Homotypic interactions of soluble and immobilized osteopontin.

Osteopontin (OPN) is an extracellular matrix protein found in bones and teeth, where it accumulates at matrix-matrix interfaces. We postulate that OPN interacts homotypically and heterotypically in the adhesion of apposing matrices. Using suspensions of OPN-coupled aldehyde/sulfate latex spheres, we measured the strength of homotypic OPN-OPN binding in vitro. Doublets formed through shear-induced collisions in a cone and plate rheoscope were subjected to shear stresses >0.6 Nm(-2) and the fraction broken up determined over 60 s. Rapid initial breakup of 35% of doublets was followed by very slow breakup of the remaining 65%. Monte Carlo simulation of the breakup kinetics pointed to the existence of low and high bond strength populations of doublets. Dynamic light scattering spectroscopy of soluble OPN showed that 27% by mass existed as dimers. We postulate that OPN dimers binding to monomers account for the low strength bonds since a strong bond has already formed between the molecules of the dimer. In contrast, OPN-OPN monomer bonds had higher tensile strength than bonds between the high-affinity interaction of IgG and protein G, previously studied. Antibody blocking studies showed that the self-binding region of OPN resides in the C-terminus. These data suggest that homotypic OPN-OPN bonds have physiologically significant strength, supporting the hypothesis that OPN-OPN binding and self-assembly participate in adhesion within mineralized tissues.

Dynamics of neutrophil aggregation in couette flow revealed by videomicroscopy: effect of shear rate on two-body collision efficiency and doublet lifetime.

During inflammation, neutrophil capture by vascular endothelial cells is dependent on L-selectin and beta(2)-integrin adhesion receptors. One of us (S.I.S.) previously demonstrated that homotypic neutrophil aggregation is analogous to this process in that it is also mediated by these receptors, thus providing a model for studying the dynamics of neutrophil adhesion. In the present work, we set out to confirm the hypothesis that cell-cell adhesion via selectins serves to increase the lifetimes of neutrophil doublets formed through shear-induced two-body collisions. In turn, this would facilitate the engagement of more stable beta(2)-integrin bonds and thus increase the two-body collision efficiency (fraction of collisions resulting in the formation of nonseparating doublets). To this end, suspensions of unstimulated neutrophils were subjected to a uniform shear field in a transparent counter-rotating cone and plate rheoscope, and the formation of doublets and growth of aggregates recorded using high-speed videomicroscopy. The dependence of neutrophil doublet lifetime and two-body collision-capture efficiency on shear rate, G, from 14 to 220 s(-1) was investigated. Bond formation during a two-body collision was indicated by doublets rotating well past the orientation predicted for break-up of doublets of inert spheres. A striking dependence of doublet lifetime on shear rate was observed. At low shear (G = 14 s(-1)), no collision capture occurred, and doublet lifetimes were no different from those of neutrophils pretreated with a blocking antibody to L-selectin, or in Ca(++)-depleted EDTA buffers. At G > or = 66 s(-1), doublet lifetimes increased, with increasing G reaching values twice those for the L-selectin-blocked controls. This correlated with capture efficiencies in excess of 20%, and, at G > or = 110 s(-1), led to the rapid formation of large aggregates, and this in the absence of exogenous chemotactic stimuli. Moreover, the aggregates almost completely broke up when the shear rate was reduced below 66 s(-1). Partial inhibition of aggregate formation was achieved by blocking beta(2)-integrin receptors with antibody. By direct observation of the shear-induced interactions between neutrophils, these data reveal that steady application of a threshold level of shear rate is sufficient to support homotypic neutrophil aggregation.

Time and force dependence of the rupture of glycoprotein IIb-IIIa-fibrinogen bonds between latex spheres.

