Nonlocal membrane bending: a reflection, the facts and its relevance.

About forty years ago it was realized that phospholipid membranes, because they are composed of two layers, exhibit particular, and specific mechanical properties. This led to the concept of nonlocal membrane bending, often called area difference elasticity. We present a short history of the development of the concept, followed by arguments for a proper definition of the corresponding elastic constant. The effects of the nonlocal bending energy on vesicle shape are explained. It is demonstrated that lipid vesicles, cells and cellular aggregates exhibit phenomena that can only be described in a complete manner by considering nonlocal bending.

Morphology of small aggregates of red blood cells.

Blood can be considered a two-phase liquid composed of plasma as well as cells and cell aggregates. The degree of cell aggregation is an important determinant of blood rheology: The size and shape of the aggregates affect blood viscosity. The microscopic mechanisms of red blood cell adhesion involve a complex interplay of electrostatic, van der Waals, and a range of specific biochemical inter-membrane interactions. Here we use an effective model of these interactions combined with the membrane elasticity theory to calculate the equilibrium shape of a red blood cell doublet and compare it with the experimentally observed red blood cell aggregates both in vitro and in vivo. Special attention is devoted to the shape of doublets formed by dissimilar cells. A possible effect of doublet shape on pathways of the formation of multicellular aggregates is discussed. Red blood cell rouleau formation is expected to take place at intermediate adhesion strengths where the outer doublet surfaces are either concave or flat, whereas in the strong-adhesion regime where the outer doublet surfaces are convex the cells should form rounded clump-like aggregates.

Vesicle self-reproduction: the involvement of membrane hydraulic and solute permeabilities.

Conditions for self-reproduction are sought for a growing vesicle with its growth defined by an exponential increase of vesicle membrane area and by adequate flow of the solution across the membrane. In the first step of the presumed vesicle self-reproduction process, the initially spherical vesicle must double its volume in the doubling time of the membrane area and, through the appropriate shape transformations, attain the shape of two equal spheres connected by an infinitesimally thin neck. The second step involves separation of the two spheres and relies on conditions that cause the neck to be broken. In this paper we consider the first step of this self-reproduction process for a vesicle suspended in a solution whose solute can permeate the vesicle membrane. It is shown that vesicle self-reproduction occurs only for certain combinations of the values of membrane hydraulic and solute permeabilities and the external solute concentration, these quantities being related to the mechanical properties of the membrane and the membrane area doubling time. The analysis includes also the relaxation of a perturbed system towards stationary self-reproduction behavior and the case where the final shape consists of two connected spheres of different radii.

The effect of substrate and adsorbed proteins on adhesion, growth and shape of CaCo-2 cells.

Extracellular matrix (ECM) proteins play a critical role in many cellular functions, from spreading, migration and proliferation to apoptosis. This role can be altered when proteins of the native ECM are adsorbed to different substrates which cause structural modifications that can influence their biological function. The effects on CaCo-2 cells of laminin-1, fibronectin, collagen-1 and ECM gel adsorbed to glass and to tissue culture polystyrene (PS) were compared in terms of adhesion, proliferation, shapes and spreading of cells in culture. Significant differences between glass and PS surfaces were observed for proliferation and cell shape. Protein surfaces prepared on PS substrates had, in most cases, more pronounced effects on cells than uncoated PS, especially if coated by collagen-1. Adsorbed ECM gel was the most adhesive for cells, but its effect on cell proliferation was not notably different from the controls (glass or PS). These findings indicate that the choice of the substrate can have a significant effect on experimental results and should be taken into consideration when comparing results obtained on different surfaces.

Flat and sigmoidally curved contact zones in vesicle-vesicle adhesion.

Using the membrane-bending elasticity theory and a simple effective model of adhesion, we study the morphology of lipid vesicle doublets. In the weak adhesion regime, we find flat-contact axisymmetric doublets, whereas at large adhesion strengths, the vesicle aggregates are nonaxisymmetric and characterized by a sigmoidally curved, S-shaped contact zone with a single invagination and a complementary evagination on each vesicle. The sigmoid-contact doublets agree very well with the experimentally observed shapes of erythrocyte aggregates. Our results show that in identical vesicles with large to moderate surface-to-volume ratio, the sigmoid-contact shape is the only bound morphology. We also discuss the role of sigmoid contacts in the formation of multicellular aggregates such as erythrocyte rouleaux.

