Detachment of agglutinin-bonded red blood cells. II. Mechanical energies to separate large contact areas.

As detailed in a companion paper (Berk, D., and E. Evans. 1991. Biophys. J. 59:861-872), a method was developed to quantitate the strength of adhesion between agglutinin-bonded membranes without ambiguity due to mechanical compliance of the cell body. The experimental method and analysis were formulated around controlled assembly and detachment of a pair of macroscopically smooth red blood cell surfaces. The approach provides precise measurement of the membrane tension applied at the perimeter of an adhesive contact and the contact angle theta c between membrane surfaces which defines the mechanical leverage factor (1-cos theta c) important in the definition of the work to separate a unit area of contact. Here, the method was applied to adhesion and detachment of red cells bound together by different monoclonal antibodies to red cell membrane glycophorin and the snail-helix pomatia-lectin. For these tests, one of the two red cells was chemically prefixed in the form of a smooth sphere then equilibrated with the agglutinin before the adhesion-detachment procedure. The other cell was not exposed to the agglutinin until it was forced into contact with the rigid cell surface by mechanical impingement. Large regions of agglutinin bonding were produced by impingement but no spontaneous spreading was observed beyond the forced contact. Measurements of suction force to detach the deformable cell yielded consistent behavior for all of the agglutinins: i.e., the strength of adhesion increased progressively with reduction in contact diameter throughout detachment. This tension-contact diameter behavior was not altered over a ten-fold range of separation rates. In special cases, contacts separated smoothly after critical tensions were reached; these were the highest values attained for tension. Based on measurements reported in another paper (Evans et al. 1991. Biophys. J. 59:838-848) of the forces required to rupture molecular-point attachments, the density of cross-bridges was estimated with the assumption that the tension was proportional to the discrete rupture force x the number of attachments per unit length. These estimates showed that only a small fraction of agglutinin formed cross-bridges at initial assembly and increased progressively with separation. When critical tension levels were reached, it appeared that nearly all local agglutinin was involved as cross-bridges. Because one cell surface was chemically fixed, receptor accumulation was unlikely; thus, microscopic "roughness" and steric repulsion probably modulated formation of cross-bridges on initial contact.(ABSTRACT TRUNCATED AT 400 WORDS)     

Mechanics of spreading cells probed by atomic force microscopy

Cellular adhesion and motility are fundamental processes in biological systems such as morphogenesis and tissue homeostasis. During these processes, cells heavily rely on the ability to deform and supply plasma membrane from pre-existing membrane reservoirs, allowing the cell to cope with substantial morphological changes. While morphological changes during single cell adhesion and spreading are well characterized, the accompanying alterations in cellular mechanics are scarcely addressed. Using the atomic force microscope, we measured changes in cortical and plasma membrane mechanics during the transition from early adhesion to a fully spread cell. During the initial adhesion step, we found that tremendous changes occur in cortical and membrane tension as well as in membrane area. Monitoring the spreading progress by means of force measurements over 2.5 h reveals that cortical and membrane tension become constant at the expense of excess membrane area. This was confirmed by fluorescence microscopy, which shows a rougher plasma membrane of cells in suspension compared with spread ones, allowing the cell to draw excess membrane from reservoirs such as invaginations or protrusions while attaching to the substrate and forming a first contact zone. Concretely, we found that cell spreading is initiated by a transient drop in tension, which is compensated by a decrease in excess area. Finally, all mechanical parameters become almost constant although morphological changes continue. Our study shows how a single cell responds to alterations in membrane tension by adjusting its overall membrane area. Interference with cytoskeletal integrity, membrane tension and excess surface area by administration of corresponding small molecular inhibitors leads to perturbations of the spreading process.     