We studied the shear-induced breakup of doublets of aldehyde/sulfate (A/S) latex spheres covalently linked with purified platelet GPIIb-IIIa receptor, and cross-linked by fibrinogen. Flow cytometry with fluorescein isothiocyanate-fibrinogen showed than an average of 22,500 molecules of active GPIIb-IIIa were captured per sphere, with a mean K(d) = 56 nM for fibrinogen binding. The spheres, suspended in buffered 19% Ficoll 400 containing 120 or 240 pM fibrinogen, were subjected to Couette flow in a counter-rotating cone-plate rheoscope. Doublets, formed by two-body collisions at low shear rate (G = 8 s(-1)) for < or =15 min, were subjected to shear stress from 0.6 to 2.9 Nm(-2), their rotations recorded until they broke up or were lost to view. Although breakup was time dependent, occurring mostly in the first 2 rotations after the onset of shear, the percentage of doublets broken up after 10 rotations were almost independent of normal hydrodynamic force, F(n): at 240 pN, 15.6, 16.0, and 17.0% broke up in the force range 70-150 pN, 150-230 pN, and 230-310 pN. Unexpectedly, at both [fibrinogen], the initial rate of breakup was highest in the lowest force range, and computer simulation using a stochastic model of breakup was unable to simulate the time course of breakup. When pre-sheared at low G for >15 min, no doublets broke up within 10 rotations at 70 < F(n) < 310 pN; it required >3 min shear (>1110 rotations) at F(n) = 210 pN for significant breakup to occur. Other published work has shown that binding of fibrinogen to GPIIb-IIIa immobilized on plane surfaces exhibits an initial fast reversible process with relative low affinity succeeded by transformation of GPIIb-IIIa to a stable high-affinity complex. We postulate that most doublet breakups observed within 10 rotations were from a population of young doublets having low numbers of bonds, by dissociation of the initial receptor complex relatively unresponsive to force. The remaining, older doublets with GPIIb-IIIa in the high-affinity complex were not broken up in the time or range of forces studied.

Probabilistic modeling of shear-induced formation and breakage of doublets cross-linked by receptor-ligand bonds.

A model was constructed to describe previously published experiments of shear-induced formation and breakage of doublets of red cells and of latexes cross-linked by receptor-ligand bonds (. Biophys. J. 65:1318-1334; Tees and Goldsmith. 1996. Biophys. J. 71:1102-1114;. Biophys. J. 71:1115-1122). The model, based on McQuarrie's master equations (1963. J. Phys. Chem. 38:433-436), provides unifying treatments for three distinctive time periods in the experiments of particles in a Couette flow in which a doublet undergoes 1) formation upon two-body collision between singlets; 2) evolution of bonds at low shear rate; and 3) break-up at high shear rate. Neglecting the applied force at low shear rate, the probability of forming a doublet per collision as well as the evolution of probability distribution of bonds in a preformed doublet were solved analytically and found to be in quite good agreement with measurements. At high shear rate with significant force acting to accelerate bond dissociation, the predictions for break-up of doublets were obtained numerically and compared well with data in both individual and population studies. These comparisons enabled bond kinetic parameters for three types of particles cross-linked by two receptor-ligand systems to be calculated, which agreed well with those computed from Monte Carlo simulations. This work can be extended to analyze kinetics of receptor-ligand binding in cell aggregates, such as those of neutrophils and platelets in the circulation.

The kinetics of thrombin- and SFLLRN-induced aggregation of human platelets in flow through tubes.

