation profile predicted from continuum elastic bilayer models. Our MD simulations at low and high gA:lipid molar ratios and different membrane compositions indicate that the gA channel's effective hydrophobic length is ∼26 Å. Using this effective hydrophobic length, ΔG(DLPC → DMPC) determined here is in excellent agreement with predictions based on continuum elastic models (-3.0 to -2.2 kcal/mol) where the bilayer deformation energy is approximated as a harmonic function of the mismatch between the channel's effective hydrophobic length and the hydrophobic thickness of the bilayer. The free energy profile for gA in the BBS includes a barrier at the interface between the two bilayers which can be attributed to the line tension at the interface between two bilayers with different hydrophobic thicknesses. This observation implies that translation of a peptide between two different regions of a cell membrane (such as between the liquid ordered and disordered phases) may include effects of a barrier at the interface in addition to the relative free energies of the species far from the interface. The BBS allows for direct transfer free energy calculations between bilayers without a need of a reference medium, such as bulk water, and thus provides an efficient simulation protocol for the quantitative characterization of protein-lipid interactions at all-atom resolution.

Dynamic modulation of the lipid translocation groove generates a conductive ion channel in Ca2+-bound nhTMEM16

Both lipid and ion translocation by Ca²⁺-regulated TMEM16 transmembrane proteins utilizes a membrane-exposed hydrophilic groove. Several conformations of the groove are observed in TMEM16 protein structures, but how these conformations form, and what functions they support, remains unknown. From analyses of atomistic molecular dynamics simulations of Ca²⁺-bound nhTMEM16 we find that the mechanism of a conformational transition of the groove from membrane-exposed to occluded from the membrane involves the repositioning of transmembrane helix 4 (TM4) following its disengagement from a TM3/TM4 interaction interface. Residue L302 is a key element in the hydrophobic TM3/TM4 interaction patch that braces the open-groove conformation, which should be changed by an L302A mutation. The structure of the L302A mutant determined by cryogenic electron microscopy (cryo-EM) reveals a partially closed groove that could translocate ions, but not lipids. This is corroborated with functional assays showing severely impaired lipid scrambling, but robust channel activity by L302A.

A membrane-exposed groove in Ca²⁺-gated TMEM16 scramblases forms the translocation pathway for ions and lipids. Here authors combine molecular dynamics with cryo-EM and functional assays to uncover the conformational transitions of the groove leading to a non-selective ion channel pore.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

A multiscale model of mechanotransduction by the ankyrin chains of the NOMPC channel

Our senses of touch and hearing are dependent on the conversion of external mechanical forces into electrical impulses by the opening of mechanosensitive channels in sensory cells. This remarkable feat involves the conversion of a macroscopic mechanical displacement into a subnanoscopic conformational change within the ion channel. The mechanosensitive channel NOMPC, responsible for hearing and touch in flies, is a homotetramer composed of four pore-forming transmembrane domains and four helical chains of 29 ankyrin repeats that extend 150 Å into the cytoplasm. Previous work has shown that the ankyrin chains behave as biological springs under extension and that tethering them to microtubules could be involved in the transmission of external forces to the NOMPC gate. Here we combine normal mode analysis (NMA), full-atom molecular dynamics simulations, and continuum mechanics to characterize the material properties of the chains under extreme compression and extension. NMA reveals that the lowest-frequency modes of motion correspond to fourfold symmetric compression/extension along the channel, and the lowest-frequency symmetric mode for the isolated channel domain involves rotations of the TRP domain, a putative gating element. Finite element modeling reveals that the ankyrin chains behave as a soft spring with a linear, effective spring constantof 22 pN/nm for deflections ≤15 Å. Force-balance analysis shows that the entire channel undergoes rigid body rotation during compression, and more importantly, each chain exerts a positive twisting moment on its respective linker helices and TRP domain. This torque is a model-independent consequence of the bundle geometry and would cause a clockwise rotation of the TRP domain when viewed from the cytoplasm. Force transmission to the channel for compressions >15 Å depends on the nature of helix-helix contact. Our work reveals that compression of the ankyrin chains imparts a rotational torque on the TRP domain, which potentially results in channel opening.

Directed Supramolecular Organization of N-BAR Proteins through Regulation of H0 Membrane Immersion Depth

Many membrane remodeling events rely on the ability of curvature-generating N-BAR membrane proteins to organize into distinctive supramolecular configurations. Experiments have revealed a conformational switch in N-BAR proteins resulting in vesicular or tubular membrane shapes, with shallow membrane immersion of the H0 amphipathic helices of N-BAR proteins on vesicles but deep H0 immersion on tubes. We develop here a minimal elastic model of the local thinning of the lipid bilayer resulting from H0 immersion. Our model predicts that the observed conformational switch in N-BAR proteins produces a corresponding switch in the bilayer-mediated N-BAR interactions due to the H0 helices. In agreement with experiments, we find that bilayer-mediated H0 interactions oppose N-BAR multimerization for the shallow H0 membrane immersion depths measured on vesicles, but promote self-assembly of supramolecular N-BAR chains for the increased H0 membrane immersion depths measured on tubes. Finally, we consider the possibility that bilayer-mediated H0 interactions might contribute to the concerted structural reorganization of N-BAR proteins suggested by experiments. Our results indicate that the membrane immersion depth of amphipathic protein helices may provide a general molecular control parameter for membrane organization.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

