Membrane Spontaneous Curvature Research Articles

Resting shape and spontaneous membrane curvature of red blood cells

A boundary-value problem is formulated describing the biconcave resting shape of normal red blood cells, based on local constitutive equations for the membrane tensions and bending moments. The fundamental physical assumption is that curvature-dependent anisotropic membrane stress resultants accompanied by isotropic bending moments arise from isotropic tensions developing in each leaflet of the lipid bilayer, while the cytoskeleton is unstressed in the resting configuration. Families of equilibrium resting shapes parametrized by the spontaneous bilayer curvature and cell sphericity compare favourably with the average shape of normal red blood cells. The successful comparison supports Helfrich's notion of a non-zero spontaneous curvature whose magnitude is nearly equal to the negative of the equivalent cell radius defined with respect to the membrane surface area. The structure of the solution space suggests a minimum spontaneous curvature below which the cell sphericity is lower than that of the red blood cell, independent of the transmural pressure. The computed cell shapes also compare favourably with the shapes of swollen red blood cells, though for a different value of the spontaneous curvature. The dependence of the spontaneous curvature on the cell volume is attributed to in-plane elastic tensions developing due to the deformation of the cytoskeleton. An alternative formulation based on a non-local model for the monolayer tensions is found to be incapable of predicting non-spherical shapes.

Modeling receptor-mediated endocytosis via mechanics of cell adhesion

AbstractA mathematical model describing how a cell membrane with diffusive mobile receptors wraps around a ligand coated cylindrical or spherical particle has been recently developed to model particle size effects in receptor mediated endocytosis. The model predicted an optimal particle size for the smallest wrapping time, as well as a minimum and a maximum particle size for successful wrapping. The results showed that particles in the size range of tens to hundreds of nanometers can enter cells even in the absence of clathrin or caveolin coats. Here we report some further progresses on modeling a spontaneous membrane curvature induced by clathrin or caveolin coats at the inner membrane leaflet as well as simultaneous entry of many particles into cells. It is found that a spontaneous membrane curvature narrows the particle size range for successful wrapping and there exists an optimal particle density for maximum particle adsorptivity.

Thermodynamics of mechanosensitivity

Mechanosensitivity of ion channels is conventionally interpreted as being driven by a change of their in-plane cross-sectional area Amsc. This, however, does not include any factors relating to membrane stiffness, thickness, spontaneous curvature or changes in channel shape, length or stiffness. Because the open probability of a channel is sensitive to all these factors, we constructed a general thermodynamic formalism. These equations provide the basis for the analysis of the behaviour of mechanosensitive channels in lipids of different geometric and chemical properties such as the hydrophobic mismatch at the boundary between the protein and lipid or the effects of changes in the bilayer intrinsic curvature caused by the adsorption of amphipaths. This model predicts that the midpoint γ1/2 and the slope1/2 of the gating curve are generally not independent. Using this relationship, we have predicted the line tension at the channel/lipid border of MscL as ∼10 pN, and found it to be much less than the line tension of aqueous pores in pure lipid membranes. The MscL channel appears quite well matched to its lipid environment. Using gramicidin as a model system, we have explained its observed conversion from stretch-activated to stretch-inactivated gating as a function of bilayer thickness and composition.

A relationship between membrane properties forms the basis of a selectivity mechanism for vesicle self-reproduction.

Self-reproduction and the ability to regulate their composition are two essential properties of terrestrial biotic systems. The identification of non-living systems that possess these properties can therefore contribute not only to our understanding of their functioning but also hint at possible prebiotic processes that led to the emergence of life. Growing lipid vesicles have been previously established as having the capacity to self-reproduce. Here it is demonstrated that vesicle self-reproduction can occur only at selected values of vesicle properties. We treat as an example a simple vesicle with membrane elastic properties defined by a membrane bending modulus kappa and spontaneous curvature C0, whose volume variation depends on the membrane hydraulic permeability Lp and whose membrane area doubles in time Td. Vesicle self-reproduction is described as a process in which a growing vesicle first transforms its shape from a sphere into a budded shape of two spheres connected by a narrow neck, and then splits into two spherical daughter vesicles. We show that budded vesicle shapes can be reached only under the condition that Td Lpkappa C0(4)> or =1.85. Thus, in a growing vesicle population containing vesicles of different composition, only the vesicles for which this condition is fulfilled can increase their number in a self-reproducing manner. The obtained results also suggest that at times much longer than Td the number of vesicles with their properties near the "edge" in the system parameter space defined by the minimum value of the product Td Lpkappa C0(4), will greatly exceed the number of any other vesicles.