Annexin A5 binding to giant phospholipid vesicles is differentially affected by anti-beta2-glycoprotein I and anti-annexin A5 antibodies.

OBJECTIVES: Anti-phospholipid antibodies have been recognized to play a role in vascular thrombosis and pregnancy morbidity. They were first thought to be directed to phospholipids, but it is now known that the majority of pathogenic antibodies recognizes epitopes on phospholipid-binding plasma proteins such as beta2-glycoprotein I (beta2GPI) or possibly also annexin A5 (ANXA5). The mechanism of their prothrombotic action is still not completely understood. The aim of the present study was to observe the effect of antibodies against ANXA5 (aANXA5) and antibodies against beta2GPI (abeta2GPI) on the binding of ANXA5 to the negatively charged phospholipid membrane. METHODS: Giant phospholipid vesicles (GPVs) were used as a simple model of the membrane surface. GPVs composed of phosphatidylserine and phosphatidylcholine were produced in an aqueous medium. A single GPV was transferred to the solution containing ANXA5 conjugated with Alexa Fluor 488 (FANXA5) and (i) aANXA5 or abeta2GPI and (ii) different concentrations of abeta2GPI together with beta2GPI. The emission of the fluorescent light from the GPV surface, as the result of FANXA5 binding, was measured. RESULTS: Beta2GPI together with abeta2GPI reduced the binding of FANXA5 to GPVs. On the contrary, aANXA5 enhanced the binding of ANXA5 to the GPV surface. CONCLUSIONS: Our results point to the competition between FANXA5 and complexes of beta2GPI-abeta2GPI for the same binding sites and therefore support the hypothesis of the disruption of the ANXA5 protective shield on procoagulant phospholipid surface. The influence of increased cell surface ANXA5 concentration in the presence of aANXA5 on coagulation needs to be further studied.

Phospholipid membrane bending as assessed by the shape sequence of giant oblate phospholipid vesicles.

Vesicle shape transformations caused by decreasing the difference between the equilibrium areas of membrane monolayers were studied on phospholipid vesicles with small volume to membrane area ratios. Slow transformations of the vesicle shape were induced by lowering of the concentration of lipid monomers in the solution outside the vesicle. The complete sequence of shapes consisted of a string of pearls, and wormlike, starfish, discocyte and stomatocyte shapes. The transformation from discocyte to stomatocyte vesicle shapes was analyzed theoretically to see whether these observations accord with the area difference elasticity (ADE) model. The membrane shape equation and boundary conditions were derived for axisymmetrical shapes for low volume vesicles, part of whose membranes are in contact. Calculated shapes were arranged into a phase diagram. The theory predicts that the transition between discocyte and stomatocyte shapes is discontinuous for relatively high volumes and continuous for low volumes. The calculated shape sequences matched well with the observed ones. By assuming a linear decrease of the equilibrium area difference with time, the ratio between the nonlocal and local bending constants is in agreement with reported values.

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.

Elastic properties of the red blood cell membrane that determine echinocyte deformability.

The natural biconcave shape of red blood cells (RBC) may be altered by injury or environmental conditions into a spiculated form (echinocyte). An analysis is presented of the effect of such a transformation on the resistance of RBC to entry into capillary sized cylindrical tubes. The analysis accounts for the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending, the latter corresponding to different area strains in the two leaflets of the bilayer. The shape transformation is assumed to be driven by the equilibrium area difference (delta A(0), the difference between the equilibrium areas of the bilayer leaflets), which also affects the energy of deformation. The cell shape is approximated by a parametric model. Shape parameters, skeleton shear deformation, and the skeleton density of deformed membrane relative to the skeleton density of undeformed membrane are obtained by minimization of the corresponding thermodynamic potential. Experimentally, delta A(0) is modified and the corresponding discocyte-echinocyte shape transition obtained by high-pressure aspiration into a narrow pipette, and the deformability of the resulting echinocyte is examined by whole cell aspiration into a larger pipette. We conclude that the deformability of the echinocyte can be accounted for by the mechanical behavior of the normal RBC membrane, where the equilibrium area difference delta A(0) is modified.

