Membrane-Mediated Aggregation of Curvature-Inducing Nematogens and?Membrane Tubulation

The shapes of cell membranes are largely regulated by membrane-associated, curvature-active proteins. Herein, we use a numerical model of the membrane, recently developed by us, with elongated membrane inclusions possessing spontaneous directional curvatures that could be different along, and perpendicular to, the membrane’s long axis. We show that, due to membrane-mediated interactions, these curvature-inducing membrane-nematogens can aggregate spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometimes the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these protein lattices. Furthermore, the elastic properties of the tubes, such as their compressional stiffness and persistence length, are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes.     

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.     

Membrane-Mediated Interactions Measured Using Membrane Domains

Cell membrane organization is the result of the collective effect of many driving forces. Several of these, such as electrostatic and van der Waals forces, have been identified and studied in detail. In this article, we investigate and quantify another force, the interaction between inclusions via deformations of the membrane shape. For electrically neutral systems, this interaction is the dominant organizing force. As a model system to study membrane-mediated interactions, we use phase-separated biomimetic vesicles that exhibit coexistence of liquid-ordered and liquid-disordered lipid domains. The membrane-mediated interactions between these domains lead to a rich variety of effects, including the creation of long-range order and the setting of a preferred domain size. Our findings also apply to the interaction of membrane protein patches, which induce similar membrane shape deformations and hence experience similar interactions.     

On the role of anisotropy of membrane constituents in formation of a membrane neck during budding of a multicomponent membrane

The expression for the isotropic membrane bending energy was generalized for the case of a multicomponent membrane where the membrane constituents (single molecules or small complexes of molecules-membrane inclusions) were assumed to be anisotropic. Using this generalized expression for the membrane energy it was shown that the change of intrinsic shape of membrane components may induce first-order-like shape transitions leading to the formation of a membrane neck. The predicted discontinuous membrane shape transition and the concomitant lateral segregation of membrane components were applied to study membrane budding. Based on the results presented we conclude that the budding process might be driven by accumulation of anisotropic membrane components in the necks connecting the bud and the parent membrane, and by accumulation of isotropic (conical) membrane components on the bud. Both processes may strongly depend on the intrinsic shape of membrane components and on the direct interactions between them.     

Static light scattering to characterize membrane proteins in detergent solution

Determination of the oligomeric state or the subunit stoichiometry of integral membrane proteins in detergent solution is notoriously difficult, because the amount of detergent (and lipid) associated with the proteins is usually not known. Only two classical methods (sedimentation equilibrium centrifugation and static light scattering) can measure directly the absolute molecular mass of a protein present in a protein/detergent micelle, without any assumption on the amount of detergent bound, or the shape of the proteins. Here the theoretical background and practical aspects of static light scattering analysis of membrane proteins are reviewed using a number of examples from our lab to highlight potential pitfalls. A brief comparison with sedimentation equilibrium centrifugation is given and a detailed protocol of how we perform light scattering analyses is provided.     

Membrane shape changes at initial stage of membrane fusion under the action of proteins inducing spontaneous curvature

This paper studies change of membrane shape at the initial stage of the fusion process due to the fusion proteins inducing spontaneous curvature in the membrane. As protein inclusions are embedded into the membrane, a highly curved surface forms in the center of the membrane; it facilitates the formation of short-lived hydrophobic defects and leads to the merger of the contact monolayers of the membranes. Membrane is considered as continuous liquid-crystal medium subject to elastic deformations. One deformational mode of splay is taken into account; energy is calculated in the quadratic approximation on this deformation. In case of positive spontaneous curvature induced by the protein there is no bulge on the top of the membrane despite high deviation of membrane shape from the equilibrium state. In case of negative spontaneous curvature a bulge is formed and its height and curvature increase with the increase of the membrane curvature in the initial state.     

Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

A statistical mechanical model for voltage-gated ion channels in cell membranes is proposed using the transfer matrix method. Equilibrium behavior of the system is studied. Representing the distribution of channels over the cellular membrane on a one-dimensional array with each channel having two states (open and closed) and incorporating channel–channel cooperative interactions, we calculate the fraction of channels in the open state at equilibrium. Experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon, using the cut-open axon technique, is best fit by the model when there is no interaction between the channels.     