The kinetics of aggregation of human platelets activated by alpha-thrombin (0.17-0.35 nM) and the hexapeptide SFLLRN (2-10 microM) was studied in plasma-free washed cell suspensions undergoing Poiseuille flow at 37 degrees C using a previously described double infusion technique. Platelet-rich Tyrodes, prepared from venous blood by multiple centrifugation, and agonist were rapidly mixed in a small chamber and the suspension flowed through various lengths of 1.19 and 0.76 mm diameter polyethylene tubing at mean transit times t from 0.2 to 43 s and mean tube shear rates = 41.9, 335, and 1335 s-1. Effluent was collected in 0.5% glutaraldehyde and single cells and aggregates in the volume range 1-10(5) micron 3 counted and sized using an aperture impedance counter. The rate and extent of aggregation with thrombin increased with increasing [thrombin] and , and although characterized by a small initial lag time, exhibited a very rapid growth of aggregates to macroscopic size, >> 10(5) micron 3, at low and moderate shear rates. With SFLLRN, the initial lag times were appreciably longer, but subsequently aggregates also rapidly grew to macroscopic size. We hypothesize that the initial lag time is due to the time required for sufficient secretion and surface organization of ligands such as vWF (known to be released by the platelet) to occur, in order for cross-bridging of the GPIIb-IIIa receptors on adjacent platelets to take place. It appears that thrombin, which, at the low concentrations used, primarily activates the platelet via binding to the GPIb alpha receptor, can more rapidly facilitate secretion of the ligand than SFLLRN, which activates the cell via binding to the seven transmembrane domain receptor.

Surface-secreted von Willebrand factor mediates aggregation of ADP-activated platelets at moderate shear stress: facilitated by GPIb but controlled by GPIIb-IIIa.

We previously showed that ADP activation of washed human platelets in plasma-free suspensions supports aggregation at moderate shear stress (0.4-1.6 Nm-2) in Poiseuille flow. Although most activated platelets expressed maximal fibrinogen-occupied GPIIb-IIIa receptors, aggregation appeared to be independent of bound fibrinogen, but blocked by the hexapeptide GRGDSP. Here, we tested the hypothesis that von Willebrand factor (vWF) secreted and expressed on activated platelets mediates aggregation at moderate shear rates from 300 to 1000 s-1 corresponding to shear stresses from 0.3 to 1.1 Nm-2. Relatively unactivated platelets (< 15% expressing prebound fibrinogen) were prepared from acidified citrated platelet rich plasma (cPRP) by single centrifugation with 50 nM stable prostacyclin derivative ZK 36374 and resuspended in Tyrodes-albumin at 5 x 10(4) cells microliter-1. Flow cytometric measurements with monoclonal antibody (mAb) 2.2.9 reporting on surface-bound vWF, and with mAb S12 reporting on alpha-granule secreted P-selectin, showed that 65% and 80%, respectively, of all platelets were maximally activated with respect to maximal secretion and surface expression of these proteins. "Resting" washed platelets exhibited both surface-bound vWF and significant P-selectin secretion. We showed that mAbs 6D1 and NMC4, respectively blocking the adhesive domains on the GPIb receptor recognizing vWF, and on the vWF molecule recognizing the GPIb receptor, partially inhibited ADP-induced aggregation under shear in Couette flow, the degree of inhibition increasing with increasing shear stress. In contrast, mAb 10E5, blocking the vWF binding domain on GPIIb-IIIa, essentially blocked all aggregation at the shear rates tested. We conclude that vWF, expressed on ADP-activated platelets, is at least the predominant cross-bridging molecule mediating aggregation at moderate shear stress. There is an absolute requirement for free activated GPIIb-IIIa receptors, postulated to interact with platelet-secreted, surface bound vWF. The GPIb-vWF cross-bridging reaction plays a facilitative role becoming increasingly important with increasing shear stress. Since aurin tricarboxylic acid, which blocks the GPIb binding domain on vWF, was also found to completely block aggregation in Poiseuille flow, we conclude that it too affects the GPIIb-IIIa interaction.

Kinetics and locus of failure of receptor-ligand-mediated adhesion between latex spheres. I. Protein-carbohydrate bond.

