Aggregation and disaggregation kinetics of human blood platelets: Part I. Development and validation of a population balance method.

Hydrodynamic shear stress of sufficient intensity is known to cause platelet activation and aggregation and to alter the effects of biochemical platelet agonists and antagonists. In this work, a population balance equation (PBE) model is developed for analysis of platelet aggregation and disaggregation kinetics under the influence of a shear field. The model incorporates both aggregation and disaggregation by splitting and/or erosion mechanisms. This paper, the first of a series of three, deals with the formulation, simplification, and validation of the PBE and with the estimation of parameters involved in the PBE. These population parameters include collision efficiency, void fraction (related to the particle collision diameter), and the breakage rate coefficient. The platelet particle size distribution is determined experimentally, both initially and at some later times. The PBE can then be used to match satisfactorily the observed particle histograms, by appropriate choice of parameters of the model as functions of time, platelet size, and magnitude of physical or chemical stimuli. Besides providing information on adhesive forces and on the rates of aggregation and disaggregation, these parameters infer the physical properties of platelets and platelet aggregates. These properties are of potential value in increasing our understanding of the processes involved in thrombotic disease and/or therapy. A numerical procedure for solving the PBE is validated by application to simple cases for which analytical solutions are available. The model is applied to analysis of experiments, and parameter sensitivity studies are used to order the importance of the parameters and to reduce the complexity of the model. The simplified model is shown to give good agreement with experimental observations.     

Aggregation and disaggregation kinetics of human blood platelets: Part III. The disaggregation under shear stress of platelet aggregates.

In the preceding two papers (1, 2), a population balance equation (PBE) mathematical model was developed, validated, and applied to the analysis of platelet aggregation kinetics under the influence of hydrodynamic shear stress. The present work involves the application of the model to the analysis of platelet reactions under shear stress in circumstances where disaggregation processes are of dominant importance: the disaggregation of aggregates formed in response to added agonists. Aggregation-disaggregation experiments were performed in the constant shear field of a rotational viscometer, and the evolution of the particle size distribution was determined by use of an electronic particle counter. The PBE model was used to simulate the experimental results. Exploratory calculations made it possible to reduce a rather complete, complex model to a more tractable form which retains the capability of simulating the experimental observations. For the experimental conditions studied, disaggregation by a splitting mechanism was found to be of dominant importance. The surface erosion mechanism can be neglected without significant impact on results. Physical reasoning confirmed by exploratory calculations showed that a discontinuous form of the breakage rate expression which incorporates a minimum friable particle size, gives significantly better results than a continuous expression. A simple step function void fraction parameter was found to be at least as successful as a more complicated, continuous function. The resulting simplified model has the potential of increasing our understanding of kinetics and mechanisms of platelet reactions, and of characterizing the state of platelet activity. Hence, it may be useful in efforts to understand thrombotic and hemostatic processes.     

Platelet adhesive dynamics. Part I: characterization of platelet hydrodynamic collisions and wall effects

Abnormally high shear stresses encountered in vivo induce spontaneous activation of blood platelets and formation of aggregates, even in the absence of vascular injury. A three-dimensional multiscale computational model—platelet adhesive dynamics—is developed and applied in Part I and Part II articles to elucidate key biophysical aspects of GPIbα-von-Willebrand-factor-mediated interplatelet binding that characterizes the onset of shear-induced platelet aggregation. In this article, the hydrodynamic effects of the oblate spheroidal shape of platelets and proximity of a plane wall on the nature of cell-cell collisions are systematically investigated. Physical quantities characterizing the adhesion probabilities between colliding platelet surfaces for the entire range of near-wall encounters between two platelets are obtained for application in platelet adhesive dynamics simulations of platelet aggregation explored in a companion article. The technique for matching simulation predictions of interplatelet binding efficiency to experimentally determined efficiencies is also described. Platelet collision behavior is found to be strikingly different from that of spheres, both close to and far from a bounding wall. Our results convey the significant effects that particle shape and presence of a bounding wall have on the particle trajectories and collision mechanisms, collision characteristics such as collision time and contact area, and collision frequency.     

