Equilibrium mechanics of monolayered epithelium.

In order to fully understand the epithelial mechanics it is essential to integrate different levels of epithelial organization. In this work, we propose a theoretical approach for connecting the macroscopic mechanical properties of a monolayered epithelium to the mechanical properties at the cellular level. The analysis is based on the established mechanical models-at the macroscopic scale the epithelium is described within the mechanics of thin layers, while the cellular level is modeled in terms of the cellular surface (cortical) tension and the intercellular adhesion. The macroscopic elastic energy of the epithelium is linked to the energy of an average epithelial cell. The epithelial equilibrium state is determined by energy minimization and the macroscopic elastic moduli are calculated from deformations around the equilibrium. The results indicate that the epithelial equilibrium state is defined by the ratio between the adhesion strength and the cellular surface tension. The lower and the upper bounds for this ratio are estimated. If the ratio is small, the epithelium is cuboidal, if it is large, the epithelium becomes columnar. Importantly, it is found that the cellular cortical tension and the intercellular adhesion alone cannot produce the flattened squamous epithelium. Any difference in the surface tension between the apical and basal cellular sides bends the epithelium towards the side with the larger surface tension. Interestingly, the analysis shows that the epithelial area expansivity modulus and the shear modulus depend only on the cellular surface tension and not on the intercellular adhesion. The results are presented in a general analytical form, and are thus applicable to a variety of monolayered epithelia, without relying on the specifics of numerical finite-element methods. In addition, by using the standard theoretical tools for multi-laminar systems, the results can be applied to epithelia consisting of layers with different mechanical properties.

The response of giant phospholipid vesicles to pore-forming peptide melittin.

The interaction between the pore-forming peptide melittin (MLT) and giant phospholipid vesicles was explored experimentally. Micromanipulation and direct optical observation of a vesicle (loaded with sucrose solution and suspended in isomolar glucose solution) enabled the monitoring of a single vesicle response to MLT. Time dependences of the vesicle size, shape and the composition of the inner solution were examined at each applied concentration of MLT (in the range from 1 to 60 microg/ml). The response varied with MLT concentration from slight perturbation of the membrane to disintegration of the vesicle. A model for MLT-vesicle interaction is proposed that explains the observed phenomena in the entire span of MLT concentrations and is consistent with deduced underlying mechanisms of MLT action: trans-membrane positioning and dimerization of MLT, the lipid flow from the outer to the inner membrane leaflet induced by MLT translocation, formation of pores and the consequent transport of small molecules through the membrane. The results of the theoretical analysis stress the role of dimers in the MLT-membrane interaction and demonstrate that the MLT-induced membrane permeability for sugar molecules in this experimental set-up depends on both MLT concentration and time.

A novel strain energy relationship for red blood cell membrane skeleton based on spectrin stiffness and its application to micropipette deformation.

Red blood cell (RBC) membrane skeleton is a closed two-dimensional elastic network of spectrin tetramers with nodes formed by short actin filaments. Its three-dimensional shape conforms to the shape of the bilayer, to which it is connected through vertical linkages to integral membrane proteins. Numerous methods have been devised over the years to predict the response of the RBC membrane to applied forces and determine the corresponding increase in the skeleton elastic energy arising either directly from continuum descriptions of its deformation, or seeking to relate the macroscopic behavior of the membrane to its molecular constituents. In the current work, we present a novel continuum formulation rooted in the molecular structure of the membrane and apply it to analyze model deformations similar to those that occur during aspiration of RBCs into micropipettes. The microscopic elastic properties of the skeleton are derived by treating spectrin tetramers as simple linear springs. For a given local deformation of the skeleton, we determine the average bond energy and define the corresponding strain energy function and stress-strain relationships. The lateral redistribution of the skeleton is determined variationally to correspond to the minimum of its total energy. The predicted dependence of the length of the aspirated tongue on the aspiration pressure is shown to describe the experimentally observed system behavior in a quantitative manner by taking into account in addition to the skeleton energy an energy of attraction between RBC membrane and the micropipette surface.

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.

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.

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.

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 cooperative role of membrane skeleton and bilayer in the mechanical behaviour of red blood cells.

Red blood cell (RBC) shape, behaviour and deformability can be consistently accounted for by a model for the elastic properties of the RBC membrane that includes the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending. The role of the corresponding energy terms in different RBC shape and deformation situations is analyzed. RBC shape transformations are compared to the shape transformations of phospholipid vesicles that are driven by the difference between the equilibrium areas of the bilayer leaflets (DeltaA0). It is deduced that the skeleton energy contributions play a crucial role in the formation of an echinocyte. The effect of a transformation of the natural biconcave RBC shape into an echinocyte on its resistance to entry into capillary-sized cylindrical tubes is analyzed. It is shown that, during the aspiration of an echinocyte into a pipette, there are two competing skeleton deformation effects, which arise due to skeleton density changes, one due to spicule formation and the other due to deformation induced by micropipette aspiration. Furthermore, the shift of the observed dependence of the projection length on the aspiration pressure of more crenated cells towards higher aspiration pressures can be accounted for by an increase of the equilibrium area difference DeltaA0 and consequent modification of the nonlocal contribution to the cell elastic energy.

