Aydin Tozeren

Strain Energy Function of Red Blood Cell Membranes

The several widely different values of the elastic modulus of the human red blood cell membrane which have been reported in the literature are incorporated into a single strain energy function consisting of two terms. One term gives the small stresses and low elastic modulus which is observed when the red cell membrane is deformed at constant area. The second term contributes a large isotropic stress dependent on the change of area. The strain energy function is applied to the process of sphering of red blood cells in a hypotonic solution. It is shown that a nearly perfect sphere can result even though the red blood cell membrane is homogeneous in all areas of the cell. Results pertinent to sieving and micropipette experiments are also explored.

Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane

The deformation of a portion of erythrocyte during aspirational entry into a micropipette has been analyzed on the basis of a constant area deformation of an infinite plane membrane into a cylindrical tube. Consideration of the equilibrium of the membrane at the tip of the pipette has generated the relation between the aspirated length and the dimensionless time during deformational entry as well as during relaxation after the removal of aspiration pressure. Experimental studies on deformation and relaxation of normal human erythrocytes were performed with the use of micropipettes and a video dimension analyzer which allowed the continuous recording of the time-courses. The deformation consisted of an initial rapid phase with a membrane viscosity (range 0.6 x 10(-4) to 4 x 10(-4) dyn.s/cm) varying inversely with the degree of deformation and a later slow phase with a high membrane viscosity (mean 2.06 x 10(-2) dyn.s/cm) which was not correlated with the degree of deformation. The membrane viscosity of the recovery phase after 20 s of deformation (mean 5.44 x 10(-4) dyn.s/cm) was also independent of the degree of deformation. When determined after a short period of deformation (e.g., 2 s), however, membrane viscosity of the recovery phase became lower and agreed with that of the deformation phase. These results suggest that the rheological properties of the membrane can undergo dynamic changes depending on the extent and duration of deformation, reflecting molecular rearrangement in response to membrane strain.

How do selectins mediate leukocyte rolling in venules

At the onset of inflammation, 20-80% of all leukocytes passing postcapillary venules roll along the endothelium. Recent blocking experiments with antibodies and soluble adhesion receptor molecules, as well as in vitro reconstitution experiments, suggest that leukocyte rolling is mediated by adhesion molecules that belong to the selectin family. What differentiates a selectin-counterreceptor interaction that leads to leukocyte rolling from others that mediate firm adhesion after static incubation but no adhesion when incubated under flow conditions? Here, we explore this question by introducing a quantitative biophysical model that is compatible with the laws of mechanics as applied to rolling leukocytes and the present biochemical and biophysical data on selectin mediated interactions. Our computational experiments point to an adhesion mechanism in which the rate of bond formation is high and the detachment rate low, except at the rear of the contact area where the stretched bonds detach at a high uniform rate. The bond length and bond flexibility play a critical role in enhancing leukocyte rolling at a wide range of fluid shear rates.

Flow past an array of cells that are adherent to the bottom plate of a flow channel

Abstract Parallel-plate flow channels are used extensively in cell-biological research to investigate cell-substrate adhesion. However, an analytical relationship between the fluid force acting on a cell that is adherent to the bottom plate of a channel and the flow rate into the channel is yet to be established. A finite-difference scheme was used to evaluate the three-dimensional laminar flow past an array of uniformly distributed cells that are adherent to the bottom plate of a parallel-plate flow channel. Computational results indicated that the fluid force acting on a spherical cell can be computed within 10% accuracy by using the solution given by Goldman et al . [Goldman, A. J., Cox, R. G. and Brenner, H., Slow viscous motion of a sphere parallel to a plane wall. I. Motion through quiescent fluid. Chem. Engng Sci. , 1967, 22 , 637–651. Goldman, A. J., Cox, R. G. and Brenner, H., Slow viscous motion of a sphere parallel to a plane wall. II. Couette flow. Chem. Engng Sci. , 1967, 22 , 653–660.] — for a single sphere in contact with a planar wall in infinite shear flow — when the ratio of the cell radius ( R S ) to the gap thickness between parallel plates ( h ) is less than (1/15). Goldman et al .s solution begins to significantly overestimate the actual fluid force as the ( R S / h ) ratio becomes larger than 1/15. When R S / h ) = 1/5, the fluid force computed by Goldman et al . is greater than the actual force by 30%. As an originally spherical cell aligns and elongates in the direction of flow, the fluid force acting on it decreases by 25%. In all cases, cell spreading leads to a more uniform distribution of fluid shear stress on the cell surface. Further computations indicate that fluid force on a spherical cell with surface projections (rough cell) is slightly smaller than that for a smooth spherical cell whose radius is equal to the maximum radial dimension of the rough cell.