Leukocyte rolling on P-selectin: a three-dimensional numerical study of the effect of cytoplasmic viscosity

Rolling leukocytes deform and show a large area of contact with endothelium under physiological flow conditions. We studied the effect of cytoplasmic viscosity on leukocyte rolling using our three-dimensional numerical algorithm that treats leukocyte as a compound droplet in which the core phase (nucleus) and the shell phase (cytoplasm) are viscoelastic fluids. The algorithm includes the mechanical properties of the cell cortex by cortical tension and considers leukocyte microvilli that deform viscoelastically and form viscous tethers at supercritical force. Stochastic binding kinetics describes binding of adhesion molecules. The leukocyte cytoplasmic viscosity plays a critical role in leukocyte rolling on an adhesive substrate. High-viscosity cells are characterized by high mean rolling velocities, increased temporal fluctuations in the instantaneous velocity, and a high probability for detachment from the substrate. A decrease in the rolling velocity, drag, and torque with the formation of a large, flat contact area in low-viscosity cells leads to a dramatic decrease in the bond force and stable rolling. Using values of viscosity consistent with step aspiration studies of human neutrophils (5-30 Pa·s), our computational model predicts the velocities and shape changes of rolling leukocytes as observed in vitro and in vivo.     

A sensitive measure of surface stress in the resting neutrophil.

The simplest parameterized model of the "passive" or "resting receptive" neutrophil views the cell as being composed of an outer cortex surrounding an essentially liquid-like highly viscous cytoplasm. This cortex has been measured to maintain a small persistent tension of approximately 0.035 dyn/cm (Evans and Yeung. 1989. Biophys. J. 56:151-160) and is responsible for recovering the spherical shape of the cell after large deformation. The origin of the cortical tension is at present unknown, but speculations are that it may be an active process related to the sensitivity of a given cell to external stimulation and the "passive-active" transition. In order to characterize further this feature of the neutrophil we have used a new micropipet manipulation method to give a sensitive measure of the surface stress as a function of the surface area dilation of the highly ruffled cellular membrane. In the experiment, a single cell is driven down a tapered pipet in a series equilibrium deformation positions. Each equilibrium position represents a balance between the stress in the membrane and the pressure drop across the cell. For most cells that seemed to be "passive," as judged by their spherical appearance and lack of pseudopod activity, area dilations of approximately 30% were accompanied by only a small increase in the membrane tension, indicative of a very small apparent elastic area expansion modulus (approximately 0.04 dyn/cm). Extrapolations back to zero area dilation gave a value for the tension in the resting membrane of 0.024 +/- 0.003 dyn/cm, in close agreement with earlier measures.(ABSTRACT TRUNCATED AT 250 WORDS)     

A theoretical analysis for the effect of focal contact formation on cell-substrate attachment strength.

For many cell types, growth, differentiation, and motility are dependent on receptor-mediated adhesion to ligand-coated surfaces. Focal contacts are strong, specialized, adhesive connections between cell and substrate in which receptors aggregate and connect extracellular ligand to intracellular cytoskeletal molecules. In this paper, we present a mathematical model to examine how focal contact formation affects cellular adhesive strength. To calculate adhesive strength with and without focal contacts, we use a one-dimensional tape peeling analysis to determine the critical tension necessary to peel the membrane. Receptor-ligand bonds are modeled as adhesive springs. In the absence of focal contacts, we derive analytic expressions for the critical tension at low and high ligand densities and show how membrane morphology affects adhesion. Then, focal contacts are modeled as cytoplasmic nucleation centers which bind adhesion receptors. The extent of adhesive strengthening upon focal contact formation depends on the elastic rigidity of the cytoskeletal connections, which determines the structural integrity of the focal contact itself. We consider two limits to this elasticity, very weak and rigid. Rigid cytoskeletal connections give much greater attachment strengths. The dependence of attachment strength on measurable model parameters is quite different in these two limits, which suggests focal contact structure might be deduced from properly performed adhesion experiments. Finally, we compare our model to the adhesive strengthening response reported for glioma cell adhesion to fibronectin (Lotz et al., 1989. J. Cell Biol. 109:1795-1805). Our model successfully predicts the observed detachment forces at 4 degrees C and yields values for the number of fibronectin receptors per glioma cell and the density of cytoskeletal connection molecules (talin) involved in receptor clusters which are consistent with measurements for other cell types. Comparison of the model with data at 37 degrees C suggests that while cytoskeletal cross-linking and clustering of fibronectin receptors significantly increases adhesion strength, specific glioma cell-substratum attachment sites possess little mechanical rigidity and detach through a peeling mechanism, consistent with the view that these sites of < or = 15 nm cell-substrate separation are precursors to fully formed, elastically rigid focal contacts.     

