Bojan Božič

Vesicle deformation by an axial load: From elongated shapes to tethered vesicles

A sufficiently large force acting on a single point of the fluid membrane of a flaccid phospholipid vesicle is known to cause the formation of a narrow bilayer tube (tether). We analyze this phenomenon by means of general mathematical methods allowing us to determine the shapes of strongly deformed vesicles including their stability. Starting from a free vesicle with an axisymmetric, prolate equilibrium shape, we consider an axial load that pulls (or pushes) the poles of the vesicle apart. Arranging the resulting shapes of strained vesicles in dependence of the axial deformation and of the area difference of monolayers, phase diagrams of stable shapes are presented comprising prolate shapes with or without equatorial mirror symmetry. For realistic values of membrane parameters, we study the force-extension relation of strained vesicles, and we demonstrate in detail how the initially elongated shape of an axially stretched vesicle transforms into a shape involving a membrane tether. This tethering transition may be continuous or discontinuous. If the free vesicle is mirror symmetric, the mirror symmetry is broken as the tether forms. The stability analysis of tethered shapes reveals that, for the considered vesicles, the stable shape is always asymmetric (polar), i.e., it involves only a single tether on one side of the main vesicle body. Although a bilayer tube formed from a closed vesicle is not an ideal cylinder, we show that, for most practical purposes, it is safe to assume a cylindrical geometry of tethers. This analysis is supplemented by the documentation of a prototype experiment supporting our theoretical predictions. It shows that the currently accepted model for the description of lipid-bilayer elasticity (generalized bilayer couple model) properly accounts for the tethering phenomenon.

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 κ 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 TdLpκC04≥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 TdLpκC04, will greatly exceed the number of any other vesicles.

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.

Equilibrium Shapes of Erythrocytes in Rouleau Formation

A well known physiological property of erythrocytes is that they can aggregate and form a rouleau. We present a theoretical analysis of erythrocyte shapes in a long rouleau composed of cells with identical sizes. The study is based on the area difference elasticity model of lipid membranes, and takes into consideration the adhesion of curved axisymmetric membranes. The analysis predicts that the erythrocytes in the rouleau can have either a discoid or a cup-like shape. These shapes are analogous to the discoid and stomatocyte shapes of free erythrocytes. The transitions between the discoid and cup-like shapes in the rouleau are characterized. The occurrence of these transitions depends on three model parameters: the cell relative volume, the preferred difference between the areas of the membrane bilayer leaflets, and the strength of the adhesion between the membranes. The cup-like shapes are favored at small relative volumes and small preferred area differences, and the discoid shapes are favored at large values of these parameters. Increased adhesion strength enlarges the contact area between the cells, flattens the cells, and consequently promotes the discoid shapes.

Torocyte shapes of red blood cell daughter vesicles.

The shape of the newly described torocyte red blood cell endovesicles induced by octaethyleneglycol dodecylether (C12E8) is characterized. A possible explanation for the origin and stability of the observed torocyte endovesicles is suggested. Three partly complementary mechanisms are outlined, all originating from the interaction of C12E8 molecules with the membrane. The first is a preferential intercalation of the C12E8 molecule into the inner membrane layer, resulting in a membrane invagination which may finally close, forming an inside-out endovesicle. The second is a preference of the C12E8-induced membrane inclusions (clusters) for small local curvature which would favour torocyte endovesicle shape with large regions of small or even negative membrane mean curvatures, the C12E8 membrane inclusion being defined as a complex composed of the embedded C12E8 molecule and some adjacent phospholipid molecules which are significantly distorted due to the presence of the embedded C12E8 molecule. The preference of the C12E8 inclusions for zero or negative local curvature may also lead to the nonhomogeneous lateral distribution of the C12E8 inclusions resulting in their accumulation in the membrane of torocyte endovesicles. The third possible mechanism is orientational ordering of the C12E8-induced inclusions in the regions of torocyte endovesicles with high local membrane curvature deviator.

Shapes of Discoid Intracellular Compartments with Small Relative Volumes

A prominent feature of many intracellular compartments is a large membrane surface area relative to their luminal volume, i.e., the small relative volume. In this study we present a theoretical analysis of discoid membrane compartments with a small relative volume and then compare the theoretical results to quantitative morphological assessment of fusiform vesicles in urinary bladder umbrella cells. Specifically, we employ three established extensions of the standard approach to lipid membrane shape calculation and determine the shapes that could be expected according to three scenarios of membrane shaping: membrane adhesion in the central discoid part, curvature driven lateral segregation of membrane constituents, and existence of stiffer membrane regions, e.g., support by protein scaffolds. The main characteristics of each scenario are analyzed. The results indicate that even though all three scenarios can lead to similar shapes, there are values of model parameters that yield qualitatively distinctive shapes. Consequently, a distinctive shape of an intracellular compartment may reveal its membrane shaping mechanism and the membrane structure. The observed shapes of fusiform vesicles fall into two qualitatively different classes, yet they are all consistent with the theoretical results and the current understanding of their structure and function.

