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.     

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.     

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.     

Interaction forces between red cells agglutinated by antibody. II. Measurement of hydrodynamic force of breakup.

The expressions derived in the previous paper for the respective normal, F3, and shear forces, Fshear, acting along and perpendicular to the axis of a doublet of rigid spheres, were used to determine the hydrodynamic forces required to separate two red cell spheres of antigenic type B crosslinked by the corresponding antibody. Cells were sphered and swollen in isotonic buffered glycerol containing 8 X 10(-5) M sodium dodecyl sulfate, fixed in 0.085% glutaraldehyde, and suspended in aqueous glycerol (viscosity: 15-34 mPa s), containing 0.15 M NaCl and anti-B antibody from human hyperimmune antiserum at concentrations from 0.73 to 3.56 vol%. After incubating and mixing for 12 h, doublets were observed through a microscope flowing in a 178-micron tube by gravity feed between two reservoirs. Using a traveling microtube apparatus, the doublets were tracked in a constantly accelerating flow and the translational and rotational motions were recorded on videotape until breakup occurred. From a frame by frame replay of the tape, the radial position, velocity and orientation of the doublet were obtained and the normal and shear forces of separation at breakup computed. Both forces increased significantly with increasing antiserum concentration, the mean values of F3 increasing from 0.060 to 0.197 nN, and Fshear from 0.023 to 0.072 nN. There was no significant effect of glycerol viscosity on the forces of separation. It was not possible to determine whether the shear or normal force was responsible for doublet separation. Measurements of the mean dimensionless period of rotation, TG, of doublets in suspensions containing 0.73 and 2.40% antiserum undergoing steady flow were also made to test whether the spheres were rigidly linked or capable of some independent rotation. A fairly narrow distribution in TG about the value 15.64, predicted for rigidly-linked doublets, was obtained at both antiserum concentrations.     

Interaction forces between red cells agglutinated by antibody. III. Micromanipulation.

In the flow studies described in two previous papers (Tha, S. P., and H. L. Goldsmith, 1986, Biophys. J. 50:1109-1116; Tha, S. P., J. Shuster, and H. L. Goldsmith, 1986, Biophys. J. 50:1117-1126), hydrodynamic forces of the order of 10(-11) N (mu dyn) were applied to measure the force of separation of doublets of hardened, sphered human red blood cells cross-linked by anti-B antibody. The same cell preparation and hyperimmune antiserum has here been used to carry out experiments with micropipet aspiration techniques. One cell of a doublet was aspirated onto a holding pipet, and a second aspiration pipet was brought into proximity of the other cell so that the two pipets and the doublet were colinear. Suction was then raised until the two cells separated. Some doublets were assembled by aspiration of a singlet, bringing a second singlet into apposition with the first, and releasing it from the pipet which was then withdrawn. Cells could be repeatedly assembled and separated. At 3.56% vol/vol antiserum, the mean normal force of separation was 0.45 +/- 0.11 nN in phosphate-buffered saline suspensions containing 2.5 x 10(4) cells/microliter; at 1.22% vol/vol antiserum, the value was 0.22 +/- 0.11 nN. The above values of the force were approximately 2.5 x greater than those from the flow studies. The data could be fitted to a Poisson distribution with 0.05 nN as the force needed to break a single cross-bridge (c.f. 0.024 nN from the previous hydrodynamic data). The forces of separation of randomly assembled doublets were lower than those of preexisting doublets. Repeated assembly and separation of doublets showed that the cell surfaces are nonuniform in adhesion strength both over the local scale less than 0.25 micron2 and the cell population.     

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.     

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.     

Interaction forces between red cells agglutinated by antibody. I. Theoretical.

A general method of calculating forces, torques, and translational and rotational velocities of rigid, neutrally buoyant spheres suspended in viscous liquids undergoing a uniform shear flow has been given by Arp and Mason (1977). The method is based on the matrix formulation of hydrodynamic resistances in creeping flow by Brenner and O'Neill (1972). We describe the solution of the Brenner-O'Neill force-torque vector equation in terms of the particle and external flow field coordinates and derive expressions for the normal force acting along, and the shear force acting perpendicular to, the axis of the doublet of spheres, the latter explicitly given for the first time. The equations consist of a term comprising force and torque coefficients obtained from the matrices of the hydrodynamic resistances (functions of the distance h between sphere surfaces which have been computed), and terms comprising the orientation of the doublet axis relative to the coordinates of the external flow field and the shear stress (which can be experimentally determined). We have applied the theory to a system of doublets of sphered, hardened human red cells of group A or B antigenic type cross-linked by the corresponding antibody at a fixed interparticle distance. Working from studies of the breakup of doublets of red cells in an accelerating Poiseuille flow, given in the succeeding paper, we are able to compute the hydrodynamic force required to separate the two spheres. Previous work has shown that the theory can be applied to doublets in a variable shear, Poiseuille flow, provided the ratio of particle to tube diameter is small. In calculating the force-torque coefficients it was assumed that the cells are crosslinked by antibody with h = 20 nm.     