We previously described the use of a counter-rotating cone and plate rheoscope to measure the time and force dependence of break-up of doublets of sphered, swollen, and fixed red cells (SSRC) cross-linked by monoclonal IgM antibody. It has been shown that doublet break-up can occur by extraction of receptors from the membrane, rather than by antibody-antigen bond break-up, and is a stochastic process. We therefore prepared 4.62-microns carboxyl modified latex spheres with a covalently coupled synthetic blood group B antigen trisaccharide. Using a two-step carbodiimide process, ethylene diamine was covalently linked to the carboxyl modified latex spheres, and the trisaccharide, having an eight carbon spacer modified to bear a terminal carboxyl group, was linked to the ethylene diamine. Using these antigen spheres we carried out studies in Couette flow, in a transparent cone and plate rheoscope, of the shear-induced break-up of doublets cross-linked by monoclonal IgM anti-B antibody in 19% and 15% Dextran 40. As previously found with SSRC, over a range of normal force from 55 to 175 pN, there was a distribution in times to break-up. However, the fraction of antigen sphere doublets broken up, which increased from 0.08 to 0.43 at 75 pM IgM, and from 0.06 to 0.20 at 150 pM IgM, was significantly lower than that for the SSRC, where the fraction broken up at 150 pM IgM increased from 0.10 to 0.47. Thus, significantly higher forces were required to achieve the same degree of break-up for doublets of antigen-linked spheres than for SSRC. Computer simulation using a stochastic model of break-up showed that the differences between antigen sphere and SSRC doublet break-up were due to a change in bond character (the range and depth of the bond energy minimum) rather than to an increase in the number of bonds linking antigen-sphere doublets. This supports the notion that antibody-antigen bonds are ruptured in the case of antigen spheres, whereas antigen is able to be extracted from the membrane of SSRC, although changes of receptor substrate from cell to latex and the possibility of latex strand extraction from the microspheres are potential complicating factors.

Kinetics and locus of failure of receptor-ligand-mediated adhesion between latex spheres. II. Protein-protein bond.

In an extension of the previous paper, we describe the force dependence of break-up of doublets of latex spheres cross-linked by protein G-IgG bonds via the Fc region of the antibody. The receptor, the monoclonal Bear-1 antibody, was either covalently linked to 4.75-microns aldehyde/sulfate (A/S) latex spheres in a one-step reaction, or physically adsorbed to the 4.63-microns carboxyl-modified latex spheres used in Part I of this paper. The spheres were suspended in 19% buffered Dextran 40 containing the ligand, the bivalent recombinant protein G (Gamma-Bind G), and observed in the counter-rotating cone and plate Rheoscope. Break-up of doublets, tracked individually under the microscope, as well as in populations of 50-150 particles, was studied over a range of normal force from 20 to 260 pN. In individual particle studies, the fraction of doublets of spheres with covalently linked IgG breaking up in the first 10 rotations, increased from 16% in the low-force to 63% in the high-force range. In population studies, the fraction broken up increased with duration and magnitude of the applied force, and decreased with increasing ligand concentration. Moreover, doublets of physically adsorbed IgG spheres required significantly lower force than doublets of covalently linked IgG spheres for the same degree of break-up, possibly because of surface detachment of IgG molecules rather than rupture of receptor-ligand bonds. Computer simulation, using the Bell stochastic model of break-up and a Poisson distribution for the number of bonds, described in Part I, showed that the parameters of the protein-protein bond differed significantly from those of the carbohydrate-protein bond studied in Part I of this paper, the former being much more responsive to force than the latter.

Physical and chemical effects of red cells in the shear-induced aggregation of human platelets.

