Saša Svetina

Role of lamellar membrane structure in tether formation from bilayer vesicles

A theoretical analysis is presented of the formation of membrane tethers from micropipette-aspirated phospholipid vesicles. In particular, it is taken into account that the phospholipid membrane is composed of two layers which are in contact but unconnected. The elastic energy of the bilayer is taken to be the sum of contributions from area expansivity, relative expansivity of the two monolayers, and bending. The vesicle is aspirated into a pipette and a constant point force is applied at the opposite side in the direction away from the pipette. The shape of the vesicle in approximated as a cylindrical projection into the pipette with a hemispherical cap, a spherical section, and a cylindrical tether with a hemispherical cap. The dimensions of the different regions of the vesicle are obtained by minimizing its elastic energy subject to the condition that the volume of the vesicle is fixed. The range of values for the parameters of the system is determined at which the existence of a tether is possible. Stability analysis is performed showing which of these configurations are stable. The importance of the relative expansion and compression of the constituent monolayers is established by recognizing that local bending energy by itself does not stabilize the vesicle geometry, and that in the limit as the relative expansivity modulus becomes infinitely large, a tether cannot be formed. Predictions are made for the functional relationships among experimentally observable quantities. In a companion report, the results of this analysis are applied to experimental measurements of tether formation, and used to calculate values for the membrane material coefficients.

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.

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.

Growth and shape transformations of giant phospholipid vesicles upon interaction with an aqueous oleic acid suspension.

The interaction of two types of vesicle systems was investigated: micrometer-sized, giant unilamellar vesicles (GUVs) formed from 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and submicrometer-sized, large unilamellar vesicles (LUVs) formed from oleic acid and oleate, both in a buffered aqueous solution (pH 8.8). Individual POPC GUVs were transferred with a micropipette into a suspension of oleic acid/oleate LUVs, and the shape changes of the GUVs were monitored using optical microscopy. The behavior of POPC GUVs upon transfer into a 0.8mM suspension of oleic acid, in which oleic acid/oleate forms vesicular bilayer structures, was qualitatively different from the behavior upon transfer into a 0.3mM suspension of oleic acid/oleate, in which oleic acid/oleate is predominantly present in the form of monomers and possibly non-vesicular aggregates. In both cases, changes in vesicle morphology were observed within tens of seconds after the transfer. After an initial increase of the vesicle cross-section, the vesicle started to evaginate, spawning dozens of satellite vesicles connected to the mother vesicle with narrow necks or tethers. In 60% of the cases of transfer into a 0.8mM oleic acid suspension, the evagination process reversed and proceeded to the point where the membrane formed invaginations. In some of these cases, several consecutive transitions between invaginated and evaginated shapes were observed. In the remaining 40% of the cases of transfer into the 0.8mM oleic acid suspension and in all cases of vesicle transfer into the 0.3mM oleic acid suspension, no invaginations nor subsequent evaginations were observed. An interpretation of the observed vesicle shape transformation on the basis of the bilayer-couple model is proposed, which takes into account uptake of oleic acid/oleate molecules by the POPC vesicles, oleic acid flip-flop processes and transient pore formation.

Vesicle Budding and the Origin of Cellular Life

This Minireview provides an appropriate opportunity to demonstrate the connection between the results of some early experimental and theoretical investigations of vesicle budding and the more recent application of the concepts developed there to the process of vesicle self-reproduction. Herein, we also explain why vesicle budding could have preceded the establishment of cellular life.

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.

The contribution of hydrogen bonds to the surface tension of water

Abstract The surface energy, the surface free energy and the surface entropy of liquid water are calculated from the decrease in the number of hydrogen bonds in the surface layer, estimated on the bash of a simplified aater structure scheme. In the calculations of the free energy density function only the hydrogen-bond interactions between molecules are taken into consideration. The resulting surface free energy of water is ≈43 mN/m at 25°C. The calculated temperature dependence is consistent with that observed.

Myelin-like protrusions of giant phospholipid vesicles prepared by electroformation

Abstract Quasistable shapes of phospholipid bilayer vesicles obtained by formation in an alternating electric field [M.I. Angelova, S. Soleau, Ph. Meleard, J.F. Faucon, P. Bothorel, Prog. Colloid Polym. Sci. 89 (1992) 127; V. Heinrich, R.E. Waugh, Ann. Biomed. Eng. 24 (1996) 595] are observed. The vesicles appearing as composed of a mother sphere and a thin tubular myelin-like protrusion, are found to be a common phase in the spontaneous slow shape transformation that yields giant fluctuating phospholipid vesicles of different shapes. In the shape transformation, the myelin-like protrusion, which acts as a reservoir for the membrane area, is integrated into the mother vesicle.

Membrane bending energy in relation to bilayer couples concept of red blood cell shape transformations

Abstract A simple four parameter geometrical model is introduced to approximately simulate the axisymmetrically shaped red blood cells. Possible shapes are calculated according to the requirement that the cell volume and areas of the two constituent monolayers of the membrane are constant during cell shape transformations. The intervals for the geometrical parameters are determined within which the cell can have a series of rotationally symmetrical shapes. The cell shape at given values of the above three cell properties is obtained by finding the minimum value of the membrane bending energy. The presented picture of red blood cell shape transformations is shown to be in agreement with the concept of bending energy as well as with the bilayer couples concept.

Effect of pH on red blood cell deformability.

Abstract 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.