Diacylglycerol-Rich Domain Formation in Giant Stearoyl-Oleoyl Phosphatidylcholine Vesicles Driven by Phospholipase C Activity

We have studied the effect of phospholipase C from Bacillus cereus and Clostridium perfringens (α-toxin) on giant stearoyl-oleoyl phosphatidylcholine (SOPC) vesicles. Enzyme activity leads to a binary mixture of SOPC and the diacylglycerol SOG, which phase separates into a SOPC-rich bilayer phase and a SOG-rich isotropic bulk-like domain embedded within the membrane, as seen directly by phase contrast microscopy. After prolonged enzymatic attack, all bilayer membranes are transformed into an isotropic pure SOG phase as characterized by fluorescence microscopy, differential scanning calorimetry, fluorescence anisotropy measurements, and small angle x-ray scattering. These domains may have biological relevance, serving as storage compartments for hydrophobic molecules and/or catalyzing cellular signaling events at their boundaries. Furthermore, in the early stages of asymmetric enzymatic attack to the external monolayer of giant vesicles, we observe a transient coupling of the second-messenger diacylglycerol to membrane spontaneous curvature, which decreases due to enzyme activity, before domain formation and final vesicle collapse occurs.

Flunitrazepam partitioning into natural membranes increases surface curvature and alters cellular morphology

In recent studies, we showed that flunitrazepam (FNTZ) and other benzodiazepines interact with artificial phospholipid membranes locating at the polar head group region, inducing a membrane expansion, reducing the molecular packing and reorganising molecular dipoles. In the present paper we investigated the possibility that those phenomena could be transduced into changes in the curvature of membranes from natural origin. Hence we studied the effect of FNTZ on cellular morphology using human erythrocyte as a natural assay system. Shape changes of erythrocytes were evaluated by light microscopy and expressed as a morphological index (MI). FNTZ induced echinocytosis in a time-dependent manner with MI values significantly higher than those of control (without drug) or DMSO (vehicle) samples. Lidocaine, a local anesthetic known to induce stomatocytosis by incorporating in the inner monolayer, counterbalanced the concentration-dependent FNTZ crenating effects. FNTZ induced protective effects, compared with control and DMSO, against time-dependent hemolysis. Hypotonic-induced hemolysis, was also lowered by FNTZ in a concentration-dependent manner. Both antihemolytic effects suggested a drug-induced membrane expansion allowing a greater increase in cell volume before lysis. In such a complex system like a cell, curvature changes triggered by drug partitioning towards the plasma membrane, might be an indirect effect exerted through modifications of ionic-gradients or by affecting cytoskeleton–membrane linkage. In spite of that, the curvature changes can be interpreted as a mechanism suitable to relieve the tension generated initially by drug incorporation into the bilayer and may be the resultant of the dynamic interactions of many molecular fluxes leading to satisfy the spontaneous membrane curvature.

Correlation between the free energy of a channel-forming voltage-gated peptide and the spontaneous curvature of bilayer lipids.

