Membrane sorting via the extracellular matrix

We consider the coupling between a membrane and the extracellular matrix. Computer simulations demonstrate that the latter coupling is able to sort lipids. It is assumed that membranes are elastic manifolds, and that this manifold is disrupted by the extracellular matrix. For a solid-supported membrane with an actin network on top, regions of positive curvature are induced below the actin fibers. A similar mechanism is conceivable by assuming that the proteins which connect the cytoskeleton to the membrane induce local membrane curvature. The regions of non-zero curvature exist irrespective of any phase transition the lipids themselves may undergo. For lipids that prefer certain curvature, the extracellular matrix thus provides a spatial template for the resulting lateral domain structure of the membrane.     

Nonlinear sorting, curvature generation, and crowding of endophilin N-BAR on tubular membranes

The curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis.     

Coupling field theory with mesoscopic dynamical simulations of multicomponent lipid bilayers

A method for simulating a two-component lipid bilayer membrane in the mesoscopic regime is presented. The membrane is modeled as an elastic network of bonded points; the spring constants of these bonds are parameterized by the microscopic bulk modulus estimated from earlier atomistic nonequilibrium molecular dynamics simulations for several bilayer mixtures of DMPC and cholesterol. The modulus depends on the composition of a point in the elastic membrane model. The dynamics of the composition field is governed by the Cahn-Hilliard equation where a free energy functional models the coupling between the composition and curvature fields. The strength of the bonds in the elastic network are then modulated noting local changes in the composition and using a fit to the nonequilibrium molecular dynamics simulation data. Estimates for the magnitude and sign of the coupling parameter in the free energy model are made treating the bending modulus as a function of composition. A procedure for assigning the remaining parameters in the free energy model is also outlined. It is found that the square of the mean curvature averaged over the entire simulation box is enhanced if the strength of the bonds in the elastic network are modulated in response to local changes in the composition field. We suggest that this simulation method could also be used to determine if phase coexistence affects the stress response of the membrane to uniform dilations in area. This response, measured in the mesoscopic regime, is already known to be conditioned or renormalized by thermal undulations.     

Coupling field theory with continuum mechanics: a simulation of domain formation in giant unilamellar vesicles

Domain formation is modeled on the surface of giant unilamellar vesicles using a Landau field theory model for phase coexistence coupled to elastic deformation mechanics (e.g., membrane curvature). Smooth particle applied mechanics, a form of smoothed particle continuum mechanics, is used to solve either the time-dependent Landau-Ginzburg or Cahn-Hilliard free-energy models for the composition dynamics. At the same time, the underlying elastic membrane is modeled using smooth particle applied mechanics, resulting in a unified computational scheme capable of treating the response of the composition fields to arbitrary deformations of the vesicle and vice versa. The results indicate that curvature coupling, along with the field theory model for composition free energy, gives domain formations that are correlated with surface defects on the vesicle. In the case that external deformations are included, the domain structures are seen to respond to such deformations. The present simulation capability provides a significant step forward toward the simulation of realistic cellular membrane processes.     

Calcium-Actin Waves and Oscillations of Cellular Membranes

We propose a mechanism for the formation of membrane oscillations and traveling waves, which arise due to the coupling between the actin cytoskeleton and the calcium flux through the membrane. In our model, the fluid cell membrane has a mobile but constant population of proteins with a convex spontaneous curvature, which act as nucleators of actin polymerization and adhesion. Such a continuum model couples the forces of cell-substrate adhesion, actin polymerization, membrane curvature, and the flux of calcium through the membrane. Linear stability analysis shows that sufficiently strong coupling among the calcium, membrane, and protein dynamics may induce robust traveling waves on the membrane. This result was checked for a reduced feedback scheme and is compared to the results without the effects of calcium, where permanent phase separation without waves or oscillations is obtained. The model results are compared to the published observations of calcium waves in cell membranes, and a number of testable predictions are proposed.     

