Variation in the velocity, deformation, and adhesion energy density of leukocytes rolling within venules

Leukocyte rolling along the endothelium in inflammation is caused by continuous formation and breakage of bonds between selectin adhesion molecules and their ligands. We investigated trauma-induced leukocyte rolling in venules (diameter, 23 to 58 microns; wall shear stress, 1.2 to 35 dyne/cm2) of the exteriorized rat mesentery using high-resolution intravital microscopy. While rolling, the leukocytes deformed into a tear-droplike shape. Deformation continued to increase with shear stress up to the highest values observed (35 dyne/cm2). Successive leukocytes had similar rolling velocities at the same axial positions along each vessel, suggesting that heterogeneity of endothelial adhesiveness is responsible for velocity variation. Adhesion energy density varied inversely with instantaneous rolling velocity and directly with instantaneous deformation. Adhesion energy density reached a maximum of 0.36 dyne/cm, similar to values found for lymphocyte function-associated antigen-1-dependent adhesion of stimulated T cells to isolated intercellular adhesion molecule-1. We conclude that selectin-mediated adhesion during rolling produces adhesion energy densities comparable to those observed for integrin-mediated adhesion events in other experimental systems.

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.

E-selectin-mediated dynamic interactions of breast- and colon-cancer cells with endothelial-cell monolayers

The molecular mechanisms involved in the dynamic interaction of human breast carcinoma cells with the endothelial cell lining of lymphatic vessels and post-capillary blood venules are largely unknown. In the present study, laminar flow assays were used to investigate the ability of various normal breast cells and of breast- and colon-tumor cells to adhere to human umbilical cord endothelial cell monolayers. MCF-10A breast, MCF-7 and T-47D breast-carcinoma and clone A, RKO, and HT-29 colon-carcinoma cells accumulated and rolled, in the presence of flow, on tumor necrosis factor (TNF)-stimulated but not on unstimulated endothelial cell monolayers. Non-tumor and tumor cells continued to form transient adhesions with TNF-stimulated endothelial cells even when the flow rate was increased to levels found in arteries. Incubation of TNF-stimulated endothelial cells with an E-selectin-specific monoclonal antibody (MAb) partially or completely inhibited dynamic interactions and diminished adhesion strength, whereas integrin beta 1- and integrin alpha 6-specific MAbs had no effect. A set of highly invasive breast-carcinoma cells (MDA-231, BT-549, HS-578t) neither adhered to nor rolled on resting or TNF-stimulated endothelial cell monolayers. However, after 5 min of static incubation, a fraction of these cells attached strongly to resting and TNF-stimulated endothelial cells and this static adhesion could not be blocked by an E-selectin-specific monoclonal antibody. Our results suggest that E-selectin is a major homing receptor in the metastasis of some breast and colon cancers.

Integrin alpha 6 beta 4 mediates dynamic interactions with laminin

We present here a novel form of dynamic adhesion in which both the integrin receptor and the ligand supporting dynamic adhesion have been identified. Laminar flow assays showed that laminin supported attachment of alpha 6 beta 4-positive cells in the presence of fluid shear stress (tau < or = 2 dyn/cm2), indicating that these cells adhered to laminin within a fraction of a second. Further increases in flow rate (3.5 dyn/cm2 < or = tau < or = 100 dyn/cm2) initiated rolling of attached cells in the direction of flow, suggesting that rapidly formed adhesion is reversible and repeatable. Laminin fragment E8, which interacts with alpha 6 integrins, supported dynamic attachment and rolling but extracellular matrix glycoprotein fibronectin did not. In cell lines that express alpha 6 beta 4 but not alpha 6 beta 1 an anti-alpha 6 monoclonal antibody inhibited attachment to laminin in the presence of flow and following 5 minutes of static incubation. Infusion of this antibody onto cells adherent to laminin-coated slides led to rapid detachment of cells from the substratum. An anti-beta 1 monoclonal antibody diminished adhesion strength following static incubation but did not inhibit rapid attachment and flow-initiated rolling. These results indicate that in some alpha 6 beta 4-expressing epithelial and carcinoma cell lines, integrin alpha 6 beta 4 mediates rapidly formed dynamic interactions with laminin.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.