Both chemical and physical effects of red cells have been implicated in the spontaneous aggregation of platelets in sheared whole blood (WB). To determine whether the chemical effect is due to ADP leaking from the red cells, a previously described technique for measuring the concentration and size of single platelets and aggregates was used to study the shear-induced aggregation of platelets in WB flowing through 1.19-mm-diameter polyethylene tubing in the presence and absence of the ADP scavenger enzyme system phosphocreatine-creatine phosphokinase (CP-CPK). Significant spontaneous aggregation was observed at mean tube shear rates, (G) = 41.9 and 335 s-1 (42% and 13% decrease in single platelets after a mean transit time (t) = 43 s, compared to 89 and 95% decrease with 0.2 microM ADP). The addition of CP-CPK, either at the time of, or 30 min before each run, completely abolished aggregation. In the presence of 0.2 microM ADP, CP-CPK caused a reversal of aggregation at (t) = 17 s after 30% of single cells had aggregated. To determine whether red cells exert a physical effect by increasing the time of interaction of two colliding platelets (thereby increasing the proportion of collisions resulting in the formation of aggregates), an optically transparent suspension of 40% reconstituted red cell ghosts in serum containing 2.5-micron-diameter latex spheres (3 x 10(5)/microliters) flowing through 100-microns-diameter tubes was used as a model of platelets in blood, and the results were compared with those obtained in a control suspension of latex spheres in serum alone. Two-body collisions between microspheres in the interior of the flowing ghost cell or serum suspensions at shear rates from 5 to 90 s-1 were recorded on cine film. The films were subsequently analyzed, and the measured doublet lifetime, tau meas, was compared with that predicted by theory in the absence of interactions with other particles, tau theor. The mean (tau meas/tau theor) for doublets in ghost cell suspensions was 1.614 +/- 1.795 (SD; n = 320), compared to a value of 1.001 +/- 0.312 (n = 90) for doublets in serum. Whereas 11% of doublets in ghost cell suspensions had lifetimes from 2.5 to 5 times greater than predicted, in serum, no doublets had lifetimes greater than 1.91 times that predicted. There was no statistically significant correlation between tau meas/tau theor and shear rate, but the values of tau meas/tau theor for low-angle collisions in ghost cell suspensions were significantly greater than for high-angle collisions.

Effect of hematocrit on adenosine diphosphate-induced aggregation of human platelets in tube flow.

Both chemical and physical effects of red cells are known to play a role in the adenosine diphosphate (ADP)-induced aggregation of human platelets in sheared blood. Using a previously described double infusion technique (Bell et al., 1989a), we studied the effect of increasing hematocrit from 10 to 60% on the rate and extent of platelet aggregation with 0.2 microM ADP in citrated whole blood undergoing tube flow. Blood and agonist were rapidly mixed in a small chamber and the suspensions flowed through lengths of 1.19 mm-diameter polyethylene tubing at mean transit times from 0.2 to 42.8 s at a mean tube shear rate = 335 s-1. Effluent was collected into 0.5% glutaraldehyde, the red cells removed by centrifugation through Percoll, and all single platelets and aggregates in the volume range 1-10(5) microns3 counted and sized using an aperture impedance counter. Both the initial rate (over the first 8.6 s) and the extent of aggregation with time increased with increasing mean hematocrit up to 35.8%, being significantly greater than in citrated plasma (cPRP). However, at 61.5% hematocrit, the extent of aggregation decreased markedly to a level close to that in cPRP. We also studied the effect of washed red cells at 39% hematocrit on the aggregation of washed platelets in Tyrodes-albumin fibrinogen-free suspensions. It had previously been shown that, at > or = 335 s-1, washed platelets in platelet-rich Tyrodes (PRT) aggregated with 0.7 microM ADP. We found that red cells markedly increased the extent of aggregation from that in PRT, and promoted the formation of large aggregates, absent in PRT. Spontaneous aggregation in whole blood or washed cell suspensions in the absence of added ADP at = 42.8 s was < 10% of that in the presence of ADP. The results indicate that a physical effect of red cells, likely manifested as an increase in the efficiency of aggregate formation (Goldsmith et al., 1995), plays an important role at low and normal hematocrits; however, at high hematocrits, particle crowding impedes the formation of aggregates.

Flow-induced detachment of red blood cells adhering to surfaces by specific antigen-antibody bonds.