Analysis of shear-induced platelet aggregation with population balance mathematics.

Suspensions of blood platelets aggregate and degranulate when subjected to a shearing flow of sufficient intensity. This work examines, by means of a population balance technique, the kinetics of platelet aggregation in a shear field. The particle collision efficiency, epsilon, and the particle void volume fraction, phi, are estimated from particle number density data. The collision efficiency represents the fraction of particle collisions that result in the binding together of the involved particles. We term epsilon and phi population balance properties because they refer to physical characteristics of platelets and aggregates that are pertinent to their aggregation behavior. Experiments focused on the dependence of epsilon on platelet concentration, shearing rate, and time in a controlled shear field. The collision efficiency is lower in dilute platelet suspensions. This finding supports an ADP-mediated mechanism for shear aggregation. The collision efficiency passes through a maximum with respect to shearing rate, suggesting a competition between the opposing effects of increasing platelet activation and increasing collision violence. The collision efficiency is highest during the first ten seconds in the shear field and declines significantly thereafter. Even at its maximum, however, epsilon for shear aggregation is small: only about one in every thousand particle collisions results in binding.     

Adenosine diphosphate-induced aggregation of human platelets in flow through tubes. I. Measurement of concentration and size of single platelets and aggregates.

A double infusion flow system and particle sizing technique were developed to study the effect of time and shear rate on adenosine diphosphate-induced platelet aggregation in Poiseuille flow. Citrated platelet-rich plasma, PRP, and 2 microM ADP were simultaneously infused into a 40-microliters cylindrical mixing chamber at a fixed flow ratio, PRP/ADP = 9:1. After rapid mixing by a rotating magnetic stirbar, the platelet suspension flowed through 1.19 or 0.76 mm i.d. polyethylene tubing for mean transit times, t, from 0.1 to 86 s, over a range of mean tube shear rate, G, from 41.9 to 1,000 s-1. Known volumes of suspension were collected into 0.5% buffered glutaraldehyde, and all particles in the volume range 1-10(5) microns 3 were counted and sized using a model ZM particle counter (Coulter Electronics Inc., Hialeah, FL) and a logarithmic amplifier. The decrease in the single platelet concentration served as an overall index of aggregation. The decrease in the total particle concentration was used to calculate the collision capture efficiency during the early stages of aggregation, and aggregate growth was followed by changes in the volume fraction of particles of successively increasing size. Preliminary results demonstrate that both collision efficiency and particle volume fraction reveal important aspects of the aggregation process not indicated by changes in the single platelet concentration alone.     

Platelet adhesive dynamics. Part II: high shear-induced transient aggregation via GPIbalpha-vWF-GPIbalpha bridging

A three-dimensional multiscale computational model, platelet adhesive dynamics (PAD), is developed and applied in Part I and Part II articles to characterize and quantify key biophysical aspects of GPIbα-von-Willebrand-factor (vWF)-mediated interplatelet binding at high shear rates, a necessary and enabling step that initiates shear-induced platelet aggregation. In this article, an adhesive dynamics model of the transient aggregation of two unactivated platelets via GPIbα-vWF-GPIbα bridging is developed and integrated with the three-dimensional hydrodynamic flow model discussed in Part I. Platelet binding efficiencies predicted by PAD are in good agreement with platelet aggregation behavior observed experimentally, as documented in the literature. Deviations from average vWF ligand size or healthy GPIbα-vWF-A1 binding kinetics are observed in simulations to have significant effects on the dynamics of transient platelet aggregation, i.e., the efficiency of platelet aggregation and characteristics of bond failure, in ways that typify diseased conditions. The GPIbα-vWF-A1 bond formation rate is predicted to have piecewise linear dependence on the prevailing fluid shear rate, with a sharp transition in fluid shear dependency at 7200 s⁻¹. Interplatelet bond force-loading is found to be complex and highly nonlinear. These results demonstrate PAD as a powerful predictive modeling tool for elucidating platelet adhesive phenomena under flow.     

Modeling the reversible kinetics of neutrophil aggregation under hydrodynamic shear.