A semianalytical model to study the effect of cortical tension on cell rolling

Cell rolling on the vascular endothelium plays an important role in trafficking of leukocytes, stem cells, and cancer cells. We describe a semianalytical model of cell rolling that focuses on the microvillus as the unit of cell-substrate interaction and integrates microvillus mechanics, receptor clustering, force-dependent receptor-ligand kinetics, and cortical tension that enables incorporation of cell body deformation. Using parameters obtained from independent experiments, the model showed excellent agreement with experimental studies of neutrophil rolling on P-selectin and predicted different regimes of cell rolling, including spreading of the cells on the substrate under high shear. The cortical tension affected the cell-surface contact area and influenced the rolling velocity, and modulated the dependence of rolling velocity on microvillus stiffness. Moreover, at the same shear stress, microvilli of cells with higher cortical tension carried a greater load compared to those with lower cortical tension. We also used the model to obtain a scaling dependence of the contact radius and cell rolling velocity under different conditions of shear stress, cortical tension, and ligand density. This model advances theoretical understanding of cell rolling by incorporating cortical tension and microvillus extension into a versatile, semianalytical framework.     

Neutrophil adhesive contact dependence on impingement force

Neutrophil capture and recruitment from the circulation requires the formation of specific receptor/ligand bonds under hydrodynamic forces. In the present study we examine bond formation between beta2-integrins on neutrophils and immobilized ICAM-1 while using micropipettes to control the force of contact between the cell and substrate. Magnesium was used to induce the high affinity conformation of the integrins, and bond formation was assessed by measuring the probability of adhesion during repeated contacts. Increasing the impingement force caused an increase in the contact area and led to a proportional increase in adhesion probability (from approximately 20 to 50%) over the range of forces tested (50-350 pN). In addition, different-sized beads were used to change the force per unit area in the contact zone (contact stress). We conclude that for a given contact stress, the rate of bond formation increases linearly with contact area, but that increasing contact stress results in higher intrinsic rates of bond formation.     

Viscosity of passive human neutrophils undergoing small deformations.

At issue is the type of constitutive equation that can be used to describe all possible types of deformation of the neutrophil. Here a neutrophil undergoing small deformations is studied by aspirating it into a glass pipet with a diameter that is only slightly smaller than the diameter of the spherically shaped cell. After being held in the pipet for at least seven seconds, the cell is rapidly expelled and allowed to recover its undeformed, spherical shape. The recovery takes approximately 15 s. An analysis of the recovery process that treats the cell as a simple Newtonian liquid drop with a constant cortical (surface) tension gives a value of 3.3 x 10(-5) cm/s for the ratio of the cortical tension to cytoplasmic viscosity. This value is about twice as large as a previously published value obtained with the same model from studies of large deformations of neutrophils. This discrepancy indicates that the cytoplasmic viscosity decreases as the amount of deformation decreases. An extrapolated value for the cytoplasmic viscosity at zero deformation is approximately 600 poise when a value for the cortical tension of 0.024 dyn/cm is assumed. Clearly the neutrophil does not behave like a simple Newtonian liquid drop in that small deformations are inherently different from large deformations. More complex models consisting either of two or more fluids or multiple shells must be developed. The complex structure inside the neutrophil is shown in scanning electron micrographs of osmotically burst cells and cells whose membrane has been dissolved away.     

Passive mechanical behavior of human neutrophils: effect of cytochalasin B.