Theoretical and experimental studies on cross-bridge migration during cell disaggregation

A micromanipulation method is used to determine the adhesive energy density (gamma) between pairs of cytotoxic T cells (F1) and their target cells (JY: HLA-A2-B7-DR4,W6). gamma is defined as the energy per unit area that must be supplied to reduce the region of contact between a conjugated cell pair. Our analysis of the data indicates that the force applied by the micropipette on the cell is not uniformly distributed throughout the contact region as we had previously assumed (Sung, K. L. P., L. A. Sung, M. Crimmins, S. J. Burakoff, and S. Chien. 1986. Science (Wash. DC). 234: 1405-1408), but acts only at the edges of the contact region. We show that gamma is not constant during peeling but increases with decreasing contact area of the conjugated cell pairs F1-JY, F1-F1, and JY-JY in contrast to the constancy of gamma for typical engineering adhesives. This finding supports the notion that the cross-linking protein molecules slide towards the conjugated area across the leading edge of the separation while remaining attached to both cells. Our mathematical analysis shows that the elastic energy stored in the cross-links by the membrane tensions balances the diffusive forces that act against cross-bridge migration. The binding affinity between F1-JY is found to be approximately 15-20 times larger than the corresponding affinity for F1-F1. The number of binding sites of F1 for attachment to JY is approximately the same for binding F1 to another F1 and vary between 10(5) and 10(6).

Micromanipulation of adhesion of phorbol 12-myristate-13-acetate-stimulated T lymphocytes to planar membranes containing intercellular adhesion molecule-1

This paper presents an analytical and experimental methodology to determine the physical strength of cell adhesion to a planar membrane containing one set of adhesion molecules. In particular, the T lymphocyte adhesion due to the interaction of the lymphocyte function associated molecule 1 on the surface of the cell, with its counter-receptor, intercellular adhesion molecule-1 (ICAM-1), on the planar membrane, was investigated. A micromanipulation method and mathematical analysis of cell deformation were used to determine (a) the area of conjugation between the cell and the substrate and (b) the energy that must be supplied to detach a unit area of the cell membrane from its substrate. T lymphocytes stimulated with phorbol 12-myristate-13-acetate (PMA) conjugated strongly with the planar membrane containing purified ICAM-1. The T lymphocytes attached to the planar membrane deviated occasionally from their round configuration by extending pseudopods but without changing the size of the contact area. These adherent cells were dramatically deformed and then detached when pulled away from the planar membrane by a micropipette. Detachment occurred by a gradual decrease in the radius of the contact area. The physical strength of adhesion between a PMA-stimulated T lymphocyte and a planar membrane containing 1,000 ICAM-1 molecules/micron 2 was comparable to the strength of adhesion between a cytotoxic T cell and its target cell. The comparison of the adhesive energy density, measured at constant cell shape, with the model predictions suggests that the physical strength of cell adhesion may increase significantly when the adhesion bonds in the contact area are immobilized by the actin cytoskeleton.