Neutrophil emigration into inflamed tissue is mediated by beta 2-integrin and L-selectin adhesion receptors. Homotypic neutrophil aggregation is also dependent on these molecules, and it provides a model system in which to study adhesion dynamics. In the current study we formulated a mathematical model for cellular aggregation in a linear shear field based on Smoluchowski's two-body collision theory. Neutrophil suspensions activated with chemotactic stimulus and sheared in a cone-plate viscometer rapidly aggregate. Over a range of shear rates (400-800 s-1), approximately 90% of the single cells were recruited into aggregates ranging from doublets to groupings larger than sextuplets. The adhesion efficiency fit to these kinetics reached maximum levels of > 70%. Formed aggregates remained intact and resistant to shear up to 120 s, at which time they spontaneously dissociated back to singlets. The rate of cell disaggregation was linearly proportional to the applied shear rate, and it was approximately 60% lower for doublets as compared to larger aggregates. By accounting for the time-dependent changes in adhesion efficiency, disaggregation rate, and the effects of aggregate geometry, we succeeded in predicting the reversible kinetics of aggregation over a wide range of shear rates and cell concentrations. The combination of viscometry with flow cytometry and mathematical analysis as presented here represents a novel approach to differentiating between the effects of hydrodynamics and the intrinsic biological processes that control cell adhesion.     

Adenosine diphosphate-induced aggregation of human platelets in flow through tubes. II. Effect of shear rate, donor sex, and ADP concentration.

The effect of shear rate on the adenosine diphosphate-induced aggregation of human platelets in Poiseuille flow was studied using the method described in part I (Bell, D.N., S. Spain, and H.L. Goldsmith. 1989. Biophys. J. 56:817-828). The rate and extent of aggregation in citrated platelet-rich plasma were measured over a range of mean transit time from 0.2 to 8.6 s and mean tube shear rate, G, from 41.9 to 1,920 s-1. At 0.2 microM ADP, changes in the single platelet concentration with time suggest that more than one type of platelet-platelet bond mediates platelet aggregation at physiological shear rates. At low G, a high initial rate of aggregation reflects the formation of a weak bond of high affinity, the strength of which diminishes with time. Here, the fraction of collisions yielding stable doublets, the collision efficiency, reached a maximum of 26%. The collision efficiency decreased with increasing G and was accompanied by a progressive delay in the onset of aggregation. However, the gradual expression of a more shear rate-resistant bond at high shear rates and long mean transit times produced a subsequent increase in collision efficiency and a corresponding increase in the rate of aggregation. Although the collision efficiencies here were less than 1%, the high collision frequencies were able to sustain a high rate of aggregation. At 0.2 microM ADP, aggregate size generally decreased with increasing G. At 1.0 microM ADP, aggregate size was still limited at high shear rates even though the rate of single platelet aggregation was much higher than at 0.2 microM ADP. Platelet aggregation was greater for female than for male donors, an effect related to differences in the hematocrit of donors before preparing platelet-rich plasma.     

The effects of elongational stress exposure on the activation and aggregation of blood platelets.

Hemodynamic shear is known to stimulate blood and endothelial cells and induce platelet activation. Many studies of shear-induced platelet stimulation have employed rotational viscometers in which secondary flow effects are assumed to be negligible. Shear induced platelet activation occurs at elevated shear rates where secondary flows may contribute a significant percentage of the total hydrodynamic force experienced by the sample. Elongational stress, one component of this secondary flow, has been shown to alter transmembrane ion flux in intact cell and the permeability of synthetic membrane preparations. Elongational flow also occurs in the vasculature at sites of elevated shear stress. Secondary flow components may contribute to platelet activation induced during shear stress application in rotational viscometry. A unique 'constrained convergence' elongational flow chamber was designed and fabricated to study platelet response to elongational stress exposure. The elongational flow chamber was capable of producing an elongation rate of 2.1 s-1 with a corresponding volume averaged shear rate of 58.33 s-1. Significant changes were observed in the total platelet volume distribution and measured response to added chemical antagonists after elongational stress exposure. The total platelet volume histogram shifted toward larger particle sizes, suggesting the formation of large aggregates as a result of elongational stress exposure. Platelets exposed to elongational stress demonstrated a dose dependent decrease in added ADP-induced aggregation rate and extent of aggregation.     