Actin is a ubiquitous protein in eukaryotic cells. It plays a major role in cell motility and in the maintenance and control of cell shape. In this article, we intend to address the contribution of actin to the passive mechanical properties of human neutrophils. As a framework for assessing this contribution, the neutrophil is modeled as a simple viscous fluid drop with a constant cortical ("surface") tension. The reagent cytochalasin B (CTB) was used to disrupt the F-actin structure, and the neutrophil cortical tension and cytoplasmic viscosity were evaluated by single-cell micropipette aspiration. The cortical tension was calculated by simple force balance, and the viscosity was calculated according to a numerical analysis of the cell entry into the micropipette. CTB reduced the cell cortical tension in a dose-dependent fashion: by 19% at a concentration of 3 microM and by 49% at 30 microM. CTB also reduced the cytoplasmic viscosity by approximately -25% at a concentration of 3 microM and by approximately 65% at a concentration of 30 microM when compared at the same aspiration pressures. All three groups of neutrophils, normal cells, and cells treated with either 3 or 30 microM CTB, exhibited non-Newtonian behavior, in that the apparent viscosity decreased with increasing shear rate. The dependence of the cytoplasmic viscosity on deformation rate can be described empirically by mu = mu c(gamma m/gamma c)-b, where mu is cytoplasmic viscosity, gamma m is mean shear rate, mu c is the characteristic viscosity at the characteristic shear rate gamma c, and b is a material coefficient.(ABSTRACT TRUNCATED AT 250 WORDS)     

Shear induced adhesion: contact mechanics of biological spatula-like attachment devices

Most biological hairy adhesive systems of insects, arachnids, and reptiles, involved in locomotion, rely not on flat punches on their tips, but rather on spatulate structures. Several hypotheses have been previously proposed to explain the functional importance of this particular contact geometry: (1) enhancement of adaptability to the rough substrate; (2) contact formation by shear force rather than by normal load; (3) increase in total peeling line due to the use of an array of multiple spatulae; (4) contact breakage by peeling off. In the present paper, we used numerical approach to study dynamics of spatulate tips during contact formation on rough substrates. The model clearly demonstrates that the contact area increases under applied shear force, especially when spatulae are misaligned prior to the contact formation. Applied shear force has an optimum describing the situation when maximal contact is formed but no slip occurs. At such equilibrium, maximal adhesion can be generated. This principle manifests the crucial role of spatulate terminal elements in biological fibrillar adhesion.     

Affinity of red blood cell membrane for particle surfaces measured by the extent of particle encapsulation.

An experimental technique and a simple analysis are presented that can be used to quantitate the affinity of red blood cell membrane for surfaces of small beads or microsomal particles up to 3 micrometers Diam. The technique is demonstrated with an example of dextran-mediated adhesion of small spherical red cell fragments to normal red blood cells. Cells and particles are positioned for contact by manipulation with glass micropipets. The mechanical equilibrium of the adhesive contact is represented by the variational expression that the decrease in interfacial free energy due to a virtual increase in contact area is balanced by the increase in elastic energy of the membrane due to virtual deformation. The surface affinity is the reduction in free energy per unit area of the interface associated with the formation of adhesive contact. From numerical computations of equilibrium configurations, the surface affinity is derived as a function of the fractional extent of particle encapsulation. The range of surface affinities for which the results are applicable is increased over previous techniques to several times the value of the elastic shear modulus. It is shown that bending rigidity of the membrane has little effect on the analytical results for particles 1--3 micrometers Diam and that results are essentially the same for both cup- and disk-shaped red cells. A simple analytical model is shown to give a good approximation for surface affinity (normalized by the elastic shear modulus) as a function of the fractional extent of particle encapsulation. The model predicts that a particle would be almost completely vacuolized for surface affinities greater than or equal to 10 times the elastic shear modulus. Based on an elastic shear modulus of 6.6 x 10(-3) dyn/cm, the range for the red cell-particle surface affinity as measured by this technique is from approximately 7 x 10(-4) to 7 x 10(-2) erg/cm2. Also, an approximate relation is derived for the level of surface affinity necessary to produce particle vacuolization by a phospholipid bilayer surface which possesses bending rigidity and a fixed tension.     

Mechanical forces induced by the transendothelial migration of human neutrophils

The mechanisms regulating neutrophil transmigration of vascular endothelium are not fully elucidated, but involve neutrophil firm attachment and passage through endothelial cell-cell junctions. The goal of this study was to characterize the tangential forces exerted by neutrophils during transendothelial migration at cell-cell junctions using an in vitro laminar shear flow model in which confluent activated endothelium is grown on a microfabricated pillar substrate. The tangential forces are deduced from the measurement of pillar deflection beneath the endothelial cell-cell junction as neutrophils transmigrate. The force diagram displays an initial force increase, which coincides with neutrophil penetration into the intercellular space and formation of a gap in VE-cadherin staining. This is followed by a rapid and large increase of traction forces exerted by endothelial cells on the substrate in response to the transmigration process and the disruption of cell-cell contacts. The average maximum force exerted by an actively transmigrating neutrophil is three times higher than the force generated by an adherent neutrophil that does not transmigrate. Furthermore, we show that substrate rigidity can modify the mechanical forces induced by the transmigration of a neutrophil through the endothelium. Our data suggest that the force induced by neutrophil transmigration plays a key role in the disruption of endothelial adherens junctions.     

Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism

The transition of cell-matrix adhesions from the initial punctate focal complexes into the mature elongated form, known as focal contacts, requires GTPase Rho activity. In particular, activation of myosin II-driven contractility by a Rho target known as Rho-associated kinase (ROCK) was shown to be essential for focal contact formation. To dissect the mechanism of Rho-dependent induction of focal contacts and to elucidate the role of cell contractility, we applied mechanical force to vinculin-containing dot-like adhesions at the cell edge using a micropipette. Local centripetal pulling led to local assembly and elongation of these structures and to their development into streak-like focal contacts, as revealed by the dynamics of green fluorescent protein-tagged vinculin or paxillin and interference reflection microscopy. Inhibition of Rho activity by C3 transferase suppressed this force-induced focal contact formation. However, constitutively active mutants of another Rho target, the formin homology protein mDia1 (Watanabe, N., T. Kato, A. Fujita, T. Ishizaki, and S. Narumiya. 1999. Nat. Cell Biol. 1:136-143), were sufficient to restore force-induced focal contact formation in C3 transferase-treated cells. Force-induced formation of the focal contacts still occurred in cells subjected to myosin II and ROCK inhibition. Thus, as long as mDia1 is active, external tension force bypasses the requirement for ROCK-mediated myosin II contractility in the induction of focal contacts. Our experiments show that integrin-containing focal complexes behave as individual mechanosensors exhibiting directional assembly in response to local force.     

Mechanical Checkpoint For Persistent Cell Polarization In Adhesion-Naive Fibroblasts

Cell polarization is a fundamental biological process implicated in nearly every aspect of multicellular development. The role of cell-extracellular matrix contacts in the establishment and the orientation of cell polarity have been extensively studied. However, the respective contributions of substrate mechanics and biochemistry remain unclear. Here we propose a believed novel single-cell approach to assess the minimal polarization trigger. Using nonadhered round fibroblast cells, we show that stiffness sensing through single localized integrin-mediated cues are necessary and sufficient to trigger and direct a shape polarization. In addition, the traction force developed by cells has to reach a minimal threshold of 56 ± 1.6 pN for persistent polarization. The polarization kinetics increases with the stiffness of the cue. The polarized state is characterized by cortical actomyosin redistribution together with cell shape change. We develop a physical model supporting the idea that a local and persistent inhibition of actin polymerization and/or myosin activity is sufficient to trigger and sustain the polarized state. Finally, the cortical polarity propagates to an intracellular polarity, evidenced by the reorientation of the centrosome. Our results define the minimal adhesive requirements and quantify the mechanical checkpoint for persistent cell shape and organelle polarization, which are critical regulators of tissue and cell development.     

Mechanical Checkpoint For Persistent Cell Polarization In Adhesion-Naive Fibroblasts

Cell polarization is a fundamental biological process implicated in nearly every aspect of multicellular development. The role of cell-extracellular matrix contacts in the establishment and the orientation of cell polarity have been extensively studied. However, the respective contributions of substrate mechanics and biochemistry remain unclear. Here we propose a believed novel single-cell approach to assess the minimal polarization trigger. Using nonadhered round fibroblast cells, we show that stiffness sensing through single localized integrin-mediated cues are necessary and sufficient to trigger and direct a shape polarization. In addition, the traction force developed by cells has to reach a minimal threshold of 56 ± 1.6 pN for persistent polarization. The polarization kinetics increases with the stiffness of the cue. The polarized state is characterized by cortical actomyosin redistribution together with cell shape change. We develop a physical model supporting the idea that a local and persistent inhibition of actin polymerization and/or myosin activity is sufficient to trigger and sustain the polarized state. Finally, the cortical polarity propagates to an intracellular polarity, evidenced by the reorientation of the centrosome. Our results define the minimal adhesive requirements and quantify the mechanical checkpoint for persistent cell shape and organelle polarization, which are critical regulators of tissue and cell development.     

