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Selectin catch–slip kinetics encode shear threshold adhesive behavior of rolling leukocytes

Edited by Shu Chien, University of California at San Diego, La Jolla, CA, and approved October 27, 2008 (received for review August 19, 2008)
Abstract
The selectin family of leukocyte adhesion receptors is principally recognized for mediating transient rolling interactions during the inflammatory response. Recent studies using ultrasensitive force probes to characterize the force–lifetime relationship between P and Lselectin and their endogenous ligands have underscored the ability of increasing levels of force to initially extend the lifetime of these complexes before disrupting bond integrity. This socalled “catch–slip” transition has provided an appealing explanation for shear threshold phenomena in which increasing levels of shear stress stabilize leukocyte rolling under flow. We recently incorporated catch–slip kinetics into a mechanical model for cell adhesion and corroborated this hypothesis for neutrophils adhering via Lselectin. Here, using adhesive dynamics simulations, we demonstrate that biomembrane force probe measurements of various P and Lselectin catch bonds faithfully predict differences in cell adhesion patterns that have been described extensively in vitro. Using phenomenological parameters to characterize the dominant features of molecular force spectra, we construct a generalized phase map that reveals that robust shearthreshold behavior is possible only when an applied force very efficiently stabilizes the bound receptor complex. This criteria explains why only a subset of selectin catch bonds exhibit a shear threshold and leads to a quantitative relationship that may be used to predict the magnitude of the shear threshold for families of catch–slip bonds directly from their force spectra. Collectively, our results extend the conceptual framework of adhesive dynamics as a means to translate complex singlemolecule biophysics to macroscopic cell behavior.
By associating with cognate ligands on apposed surfaces, selectins expressed inducibly on the endothelial lumen (E and Pselectin) and constitutively on the microvillar tips of peripheral blood leukocytes (Lselectin) mediate cell tethering and rolling adhesion (1). Stable rolling through Lselectin requires a threshold level of fluid shear stress, an unexpected but important consequence that prevents homotypic aggregation and inappropriate adhesion in lowshear environments (2–4). Much attention has focused on the underlying molecular kinetics to understand this behavior, with particular emphasis on the role of convective transport (5–8) and the molecular response to mechanical strain (9, 10). Several studies have now firmly established that fluid shear rate controls the tethering rate at which cells initially adhere to the substrate (6–8). Although a ratecontrolled model of rolling adhesion does account for observed changes in adherent cell flux to a surface above and below the shear threshold, it does not provide a satisfactory explanation for why rolling cells in continuous contact with the surface roll progressively slower as the optimal level of fluid shear is approached. Rather, the favored hypothesis for the shear threshold postulates that the fluid force, translated through molecular linkages, regulates the lifetime and stability of adhesive contacts at the trailing edge of the rolling cell (6, 11).
Although initial experiments suggested that the rate of ligand dissociation increased exponentially with applied tension (9, 12), a number of studies have since demonstrated that low levels of force (<100 pN) initially prolong the lifetime of P and Lselectin bonds with their complementary ligand, Pselectin glycoprotein1 (PSGL1) (2, 13–15). Beyond this regime, unbinding becomes accelerated by force. Such evidence for socalled “catch–slip” kinetics has provided a compelling rationale for sheardependent leukocyte adhesion; however, the molecular basis for variations among P, L, and Eselectinmediated rolling dynamics remains unclear. Unlike Lselectin, a shear threshold is not consistently observed for leukocytes adhering to P or Eselectin (2–4), even though both share homologous structures with Lselectin, and Pselectin has been extensively characterized as a bona fide catch bond (13, 16). Recent attempts to understand these differences by using sitedirected mutagenesis and selectin chimeras have revealed a role for allosteric regulation at the interdomain hinge linking the lectin headpiece to the EGFlike stalk (17, 18). Greater hinge flexibility appears to be associated with a transition to the resilient molecular conformation at lower levels of shear stress and leads to an overall enhancement in rolling adhesion.
To unravel the complex link between catch–slip kinetics and the shear threshold for leukocyte adhesion, we have coupled experimental measurements of selectin–ligand force spectra with mechanochemical simulations of adhesion dynamics over a range of fluid shear stress. We demonstrate that precise knowledge of the catch–slip mechanism is not required to accurately simulate shear threshold rolling dynamics and that features of the force spectra can be appropriately coarsegrained by phenomenological parameters characterizing the force scale and allosteric efficiency of the catch–slip transition. In turn, simulating a wide spectrum of possible catch bond behaviors reveals empirical criteria that differentiate whether and to what extent cells adhering through a given catch bond will exhibit a shear threshold.