Aggregation efficiency of activated normal or fixed platelets in a simple shear field: effect of shear and fibrinogen occupancy.

Shear rate can affect protein adsorption and platelet aggregation by regulating both the collision frequency and the capture efficiency (alpha). These effects were evaluated in well defined shear field in a micro-couette for shear rate G = 10 - 1000 s-1. The rate of protein binding was independent of G, shown for adsorption of albumin to latex beads and PAC1 to activated platelets. The initial aggregation rate for ADP-activated platelets in citrated platelet-rich plasma followed second order kinetics at the initial platelet concentrations between 20,000 and 60,000/microliters. alpha values, which dropped nearly fivefold for a 10-fold increase in G, were approximately proportional to G-1, contrary to a minor drop predicted by the theory that includes protein cross-bridging. Varying ADP concentration did not change alpha of maximally activated platelet subpopulations, suggesting that aggregation between unactivated and activated platelets is negligible. Directly blocking the unoccupied but activated GPIIb-IIIa receptors without affecting pre-bound Fg on "RGD"-activated, fixed platelets (AFP) by GRGDSP or Ro 43-5054 eliminated aggregation, suggesting that cross-bridging of GPIIb-IIIa on adjacent platelets by fibrinogen mediates aggregation. Alpha for AFP remained maximal (approximately 0.24) over 25-75% Fg occupancy, otherwise decreasing rapidly, with a half-maximum occurring at around 2% occupancy, suggesting that very few bound Fg were required to cause significant aggregation.     

Kinetics of beta2-integrin and L-selectin bonding during neutrophil aggregation in shear flow.

Activated neutrophils aggregate in a shear field via bonding of L-selectin to P-selectin glycoprotein ligand-1 (PSGL-1) followed by a more stable bonding of LFA-1 (CD11a/CD18) to intercellular adhesion molecule 3 (ICAM-3) and Mac-1 (CD11b/CD18) to an unknown counter receptor. Assuming that the Mac-1 counter receptor is ICAM-3-like in strength and number, rate processes were deconvoluted from neutrophil homoaggregation data for shear rates (G) of 100-3000 s-1 with a two-body hydrodynamic collision model (. Biophys. J. 73:2819-2835). For integrin-mediated aggregation (characteristic bond strength of 5 microdynes) in the absence of L-selectin contributions, an average forward rate of kf = 1.57 x 10(-12) cm2/s predicted the measured efficiencies for G = 100-800 s-1. For a selectin bond formation rate constant equal to the integrin bond formation rate constant, the colloidal stability of unactivated neutrophils was satisfied for a reverse rate of the L-selectin-PGSL bond corresponding to an average bond half-life of 10 ms at a characteristic bond strength of 1 microdyne. Colliding neutrophils initially bridged by at least one L-selectin-PSGL-1 bond were calculated to rotate from 8 to 50 times at G = 400 to 3000 s-1, respectively, before obtaining mechanical stability in sheared fluid of either 0.75 or 1.75 cP viscosity. Thus for G > 400 s-1, the interaction time needed for the rotating aggregates to become stable was relatively constant at 52.5 +/- 8.5 ms, largely independent of shear rate or shear stress. Aggregation data and the colloidal stability criterion can provide a consistent set of forward and reverse rate constants and characteristic bond strengths for a known time-dependent stoichiometry of receptors on cells interacting in a shear flow field.     

Molecular dynamics of the transition from L-selectin- to beta 2-integrin-dependent neutrophil adhesion under defined hydrodynamic shear.