Time-dependent recovery of passive neutrophils after large deformation.

Experiments are performed in which a passive human neutrophil is deformed into an elongated "sausage" shape by aspirating it into a small glass pipette. When expelled from the pipette the neutrophil recovers its natural spherical shape in approximately 1 minute. This recovery process is analyzed according to a Newtonian, liquid-drop model in which a variational method is used to simultaneously solve the hydrodynamic equations for low Reynolds-number flow and the equations for membrane equilibrium with a constant membrane tension. The theoretical model gives a good fit to the experimental data for a ratio of membrane cortical tension to cytoplasmic viscosity of approximately 1.7 x 10(-5) cm/s (0.17 micron/s). However, when the cell is held in the pipette for only a short time period of 5 s or less, and then expelled, the cell undergoes an initial, rapid elastic rebound suggesting that the cell behaves in this instance as a Maxwell viscoelastic liquid rather than a Newtonian liquid with constant cortical tension.     

Attraction, deformation and contact of membranes induced by low frequency electric fields

The force of attraction between erythrocyte ghosts induced by low frequency electric fields (60 Hz) was measured as a function of the intermembrane separation. It varied from 10(-14) N for separation of the order of the cell diameter to 10(-12) N for close approach and contact in 20 mM sodium phosphate buffers (conductivity 260 mS/m, pH 8.5). For large separations the interaction force followed a dependence on separation as predicted for dipole-dipole interactions. For small separation an empirical formula was obtained. The membranes deformed at close approach (less than 1 microns) before making contact. The contact area increased with time until reaching the final equilibrium state. The ghosts separated reversibly after switching off the electric field. The membrane tension induced by the ghost interaction at contact was estimated to be of the order of 0.1 mN/m. These first quantitative measurements of the force/separation dependence for intermembrane interactions induced by low frequency electric fields indicate that attractive forces, membrane deformation and contact area of cells depend strongly on intermembrane separation and field strength. The quantitative relationship between them are important for measuring membrane surface and mechanical properties, intermembrane forces and understanding mechanisms of membrane adhesion, instability and fusion in electric fields and in general.     

Contact dynamics during keratocyte motility

BACKGROUND: Keratocytes are specialised, rapidly moving cells that generate substantial contractile force perpendicular to their direction of locomotion. Potential roles for contractile force in cell motility include cell-body transport, regulation of adhesion, and retraction of the cell's trailing edge. RESULTS: To investigate contact dynamics, we used simultaneous confocal fluorescence and interference reflection microscopy to image keratocytes injected with fluorescent vinculin. We found that contacts formed behind the leading edge and grew beneath both the lamellipodium and the cell body. Contacts in the middle of the cell remained stationary relative to the substrate and began to disassemble as the cell body passed over them. In contrast, contacts in the lobes of the cell grew continuously and more rapidly, incorporated more vinculin, and slid inwards towards the sides of the cell body. Contact sliding often led to merging of contacts before their removal from the substrate. CONCLUSIONS: We suggest a synthesis of two existing, apparently conflicting models for keratocyte motility, in which network contraction progressively reorients actin filaments using the contacts as pivots, forming bundles that then generate lateral tension by a sliding-filament mechanism. Contact dynamics vary between the middle of the cell and the lobes. We propose that laterally opposed contractile forces first enhance contact growth and stability, but escalating force eventually pulls contacts from the substrate at the back of the cell, without interfering with the cell's forward progress.     

Predicting the kinetics of cell spreading

We apply the wetting theory to predict the kinetics of fibroblast spreading onto an adhesive substrate, under simplifying assumptions on the cell structure and geometry. Three main parameters are used: cytoplasmic viscosity, cortical tension, and cell-to-substrate adhesion energy. The viscosity and tension values are taken from previous micromechanical studies. The adhesion energy, ill known, is adjusted by fitting the model predictions to available experimental data of contact radius versus time. The agreement is quite good, justifying such a "macroscopic" view of cell morphology.