The aqueous-membrane partitioning of alamethicin, a voltage-gated channel-forming peptide, was measured as a function of the membrane spontaneous curvature. EPR spectroscopy was used to measure the partitioning of the peptide in lipid compositions formed from dioleoylphosphatidylcholine (DOPC) and varied percentages of dioleoylphosphatidylethanolamine (DOPE), dioleoylphosphatidylethanolamine-N-methyl (DOPE-Me), or dioleoylphosphatidylethanolamine-N,N-dimethyl (DOPE-Me2). When the mole fraction of DOPE in mixtures of DOPC/DOPE is increased the binding of alamethicin decreases, and the increase in binding free energy is found to be linearly dependent upon the mole fraction of DOPE in the mixture. Addition of DOPE-Me or DOPE-Me2 also increases the binding free energy, except that the effect is reduced relative to that of DOPE. The free-energy increase per mole fraction of DOPE was found to be 1400 cal/mol, whereas for DOPE-Me and DOPE-Me2 the free-energy changes were 980 and 630 cal/mol, respectively. When the free-energy changes for alamethicin binding are compared with the previously determined spontaneous curvatures for mixtures of DOPC/DOPE and DOPC/DOPE-Me, the free energy of binding is found to be linearly dependent upon the spontaneous curvature of the bilayer lipids. The effects of membrane lipid unsaturation on the partitioning of alamethicin were also measured and are qualitatively consistent with this conclusion. The sensitivity to spontaneous curvature and the cooperativity that is seen in the binding curves for alamethicin are postulated to be a result of a localized thinning of the bilayer promoted by this peptide.

Dipole potentials and spontaneous curvature: membrane properties that could mediate anesthesia

General anesthetics alter both the membrane dipole potential and the membrane spontaneous curvature, two membrane properties that are likely to have a significant effect on membrane protein function. The dipole potential is a large hydrocarbon positive potential that appears to arise from the lipid carbonyl groups and/or water at the membrane–solution interface. Anesthetics reduce the magnitude of the membrane dipole potential at clinical levels of anesthetics, while non-anesthetics do not, and these changes in potential could modulate conformational transitions in membrane proteins that are electrically active. When the membrane distribution of anesthetic versus non anesthetic compounds is examined, anesthetics exhibit a preference for the membrane interface, whereas non-anesthetic compounds reside within the membrane hydrocarbon core. The preferential localization of anesthetics within the interface accounts for their effect on the membrane dipole potential, and may also serve to alter the membrane spontaneous curvature or lateral stress through the bilayer.

Electrostatics of lipid bilayer bending

The electrostatic contribution to spontaneous membrane curvature is calculated within Poisson-Boltzmann theory under a variety of assumptions and emphasizing parameters in the physiological range. Asymmetrical surface charges can be fixed with respect to bilayer midplane area or with respect to the lipid-water area, but induce curvatures of opposite signs. Unequal screening layers on the two sides of a vesicle (e.g., multivalent cationic proteins on one side and monovalent salt on the other) also induce bending. For reasonable parameters, tubules formed by electrostatically induced bending can have radii in the 50-100-nm range, often seen in many intracellular organelles. Thus membrane associated proteins may induce curvature and subsequent budding, without themselves being intrinsically curved. Furthermore, we derive the previously unexplored effects of respecting the strict conservation of charge within the interior of a vesicle. The electrostatic component of the bending modulus is small under most of our conditions and is left as an experimental parameter. The large parameter space of conditions is surveyed in an array of graphs.

Is the Mechanism of General Anesthesia Related to Lipid Membrane Spontaneous Curvature?a

Lipid bilayers in biomembranes may exist in a state of elastic curvature stress which may couple to the conformation of integral membrane proteins in a logical, and energetically significant, fashion. Many biomembranes contain sufficiently large fractions of nonlamellar-prone lipids to have monolayers under substantial curvature stress. Although very few experiments have been performed that can be used to correlate protein activity with curvature stress, the literature does contain a small number of studies that indicate that some protein function is nonspecifically modulated by the amounts of nonlamellar-prone lipid in the imbedding bilayers. The spontaneous curvature, is altered by the presence of anesthetics in physiologically relevant concentrations. This leads us to suggest that anesthetic action may be coupled to protein function via alteration of the tensions leading to the spontaneous curvature of biomembrane layers. The spontaneous curvature is also sufficiently sensitive to pressure that a mechanism for the pressure reversal of anesthesia follows if the effects of pressure are to counter changes in membrane lateral tension induced by anesthetics. It is emphasized that many more experimental data must be acquired to determine whether the ideas presented in this paper have validity. In particular, there is a need for data on the effects of different anesthetics and pressure on the spontaneous curvature and, more generally, lipid monolayer lateral tensions. Most importantly, experiments must be performed to investigate whether protein function correlates with these quantities.