Homotypic adhesion o2 neutrophils stimulated with chemoattractant is analogous to capture on vascular endothelium in that both processes depend on L-selectin and beta 2-integrin adhesion receptors. Under hydrodynamic shear, cell adhesion requires that receptors bind sufficient ligand over the duration of intercellular contact to withstand hydrodynamic stresses. Using cone-plate viscometry to apply a uniform linear shear field to suspensions of neutrophils, we conducted a detailed examination of the effect of shear rate and shear stress on the kinetics of cell aggregation. A collisional analysis based on Smoluchowski's flocculation theory was employed to fit the kinetics of aggregation with an adhesion efficiency. Adhesion efficiency increased with shear rate from approximately 20% at 100 s-1 to approximately 80% at 400 s-1. The increase in adhesion efficiency. Adhesion efficiency increased with shear rate from approximately 20% at 100 s-1 to approximately 80% at 400 s-1. The increase in adhesion efficiency with shear was dependent on L-selectin, and peak efficiency was maintained over a relatively narrow range of shear rates (400-800 s-1) and shear stresses (4-7 dyn/cm2). When L-selectin was blocked with antibody, beta 2-integrin (CD11a, b) supported adhesion at low shear rates (< 400 s-1). The binding kinetics of selectin and integrin appear to be optimized to function within discrete ranges of shear rate and stress, providing an intrinsic mechanism for the transition from neutrophil tethering to stable adhesion.     

Hydrodynamic effects and receptor interactions of platelets and their aggregates in linear shear flow.

We have modeled platelet aggregation in a linear shear flow by accounting for two body collision hydrodynamics, platelet activation and receptor biology. Considering platelets and their aggregates as unequal-sized spheres with DLVO interactions (psi(platelet) = -15 mV, Hamaker constant = 10(-19) J), detailed hydrodynamics provided the flow field around the colliding platelets. Trajectory calculations were performed to obtain the far upstream cross-sectional area and the particle flux through this area provided the collision frequency. Only a fraction of platelets brought together by a shearing fluid flow were held together if successfully bound by fibrinogen cross-bridging GPIIb/IIIa receptors on the platelet surfaces. This fraction was calculated by modeling receptor-mediated aggregation using the formalism of Bell (Bell, G. I. 1979. A theoretical model for adhesion between cells mediated by multivalent ligands. Cell Biophys. 1:133-147) where the forward rate of bond formation dictated aggregation during collision and was estimated from the diffusional limited rate of lateral association of receptors multiplied by an effectiveness factor, eta, to give an apparent rate. For a value of eta = 0.0178, we calculated the overall efficiency (including both receptor binding and hydrodynamics effects) for equal-sized platelets with 50,000 receptors/platelet to be 0.206 for G = 41.9 s(-1), 0.05 for G = 335 s(-1), and 0.0086 for G = 1920 s(-1), values which are in agreement with efficiencies determined from initial platelet singlet consumption rates in flow through a tube. From our analysis, we predict that bond formation proceeds at a rate of approximately 0.1925 bonds/microm2 per ms, which is approximately 50-fold slower than the diffusion limited rate of association. This value of eta is also consistent with a colloidal stability of unactivated platelets at low shear rates. Fibrinogen was calculated to mediate aggregation quite efficiently at low shear rates but not at high shear rates. Although secondary collisions (an orbitlike trajectory) form only a small fraction of the total number of collisions, they become important at high shear rates (>750 s(-1)), as these are the only collisions that provide enough time to result in successful aggregate formation mediated by fibrinogen. The overall method provides a hydrodynamic and receptor correction of the Smoluchowski collision kernel and gives a first estimate of eta for the fibrinogen-GPIIb/IIIa cross-bridging of platelets. We also predict that secondary collisions extend the shear rate range at which fibrinogen can mediate successful aggregation.     

Platelet lysis and aggregation in shear fields.

A rotational viscometer was used to study the effects of shear stress on platelets in human platelet-rich plasma (PRP). For 5-min exposure times, shear stresses above 160 dynes/cm2 induced platelet lysis (as determined by release of platelet lactic dehydrogenase). For 30-s exposure times, shear stresses greater than 600 dynes/cm2 were required to induce platelet lysis. The platelet counts of sheared PRP were decreased to as low as one-fifth the original count due largely to shear-induced aggregation. The count is a minimum at intermediate stress levels (200-400 dynes/cm2). Higher stresses induce disaggregation as well as lysis. The diminution in the counts was partially reversed in 2 h incubation after cessation of shearing. Experiments were carried out with three different viscometer configurations so that the shear stress and the solid surface area access could be varied independently. Surface access was not a significant variable in the conditions of the experiments. Thus aggregation and lysis may be induced by stress effects alone as well as by solid surface effects. The results also show that the response of platelets to shear stress is strongly dependent on exposure time. Platelets are much less resistant to shear stress than red cells for relatively long exposure times. However, the converse is true for very short exposure times.     

