Micromanipulation of adhesion of a Jurkat cell to a planar bilayer membrane containing lymphocyte function-associated antigen 3 molecules.

Cell adhesion plays a fundamental role in the organization of cells in differentiated organs, cell motility, and immune response. A novel micromanipulation method is employed to quantify the direct contribution of surface adhesion receptors to the physical strength of cell adhesion. In this technique, a cell is brought into contact with a glass-supported planar membrane reconstituted with a known concentration of a given type of adhesion molecules. After a period of incubation (5-10 min), the cell is detached from the planar bilayer by pulling away the pipette holding the cell in the direction perpendicular to the glass-supported planar bilayer. In particular, we investigated the adhesion between a Jurkat cell expressing CD2 and a glass-supported planar bilayer containing either the glycosyl-phosphatidylinositol (GPI) or the transmembrane (TM) isoform of the counter-receptor lymphocyte function-associated antigen 3 (LFA-3) at a concentration of 1,000 molecules/microns 2. In response to the pipette force the Jurkat cells that adhered to the planar bilayer containing the GPI isoform of LFA-3 underwent extensive elongation. When the contact radius was reduced by approximately 50%, the cell then detached quickly from its substrate. The aspiration pressure required to detach a Jurkat cell from its substrate was comparable to that required to detach a cytotoxic T cell from its target cell. Jurkat cells that had been separated from the substrate again adhered strongly to the planar bilayer when brought to proximity by micromanipulation. In experiments using the planar bilayer containing the TM isoform of LFA-3, Jurkat cells detached with little resistance to micromanipulation and without changing their round shape.

Retinoids increase cell-cell adhesion strength, beta-catenin protein stability, and localization to the cell membrane in a breast cancer cell line: a role for serine kinase activity.

In this study we show that a breast cancer cell line (SKBR3) that expresses no E-cadherin and very low levels of beta-catenin protein and exhibits a poorly adhesive phenotype in Matrigel responds to retinoic acid (RA) by a marked increase in epithelial differentiation. Specifically, treatment of cells with all-trans-RA, 9-cis-RA, or a RA receptor alpha-specific ligand resulted in a large increase in cell-cell adhesive strength and stimulated the formation of fused cell aggregates in Matrigel. A retinoid X receptor-specific ligand was ineffective. Exposure of cells to 9-cis-RA for as little as 4 h was sufficient to maintain the adhesive phenotype for at least 4 days. The effects of 9-cis-RA required protein and RNA synthesis, but were not mediated by factors secreted by stimulated cells or by direct cell contact and did not require serum. These 9-cis-RA-induced morphological effects were completely reversed by growing cells in 50 microM Ca2+, suggesting a mechanism involving a 9-cis-RA-induced increase in Ca(2+)-dependent adhesion. Consistent with this, beta-catenin protein levels were markedly elevated in the 9-cis-RA-treated cells, and beta-catenin became localized to a Triton-insoluble pool at regions of cell-cell contact. No change could be detected in beta-catenin steady state messenger RNA levels, but 9-cis-RA did increase beta-catenin protein stability. Treatment of cells with low calcium medium did not prevent the 9-cis-RA-induced increase in total beta-catenin protein, but did prevent its movement to a Triton-insoluble pool at the cell membrane. Among several kinase inhibitors, only the broad spectrum kinase inhibitor staurosporine and the protein kinase C inhibitor bisindoylmaleimide reversed the morphological changes induced by 9-cis-RA. Like treatment with low calcium medium, these inhibitors did not prevent the 9-cis-RA-induced increase in total beta-catenin protein levels, but completely prevented the movement of beta-catenin to the cell membrane. These results point to a role for beta-catenin and serine kinase activity in mediating the action of 9-cis-RA in epithelial differentiation.

Flow of particles along a deformable tube.