Fixed spherical swollen human red blood cells of blood type B adhering on a glass surface through antigen-antibody bonds to monoclonal mouse antihuman IgM, adsorbed or covalently linked on the surface, were detached by known hydrodynamic forces created in an impinging jet. The dynamic process of detachment of the specifically bound cells was recorded and analyzed. The fraction of adherent cells remaining on the surface decreased with increasing hydrodynamic force. For an IgM coverage of 0.26%, a tangential force on the order of 100 pN was able to detach almost all of the cells from the surface within 20 min. After a given time of exposure to hydrodynamic force, the fraction of adherent cells remaining increased with time, reflecting an increase in adhesion strength. The characteristic time for effective aging was approximately 4 h. Results from experiments in which the adsorbed antibody molecules were immobilized through covalent coupling and from evanescent wave light scattering of adherent cells, imply that deformation of red cells at the contact area was the principal cause for aging, rather than local clustering of the antibody through surface diffusion. Experiments with latex beads specifically bound to red blood cells suggest that, instead of breaking the antigen-antibody bonds, antigen molecules were extracted from the cell membrane during detachment.

Adenosine diphosphate-induced aggregation of human platelets in flow through tubes: III. Shear and extrinsic fibrinogen-dependent effects.

The effect of shear rate and fibrinogen concentration on adenosine diphosphate-induced aggregation of suspensions of washed human platelets in Poiseuille flow at 23 degrees C was studied using a previously described double infusion technique and resistive particle counter size analysis. Using suspensions of multiple-centrifuged and -washed cells in Tyrodes-albumin [3 x 10(5) microliters-1; (17)] with [fibrinogen] from 0 to 1.2 microM, the rate and extent of aggregation with 0.7 microM ADP in Tyrodes-albumin were measured over a range of mean transit times from 0.2 to 43 s, and at mean tube shear rates, G, = 41.9, 335 and 1,335 s-1. As measured by the decrease in singlet concentration, aggregation at 1.2 microM fibrinogen increased with increasing G up to 1,335 s-1, in contrast to that previously reported in citrated plasma, in which aggregation reached a maximum at G = 335 s-1. Without added fibrinogen, there was no aggregation at G = 41.9 s-1; at G = 335 s-1, there was significant aggregation but with an initial lag time, aggregation increasing further at G = 1,335 s-1. Without added fibrinogen, aggregation was abolished at all G upon incubation with the hexapeptide GRGDSP, but was almost unaffected by addition of an F(ab')2 fragment of an antibody to human fibrinogen. Aggregation in the absence of added fibrinogen was also observed at 37 degrees C. The activation of the multiple-washed platelets was tested using flow cytometry with the fluorescently labelled monoclonal antibodies FITC-PAC1 and FITC-9F9. It was shown that 57% of single cells in unactivated PRT expressed maximal GPIIb-IIIa fibrinogen receptors (MoAb PAC1) and 54% expressed pre-bound fibrinogen (MoAb 9F9), with further increases on ADP activation. However, incubation with GRGDSP and the F(ab')2 fragment did not inhibit the prebound fibrinogen. Moreover, relatively unactivated cells (8% expressing receptor, 14% prebound fibrinogen), prepared from acidified cPRP by single centrifugation with 50 nM of the stable prostacyclin derivative, ZK 36,374, and resuspension in Tyrodes-albumin at 5 x 10(4) microliters-1, aggregated with 2 and 5 microM ADP at G = 335 and 1,335 s-1 in the absence of added fibrinogen. We therefore postulate that a protein such as von Willebrand factor, secreted during platelet isolation or in flow at sufficiently high shear rates, may yield the observed shear-rate dependent aggregation without fibrinogen.

Kinetics of specific and nonspecific adhesion of red blood cells on glass.

