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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.

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.

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.

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.

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.

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).

In the present study we investigate the transient conjugation of cell pairs by using a mathematical model. Macromolecules responsible for adhesion (bonds) are assumed to exist in two reversible states, attached and unattached, and exert a force elastic in nature only when they cross-link the two cell surfaces (attached state). Bonds form a link between the two cell surfaces only in the attached form. The unattached bridges are assumed laterally mobile in the plane of the cell membrane. Lateral mobility of attached bonds may be limited by structures on the undersurface of the cell membrane. Using this model we show that the bond density distribution between a cytotoxic T-cell (F-1) and a cancer cell (JY:HLA-A2-B7-DR4, W6) approaches equilibrium within 10 min, the incubation period used in experiments by Sung, K.L.P., L.A. Sung, M. Crimmins, S.J. Burakoff, and S. Chien (1986. Science [Wash. DC]. 234:1405–1408). If the diffusion coefficient of attached bonds is set equal to zero in the computations the model predictions indicate accumulation of bonds at the edge of conjugation. This prediction is consistent with present experimental data on lectin-induced red blood cell aggregation (Vayo, M., R. Skalak, P. Brunn, S. Usami, and S. Chien. 1987. Fed. Proc. 46:1043). It is concluded that significant features of micromanipulation data on specific adhesion can be explained by the diffusivity properties of bonds responsible for adhesion.