Slow viscous flow of rigid particles along a deformable tube of comparable diameter is considered as a possible model for some biological flows. Lubrication theory is assumed to be valid in the fluid region. The cylindrical tube is considered to be a thin elastic shell undergoing small deflections. The mean velocity of the flow is assumed to be maintained at a constant value by the application of a pressure difference over some length including the particle, or by an external force acting directly on the particle. Numerical results are obtained for the force required to maintain the motion and for the distribution of fluid pressure and thickness along the tube as a function of the diameter ratio, dimensionless velocity parameter and the shape of the particle. Effect of the bending resistance of the tube on the flow is also discussed.

Role of cytoskeleton and deformability in laminin-mediated cell rolling.

Recent mathematical models show that molecular events that mediate rolling interactions also have an impact on the stochastic features of rolling. In spherical cells, statistical fluctuations in cell displacement were shown to be an indication that only a few adhesion bonds are involved in rolling interactions. In this study, we investigated whether cell shape and cell deformability could also modulate the stochastic features of rolling. As an experimental model we considered the flow-initiated rolling of MCF-10 breast epithelial cells on laminin. The dynamic adhesion of MCF-10A cells to laminin, which involves integrin alpha 6 beta 4, occurs slow enough to allow for an accurate determination of the trajectories of rolling cells. The data from high-magnification videomicroscopy showed that cell shape, cell deformability, and the level of fluid shear stress were all strong determinants of the rolling velocity and the extent of fluctuations in the trajectory of rolling cells. MCF-10A cells with large surface projections rolled faster and wobbled more extensively than spherical cells under the same flow conditions. The extent of wobbling decreased and the variation of rolling velocity increased with increasing fluid shear stress. MCF-10A cells treated with cytochalasin B, which increased cell deformability and caused extensive blebbing without significantly altering surface expression of laminin integrins, reduced mean rolling velocity and increased its variance. Because leukocytes change shape as they roll in postcapillary blood venules at high shear rates, results indicate the need for further expanding the present biophysical models of rolling to the case of deformable cells.

The influence of doubly attached crossbridges on the mechanical behavior of skeletal muscle fibers under equilibrium conditions.

A simple model of a double-headed crossbridge is introduced to explain the retardation of force decay after an imposed stretch in skeletal muscle fibers under equilibrium conditions. The critical assumption in the model is that once one of the heads of a crossbridge is attached to one of the available actin sites, the attachment of the second head will be restricted to a level of strain determined by the attachment of the first head. The crossbridge structure, namely the connection of both heads of a crossbridge to the same tail region, is assumed to impose this constraint on the spatial configurations of crossbridge heads. The unique feature of the model is the prediction that, in the presence of a ligand (PPi, ADP, AMP-PNP) and absence of Ca2+, the halftime of force decay is many times larger than the inverse rate of detachment of a crossbridge head measured in solution. This prediction is in agreement with measured values of half-times of force decay in fibers under similar conditions (Schoenberg, M., and E. Eisenberg. 1985. Biophys. J. 48:863-871f). It is predicted that a crossbridge head is more likely to re-attach to its previously strained position than remain unattached while the other head is attached, leading to the slow decay of force. Our computations also show that the apparent cooperativity in crossbridge binding observed in experiments (Brenner, B., L. C. Yu, L. E. Greene, E. Eisenberg, and M. Schoenberg. 1986. Biophys. J. 50:1101-1108) can be partially accounted by the double-headed crossbridge attachment. Our model predictions fit the aforementioned data best when the crossbridge stiffness does not change significantly with the dissociation of one of the two attached heads. This observation suggests that crossbridge stiffness is determined either by the extensibility (flexibility) of the double helical tail region or its junction to the thick filament backbone.

Adhesion induced by mobile cross-bridges: steady state peeling of conjugated cell pairs.