Fixed spherical human red blood cells suspended in 17% sucrose were allowed to adhere on either clean glass surfaces or glass surfaces preincubated with antibodies specific to a certain blood group antigen. The adhesion experiments were performed in an impinging jet apparatus, in which the cells are subjected to stagnation point flow. The objective of this study was to compare the efficiencies of nonspecific and specific (antigen-antibody mediated) adhesion of red blood cells on glass surfaces. The efficiency was defined as the ratio of the experimental adhesion rate to that calculated based on numerical solutions of the mass transfer equation, taking into account hydrodynamic interactions as well as colloidal forces. The efficiency for nonspecific adhesion was nearly unity at flow rates lower than 85 microliter/s (corresponding to a wall shear rate, Gw, of 30 s-1 at a radial distance of 110 microns from the stagnation point). The values of efficiency dropped at higher flow rates, due to an increase in the tangential force. The critical deposition concentration is found to occur at 120-150 mM NaCl, which is consistent with the theoretically predicted values. At low salt concentrations, the experimental values are higher than the theoretical ones. Similar discrepancies have been found in many colloidal systems. Introducing steric repulsion by adsorbing a layer of albumin molecules on the glass completely prevents nonspecific adhesion at flow rates below 60 microliter/s (Gw congruent to 15 s-1). The efficiency of specific adhesion depends both on the concentration of antibody molecules on the surface and the flow rate. Normal red cells adhere more readily through antigen-antibody bonds than fixed cells. Fixed spherical cells have a higher adhesion efficiency than fixed biconcave ones.

Interaction forces between red cells agglutinated by antibody. IV. Time and force dependence of break-up.

We report on an extension of a previously described method to measure the hydrodynamic force to separate doublets of fixed, sphered and swollen red cells cross-linked by antibody (S. P. Tha, J. Shuster, and H. L. Goldsmith. 1986. Biophys. J. 50:1117-1126). With a traveling microtube apparatus, doublets are tracked and videotaped in a slowly accelerating Poiseuille flow in 150-microns-diameter tubes, and the hydrodynamic normal force at break-up, Fn, is computed from the measured doublet velocity and radial position. Previous results showed a large range of Fn, the mean of which increased with [antiserum], and an absence of clustering at discrete values of Fn. Since it was assumed that the cells separate the instant a critical force to break all crossbridges was reached, lack of clustering could have been due to the use of a polyclonal antiserum. We therefore studied the effect of monoclonal IgM or IgA antibody on the distribution of Fn. The results showed that the data are as scattered as ever, with Fn varying from 2 to 200 pN, and exhibit no evidence of clustering. However, the scatter in Fn could be due to the stochastic nature of intercellular bonds (E. Evans, D. Berk, and A. Leung. 1991a. Biophys. J. 59:838-848). We therefore studied the force dependence of the time to break-up under constant shear stress (Fn from 30 to 200 pN), both in Poiseuille and Couette flow, the latter by using a counter-rotating cone and plate rheoscope. When 280 doublets were rapidly accelerated in the traveling microtube and then allowed to coast in steady flow for up to 180 s, 91% survived into the constant force region; 16% of these broke up after time intervals, tP, of 2-30s. Of 340 doublets immediately exposed to constant shear in the rheoscope, 37% broke after time intervals, tc, from < 1 to 10 s. Thus, doublets do indeed break up under a constant shear stress, if given time. The average time to break-up decreased significantly with increasing force, while the fraction of doublets broken up increased. At a given Fn, the fraction of break-ups decreased with increasing [IgM], suggesting that the average number of bonds had also increased. Using a stochastic model of break-up (G. I. Bell. 1978. Science (Washington DC). 200:618-627; E. Evans, D. Berk,and A. Leung. 1991. Biophys. J. 59:838-848) and a Poisson distribution for the number of bonds, Nb, break-up in slowly accelerating Poiseuille flow and in immediate shear application in Couette flow was simulated. In Poiseuille flow, the observed range and scatter in Fn could be reproduced assuming (Nb) > 5. In the rheoscope, the time intervals and number of rotations to break-up, tc, were quite well reproduced assuming (Nb) = 4. The similarity of (Fn) for monoclonal IgM and IgA for doublet break-up under constant slow acceleration is compatible with the conclusion of Evans et al. (1991 a) for normal red cells and Xia et al. (manuscript submitted for publication) for sphered and swollen red cells, that the applied force extracts the antigen from the cell membrane.