Mechanisms of equinatoxin II-induced transport through the membrane of a giant phospholipid vesicle.

Protein equinatoxin II from sea anemone Actinia equina L. was used to form pores in phospholipid membranes. We studied the effect of these pores on the net transmembrane transport of sucrose and glucose by observing single giant (cell-size) vesicles under the phase contrast microscope. Sugar composition in the vesicle was determined by measuring the width of the halo, which appears around the vesicle in the phase contrast image. The transport of sugars was induced when a vesicle, filled with the sucrose solution, was transferred into the isomolar environment of a glucose solution with added equinatoxin II. Typically, a vesicle grew to a critical size, then the membrane broke by bursting and the vesicle shrank, started to grow again, and the whole process was repeated. The consecutive membrane breaks occurred in the same spot. The observed behavior was interpreted by the diffusion flow of the glucose molecules through the equinatoxin II-induced pores and the consequent increase of the vesicle water content. The burst relaxed the critically strained membrane, which then apparently resealed. A mathematical model of the described behavior was developed and was used to obtain the equinatoxin II-induced membrane permeability for the glucose molecules. Its dependence on the equinatoxin II concentration is in agreement with the previous reports.

Fractional occurrence of defects in membranes and mechanically driven interleaflet phospholipid transport.

The picture of biological membranes as uniform, homogeneous bileaflet structures has been revised in recent times due to the growing recognition that these structures can undergo significant fluctuations both in local curvature and in thickness. In particular, evidence has been obtained that a temporary, localized disordering of the lipid bilayer structure (defects) may serve as a principal pathway for movement of lipid molecules from one leaflet of the membrane to the other. How frequently these defects occur and how long they remain open are important unresolved questions. In this report, we calculate the rate of molecular transport through a transient defect in the membrane and compare this result to measurements of the net transbilayer flux of lipid molecules measured in an experiment in which the lipid flux is driven by differences between the mechanical stress in the two leaflets of the membrane bilayer. Based on this comparison, we estimate the frequency of defect occurrence in the membrane. The occurrence of defects is rare: the probability of finding a defect in 1.0 microm2 of a lecithin membrane is estimated to be approximately 6.0x10(-6). Based on this fractional occurrence of defects, the free energy of defect formation is estimated to be approximately 1.0x10(-19) J. The calculations provide support for a model in which interleaflet transport in membranes is accelerated by mechanically driven lipid flow.

Mechanical and functional aspects of membrane skeletons.

Membrane skeletons can be characterized as cytoskeletal structures lying parallel to the bilayer part of cellular and organelle membranes. Typical examples are spectrin network and actin-myosin cortex. We approach the problem of elucidating the function of membrane skeletons by theoretically analyzing mechanical models of the cellular behavior. Membranes of different physical and chemical properties are considered. In erythrocytes and some organelles membrane bilayers are smooth and simply underlaid or overlaid by membrane skeletons. It is argued that there the role of a membrane skeleton is, either, to keep the membrane composition laterally homogeneous as it is in the case of the erythrocyte, or, that it is involved in the processes of the lateral separation of integral membrane proteins as it is happening in the case of some intermediate steps of the vesicular membrane trafficking. In the second type of membranes the bilayer part is ruffled and folded, and there the membrane skeletons play a role in the determination of the cortical tension. Here we explore in more detail the mechanical behavior of a cell with such properties of its boundary. The shape transformations are described which occur under the influence (i) of different external forces, i.e., when an originally spherical cell is aspirated into the micropipette or when such a cell is adsorbed on a flat surface, and (ii) of different internal forces on the cell boundary exerted by the cytoskeletal elements.

Membrane active compounds that affect the shape of cells and cellular organelles.

Amphiphilic membrane active compounds are considered that affect the shapes of cells and cellular organelles by intercalation into the phospholipid part of their membranes. It is taken into consideration that amphiphile-membrane interaction modifies membrane mechanical properties. The relationship between membrane mechanical properties and vesicle shapes and the concept of the bilayer couple model are shortly reviewed. Then it is put forward that the strength of the amphiphile-membrane interaction may depend on the lateral packing of phospholipid molecules. It is shown that in such a case the amphiphile molecules bind to the membrane in a cooperative manner. Moreover, the amphiphile binding makes the ratio between the nonlocal and local membrane bending constants to be effectively larger and thus widens the range of possible stable vesicle and cellular shapes.