Recent experiments on cell-cell adhesion indicate that (i) bonds between two cells migrate towards the region of conjugation during peeling, and (ii) cell membrane tension increases with the rate of peeling. Analytical methods that would allow the derivation of intrinsic parameters of adhesion from such experimental data have yet to be explored. In this study we introduce a specific adhesion model to investigate the complex interaction between rate of peeling, lateral diffusivity and the rate of detachment of bonds. Our analysis show that adhesive energy density increases with the rate of peeling and with lateral diffusivity of the bonds but decreases with increasing rate of detachment. The rate dependency of the adhesive energy is due to the modulation of the number density distribution of bonds by the speed of peeling.

Elastic properties of arteries and their influence on the cardiovascular system.

Pressure-volume relations of aorta and arteries are considered using a fiber-fluid continuum analysis. A Windkessel model is revised to investigate the effects of the exponential pressure-volume relation of the present study on the cardiovascular system. It is shown that the elastic properties of the fibers in large blood vessels play an important role in the circulation of blood in health and in disease.

Constitutive equations of skeletal muscle based on cross-bridge mechanism.

The statistical mechanics of cross-bridge action is considered in order to develop constitutive equations that express fiber tension as a function of degree of activation and time history of speed of contraction. The kinetic equation of A.F. Huxley (1) is generalized to apply to the partially activated state. The rate parameters of attachment and detachment, and cross-bridge compliance are assumed to be step functions of extension, x, with a finite number of discontinuities. This assumption enables integration of the kinetic equation and its moments with respect to x resulting in analytic equations from which x has been eliminated. When the constants in the rate parameters and the force function are chosen so that Hill's force-velocity relation and features of the transient kinetic and tension data can be fitted, the resulting cross-bridge mechanism is quite similar to the one proposed by Podolsky et al. (2). Because the derived constitutive equations simplify mathematical analysis, the influence of various cross-bridge parameters on the mechanical behavior of muscle fibers may be evaluated. For example (a) instantaneous elastic response (T0-T1) and the magnitude of rapid recovery (T2-T1) after a step length change can be adequately explained when the rate of attachment is assumed high for positive x. In that case T2 corresponds to the force generated by cross-bridges in the region of negative x. (b) Kinetic transients occur as a result of the jumps that exist in the distribution of attached cross-bridges during the isometric state. Because of the hyperbolic nature of the kinetic equation, these jumps propagate in the--x direction causing rapid changes in the speed of contraction. (c) When the number of actin sites available for attachment is assumed to depend on the degree of activation, computational results indicate that the speed of shortening is insensitive to the degree of activation at each relative load. (d) It is shown that during sinusoidal oscillation, the mean and second-order harmonics of the experimental force-time curve are strongly dependent on cross-bridge parameters. Therefore, significant information may be lost when the data is expanded into Fourier series and only the first term is considered.

Continuum rheology of muscle contraction and its application to cardiac contractility.

A set of constitutive equations is proposed to describe the mechanics of contraction of skeletal and heart muscle. Fiber tension is assumed to depend on the degree of chemical activation, the stretch ratio, and the rate of stretching of the fibers. The time rate of change of activation is governed by a differential equation. The proposed constitutive equations are used to model the time courses of isotonic and isometric twitches during contraction and relaxation phases of the muscle response to stimulation. Various contractility indices of the left ventricle are considered next by using the proposed constitutive equations. The present analysis introduces a new interpretation of the index of contractility (dP/dt)/P used in cardiac literature. It is shown that this index may not be related at all to the maximum speed of shortening and that it may be dependent on both preload and afterload. The development of pressure during isovolumetric contraction of the left ventricle is shown to be governed by a differential equation describing the time rate of change of tension during isometric contraction of myocardium fibers.

Cell-cell, cell-substrate adhesion: theoretical and experimental considerations.