Valosin-containing Protein-interacting Membrane Protein (VIMP) Links the Endoplasmic Reticulum with Microtubules in Concert with Cytoskeleton-linking Membrane Protein (CLIMP)-63

The distribution and morphology of the endoplasmic reticulum (ER) in mammalian cells depend on both dynamic and static interactions of ER membrane proteins with microtubules (MTs). Cytoskeleton-linking membrane protein (CLIMP)-63 is exclusively localized in sheet-like ER membranes, typical structures of the rough ER, and plays a pivotal role in the static interaction with MTs. Our previous study showed that the 42-kDa ER-residing form of syntaxin 5 (Syn5L) regulates ER structure through the interactions with both CLIMP-63 and MTs. Here, we extend our previous study and show that the valosin-containing protein/p97-interacting membrane protein (VIMP)/SelS is also a member of the family of proteins that shape the ER by interacting with MTs. Depletion of VIMP causes the spreading of the ER to the cell periphery and affects an MT-dependent process on the ER. Although VIMP can interact with CLIMP-63 and Syn5L, it does not interact with MT-binding ER proteins (such as Reep1) that shape the tubular smooth ER, suggesting that different sets of MT-binding ER proteins are used to organize different ER subdomains.     

Coarse-Grained Model of SNARE-Mediated Docking

Synaptic transmission requires that vesicles filled with neurotransmitter molecules be docked to the plasma membrane by the SNARE protein complex. The SNARE complex applies attractive forces to overcome the long-range repulsion between the vesicle and membrane. To understand how the balance between the attractive and repulsive forces defines the equilibrium docked state we have developed a model that combines the mechanics of vesicle/membrane deformation with an apparently new coarse-grained model of the SNARE complex. The coarse-grained model of the SNARE complex is calibrated by comparison with all-atom molecular dynamics simulations as well as by force measurements in laser tweezer experiments. The model for vesicle/membrane interactions includes the forces produced by membrane deformation and hydration or electrostatic repulsion. Combining these two parts, the coarse-grained model of the SNARE complex with membrane mechanics, we study how the equilibrium docked state varies with the number of SNARE complexes. We find that a single SNARE complex is able to bring a typical synaptic vesicle to within a distance of ∼3 nm from the membrane. Further addition of SNARE complexes shortens this distance, but an overdocked state of >4–6 SNAREs actually increases the equilibrium distance.     

Correlated Inter-Domain Motions in Adenylate Kinase

Correlated inter-domain motions in proteins can mediate fundamental biochemical processes such as signal transduction and allostery. Here we characterize at structural level the inter-domain coupling in a multidomain enzyme, Adenylate Kinase (AK), using computational methods that exploit the shape information encoded in residual dipolar couplings (RDCs) measured under steric alignment by nuclear magnetic resonance (NMR). We find experimental evidence for a multi-state equilibrium distribution along the opening/closing pathway of Adenylate Kinase, previously proposed from computational work, in which inter-domain interactions disfavour states where only the AMP binding domain is closed. In summary, we provide a robust experimental technique for study of allosteric regulation in AK and other enzymes.     

Red cell extensional recovery and the determination of membrane viscosity.

A theory of membrane viscoelasticity developed by Evans and Hochmuth in 1976 is used to analyze the time-dependent recovery of an elongated cell. Before release, the elongated cell is the static equilibrium where external forces are balanced by membrane elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of the viscoelastic solid model. It is shown that the model describes the time-dependent recovery process very well for a time constant in the range of 0.1-0.13 s. The time constant is the ratio membrane surface viscosity eta:membrane surface elasticity mu. Measurements for the shear modulus mu of 0.006 dyne/cm give a value for the surface viscosity of red cell membrane as a viscoelastic solid material of eta = mu tc = (6-8) X 10(-4) poise . cm.     

Interdomain interactions in hinge-bending transitions.

BACKGROUND: The mechanisms that allow or constrain protein movement have not been understood. Here we study interdomain interactions in proteins to investigate hinge-bending motions. RESULTS: We find a limited number of salt bridges and hydrogen bonds at the interdomain interface, in both the "closed" and the "open" conformations. Consistently, analysis of 222 salt bridges in an independently selected database indicates that most salt bridges form within rather than between independently folding hydrophobic units. Calculations show that these interdomain salt bridges either destabilize or only marginally stabilize the closed conformation in most proteins. In contrast, the nonpolar buried surface area between the moving parts can be extensive in the closed conformations. However, when the nonpolar buried surface area is large, we find that at the interdomain interface in the open conformation it may be as large or larger than in the closed conformation. Hence, the energetic penalty of opening the closed conformation is overcome. Consistently, a large nonpolar surface area buried in the closed interdomain interface accompanies limited opening of the domains, yielding a larger interface. CONCLUSIONS: Short-range electrostatic interactions are largely absent between moving domains. Interdomain nonpolar buried surface area may be large in the closed conformation, but it is largely offset by the area buried in the open conformation. In such cases the opening of the domains appears to be relatively small. This may allow prediction of the extent of domain opening. Such predictions may have implications for the shape and size of the binding pockets in drug/protein design.     

Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions

A theoretical model of a two-component bilayer membrane was used in order to describe the influence of anisotropic membrane inclusions on shapes of membrane daughter micro and nano vesicles. It was shown that for weakly anisotropic inclusions the stable vesicle shapes are only slightly out-of-round. In contrast, for strongly anisotropic inclusions the stable vesicle shapes may significantly differ from spheres, i.e. they have a flattened oblate shape at small numbers of inclusions in the membrane, and an elongated cigar-like prolate shape at high numbers of inclusions in the vesicle membrane.     

The hydrophobic insertion mechanism of membrane curvature generation by proteins

A wide spectrum of intracellular processes is dependent on the ability of cells to dynamically regulate membrane shape. Membrane bending by proteins is necessary for the generation of intracellular transport carriers and for the maintenance of otherwise intrinsically unstable regions of high membrane curvature in cell organelles. Understanding the mechanisms by which proteins curve membranes is therefore of primary importance. Here we suggest, for the first time to our knowledge, a quantitative mechanism of lipid membrane bending by hydrophobic or amphipathic rodlike inclusions which simulate amphipathic α-helices—structures shown to sculpt membranes. Considering the lipid monolayer matrix as an anisotropic elastic material, we compute the intramembrane stresses and strains generated by the embedded inclusions, determine the resulting membrane shapes, and the accumulated elastic energy. We characterize the ability of an inclusion to bend membranes by an effective spontaneous curvature, and show that shallow rodlike inclusions are more effective in membrane shaping than are lipids having a high propensity for curvature. Our computations provide experimentally testable predictions on the protein amounts needed to generate intracellular membrane shapes for various insertion depths and membrane thicknesses. We also predict that the ability of N-BAR domains to produce membrane tubules in vivo can be ascribed solely to insertion of their amphipathic helices.     

Hydrodynamic studies on chitosans in aqueous solution

Three commercial chitosans with a degree of acetylation of 25–30% were studied by light scattering (static and dynamic), analytical ultracentrifugation (sedimentation velocity and sedimentation equilibrium), and capillary viscometry in 0.02 M acetate buffer/0.1 M NaCl, pH 4.5. The molecular masses obtained by sedimentation equilibrium measurements or sedimentation and diffusion coefficients according to the Svedberg equation agreed well or fairly well with those from static light scattering whereas the molecular masses calculated via the Scheraga–Mandelkern equation were found too low by almost 50%. The various Mark–Houwink type relationships suggested a nearly free-draining flexible worm-like chain. A prolate ellipsoid of revolution with an axial ratio a/b25 was shown to be a hydrodynamically equivalent body of the flexible worm-like chain that had been derived from static light scattering. The findings illustrate the fact that a hydrodynamically strongly asymmetric shape need not mean a strongly elongated shape of the molecules in reality.     

A model of lipid rearrangements during pore formation in the DPPC lipid bilayer

Context: The molecular bases of pore formation in the lipid bilayer remain unclear, as do the exact characteristics of their sizes and distributions. To understand this process, numerous studies have been performed on model lipid membranes including cell-sized giant unilamellar vesicles (GUV). The effect of an electric field on DPPC GUV depends on the lipid membrane state: in the liquid crystalline phase the created pores have a cylinder-like shape, whereas in the gel phase a crack has been observed.

Objective: The aim of the study was to investigate the geometry of pores created in a lipid bilayer in gel and liquid crystalline phases in reference to literature experimental data.

Methods: A mathematical model of the pore in a DPPC lipid bilayer developed based on the law of conservation of mass and the assumption of constant volume of lipid molecules, independent of their conformation, allows for analysis of pore shape and accompanying molecular rearrangements.

Results: The membrane area occupied by the pore of a cylinder-like shape is greater than the membrane area occupied by lipid molecules creating the pore structure (before pore appearance). Creation of such pores requires more space, which can be achieved by conformational changes of lipid chains toward a more compact state. This process is impossible for a membrane in the most compact, gel phase.

Discussion and conclusions: We show that the geometry of the pores formed in the lipid bilayer in the gel phase must be different from the cylinder shape formed in the lipid bilayer in a liquid crystalline state, confirming experimental studies. Furthermore, we characterize the occurrence of the ‘buffer’ zone surrounding pores in the liquid crystalline phase as a mechanism of separation of neighbouring pores.     

Shape equations and curvature bifurcations induced by inhomogeneous rigidities in cell membranes

This article aims at two objectives: one is the shape equation for the equilibrium configurations of biomembranes with heterogeneous rigidities; another is the possible mechanism for curvature bifurcations in various biomembranes such as human red blood cells (RBC). The shape equation is established by treating the inhomogeneous biomembrane as a lipid bilayer vesicle containing inclusions or impurities. After careful investigation of the equation, the rigidity gradient is found to be an initial "driving force" that may destabilize the biomembrane and stimulate shape transitions, and the concept (or mechanism) termed "curvature bifurcations induced by rigidity gradients" is suggested. Various post-bifurcation modes recording the new equilibrium configurations are disclosed. A few post-bifurcation modes are found to coincide well with some practical shape transitions in cells such as the cup-like shape (stomatocyte) transition and spiculated shape (echinocyte) transition in RBC.     