Asymmetrical labeling of giant phospholipid vesicles.

The method for labeling of inner membrane leaflet in unilamellar giant POPC vesicles was developed and characterised. Symmetrically NBD-PC labeled vesicles were treated by sodium dithionite, which undergoes an irreversible chemical reaction with NBD-PC molecule making it non-fluorescent. After the addition of dithionite the fluorescence on single vesicles as well as on vesicle suspension showed a 50% decrease of its initial value corresponding to marker quenching in the outer leaflet. Hence, fluorimetry as well as fluorescence microscopy prove that dithionite quenching is a suitable method to induce an asymmetrical labeling of the NBD-PC marked giant vesicles.

Effect of pH on red blood cell deformability.

The effect of pH on the red blood cell (RBC) deformability, which is a consequence of a change of cell membrane elastic properties is studied experimentally. With the intention to reduce the effects on deformability of cell geometry and cytoplasmic viscosity, we measured the deformability of the cells with the same volume at various pH of cell suspension from 6.2 to 8.0. Constant cell volume was achieved by varying osmolarity. Deformability was quantified by measuring the elongation of RBCs subjected to velocity gradient in a transparent cone-plate rheoscope. Observed significant decrease of deformability at lower pH leads to the conclusion that membrane elastic properties could be affected by pH changes in the range from 6.2 to 8.0.

The influence of the successive depolymerization and polymerization of cytoskeleton components on the fibroblast shapes.

Monitoring the influence of the cytoskeleton polymers on the shape of fibroblasts, performing the experiments of repeated degradation and polymerization of microtubules and microfilaments, we found out that the presence of microtubules is necessary in order to regenerate the proper functional structure of microfilaments, and vice versa.

Stability analysis of micropipette aspiration of neutrophils.

During micropipette aspiration, neutrophil leukocytes exhibit a liquid-drop behavior, i.e., if a neutrophil is aspirated by a pressure larger than a certain threshold pressure, it flows continuously into the pipette. The point of the largest aspiration pressure at which the neutrophil can still be held in a stable equilibrium is called the critical point of aspiration. Here, we present a theoretical analysis of the equilibrium behavior and stability of a neutrophil during micropipette aspiration with the aim to rigorously characterize the critical point. We take the energy minimization approach, in which the critical point is well defined as the point of the stability breakdown. We use the basic liquid-drop model of neutrophil rheology extended by considering also the neutrophil elastic area expansivity. Our analysis predicts that the behavior at large pipette radii or small elastic area expansivity is close to the one predicted by the basic liquid-drop model, where the critical point is attained slightly before the projection length reaches the pipette radius. The effect of elastic area expansivity is qualitatively different at smaller pipette radii, where our analysis predicts that the critical point is attained at the projection lengths that may significantly exceed the pipette radius.

The relation between the rod-like inner structures and the shapes of the cells.

The shapes of the cells with simple rod-like inner structures are studied theoretically. Since the cell with inner structure can be bent, the possibility of non-axisymmetric shapes is considered. The equilibrium shape of the cell, obtained by minimizing the sum of the membrane bending energy and the bending energy of the rod, depends on the ratio between the bending constant of the membrane and the bending rigidity of the polymer rod. The dependence of the cell shape on the length of the rod and on the difference between inner and outer membrane layer areas is presented.

The frequency dependence of phospholipid vesicle shapes in an external electric field.

Experiments show that phospholipid vesicles exposed to AC electric field undergo a shape transition from prolate to oblate ellipsoidal shape when the frequency of the field is increased. A theoretical model, based on the minimization of total free energy of the vesicle, was devised to explain this phenomenon. The model exhibits the same frequency-dependent prolate-to-oblate shape transition as observed in the experiment.

Rotation of giant phospholipid vesicles in an uniform shear flow.

Rotation of giant "point attached" phospholipid (POPC) vesicles in a shear flow was studied. The dependence of the angular velocity on the flow gradient was measured and the experimental results were compared to the predictions of a theoretical model. A good linear correlation between the angular velocity of the vesicle and the flow gradient, as predicted, was observed.