Micropipet-based pico force transducer: in depth analysis and experimental verification.

Measurements of forces in the piconewton range are very important for the study of molecular adhesion and mechanics. Recently, a micropipet-based force transducer for this type of experiment was presented (E. Evans, K. Ritchie, and R. Merkel, 1995, Biophys. J., 68:2580-2587). In the present article we give a detailed mechanical analysis of this transducer, including nonlinear effects. An analytical expression for the transducer stiffness at small elongations is given. Using magnetic tweezers (F. Ziemann, J. Rädler, and E. Sackmann, 1994, Biophys. J., 66:2210-2216), we were able to determine the force displacement relation of this transducer experimentally. Forces from approximately 10 pN to 500 pN were applied. Theoretical predictions and experimental results coincide remarkably well.     

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

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

Effect of receptor-ligand affinity on the strength of endothelial cell adhesion.

The objective of this study was to determine the effect of receptor-ligand affinity on the strength of endothelial cell adhesion. Linear and cyclic forms of the fibronectin (Fn) cell-binding domain peptide Arg-Gly-Asp (RGD) were covalently immobilized to glass, and Fn was adsorbed onto glass slides. Bovine aortic endothelial cells attached to the surfaces for 15 min. The critical wall shear stress at which 50% of the cells detached increased nonlinearly with ligand density and was greater with immobilized cyclic RGD than with immobilized linear RGD or adsorbed Fn. To directly compare results for the different ligand densities, the receptor-ligand dissociation constant and force per bond were estimated from data for the critical shear stress and contact area. Total internal reflection fluorescence microscopy was used to measure the contact area as a function of separation distance. Contact area increased with increasing ligand density. Contact areas were similar for the immobilized peptides but were greater on surfaces with adsorbed Fn. The dissociation constant was determined by nonlinear regression of the net force on the cells to models that assumed that bonds were either uniformly stressed or that only bonds on the periphery of the contact region were stressed (peeling model). Both models provided equally good fits for cells attached to immobilized peptides whereas the peeling model produced a better fit of data for cells attached to adsorbed Fn. Cyclic RGD and linear RGD both bind to the integrin alpha v beta 3, but immobilized cyclic RGD exhibited a greater affinity than did linear RGD. Receptor affinities of Fn adsorbed to glycophase glass and Fn adsorbed to glass were similar. The number of bonds was calculated assuming binding equilibrium. The peeling model produced good linear fits between bond force and number of bonds. Results of this study indicate that 1) bovine aortic endothelial cells are more adherent on immobilized cyclic RGD peptide than linear RGD or adsorbed Fn, 2) increased adhesion is due to a greater affinity between cyclic RGD and its receptor, and 3) the affinity of RGD peptides and adsorbed Fn for their receptors is increased after immobilization.     

Direct measurement of inter-doublet elasticity in flagellar axonemes.

The outer doublet microtubules in ciliary and flagellar axonemes are presumed to be connected with each other by elastic links called the inter-doublet links or the nexin links, but it is not known whether there actually are such elastic links. In this study, to detect the elasticity of the putative inter-doublet links, shear force was applied to Chlamydomonas axonemes with a fine glass needle and the longitudinal elasticity was determined from the deflection of the needle. Wild-type axonemes underwent a high-frequency, nanometer-scale vibration in the presence of ATP. When longitudinal shear force was applied, the average position of the needle tip attached to the axoneme moved linearly with the force applied, yielding an estimate of spring constant of 2.0 (S.D.: 0.8) pN/nm for 1 microm of axoneme. This value did not change in the presence of vanadate, i.e., when dynein does not form strong cross bridges. In contrast, it was at least five times larger when ATP was absent, i.e., when dynein forms strong cross bridges. The measured elasticity did not significantly differ in various mutant axonemes lacking the central-pair microtubules, a subset of inner-arm dynein, outer-arm dynein, or the radial spokes, although it was somewhat smaller in the latter two mutants. It was also observed that the shear displacement in an axoneme in the presence of ATP often took place in a stepwise manner. This suggests that the inter-doublet links can reversibly detach from and reattach to the outer doublets in a cooperative manner. This study thus provides the first direct measure of the elasticity of inter-doublet links and also demonstrates its dynamic nature.     

Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion.

Measurements of the dimensions and membrane rotational frequency of individual erythrocytes steadily tank-treading in a rheoscope are used to deduce the surface shear viscosity of the membrane. The method is based on an integral energy principle which says that the power supplied to the tank-treading cell by the suspending fluid is equal to the rate at which energy is dissipated by viscous action in the membrane and cytoplasm. The integrals involved are formulated with the aid of an idealized mathematical model of the tank-treading red blood cell (RBC) (Keller and Skalak, 1982, J. Fluid Mech., 120:24-27) and evaluated numerically. The outcome is a surface-averaged value of membrane viscosity which is representative of a finite interval of membrane shear rate. The numerical values computed show a clear shear-thinning characteristic as well as a significant augmentation of viscosity with cell age and tend toward agreement with those determined for the rapid phase of shape recovery in micropipettes (Chien, S., K.-L. P. Sung, R. Skalak, S. Usami, and A. Tozeren, 1978, Biophys. J., 24:463-487). The computations also indicate that the rate of energy dissipation in the membrane is always substantially greater than that in the cytoplasm.     

A direct comparison of selectin-mediated transient, adhesive events using high temporal resolution

Leukocyte capture and rolling on the vascular endothelium is mediated principally by the selectin family of cell adhesion receptors. In a parallel plate flow chamber, neutrophil rolling on purified selectins or a selectin-ligand substrate was resolved by high speed videomicroscopy as a series of ratchet-like steps with a characteristic time constant (Kaplanski, G., C. Farnarier, O. Tissot, A. Pierres, A.-M. Benoliel, M. C. Alessi, S. Kaplanski, and P. Bongrand. 1993. Biophys. J. 64:1922-1933; Alon, R., D. A. Hammer, and T. A. Springer. 1995. Nature (Lond.). 374:539-542). Under shear, neutrophil arrests due to bond formation events were as brief as 4 ms. Pause time distributions for neutrophils tethering on P-, E-, L-selectin, or peripheral node addressin (PNAd) were compared at estimated single bond forces ranging from 37 to 250 pN. Distributions of selectin mediated pause times were fit to a first order exponential, resulting in a molecular dissociation constant (k(off)) for the respective selectin as a function of force. At estimated single bond forces of 125 pN and below, all three selectin dissociation constants fit the Bell and Hookean spring models of force-driven bond breakage equivalently. Unstressed k(off) values based on the Bell model were 2.4, 2.6, 2.8, 3.8 s(-1) for P-selectin, E-selectin, L-selectin, and PNAd, respectively. Bond separation distances (reactive compliance) were 0.39, 0.18, 1.11, 0.59 A for P-selectin, E-selectin, L-selectin, and PNAd, respectively. Dissociation constants for L-selectin and P-selectin at single bond forces above 125 pN were considerably lower than either Bell or Hookean spring model predictions, suggesting the existence of two regimes of reactive compliance. Additionally, interactions between L-selectin and its leukocyte ligand(s) were more labile in the presence of flow than the L-selectin endothelial ligand, PNAd, suggesting that L-selectin ligands may have different molecular and mechanical properties. Both types of L-selectin bonds had a higher reactive compliance than P-selectin or E-selectin bonds.     

The mechanical stability of immunoglobulin and fibronectin III domains in the muscle protein titin measured by atomic force microscopy.

The domains of the giant muscle protein titin (connectin) provide interaction sites for other sarcomeric proteins and fulfill mechanical functions. In this paper we compare the unfolding forces of defined regions of different titin isoforms by single-molecule force spectroscopy. Constructs comprising six to eight immunoglobulin (Ig) domains located in the mechanically active I-band part of titin are compared to those containing fibronectin III (Fn3) and Ig domains from the A-band part. The high spatial resolution of the atomic force microscope allows us to detect differences in length as low as a few amino acids. Thus constructs of different lengths may be used as molecular rulers for structural comparisons with other modular proteins. The unfolding forces range between 150 and 300 pN and differ systematically between the constructs. Fn3 domains in titin exhibit 20% lower unfolding forces than Ig domains. Fn3 domains from tenascin, however, unfold at forces only half those of titin Fn3 domains. This indicates that the tightly folded titin domains are designed to maintain their structural integrity, even under the influence of stretching forces. Hence, at physiological forces, unfolding is unlikely unless the forces are applied for a long time (longer than minutes).     