Micro-organisation of the membrane after radiation-induced apoptosis: a flow cytometry study

The aim of this study was to detect membrane fluidity modifications in blood lymphocytes that had been exposed to γ-radiation, at a graded series of depths from the surface to the centre of the membrane bilayer and as a function of cell viability. A time course was performed to verify the contribution of the membrane to radiation-induced apoptosis. In comparison with spectrofluorimetry, flow cytometry proved to be a reliable method for measuring radiation-induced membrane alterations. Late apoptotic lymphocytes were characterised by a significant decrease of the 3-SA, 6-SA and 9-SA fluorescence anisotropy values, compared to viable lymphocytes. Moreover, a highly significant difference was observed in the early apoptotic lymphocyte subpopulation between the fluorescence anisotropy values measured 24 h (radiation-induced apoptosis) and those measured 1 h (spontaneous apoptosis) after irradiation. The simultaneous assessment of cellular viability and membrane fluidity using n-(9-anthroyloxy) fatty acid probes, may be relevant for the investigation of interactions which may exist between membrane modifications and the apoptotic process. Our observations support the specificity of radiation-induced apoptosis compared to spontaneous apoptosis in terms of biophysical modifications of membrane properties. Received: 15 January 2001 / Accepted: 1 July 2001     

Statistical thermodynamic analysis of peptide and protein insertion into lipid membranes.

A statistical thermodynamic approach is used to analyze the various contributions to the free energy change associated with the insertion of proteins and protein fragments into lipid bilayers. The partition coefficient that determines the equilibrium distribution of proteins between the membrane and the solution is expressed as the ratio between the partition functions of the protein in the two phases. It is shown that when all of the relevant degrees of freedom (i.e., those that change their character upon insertion into the membrane) can be treated classically, the partition coefficient is fully determined by the ratio of the configurational integrals and thus does not involve any mass-dependent factors, a conclusion that is also valid for related processes such as protein adsorption on a membrane surface or substrate binding to proteins. The partition coefficient, and hence the transfer free energy, depend only on the potential energy of the protein in the membrane. Expressing this potential as a sum of a "static" term, corresponding to the equilibrium (minimal free energy) configuration of the protein in the membrane, and a "dynamical" term representing fluctuations around the equilibrium configuration, we show that the static term contains the "solvation" and "lipid perturbation" contributions to the transfer free energy. The dynamical term is responsible for the "immobilization" free energy, reflecting the loss of translational and rotational entropy of the protein upon incorporation into the membrane. Based on a recent molecular theory of lipid-protein interactions, the lipid perturbation and immobilization contributions are then expressed in terms of the elastic deformation free energy resulting from the perturbation of the lipid environment by the foreign (protein) inclusion. The model is formulated for cylindrically shaped proteins, and numerical estimates are given for the insertion of an alpha-helical peptide into a lipid bilayer. The immobilization free energy is shown to be considerably smaller than in previous estimates of this quantity, and the origin of the difference is discussed in detail.     

Torocyte membrane endovesicles induced by octaethyleneglycol dodecylether in human erythrocytes

Endovesicles induced in human erythrocytes by octaethyleneglycol dodecylether (C12E8) were studied by confocal laser scanning microscopy, using fluorescein isothiocyanate dextran as a nonspecific fluid marker. The endovesicles appeared to consist mainly of a ring-formed toroidal part joined with a central flat membrane segment. The torocyte contour length was several microm. There was usually one torocyte endovesicle per cell. The endovesicles seemed to be located near the cell surface. In sections of C12E8-treated erythrocytes transmission electron microscopy revealed the frequent occurrence of flat membrane structures with a bulby periphery, which apparently are cross sections of torocyte endovesicles. The possible physical mechanisms leading to the observed torocyte endovesicle shape are discussed. The torocyte endovesicles seem to be formed in a process in which an initially stomatocytic invagination loses volume while maintaining a large surface area. Because intercalation of C12E8 in the erythrocyte membrane induces inward membrane bending (stomatocytosis) we assume that C12E8 is preferentially located in the inner lipid layer of the erythrocyte membrane, i.e., in the outer lipid layer of the endovesicle membrane. It is suggested that local disturbances of the lipid molecules in the vicinity of the C12E8 molecules in the outer lipid layer of the endovesicle membrane form membrane inclusions with the effective shape of an inverted truncated cone. If the interaction between the inclusion and the membrane is weak, the membrane of such an endovesicle can be characterized by its negative spontaneous curvature, which may lead to a torocyte endovesicle shape with a small relative volume. Effects of a possible strong interaction between the C12E8-induced membrane inclusions and the membrane on the stability of the torocyte endovesicles are also indicated.