Mathematical modeling of dynamic behavior of fluid bilayer membranes under the effect of density asymmetry

Shape transformations in biological membranes are crucial in a variety of cellular processes such as transport in the Golgi apparatus and endoplasmic reticulum, shaping the cell organelles and signaling in neuronal synapses. Dynamic analysis of lipid bilayer membranes is popular among researchers as valuable information about cell functions can be retrieved. There are several limitations in experimental tests and simulations such as computational and implementation cost while in theoretical studies, different phenomena can be modeled and the effect of each parameter can be investigated. In this paper, a continuum model including elastic energies and dissipation functions is utilized with energy approach to obtain the governing equations of an enclosed lipid bilayer membrane. The governing equations are solved numerically for vesicles initially disturbed and the relaxation dynamics is studied. The stationary shape of the vesicles for different values of reduced volume and reduced area difference is obtained to explore the phase diagram and verify the governing equations. Then, the density asymmetry in bilayers caused by the change in the density or the equilibrium density of the outer monolayer is studied. This leads to the formation of buds, tubules, and pearls. This can be observed in the recruitment of proteins to the outer monolayer or pH gradients of the environment of a vesicle. The effect of density difference and curvature on creation and growth of tubules are investigated. An interesting metastable state in the adsorption of the final bud due to the increase in the density of the outer monolayer is observed in which the shape of the vesicle is almost unchanged. A prolate vesicle relaxes toward an oblate or a stomatocyte vesicle when the equilibrium density of the outer monolayer increases.

Membrane Elastic Deformations Modulate Gramicidin A Transbilayer Dimerization and Lateral Clustering

Gramicidin A (gA) is a short β-helical peptide known to form conducting channels in lipid membranes because of transbilayer dimerization. The gA conducting dimer, being shorter than the lipid bilayer thickness, deforms the membrane in its vicinity, and the bilayer elastic energy contributes to the gA dimer formation energy. Likewise, membrane incorporation of a gA monomer, which is shorter than the lipid monolayer thickness, creates a void, thereby forcing surrounding lipid molecules to tilt to fill it. The energy of membrane deformation was calculated in the framework of the continuum elasticity theory, taking into account splay, tilt, lateral stretching/compression, Gaussian splay deformations, and external membrane tension. We obtained the interaction energy profiles for two gA monomers located either in the same or in the opposite monolayers. The profiles demonstrated the long-range attraction and short-range repulsion behavior of the monomers resulting from the membrane deformation. Analysis of the profile features revealed conditions under which clusters of gA monomers would not dissipate because of diffusion. The calculated dependence of the dimer formation and decay energy barriers on the membrane elastic properties was in good agreement with the available experimental data and suggested an explanation for a hitherto contentious phenomenon.

Microscopic view of lipids and their diverse biological functions

Biological membranes and their diverse lipid constituents play key roles in a broad spectrum of cellular and physiological processes. Characterization of membrane-associated phenomena at a microscopic level is therefore essential to our fundamental understanding of such processes. Due to the semi-fluid and dynamic nature of lipid bilayers, and their complex compositions, detailed characterization of biological membranes at an atomic scale has been refractory to experimental approaches. Computational modeling and simulation offer a highly complementary toolset with sufficient spatial and temporal resolutions to fill this gap. Here, we review recent molecular dynamics studies focusing on the diversity of lipid composition of biological membranes, or aiming at the characterization of lipid-protein interaction, with the overall goal of dissecting how lipids impact biological roles of the cellular membranes.

Determination of Hydrophobic Lengths of Membrane Proteins with the HDGB Implicit Membrane Model

A protocol for predicting the hydrophobic length of membrane proteins using the heterogeneous dielectric generalized Born (HDGB) implicit membrane model is presented. The method involves optimal positioning in the membrane and identification of lipid-facing and inward-facing residues, followed by energy optimization of the implicit membrane model to obtain the hydrophobic length from the optimal membrane width. The latest HDGB version 3 (HDGBv3) and HDGB van der Waals (HDGBvdW) models were applied to a test set containing 15 proteins (seven β-barrel and eight α-helical proteins), for which matching membrane widths are available from experiment, and an additional set contains ten α-helical and ten β-barrel proteins without any experimental data. The results with the HDGB model compare favorably with predictions from methods used in the Orientations of Proteins in Membranes (OPM) and Protein Data Bank of Transmembrane Proteins (PDB-TM) databases.

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.