Selectin–Ligand Kinetics
Although a variety of mechanisms and associated kinetic models have been postulated to explain the molecular basis for catch–slip transitions (16, 19–22), there remains little consensus regarding which description is most appropriate for selectins. This uncertainty is largely a consequence of the considerable number of theoretical parameters—4 or more—used to model lowdimensional force–lifetime data. Illustrated conceptually in Fig. 1, the most general mechanism considers 2 distinct, ligandbound conformations that may reversibly interchange or dissociate along independent pathways (19–21). This 2state model has gained support from structural studies of Pselectin that suggest the existence of “bent” and “extended” molecular conformations of the lectin headpiece relative to the EGFlike domain (23). At intermediate levels of force, dynamic equilibrium between states allows mechanical tension to progressively favor the extended conformation, which is assumed to exhibit a greater resistance to failure.
From kinetic theory, the mean lifetime of the selectin–ligand bond (or equivalently, the inverse dissociation rate, k_{r}) may be estimated if a free energy landscape of the bound complex is constructed a priori. For the general 2state model, the assumed energy landscape contains 2 minima corresponding to the bent and extended molecular conformations separated by a small energetic barrier (see Fig. 1A). The ensemble average lifetime may be computed as the weighted contribution of escape events from each conformation. Transitions across putative barriers separating bound and unbound states are, in general, accelerated by mechanical force f, as predicted by Bell's model; i.e., k_{i}(f) = k_{i}^{0} exp(γf/k_{B}T), where the force dependent transition rate, k_{i}(f) is related to the intrinsic rate in the absence of force, k_{i}^{0}, the reactive compliance characterizing the force sensitivity, γ, and the thermal energy scale, k_{B}T (24). Eight kinetic parameters are therefore required to fully specify the force dependence of the 4 possible transition events and the overall dissociation rate, k_{r}(f) for the generalized 2state model (19). Importantly, not all 2state landscape variations give rise to catch–slip behavior. For a catch–slip transition to exist, the dissociation pathway of least resistance must become progressively inaccessible at higher forces (25).
Given the complexity of an 8parameter model, several groups have proposed mechanistic simplifications to the 2state formalism that reduce the parameterization of the free energy landscape. By assuming that (i) bound conformations rapidly equilibrate and (ii) the fast dissociating pathway is insensitive to applied force, Evans and coworkers (16) formulated a special case of the general model requiring only 5 parameters. Alternatively, if the bound states are energetically indistinguishable, the rates describing conformational transitions can be eliminated, reducing the kinetic model to 4 parameters (22). The corresponding mathematical formulations of τ(f) predicted by each model are included in supporting information (SI) Text. Not surprisingly, both simplified treatments retain sufficient mathematical flexibility to fit force–lifetime data with accuracy comparable to the general model (22, 26). Thus, our ability to discern the exact mechanism from the candidate models remains inherently limited by the coarse resolution of laboratory measurements.
To circumvent this ambiguity, we adopt 2 phenomenological parameters—the critical force f_{cr} and kinetic efficiency ε—that characterize the most important features of the catchbond regime independent of the underlying mechanism. Consistent with the definition given in (22), f_{cr} corresponds to the force at which bond lifetime exhibits a maximum (Fig. 1B). Here, we define ε as the ratio of maximum lifetime t_{max} = t(f_{cr}) to the minimum lifetime t_{min} below the critical force. We favor this definition of the efficiency as opposed to t(f_{cr})/t(f = 0) (27) because it excludes the assumption that bond lifetime decreases monotonically as force approaches zero. Indeed, the general 2state model predicts the intriguing possibility of 2fold “slip–catch–slip” transitions if the bent dissociation pathway displays a strong force dependence. In this case, bond lifetime exhibits a local minimum at a nonzero force before reaching t_{max} (Fig. 1C). Importantly, the critical force and kinetic efficiency may be obtained by numerical differentiation for any of the aforementioned kinetic models, regardless of the complexity of the energy landscape. For catch–slip and slip–catch–slip bonds, f_{cr} > 0 and ε > 1, whereas f_{cr} = 0 and ε = 1 for a perfect slip bond. In this respect, f_{cr} and ε represent a minimal parameterization of catchbond properties that will greatly simplify our subsequent analyses.
Because distinct mechanochemistry among selectins is thought to underlie differences in shearpromoted leukocyte rolling, we proceeded to compile a complete set of kinetic and phenomenological parameters for published catch bond interactions. Listed in Table S1, we analyzed 48 selectin dissociation experiments reporting force–lifetime data from flow chamber assays, atomic force microscopy (AFM), or biomembrane force probe (BFP) experiments (10, 13–17). For each dataset, we performed nonlinear leastsquares regression to extract kinetic parameters for the 8, 5, and 4parameter models as outlined in Methods. When available, we used published parameter values to initialize the regression routine. The resulting parameter estimates and goodnessoffit statistics may be found in Tables S2–S4. Consistent with previous reports, each model was capable of fitting the experimental data with comparable degrees of accuracy (22).