Cell-cell adhesion plays a fundamental role in tissue and organ development, cell mediated immunity and blood flow. In the present study a micro-mechanical model of specific adhesion is presented. Analytical expressions are derived for the adhesive energy density (gamma) at zero speed of peeling for the cases of immobile (trapped) as well as laterally mobile bonds. It is shown that gamma increases in both cases with the increasing density of bonds and with the binding of affinity of unstressed bonds. In the case of laterally mobile bonds gamma also increases with the extent of peeling. The analytical results are shown to be valid whether or not one takes into account of the bending stiffness of adhering membranes. It is also shown that gamma does not depend on the functional form of bond elasticity. The effect of the speed of peeling on the number density distribution of attached bonds is considered next. Numerical solutions for the energy required to separate conjugated cell pairs are presented. The theoretical predictions are then used to analyze experimental data on red cell aggregation and adhesion between a cytotoxic-T cell and its target cell. The results show that the binding affinity of unstressed bonds and their number density before conjugation can be obtained from data on slow peeling of cell-pairs. The information on the diffusivity of bonds, their stiffness and their rates of attachment and detachment are more difficult to obtain, requiring a set of experiments with increasing rates of separation (conjugation) of cell-pairs.

Cell-cell conjugation. Transient analysis and experimental implications.

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.

Assessment of fiber strength in a urinary bladder by using experimental pressure volume curves: an analytical method.

In the present study, an analytical method is developed to deduce the constitutive equations of fibers embedded in a thick shell from the time-variant pressure volume curves obtained by experimental procedures. It is assumed that the spherical shell under consideration is composed of a fiber reinforced material and undergoes radial deflection, modeling the behavior of some biological shells such as urinary bladder. The fiber stress is expressed as a function of fiber strain, rate of strain and the degree of biochemical activation. The function form is chosen such that equations of mechanical equilibrium can be integrated analytically to yield chamber pressure as a function of chamber volume, time rate of change of volume and activation. Arbitrary coefficients appearing in the fiber stress-equation are also present in the resultant time-variant pressure-volume relation. These coefficients can be determined by curve-fitting commonly used clinical data such as cystometry measurements.

Static analysis of the left ventricle.

Static analysis of the left ventricle is developed to estimate the local stresses and deformations that occur during the heart cycle. The left ventricle is represented as a thick hollow tube composed of solid fibers embedded in an inviscid fluid matrix. A finite deformation analysis is developed to estimate the variation of the pressure, fiber tension and fiber extension across the thickness of the left ventricle. Pressure-volume relations are obtained for the diastolic and the systolic peak isovolumetric phases. The fiber stress distribution and pressure variation are estimated as a function of the initial fiber orientation distribution, relative thickness of the ventricle, inner volume of the ventricle and the various tension-extension relations proposed for the fibers of the heart muscle. It is concluded that the diastolic pressure-volume relation is not very sensitive to either the fiber orientation distribution or the thickness of the ventricle. However, the pumping efficiency of the modeled ventricle is shown to increase with increasing thickness of the modeled left ventricle and with increasing contractility of the heart muscle fibers.

The effect of cross-bridge clustering and head-head competition on the mechanical response of skeletal muscle under equilibrium conditions.

The effect of cross-bridge clustering and head-head competition on the mechanical response of skeletal muscle under equilibrium conditions is considered. For this purpose, the recent multiple site equilibrium cross-bridge model of Schoenberg (Schoenberg, M., 1985, Biophys. J., 48:467-475) is extended in accordance with the formalism of T.L. Hill (1974, Prog. Biophys, Mol. Biol., 28:267-340) to consider the case where groups of independent cross-bridge heads compete with each other for binding to multiple actin sites. Cooperative behavior between heads is not allowed. Computations indicate that for the double-headed cross-bridge with two independent equivalent heads, the time course of force decay after a stretch is similar to that for the single-headed cross-bridge; that is, the rate constant for force decay is approximately equal to the cross-bridge head detachment rate constant. The results also show that the force decay after a stretch becomes slower than the detachment rate constant of a single head when cross-bridge heads bind adjacently in clusters so that competition between heads for binding to the available actin sites increases. However, if one assumes that the detachment rate constant of an unstrained head in a fiber is comparable to that of an S1 molecule in solution, this effect is not large enough to explain why some of the rate constants for force decay after a stretch in rigor, or in the presence of ATP analogues such as adenyl-5'-yl imidodiphosphate, appear to be significantly slower than the detachment rate constant of S1 from actin in solution.