Decreased hydrodynamic resistance in the two-phase flow of blood through small vertical tubes at low flow rates.

The aggregation of red blood cells in blood flowing through small tubes at very low shear rates leads to the two-phase flow of an inner core of rouleaux surrounded by a cell-depleted peripheral layer. The formation of this layer is known to be accompanied by a decrease in hydrodynamic resistance to flow. To quantitate this effect, we measured the pressure gradient, flow rate, and the radius of the red blood cell core in suspensions flowing through tubes of 172-microns radius at mean linear flow rates (U) from 50 to 0.15 tube diameters.sec-1. Washed red blood cells were suspended in 1.5% buffered dextran 110 at hematocrits of 34-52%. Using syringe pumps, blood flowed from a stirred reservoir through a vertical 12-cm length of tube in either the upward or downward direction. The pressure drop was measured with transducers. Mean values in distributions in the core radius were obtained by analyzing cine films of flow taken through a microscope with flow in the upward direction, measuring the core radius at five equally spaced axial positions of the tube in each of 100 frames. At 34% and 46% hematocrit, the hydrodynamic resistance increased as U decreased from 50 sec-1, reaching a maximum at U-2 sec-1. It then decreased to a minimum at U less than 0.5 sec-1 as the red blood cell core formed in the tube, and the mean core radius/tube radius ratio decreased from 0.98 to 0.74 with marked axial fluctuations at the lower U. At higher hematocrits, both the increase and decrease in hydrodynamic resistance were greater. In a red blood cell albumin-saline suspension, where there is no aggregation of red blood cells and no two-phase flow, hydrodynamic resistance increases linearly with decreasing U. The experimental results were compared with the predictions of a two-phase steady-flow model, assuming axisymmetric flow of a core surrounded by cell-free suspending medium. Two models were considered, one in which the core is solid, the other in which the rheological properties of the suspension in the core are given by the Quemada equation. The effects of sedimentation of the core resulting in a zero net flow pressure gradient were taken into account. Provided that an experimentally extrapolated value for the zero pressure gradient was used, the Quemada-fluid model gave good agreement with the experimentally observed core radius as a function of U and hematocrit.

Extracellular-free Ca++ accounts for the sex difference in the aggregation of human platelets in citrated platelet-rich plasma.

It has been shown in Poiseuille flow, that the ADP-induced aggregation of human platelets in citrated plasma from female donors is significantly greater than from male donors over a range of mean tube shear rate, G, from 41.9 s-1 to 1920 s-1 and mean transit time, t, from 0.2 to 86 s. The present work verifies the sex difference at G = 335 s-1 and t = 43 s and deals with the effect of free Ca2+ on it. An inverse correlation between the extent of single platelet aggregation and donor hematocrit, and between hematocrit and the plasma ionized calcium concentration, [Ca2+], as well as a positive correlation between the extent of single platelet aggregation and [Ca2+] was found. This indicated that the sex difference is due to hematocrit-dependent differences in the [Ca2+] that result when a fixed volume of the chelating agent citrate is used to anticoagulate blood. When the initial citrate concentration was adjusted to compensate for the variable volume dilution of citrate in plasma among donors and the [Ca2+] of males raised above that of females, the sex difference was reversed. Again, aggregation correlated with [Ca2+]. At the physiological [Ca2+] in both heparinized PRP and hirudinized PRP, the rate of aggregation and aggregate size were much greater than in citrated plasma but no sex difference was detected.