Nano- to microscale dynamics of P-selectin detachment from leukocyte interfaces. II. Tether flow terminated by P-selectin dissociation from PSGL-1

We have used a biomembrane force probe decorated with P-selectin to form point attachments with PSGL-1 receptors on a human neutrophil (PMN) in a calcium-containing medium and then to quantify the forces experienced by the attachment during retraction of the PMN at fixed speed. From first touch to final detachment, the typical force history exhibited the following sequence of events: i), an initial linear-elastic displacement of the PMN surface, ii), an abrupt crossover to viscoplastic flow that signaled membrane separation from the interior cytoskeleton and the beginning of a membrane tether, and iii), the final detachment from the probe tip most often by one precipitous step of P-selectin:PSGL-1 dissociation. Analyzing the initial elastic response and membrane unbinding from the cytoskeleton in our companion article I, we focus in this article on the regime of tether extrusion that nearly always occurred before release of the extracellular adhesion bond at pulling speeds > or =1 microm/s. The force during tether growth appeared to approach a plateau at long times. Examined over a large range of pulling speeds up to 150 microm/s, the plateau force exhibited a significant shear thinning as indicated by a weak power-law dependence on pulling speed, f(infinity) = 60 pN(nu(pull)/microm/s)(0.25). Using this shear-thinning response to describe the viscous element in a nonlinear Maxwell-like fluid model, we show that a weak serial-elastic component with a stiffness of approximately 0.07 pN/nm provides good agreement with the time course of the tether force approach to the plateau under constant pulling speed.     

Effect of ionic strength on skinned rabbit psoas fibers in the presence of magnesium pyrophosphate.

The effect of ionic strength on the kinetics of myosin cross-bridges in the presence of the ATP analogue PP, has been examined. It was found that increasing ionic strength from moderate values (mu approximately 100 mM) to high values (mu approximately 200 mM) has three effects. It causes a big decrease in the half time for the force decay after a small stretch, it causes a significant decrease in the sigmoidicity of the nucleotide analogue concentration dependence of the "apparent rate constant" of force decay after a small stretch, and it causes a big decrease in the range of rate constants necessary to describe the multiexponential force decay. It causes the last of these by causing a much larger increase in the slowest rate constants of the decay than in the fastest rate constants. The results suggest that whereas the behavior of cross-bridges in the presence of ATP is well-described by the simple independent-head equilibrium cross-bridge model of Schoenberg (1985. Biophys. J. 48:467-475), cross-bridges in the presence of the ATP analogue PPi require the more complicated double-headed equilibrium cross-bridge model of Anderson and Schoenberg (1987. Biophys. J. 52: 1077-1082) to describe their behavior.     

Equilibrium muscle cross-bridge behavior. Theoretical considerations. II. Model describing the behavior of strongly-binding cross-bridges when both heads of myosin bind to the actin filament.

A model has been developed for characterizing the interaction between strongly-binding myosin cross-bridges and actin in muscle fibers under equilibrium conditions where both heads of the myosin cross-bridge bind to actin. The model, that of Anderson and Schoenberg (1987. Biophys. J. 52:1077-1082) is quite similar to that of Schoenberg (1985. Biophys. J. 48:467-475), except that explicit account is taken of the fact that each crossbridge has two heads which can bind to actin. The key assumption that allows this model to explain a large body of data unexplained by the Schoenberg (1985) model is that the two crossbridge heads are not totally independent of one another after attachment. After the first head attaches, the second head is then free to attach only to an actin site distal to the first head. This means that when the more distally attached head subsequently detaches and reattaches (as the heads continually do), it will not reattach in a position of lesser strain and reduce the force it supports, but instead will remain attached in its strained position until the proximally attached head also detaches. This model gives an explanation for two important and otherwise unexplained observations made previously: it explains why at ionic strengths in the range of 50-120 mM, (a) the rate constant of force decay after a small stretch is a sigmoidal function of nucleotide analogue concentration, and (b) why in the presence of analogues or in rigor the rate constant of force decay after a small stretch is significantly slower than the rate constant for myosin subfragment-1 detachment from actin in solution.