Factors influencing local membrane curvature induction by N-BAR domains as revealed by molecular dynamics simulations

N-BAR domains are protein modules that bind to and induce curvature in membranes via a charged concave surface and N-terminal amphipathic helices. Recently, molecular dynamics simulations have demonstrated that the N-BAR domain can induce a strong local curvature that matches the curvature of the BAR domain surface facing the bilayer. Here we present further molecular dynamics simulations that examine in greater detail the roles of the concave surface and amphipathic helices in driving local membrane curvature. We find that the strong curvature induction observed in our previous simulations requires the stable presentation of the charged concave surface to the membrane and is not driven by the membrane-embedded amphipathic helices. Nevertheless, without these amphipathic helices embedded in the membrane, the N-BAR domain does not maintain a close association with the bilayer, and fails to drive membrane curvature. Increasing the membrane negative charge through the addition of PIP₂ facilitates closer association with the membrane in the absence of embedded helices. At sufficiently high concentrations, amphipathic helices embedded in the membrane drive membrane curvature independently of the BAR domain.     

Lateral organization of membranes and cell shapes.

The relations among membrane structure, mechanical properties, and cell shape have been investigated. The fluid mosaic membrane models used contains several components that move freely in the membrane plane. These components interact with each other and determine properties of the membrane such as curvature and elasticity. A free energy equation is postulated for such a multicomponent membrane and the condition of free energy minimum is used to obtain differential equations relating the distribution of membrane components and the local membrane curvature. The force that moves membrane components along the membrane in a variable curvature field is calculated. A change in the intramembrane interactions can bring about phase separation or particle clustering. This, in turn, may strongly affect the local curvature. The numerical solution of the set of equations for the two dimensional case allows determination of the cell shape and the component distribution along the membrane. The model has been applied to describe certain erythrocytes shape transformations.     

Stability of biphasic vesicles with membrane embedded proteins

The basic physical properties of homogeneous membranes are relatively well known, while the effects of inhomogeneities with membranes are very much an active field of study. In this paper, a biphasic lipid vesicle with membrane embedded proteins is investigated. To take into account the influences of the proteins, a simple phenomenological coupling between the local fraction of proteins and the mean curvature square is suggested. By minimizing the energy of system, the E-L equations and boundary conditions are obtained and solved analytically for vesicle with a simple shape. Besides, stability phase diagrams and stability factor are put forward by linear perturbation analysis. Our results show two different situations which are strongly dependent on the nature of the proteins: a regime of easy instability when the proteins are strongly coupled to the membrane and a regime of difficult instability.     

Molecular theory of lipid-protein interaction and the Lalpha-HII transition.

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer (Lalpha) to the inverse-hexagonal (HII) phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., "cylinder-like," "barrel-like," or "vase-like." We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape, and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the HII lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the Lalpha --> HII transition. At the transition, a peptide-poor Lalpha phase coexists with a peptide-rich HII phase.     

Variation of frequency spectrum of the erythrocyte flickering caused by aging,osmolarity, temperature and pathological changes

Frequency spectra of the surface undulations (flickering) of erythrocyte plasma membranes are measured by direct spectral analysis of the intensity fluctuations of the light passing the cells in a phase contrast microscope. Spectra are taken as a function (1) of the temperature (2) of the viscosity and osmolarity of the outer medium (3) of the aging of cells and (4) of pathological transformations. The spectra are approximately superpositions of two Lorentzian lines. At large frequencies,f, the spectra follow f^?2. This behaviour can be interpreted in terms of cell thickness fluctuations caused by thermally excited membrane undulations provided the range of wavelengths is small. The undulations are determined by the membrane curvature elasticity while the lateral tension is negligibly small for cells of discoid shape. The technique presented allows accurate measurements of relative curvature (bending) elastic constants. The spectra of freshly drawn cells are remarkably reproducible. Aging of the cells in the medium leads to an increase in the curvature elastic constant. A decrease in osmolarity causes a reduction in the intensity and line width of the spectra and the flickering vanishes if the cell approaches a spherical shape. The effect of temperature between 10 and 40°C is astonishingly small with the exception of a sudden increase in the amplitude with increasing temperature at 35°C. The flicker spectra of a large fraction of the cells from patients suffering from cronical alcoholism exhibit a reduced line width or an increase in the curvature elastic constant.     