Experimental collision efficiencies of polymer-flocculated animal cells.

The determination of particle collision kinetics is useful to decouple the effects of process parameters on individual events in flocculation. This paper discusses the effects of flocculation conditions on the collision efficiency of ATCC strain CRL 1606 hybridomas flocculated with poly-L-histidine. Experimental determinations of the collision efficiency of cells in Couette flow are presented over a range of experimental conditions. The collision efficiency correlates with the cell zeta potential to the -2.4 power at high surface coverage, consistent with literature results in latex systems. At low coverage, accounting for the distribution of polymer on the cells corrects for deviation from the high-coverage behavior. Collision is dependent on the hydrodynamic environment as well. At high surface coverage, collision efficiency is weakly dependent on hydrodynamic conditions and follows a dependency on the shear rate and viscosity to the -0.32 power. This is consistent with ionic coagulation theory. At low surface coverage, the collision efficiency is strongly dependent on the viscous fluid forces. The results versus both dose and shear rate over the entire range of surface coverages are consistent with weak intercell bonding. Collision kinetics in the presence of high molecular weight dextrans show steric hindrance to cell collision.     

Mathematical analysis of mural thrombogenesis. Concentration profiles of platelet-activating agents and effects of viscous shear flow.

The concentration profiles of adenosine diphosphate (ADP), thromboxane A2 (TxA2), thrombin, and von Willebrand factor (vWF) released extracellularly from the platelet granules or produced metabolically on the platelet membrane during thrombus growth, were estimated using finite element simulation of blood flow over model thrombi of various shapes and dimensions. The wall fluxes of these platelet-activating agents were estimated for each model thrombus at three different wall shear rates (100 s-1, 800 s-1, and 1,500 s-1), employing experimental data on thrombus growth rates and sizes. For that purpose, whole human blood was perfused in a parallel-plate flow chamber coated with type l fibrillar human collagen, and the kinetic data collected and analyzed by an EPl-fluorescence video microscopy system and a digital image processor. It was found that thrombin concentrations were large enough to cause irreversible platelet aggregation. Although heparin significantly accelerated thrombin inhibition by antithrombin lll, the remaining thrombin levels were still significantly above the minimum threshold required for irreversible platelet aggregation. While ADP concentrations were large enough to cause irreversible platelet aggregation at low shear rates and for small aggregate sizes, TxA2 concentrations were only sufficient to induce platelet shape change over the entire range of wall shear rates and thrombi dimensions studied. Our results also indicated that the local concentration of vWF multimers released from the platelet alpha-granules could be sufficient to modulate platelet aggregation at low and intermediate wall shear rates (less than 1,000 s-1). The sizes of standing vortices formed adjacent to a growing aggregate and the embolizing stresses and the torque, acting at the aggregate surface, were also estimated in this simulation. It was found that standing vortices developed on both sides of the thrombus even at low wall shear rates. Their sizes increased with thrombus size and wall shear rate, and were largely dependent upon thrombus geometry. The experimental observation that platelet aggregation occurred predominantly in the spaces between adjacent thrombi, confirmed the numerical prediction that those standing vortices are regions of reduced fluid velocities and high concentrations of platelet-activating substances, capable of trapping and stimulating platelets for aggregation. The average shear stress and normal stress, as well as the torque, acting to detach the thrombus, increased with increasing wall shear rate. Both stresses were found to be nearly independent of thrombus size and only weekly dependent upon thrombus geometry. Although both stresses had similar values at low wall shear rates, the average shear stress became the predominant embolizing stress at high wall shear rates.     