Budding of giant unilamellar vesicles induced by an amphitropic protein β2-glycoprotein I.

β(2)-glycoprotein I (β(2)GPI) is a plasma protein capable of binding reversibly to membranes, and is classified among the amphitropic proteins. Part of the protein intercalates into the outer membrane leaflet, altering the difference between the preferred areas of the membrane leaflets, which results in membrane shape transformations. Budding, as a specific example of such shape transformations, was studied using giant unilamellar vesicles. Our aim was to identify the vesicle parameters that influence the degree of membrane budding by studying this process qualitatively and quantitatively. A simple theoretical model has been developed and assessed against the experimental observations. The results show that β(2)GPI binds in a concentration dependent manner, causing transitions between vesicle shapes with increasing numbers of buds. Higher numbers of buds are characteristic of larger and/or more flaccid vesicles. When the vesicle membrane is strained, a higher β(2)GPI concentration is needed to produce the same effects as on the unstrained vesicle. Vesicles were found to be highly individual in their behaviour, so each was treated individually. Specific vesicle behaviour was found to be the consequence of the neck between the main vesicle body and the buds, which could be either open, closed for the exchange of solution, or closed for the exchange of both solution and membrane.

The role of sterols in the lipid vesicle response induced by the pore-forming agent nystatin.

The influences of ergosterol and cholesterol on the activity of the nystatin were investigated experimentally in a POPC model membrane as well as theoretically. The behavior of giant unilamellar vesicles (GUVs) under osmotic stress due to the formation of transmembrane pores was observed on single vesicles at different nystatin concentrations using phase-contrast microscopy. A significant shift of the typical vesicle behavior, i.e., morphological alterations, membrane bursts, slow vesicle ruptures and explosions, towards lower nystatin concentrations was detected in the ergosterol-containing vesicles and a slight shift towards higher nystatin concentrations was detected in the cholesterol-containing membranes. In addition, the nystatin activity was shown to be significantly affected by the ergosterol membranes molar fraction in a non-proportional manner. The observed tension-pore behavior was interpreted using a theoretical model based on the osmotic phenomena induced by the occurrence of size-selective nystatin pores. The number of nystatin pores for different vesicle behavior was theoretically determined and the role of the different mechanical characteristics of the membrane, i.e., the membranes expansivity and bending moduli, the line tension and the lysis tension, in the tension-pore formation process was quantified. The sterol-induced changes could not be explained adequately on the basis of the different mechanical characteristics, and were therefore interpreted mainly by the direct influences of the membrane sterols on the membrane binding, the partition and the pore-formation process of nystatin.

A MECHANISM FOR THE ESTABLISHMENT OF POLAR CELL MORPHOLOGY BASED ON THE CYTOSKELETON-DERIVED FORCES EXERTED ON THE CELL BOUNDARY

Abstract A mechanism for the establishment of polar cell morphology is presented, based on the internal forces that the cytoskeletal structures exert on the cell boundary. Cell shapes are determined by postulating that they correspond to the minimum of the total energy of the system, which is the sum of the bending energy of the cell boundary and the potential energies of the involved forces. Axisymmetrical cell shapes are considered, and it is assumed that the cytoskeletal structures exert an extensional axial force and are involved in controlling the area of the cell boundary. The dependence of cell shapes on the axial force is presented for different values of this area. The results show that, at increasing axial force, the cell undergoes a discontinuous transition from an oval shape, exhibiting an equatorial mirror symmetry into a polar shape. The proposed mechanism is related to previously documented specific effects of microtubule- and actin-modifying drugs on polar shapes of developing isolated retinal photoreceptor cells.

Macroscopic Properties of Phospholipid Vesicles with a Contact Angle between the Membrane Domains

Ternary mixtures of a high-melting lipid, a low-melting lipid, and cholesterol are known to form domains of a liquid-ordered and a liquid-disordered phase in bilayer membranes. We prepare giant vesicles from a sphingomyelin/dioleoylphosphocholine/cholesterol mixture and then examine them using fluorescence microscopy. NBD-labeled lipid and BODIPY-labeled cholesterol are used to identify the phase domains of the membrane. A vesicle with only two domains, one in a liquid-ordered and one in a liquid-disordered phase, is chosen because of its simple geometry, for convenient comparison of the experimental results with the theoretical predictions. A microinjector is used to gradually decrease and/or increase the volume of the vesicles by changing the osmolarity of the sugar solution. The relevant energy terms of the membrane mechanics are the elastic energies of the domains and the energy of the domain boundary. The elastic energy of the membrane domains can be described by two terms: the bending energy and the Gaussian bending energy. The energy of the domain boundary is proportional to its length. At the boundary between the domains a contact angle is taken into consideration. Then, in order to obtain values for the lateral tension and the contact angle, the areas of the domains and the characteristic dimensions of the shape are determined for different volumes. The best fits were obtained for a line tension of 6+/-3 pN and a contact angle of 1.4+/-0.3 rad.