Regulation of Membrane-Shape Transitions Induced by I-BAR Domains

I-BAR proteins are well-known actin-cytoskeleton adaptors and have been observed to be involved in the formation of plasma membrane protrusions (filopodia). I-BAR proteins contain an all-helical, crescent-shaped IRSp53-MIM domain (IMD) dimer that is believed to be able to couple with a membrane shape. This coupling could involve the sensing and even the generation of negative plasma membrane curvature. Indeed, the in vitro studies have shown that IMDs can induce inward tubulation of liposomes. While N-BAR domains, which generate positive membrane curvature, have received a considerable amount of attention from both theory and experiments, the mechanisms of curvature coupling through IMDs are comparatively less studied and understood. Here we used a membrane-shape stability assay developed recently in our lab to quantitatively characterize IMD-induced membrane-shape transitions. We determined a membrane-shape stability diagram for IMDs that reveals how membrane tension and protein density can comodulate the generation of IMD-induced membrane protrusions. From comparison to analytical theory, we determine three key parameters that characterize the curvature coupling of IMD. We find that the curvature generation capacity of IMDs is significantly stronger compared to that of endophilin, an N-BAR protein known to be involved in plasma membrane shape transitions. Contrary to N-BAR domains, where amphipathic helix insertion is known to promote its membrane curvature generation, for IMDs we find that amphipathic helices inhibit membrane shape transitions, consistent with the inverse curvature that IMDs generate. Importantly, in both of these types of BAR domains, electrostatic interactions affect membrane-binding capacity, but do not appear to affect the curvature generation capacity of the protein. These two types of BAR domain proteins show qualitatively similar membrane shape stability diagrams, suggesting an underlying ubiquitous mechanism by which peripheral proteins regulate membrane curvature.     

Membrane reshaping by protein condensates

Proteins can organize into dynamic, functionally important assemblies on fluid membrane surfaces. Phase separation has emerged as an important mechanism for forming such protein assemblies on the membrane during cell signaling, endocytosis, and cytoskeleton regulation. Protein-protein phase separation thus adds novel fluid mosaics to the classical Singer and Nicolson model. Protein condensates formed in this process can modulate membrane morphologies. This is evident from recent reports of protein condensate-driven membrane reshaping in processes such as endocytosis, autophagosome formation, and protein storage vacuole morphogenesis in plants. Lateral phase separation (on the membrane surface) of peripheral curvature coupling proteins can modulate such membrane morphological transitions. Additionally, three-dimensional protein phase separation can result in droplets that through adhesion can affect membrane shape changes. How do these condensate-driven curvature generation mechanisms contrast with the classically recognized scaffolding and amphipathic helix insertion activities of specific membrane remodeling proteins? A salient feature of these condensate-driven membrane activities is that they depend upon both macroscopic features (such as interfacial energies of the condensate, membrane, and cytosol) as well as microscopic, molecular-level interactions (such as protein-lipid binding). This review highlights the current understanding of the mechanisms underlying curvature generation by protein condensates in various biological pathways.     

Shapes of bilayer vesicles with membrane embedded molecules

The interdependence of the lateral distribution of molecules which are embedded in a membrane (such as integral membrane proteins) and the shape of a cell with no internal structure (such as phospholipid vesicles or mammalian erythrocytes) has been studied. The coupling of the lateral distribution of the molecules and the cell shape is introduced by considering that the energy of the membrane embedded molecule at a given site of the membrane depends on the curvature of the membrane at that site. Direct interactions between embedded molecules are not considered. A simple expression for the interaction of the membrane embedded molecule with the local membrane curvature is proposed. Starting from this interaction, the consistently related expressions for the free energy and for the distribution function of the embedded molecules are derived. The equilibrium cell shape and the corresponding lateral distribution of the membrane embedded molecules are determined by minimization of the membrane free energy which includes the free energy of the membrane embedded molecules and the membrane elastic energy. The resulting inhomogeneous distribution of the membrane embedded molecules affects the cell shape in a nontrivial manner. In particular, it is shown that the shape corresponding to the absolute energy minimum at given cell volume and membrane area may be elliptically non-axisymmetric, in contrast to the case of a laterally homogeneous membrane where it is axisymmetric.     