Nonlinear flow affects hydrodynamic forces and neutrophil adhesion rates in cone-plate viscometers

We present a theoretical and experimental analysis of the effects of nonlinear flow in a cone-plate viscometer. The analysis predicts that flow in the viscometer is a function of two parameters, the Reynolds number and the cone angle. Nonlinear flow occurs at high shear rates and causes spatial variations in wall shear stress, collision frequency, interparticle forces and attachment times within the viscometer. We examined the effect of these features on cellular adhesion kinetics. Based on recent data (Taylor, A. D., S. Neelamegham, J. D. Hellums, et al. 1996. Biophys. J. 71:3488-3500), we modeled neutrophil homotypic aggregation as a process that is integrin-limited at low shear and selectin-limited at high shear. Our calculations suggest that selectin and integrin on-rates lie in the order of 10(-2)-10(-4)/s. They also indicate that secondary flow causes positional variations in adhesion efficiency in the viscometer, and that the overall efficiency is dependent not only on the shear rate, but also the sample volume and the cone angle. Experiments performed with isolated neutrophils confirmed these predictions. In these experiments, enhancing secondary flow by increasing the sample volume from 100 to 1000 microl at 1500/s for a 2 degrees cone caused up to an approximately 45% drop in adhesion efficiency. Our results suggest that secondary flow may significantly influence cellular aggregation, platelet activation, and endothelial cell mechanotransduction measurements made in the viscometer over the range of conditions applied in typical biological studies.     

Fluid shear regulates the kinetics and molecular mechanisms of activation-dependent platelet binding to colon carcinoma cells

This study was undertaken to investigate the kinetics and molecular requirements of platelet binding to tumor cells in bulk suspensions subjected to a uniform linear shear field, using a human colon adenocarcinoma cell line (LS174T) as a model. The effects of shear rate (20-1000 s(-1)), shear exposure time (30-300 s), shear stress (at constant shear rate by adjusting the viscosity of the medium from 1.3-2.6 cP), cell concentration, and platelet activation on platelet-LS174T heteroaggregation were assessed. The results indicate that hydrodynamic shear-induced collisions augment platelet-LS174T binding, which is further potentiated by thrombin/GPRP-NH(2). Peak adhesion efficiency occurs at low shear and decreases with increasing shear. Intercellular contact duration is the predominant factor limiting heteroaggregation at shear rates up to 200 s(-1), whereas these interactions become shear stress-sensitive at > or = 400 s(-1). Heteroaggregation increases with platelet concentration due to an elevation of the intercellular collision frequency, whereas adhesion efficiency remains nearly constant. Moreover, hydrodynamic shear affects the receptor specificity of activation-dependent platelet binding to LS174T cells, as evidenced by the transition from a P-selectin-independent/Arg-Gly-Asp (RGD)-dependent process at 100 s(-1) to a P-selectin/alpha(IIb)beta(3)-dependent interaction at 800 s(-1). This study demonstrates that platelet activation and a fluid-mechanical environment representative of the vasculature affect platelet-tumor cell adhesive interactions pertinent to the process of blood-borne metastasis.     

Probabilistic modeling of platelet aggregation: effects of activation time and receptor occupancy

A mathematical model is constructed to predict the probability that a collision between two activated platelets results in doublet formation mediated by fibrinogen cross-bridges. The model is used to explore the effect of time from activation, looking at both simultaneous and non-simultaneous activation times. Also considered are the impact of blood fibrinogen concentration and various shear rates. The idea of hydrodynamic efficiency [Tandon & Diamond (1997) Biophys. J.73, 2819-2835] is extended by varying the separation distance which is considered to be a collision. From fitting the model to data [Xia & Frojmovic (1994) Biophys. J.66, 2190-2201], it is found that the hydrodynamic efficiency corresponds to short interaction distances ( approximately 14 nm). The model predicts that the probability of forming a doublet increases quickly after activation, remains near its maximum for a significant time interval, and then declines. This may contribute to the regulation of the time and location of platelet aggregation, by ensuring that platelets are more likely to aggregate near an injury, rather than downstream in the vascular system. A newly activated platelet has a high probability of cross-bridging with an already activated platelet. Fibrinogen concentration strongly affects the time course and the equilibrium values of the aggregation probability. These results indicate the importance of considering the progression of the reaction between solution fibrinogen and surface receptors in determining a platelet's ability to aggregate.     

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.