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.

The necessary condition that the cluster expansion as developed to determine the approximate free energy of hydrogen-bonded ferroelectrics [1] is thermodynamically consistent, is discussed, and the convergence of the series tested for the case of the KD2PO4 model Hamiltonian.

We investigate a new screwlike liquid-crystalline ordering in solutions of helical biopolymers and its influence on the state of individual molecules. In the resulting mesophase translational and rotational motions of molecules are coupled in screw fluctuations. We show that in contrast to the case of conventional chiral liquid crystals the elastic distortion does not twist the screw order but leads to overwinding of individual helical molecules. This explains the peculiarities of high-density DNA mesophases.

We propose a unified mechanism of phase transitions in the high density solutions of Nucleosomal Core Particles. We demonstrate its relation with the high shape and charge anisotropy of the NCP due to the DNA wrapping around the histone protein core. Hexagonal-to-lantellar transition in the solution of NCP columnar aggregates is shown to be driven by the condensation of the periodic antiparallel polar vector field. The transition results in the polar dyadic axes correlations. Fine structure of the NCP organization is also explained, namely the correlated tilting of NCP with respect to the column axis.

ABSTRACT When an external electric field is applied to short pitch polar smectics, their helical structures distort and unwind. The final transition to completely unwound structure can be continuous or discontinuous. Within the discrete phenomenological model the nature of the transition depends on the existence of the next-nearest neighboring layers interactions. If they are present, the transition is discontinuous. We try to elucidate this phenomenon.

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.

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 (ΔA 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, ΔA 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 ΔA 0 is modified.

It is generally accepted that the doping of chiral materials with achiral molecules diminishes the chirality of the system. Here we report the opposite phenomenon. It was found that the structural chirality of smectic phases made of rodlike molecules, Sm-C(*) or Sm-C(*)(A) phases, measured as the reverse length of the helical pitch, is enhanced by adding small amount of achiral bent-shaped molecules. The effect is due to the chirality transfer between host and guest systems. Achiral bent-shaped molecules become structurally chiral due to the interactions with the chiral host that induces tilt and polar order of bent-shaped molecules. This induced chirality is then transferred back to the host.

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.

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.

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.

The free energy of antiferroelectric smectic liquid crystals which takes into account polar order explicitly is presented. Steric, van der Waals, piezoelectric, and flexoelectric interactions to the nearest layers, and dipolar electrostatic interactions to the nearest and to the next-nearest layers, induce indirect tilt interactions with chiral and achiral properties. which extend to the third- and to the fourth-nearest layers. Although the strength of microscopic interactions changes monotonically with decreasing temperature, the effective interlayer interactions change nonmonotonically and give rise to a nonmonotonic change of the modulation period through various phases. Increased chirality changes the phase sequence.

We investigate the orientational order of transverse polarization vectors of long, stiff polymer molecules and their coupling to bond orientational and positional order in high density mesophases. Homogeneous ordering of transverse polarization vector promotes distortions in the hexatic phase, whereas inhomogeneous ordering precipitates crystallization of the 2D sections with different orientations of the transverse polarization vector on each molecule in the unit cell. We propose possible scenarios for going from the hexatic phase, through the distorted hexatic phase, to the crystalline phase with an orthorhombic unit cell observed experimentally for the case of DNA.

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.

This paper considers cellular processes that involve changes in membrane conformation. A general overview of the relationship between the mechanical properties of lamellar membranes and the shapes of vesicles and cells is given. Variational procedures are described for calculating the equilibrium shapes of simple vesicular objects, based on the assumption that these shapes correspond to the minimum of the sum of the membrane local and nonlocal bending energies. The two properties of closed lamellar membranes which could form a physical basis for biological processes axe proposed to be the symmetry breaking in vesicle shape behavior and vesicle budding. The cellular processes are discussed on the basis of the hypothesis that the shape behavior of simple vesicular objects may serve as a framework for their analysis. It is proposed that the description of certain cellular processes requires the inclusion of energy contributions additional to the membrane bending energy, and/or the involvement of cytoplasmic structures which exert forces on the membrane. Several specific examples are used to demonstrate that such generalizations may help reveal the functional role of certain cell constituents.

Electrostatic dipolar interactions between transversal polarizations of the finite and parallel surface smectic layers are shown to stabilize the anticlinic smectic-C surfaces in freely suspended smectic films formed from (anti) ferroelectric liquid crystals.

: Shapes of nearly cylindrical sections of axisymmetric phospholipid membranes are studied theoretically. Describing the shape of such sections by their deviation from a reference cylinder, the well-established shape equation for axisymmetric bilayer membranes is expanded in terms of this deviation, and it is then solved analytically. The phase diagram shows the resulting stationary shapes as functions of system parameters and external conditions, i.e. , the pressure difference across the membrane, the membrane tension, the difference between the tensions of the two monolayers, and the axial force acting on the vesicle. The accuracy of the approximate analytical solution is demonstrated by comparison with numerical results. The obtained analytical solution allows to extend the analysis to include shapes where numerical methods have failed.

The deposition of AgCl in the human tooth dentine was studied as a function of the time and dc electrical field using a scanning electron microscope and by measurements of the frequency-dependent complex dielectric constant. Dielectric properties of the tooth dentine can be well described by the model which was recently developed for the dielectric response of hydrating porous cement paste. The fractal dimension of the tooth dentine was determined by the electron microscopy and dielectric spectroscopy techniques.

Phenomenological model of chiral polar smectics is introduced with interactions up to the fourth neighboring layers. The minimization of the free energy gives three stable structures: the ferroelectric Sm C$^*$ phase, the antiferroelectric Sm C$^*_A$ phase and the hellicoidally modulated structure of the Sm C$^*_H$ phase. The phase Sm C$^*_\alpha$ can be recognized as the Sm C$^*_H$ phase below Sm A phase and as the Sm C$^*_{FI2}$ phase or as the Sm C$^*_{FI1}$ phase when appearing between the Sm C$^*$ phase and the Sm C$^*_A$ phase. Stability of these phases is analyzed and the phase diagram in the space of model parameters is presented.