Otolith responses to dynamical stimuli: results of a numerical investigation

To investigate the dynamic effects of external forces on the displacement of the otolith membrane and subsequent neuronal responses of otoliths, we performed numerical analyses of otolith membrane displacements. In these studies we included the full geometry of the human otolith maculae, including their 3D curvature. The first part focuses on mechanical aspects of the otolith membrane. While it was found that the mechanical coupling of distant parts of the otolith membrane is only weak, these simulations indicate that curvature may have considerable local effects on displacements. They further suggest that the movements of the otoconia, embedded in the interotoconial matrix, show a resonance in a range between 100 and 2000 Hz. In the second part of the article we also investigate the tonic-phasic responses in the vestibular nerve emanating from hair cells in the striola region. Small head tilts away from head upright position are used. The simulations indicate that the direction of head tilt is coded in characteristic response patterns along the striola.     

Equilibrium Shape Equation and Geometrically Permissible Condition for Two-Component Lipid Bilayer Vesicles

Equilibrium shapes of vesicles composed of a mixture of partially miscible amphiphiles are investigated. To take into account the influences of the composition, a simple phenomenological coupling between the co mposition and the curvatures, including the mean curvature and the Gauss curvature of the membrane surface, is suggested. By minimizing the potential functional, the general shape equation is obtained and solved analytically for vesicles with simple shapes. Besides, the geometrical constraint equation and geometrically permissible condition for the two-component lipid vesicles are put forward. The influences of physical parameters on the geometrically permissible phase diagrams are predicted. The close relations between the predictions and existing experimental phenomena published recently are shown.     

Budding and fission of vesicles.

We report on budding and fission of protein-free vesicles swollen from a natural lipid mixture of bovine brain sphingomyelins. Budding was induced by increasing the area-to-volume ratio through heating. Morphological changes were monitored by phase contrast microscopy and correlated with the thermal behavior of the bilayer by differential scanning calorimetry. Freeze fracture electron microscopy revealed that budding and fission are not restricted to giant vesicles but also occur on length scales relevant for cellular processes. We also observed osmotically induced budding and fission in mixtures of dimyristoyl phosphatidylcholine with cholesterol. We find that these shape transitions are driven by liquid/gel domain formation and/or coupling of the spontaneous curvature of the membrane to the local lipid composition. Our results provide evidence that coat proteins are not necessary for budding and fission of vesicles. The physics of the lipid bilayer is rich enough to explain the observed behavior.     

Formation of inverted hexagonal phase in SDPE as observed by solid-state (31)P NMR

Docosahexaenoic acid (DHA), the longest and most unsaturated fatty acid commonly found in biological membranes, is known to affect various membrane properties. In a variety of cell membranes, DHA is primarily incorporated in phosphatidylethanolamines, where its function remains poorly understood. In order to understand the role of DHA in influencing membrane structure, we utilize (31)P NMR spectroscopy to study the phase behavior of 1-stearoyl-2-docosahexaenoyl-sn-glycerophosphoethanolamine (SDPE) in comparison to 1-palmitoyl-2-oleoyl-sn-glycerophosphoethanolamine (POPE) from 20 to 50 degrees C. Spectra of SDPE phospholipids show the formation of inverted hexagonal phase (H(II)) from 20 to 50 degrees C; in contrast, POPE mutilamellar dispersions exist in a lamellar liquid-crystalline phase (L(alpha)) at the same temperatures. The ability of SDPE to adopt nonbilayer phases at a physiological temperature may indicate its role in imparting negative curvature stress upon the membrane and may affect local molecular organization including the formation of lipid microdomains within biological membranes.     