Modeling of time-variant coupling between left ventricle and aorta in cardiac cycle.

An analytical model is developed to study the interaction between the left ventricle and vascular system. Ventricular pressure is expressed as a function of the chamber volume, volumetric strain rate, and the degree of activation. A three-element Wind-kessel model is employed to represent the hydraulic properties of the vascular system. Conditions of interaction between the left ventricle and the vascular system are formulated in mathematical terms. Numerical solutions are obtained for the mechanical events occurring during a cardiac cycle as a function of time. The time variations of aortic pressure and ventricular volume predicted by the model compare well with the experimental results of Sunagawa and co-workers [Am. J. Physiol. 243 (Heart Circ. Physiol. 12): H346-H350, 1982, and Am. J. Physiol. 245 (Heart Circ. Physiol. 14): H773-H780, 1983]. Furthermore, the application of the present model to the experimental data has allowed the derivation of the intrinsic contractility parameters in these experiments. The unique features of this analytical model are that 1) it provides the time-variant pressure and volume curves of the left ventricle in relation to the aorta, 2) it generates information on the effects of heart rate on these hemodynamic parameters, and 3) it allows the derivation of intrinsic contractility parameters from experimental data.

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.

Physical response of collagen gels to tensile strain.

Extra cellular matrix, which provides physical support to epithelial and endothelial cells and to fibroblasts, also affects a number of important cell biological phenomena, such as cell motility and angiogenesis. Although type I collagen has long been recognized as the primary structural component of the extra cellular matrix, little is known about the physical properties of collagen gels. In this study, we used a servo-controlled linear actuator to impose quick stretches on dilute collagen gels. An axial strain imposed on the gel within few milliseconds resulted in a rapid development of gel tension in the direction of the strain. The gel tension then decayed toward a steady-state value within several seconds. The instantaneous gel stiffness increased and the relaxed gel stiffness decreased with the extent of gel stretching. These rheological parameters were also dependent on the density of the collagen network. Taken together the results indicated that collagen gels possess nonlinear viscoelastic properties.

Estimation of viscous dissipation inside an erythrocyte during aspirational entry into a micropipette.

Viscous dissipation inside the erythrocyte during its aspirational entry into a micropipette is analyzed. The motion of the intracellular fluid is approximated by a flow into the micropipette orifice from a half space (the portion of the erythrocyte outside the micropipette). The stream function and intracellular pressure (p) in the half space are obtained as a function of radial and axial positions near the orifice. Solution of the boundary value problem for a uniform stream entering a circular hole gives p = 2 eta HQ/pi R3p, where eta H is the intracellular viscosity, Q is the total discharge, and Rp is the pipette radius. The results indicate that the moving erythrocyte membrane helps to drive the intracellular fluid into the orifice. For normal erythrocytes, p is only approximately 0.5% of the total aspiration pressure (delta P). The contribution of p to delta P, however, may become significant when there is a large increase in eta H due to a markedly elevated intracellular hemoglobin concentration or an alteration of the physical state of hemoglobin.

A bladder contractility constant.

Muscle contractility can be characterized by two related properties: force and velocity. The initial velocity of a tetanic contraction is inversely related to preload. This was demonstrated experimentally by Hill and quantified in his well-known empiric equation. Subsequent investigators argued that a theoretical maximum contractile element velocity (V max) could be predicted from the rate of change of isometric force. V max has been applied clinically in heart studies, prompting others to use similar methods to evaluate bladder contractility. These attempts have so far been unsuccessful. The present study shows for whole canine bladders that the time to reach maximum isometric force from the moment of onset of active contraction is a constant independent of muscle length, preload, and maximum force. This can be expressed as a frequency constant (omega) whose calculation appears similar to that for V max. In contrast to V max, omega is obtained only from the active component of pressure.

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).