Electric-field-induced transition between the anticlinic and the synclinic smectic-C surfaces in free-standing films.

Anticlinic smectic-C surfaces were found experimentally as ground state structures in free-standing films made of smectic liquid crystals with no anticlinic bulk phases. A mean-field interpretation of this observation is given within a discrete phenomenological model of antiferroelectric liquid crystals, which additionally considers the enhanced order present at the surfaces of the free-standing films. The temperature dependence of the critical electric field that drives the transition between the anticlinic and synclinic smectic-C surfaces is evaluated, and fair agreement with the experimental data is found.

Devil's staircase and harmless staircase in the smectic-C*alpha phase in an electric field.

The unwinding of the short pitch helical smectic-C*alpha structure in an external electric field is studied within a discrete phenomenological model. It is found that the pitch increases quasicontinuously at low electric fields and is commensurate with the smectic layer thickness at any field. The sequence of stable structures recalls the once popular and then abandoned devil's staircase model. At larger fields the pitch grows discontinuously in steps of one smectic layer, forming a harmless staircase. Taking into account the achiral next-nearest-layer interactions the final transition to the unwound structure is found to be discontinuous.

Mechanism of sign inversion of spontaneous polarization in ferroelectric SmC* liquid crystals.

The ferroelectric liquid crystal FLC-117, which is known to exhibit at a certain temperature the sign inversion of spontaneous polarization P(s), is studied under an electric field. From the analysis of the electro-optic response and the direct texture observations, it is concluded that the inversion temperature of P(s) has the applied voltage dependence. To interpret our experimental result, we introduce a coupling term between the molecular dipole moments and the magnitude of the applied electric fields to the asymmetric rotational potential about the molecular long axis. The simulated results using this potential are in accordance with our experimental result.

Theoretical analysis of continuous pitch evolution and reversed phase sequence in antiferroelectric liquid crystals.

Recent studies reported continuous shortening of the pitch from more than four layers to less than four layers in the helicoidally modulated tilted Sm C(alpha)* phase. In a different system, the reversed phase sequence was found: the ferroelectric tilted Sm C* phase appeared below the four-layer Sm CFI2* phase upon cooling. In this contribution we quantitatively explain the behavior within the discrete phenomenological model and we found that both behaviors are the consequence of the same reason: the quadrupolar interlayer interactions.

Shape behavior of lipid vesicles as the basis of some cellular processes.

The basic principles that govern the shape behavior of phospholipid vesicle shapes are discussed. The important membrane parameters of the system are defined by presenting the expressions for the relevant contributions to the system's mechanical energy. In the description of the rather unique shape behavior of lipid vesicles, the emphasis is on providing a qualitative understanding of the dependence of vesicle shape on the parameters of the system. The vesicle shape behavior is then related to biologically important phenomena. Some examples are given of how the results of the shape behavior of lipid vesicles can be applied to the analysis of cellular systems. Red blood cell shape and shape transformations, vesicle fission and fusion processes, and the phenomenon of cellular polarity are considered. It is reasoned that the current biological processes that involve changes of membrane conformation may have their origin in the general shape behavior of closed lamellar membranes.

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.

Shapes of phospholipid [correction of phosholipid] vesicles with beadlike protrusions.

Giant phospholipid vesicles obtained by the method of electroformation were observed by the phase contrast microscope. Most of these vesicles contain a protrusion which shortens in a slow shape transformation process until it is absorbed into the main vesicle body. We are concerned with the last stages of this shape transformation process, where the protrusions attain a beadlike shape. The number of "beads" decreases one by one in consecutive steps, and it is demonstrated that each such step consists of two distinguishable phases. During the first phase the beadlike shape does not change and the necks connecting the "beads" are narrow. During the second phase the width of the protrusion necks increases. On the basis of the assumption that these shape transformations are driven by the decrease of the equilibrium difference between the outer and the inner membrane monolayers areas, the system behavior is analyzed in terms of the generalized bilayer couple model. The theoretical results confirm the observed time sequence: at a given number of "beads" the protrusion has in the first phase the shape that consists of spheres connected by infinitesimal necks, and during the second phase the protrusion is a single prolate unit with open necks. The discrepancies between the observed and the predicted widths of the necks are interpreted by the repulsive forces between the neighboring "beads" induced by the membrane thermal fluctuations. The analysis presented extends the existing catalog of vesicle shapes to the region of larger differences between the areas of membrane monolayers, and confirms the applicability of the generalized bilayer couple model to the description of the shape behavior of phospholipid vesicles containing beadlike protrusions.