Theory of vesicle budding

The formation of a small daughter vesicle from a large mother vesicle is considered, the two being connected by a narrow constriction. This budding is achieved by either decreasing the enclosed volume or increasing the membrane spontaneous curvature of a nearly spherical vesicle while the other quantity and the membrane area are constant. The activation energy of the discontinuous transition is identified and found to decrease to zero as the respective parameter change progresses.

Membrane bending energy and shape determination of phospholipid vesicles and red blood cells.

A procedure is developed to calculate red blood cell and phospholipid vesicle shapes within the bilayer couple model of the membrane. The membrane is assumed to consist of two laterally incompressible leaflets which are in close contact but unconnected. Shapes are determined by minimizing the membrane bending energy at a given volume of a cell (V), given average membrane area (A) and given difference of the areas of two leaflets (delta A). Different classes of shapes exist in parts of the v/delta a phase diagram, where v and delta a are the volume and the leaflet area difference relative to the sphere with area A. The limiting shapes are composed of sections of spheres with only two values allowed for their radii. Two low energy axisymmetrical classes, which include discocyte and stomatocyte shapes are studied and their phase diagrams are analyzed. For v= 0.6, the discocyte is the lowest energy shape, which transforms by decreasing delta a continuously into a stomatocyte. The spontaneous membrane curvature (C0) and compressibility of membrane leaflets can be incorporated into the model. A model, where delta A is free and C0 determines the shapes at given V and A, is also studied. In this case, by decreasing C0, a discocyte transforms discontinuously into an almost closed stomatocyte.

Influence of red cell surface charge on red cell membrane curvature.

The wellknown biconcave shape of resting RBC reflects an intrinsic overall negative spontaneous membrane curvature. It depends to a high degree on the integrity of the spectrin-actin-ankyrin-Band-3 hetero-complex. Alterations of this complex have previously been shown to be associated with shape transitions, which have been abolished by treatment with enzymes reducing the surface charge of the RBC. In this report we show that treatment of erythrocytes with enzymes reducing the surface charge (e.g. neuraminidase, trypsin, chymotrypsin and pronase), consistently exerts a "stomatocytogenic" effect, i.e. it reduces mean mean curvature. Also the time dependency for the charge reduction and for the correlated decrease of mean mean curvature is shown. So-called stomatocytogenic agents (e.g. clorpromazine, tetracain and triton X100) and so-called echinocytogenic agents (e.g. dinitrophenol and Na-salicylate) are known to change membrane curvature in a dose dependent manner. It is further shown that by prior reduction of surface charge by various enzymes the dose response curves of all stomatocytogenic and echinocytogenic agents tested is shifted towards higher degrees of stomatocytosis or lesser degrees of echinocytosis. The data show, that in RBC pronounced curvature influences are produced by the surface charge located on the sialic acid residues in the glycocalix.

Tangent counting for objective assessment of erythrocyte shape changes.

The resting shape of the human erythrocyte is maintained mainly by the elastic properties of its membrane. There is evidence that negative spontaneous membrane curvature is the cause of the biconcave shape; also negative membrane curvature is thought to be enhanced under "stomatocytogenic" influences and reduced under "echinocytogenic" influences. Experimental tests of these hypotheses are difficult in the absence of objective methods to quantify cell shape and/or membrane curvature. A new method is introduced to estimate the changes in convex and concave curvatures of the cell outlines in larger populations of RBC. It is based on the so-called "tangent count" procedure, carried out on microphotographs of freely suspended, randomly oriented RBCs in isotonic solutions. The method was validated by subjective shape assessment according to BESSIS' classification. It proved to be most sensitive in the range of moderate shape changes (classified subjectively as echinocyte II and stomatocyte II).

An instability of the red blood cell shape

The infinitesimal stability of fluid vesicle shapes is studied as a function of vesicle volume and spontaneous membrane curvature at fixed area. It is found that the azimuthally symmetric shapes are infinitesimally unstable for some values of these parameters. A possible connection with the sickling of red blood cells is pointed out.