Interaction of stress and growth in a fibrous tissue

The influence of stress on the growth and remodeling of a soft biological tissue is considered. For this purpose, the soft tissue is idealized as a fiber network. The stress-free lengths of the fibers composing the network are not fixed as in an inert elastic solid, but are assumed to evolve as a result of growth and stress adaptation. Similarly, the topology of the fiber network may also evolve under the application of stress. A set of constitutive equations are proposed which relate the tissue stress to the deformation of the tissue as well as to its growth and microstructure. It is shown that distinctly different growth patterns which may arise during initial growth or wound healing can be modeled by the proposed mathematical analysis.

Viscoelastic behavior of erythrocyte membrane.

A nonlinear viscoelastic relation is developed to describe the viscoelastic properties of erythrocyte membrane. This constitutive equation is used in the analysis of the time-dependent aspiration of an erythrocyte membrane into a micropipette. Equations governing this motion are reduced to a nonlinear integral equation of the Volterra type. A numerical procedure based on a finite difference scheme is used to solve the integral equation and to match the experimental data. The data, aspiration length vs. time, is used to determine the relaxation function at each time step. The inverse problem of obtaining the time dependence of the aspiration length from a given relaxation function is also solved. Analytical results obtained are applied to the experimental data of Chien et al. 1978. Biophys. J. 24:463-487. A relaxation function similar to that of a four-parameter solid with a shear-thinning viscous term is proposed.

Constitutive equations of erythrocyte membrane incorporating evolving preferred configuration.

The erythrocyte membrane is modeled as a two-dimensional viscoelastic continuum that evolves under the application of stress. The present analysis of the erythrocyte membrane is motivated by the recent development of knowledge about its molecular structure. The constitutive equations proposed in the present analysis explain in a consistent manner the data on both the deformation and recovery phases of the micropipette experiment. The rheological equations of the present study are applied in a later section to the analysis of a plane membrane deformation that is quantitatively similar to the tank-treading motion of the erythrocytes in a shear field. The computations yield useful information on how the membrane viscosity becomes a more dominant feature in tank-treading motion. The material constants appearing in the proposed constitutive equations may be useful indications of the biochemical state of the membrane in health and disease.

Vinculin and Cell-Cell Adhesion

Vinculin, a 117-kDa protein, is a constituent of adhesion plaques and adherence junctions in non-muscle cells. We investigated the role of vinculin on the physical strength of cell-cell adhesion by conducting disaggregation assays on aggregates of parental wild-type F9 mouse embryonal carcinoma cells (clone BIM), two vinculin-depleted F9 cell lines, gamma 227 and gamma 229, and a reconstituted gamma 229 cell line (R3) that re-express vinculin. Immunoblotting demonstrated that the four cell lines used in the study had similar expressions of the cell-cell adhesion molecule E-cadherin and associated membrane proteins alpha- and beta-catenin. Double immunofluorescence analysis showed that, in contrast to the vinculin-null cell lines. BIM and R3 cells expressed abundant vinculin at the cell margins in adhesion plaques and in cell-cell margins that also contained actin. Laminar flow assays showed that both the vinculin-positive and vinculin-negative cell aggregates that were formed in culture in the course of 24 to 48 hours largely remained intact despite the imposition of shear flow at high shear rates. Since laminar flow imposed on cell aggregates act to separate cells from each other, our data indicate that F9 cells that were adherent to a substrate formed strong cell-cell adhesion bonds independent of vinculin expression. On the other hand, aggregates of vinculin-depleted gamma 229 and gamma 227 cells that were formed in suspension during a two-hour static incubation at 37 degrees C were desegregated more easily with the imposition of shear flow than the BIM and R3 cell aggregates formed under identical conditions. Loss of vinculin was associated with a reduction in cell-cell adhesion strength only among those cells lacking contact to a substrate. Overall, the results indicate that vinculin is not needed for forming strong cell-cell adhesion bonds between neighboring carcinoma cells which are adherent to the basal lamina.