Field theoretic study of bilayer membrane fusion. I. Hemifusion mechanism

Self-consistent field theory is used to determine structural and energetic properties of metastable intermediates and unstable transition states involved in the standard stalk mechanism of bilayer membrane fusion. A microscopic model of flexible amphiphilic chains dissolved in hydrophilic solvent is employed to describe these self-assembled structures. We find that the barrier to formation of the initial stalk is much smaller than previously estimated by phenomenological theories. Therefore its creation it is not the rate-limiting process. The relevant barrier is associated with the rather limited radial expansion of the stalk into a hemifusion diaphragm. It is strongly affected by the architecture of the amphiphile, decreasing as the effective spontaneous curvature of the amphiphile is made more negative. It is also reduced when the tension is increased. At high tension the fusion pore, created when a hole forms in the hemifusion diaphragm, expands without bound. At very low membrane tension, small fusion pores can be trapped in a flickering metastable state. Successful fusion is severely limited by the architecture of the lipids. If the effective spontaneous curvature is not sufficiently negative, fusion does not occur because metastable stalks, whose existence is a seemingly necessary prerequisite, do not form at all. However if the spontaneous curvature is too negative, stalks are so stable that fusion does not occur because the system is unstable either to a phase of stable radial stalks, or to an inverted-hexagonal phase induced by stable linear stalks. Our results on the architecture and tension needed for successful fusion are summarized in a phase diagram.     

Evidence of cholesterol accumulated in high curvature regions: implication to the curvature elastic energy for lipid mixtures

Recent experiments suggested that cholesterol and other lipid components of high negative spontaneous curvature facilitate membrane fusion. This is taken as evidence supporting the stalk-pore model of membrane fusion in which the lipid bilayers go through intermediate structures of high curvature. How do the high-curvature lipid components lower the free energy of the curved structure? Do the high-curvature lipid components modify the average spontaneous curvature of the relevant monolayer, thereby facilitate its bending, or do the lipid components redistribute in the curved structure so as to lower the free energy? This question is fundamental to the curvature elastic energy for lipid mixtures. Here we investigate the lipid distribution in a monolayer of a binary lipid mixture before and after bending, or more precisely in the lamellar, hexagonal, and distorted hexagonal phases. The lipid mixture is composed of 2:1 ratio of brominated di18:0PC and cholesterol. Using a newly developed procedure for the multiwavelength anomalous diffraction method, we are able to isolate the bromine distribution and reconstruct the electron density distribution of the lipid mixture in the three phases. We found that the lipid distribution is homogenous and uniform in the lamellar and hexagonal phases. But in the distorted hexagonal phase, the lipid monolayer has nonuniform curvature, and cholesterol almost entirely concentrates in the high curvature region. This finding demonstrates that the association energies between lipid molecules vary with the curvature of membrane. Thus, lipid components in a mixture may redistribute under conditions of nonuniform curvature, such as in the stalk structure. In such cases, the spontaneous curvature depends on the local lipid composition and the free energy minimum is determined by lipid distribution as well as curvature.     

Oscillation of the electric potential of frog skin under the effect of Li+: Experimental approach

Summary When a frog skin is used to separate two compartments, and lithium is added to the external medium, transmembrane electric potential oscillations frequently occur. When no external current is imposed, sustained oscillations, with a period of about 10 min, are maintained for several hours. An oscillation of the Na⁺ influx accompanies the electric oscillation, though the two oscillations are out of phase to a greater or less extent.Theophyllin promotes a significant decrease in the mean electric potential of the skin, but it does not affect very much the characteristics of the oscillation. Important factors influencing the oscillation are temperature, permeability of the external membrane to lithium, and potassium concentration in the internal medium. No correlation can be detected between oscilation characteristics and skin area. This suggests that the oscillation is of a local nature, possibly originating at the cellular level. Occurrence of macroscopic oscillations implies coupling between local oscillators. Coupling between two epithelia has been studied under diverse conditions. The coupling is of an electrical nature: by varying the value of the coupling resistance, it is possible to control synchronization of the oscillations.