As demonstrated in Fig. 2 for Lselectin/PSGL1, our analysis revealed good agreement among datasets obtained by using a common experimental technique but considerable discrepancies between data obtained from distinct force probes. BFP data collected at the highest temporal resolution (<1 ms) consistently reported shorter bond lifetimes at low levels of force, indicating that temporal aliasing limits accuracy at slower acquisition rates. Furthermore, bond lifetimes peaked at relatively higher forces in tethering experiments, suggesting an underlying bias in the force calibration. Although AFM and BFP force measurements may be calibrated to high precision (±1 pN), the force resolution of flow chamber measurements (±10 pN) is fixed by the optical determination of the lever arm length of the bound tether (9, 15). Given these limitations, we concluded that BFP experiments provide the most accurate measure of force–lifetime behavior for P and Lselectin and their respective ligands. Differentiating the regressed kinetic models for these data yielded the corresponding phenomenological parameters f_{cr} and ε, which are given in Table S5.
Predicting SelectinMediated Adhesion Dynamics
Provided with quantitative models for complex dissociation kinetics, we wished to elucidate how differences in the molecular behavior among selectin catch bonds relate to the dynamics of cell motion under flow by using adhesive dynamics simulations. Adhesive dynamics has been used extensively to investigate the biophysics of cell adhesion (28, 29), and we recently demonstrated that integrating catch–slip mechanochemistry can account for shearpromoted rolling behavior (30). We first evaluated the ability of each parameter set to accurately predict the rolling dynamics of human neutrophils on a PSGL1 substrate observed from 0 to 2 dynes/cm^{2} wall shear stress. Leukocyte rolling in vitro is frequently quantified by the total flux of adherent or rolling cells in the frame of view (cells per area per time). Although this simple metric clearly highlights the shear threshold required to promote robust rolling, accumulation is directly related to the concentration of flowing cells near the substrate (31), which is difficult to measure and not generally reported. We rely instead on more precise measurements of cell kinematics that may be obtained from highspeed video microscopy, namely cell velocity and stoptime distributions. For validation, we compared our predictions to the rolling dynamics reported by Yago and coworkers (15) for neutrophils rolling on soluble, monomeric PSGL1 (sPSGL1) substrates in a parallelplate flow chamber. The surface densities of Lselectin and PSGL1 on simulated neutrophils and substrates were specified to match the corresponding estimates provided by the authors (251 Lselectin per μm^{2}, 140 sPSGL1 per μm^{2}).
Fig. 3 illustrates the comparison between experimental rolling dynamics of fixed and unfixed neutrophils from (15) and those simulated by using kinetic parameters obtained from BFP experiments. Predicted cell velocity initially increases rapidly with increasing shear stress before reaching a maximum, then falls and exhibits a more gradual increase with rising shear stress, mirroring the experimental measurements (Fig. 3A). Agreement between simulation and experiment is excellent except at the lowest reported shear stress of 0.1 dyne/cm^{2}. Similarly, the calculated mean stop time transitions through a maximum with rising shear between 0.5 and 1.0 dyne/cm^{2}, showing good agreement with experiment >0.1 dyne/cm^{2} (Fig. 3B). Below this level of shear, Brownian fluctuations reduce the signaltonoise ratio of detected rolling steps and, although filtered, contribute to an overestimation in the observed cell velocity and pause times (32). Our predictions of cell velocity and pause time faithfully predict a shear threshold in neutrophil adhesion at a shear optimum of ≈0.8 dyne/cm^{2} for Lselectin/PSGL1 interactions.
When embedded in adhesive dynamics, we found that kinetic data obtained from BFP experiments yielded the most accurate prediction of cell motion. By comparison, parameters derived from flow chamber and AFM lifetime data consistently predicted faster rolling velocities and lower overall pause times relative to those observed experimentally (Fig. S1). To confirm that we could predict more general features of the shear threshold using this dataset, we also performed simulations over a variable range of substrate adhesiveness. Multiple studies have demonstrated that the shear threshold for adhesion is evident only when the density of substrate ligand is low, and absent at high ligand density (3, 33). Consistent with these reports, cells rolled slowly on densities >300 μm^{−2} but ceased to exhibit a minimum in rolling velocity (Fig. 3C). By contrast, cell adhesion became saltatory at densities <10 μm^{−2}, with continuous periods of rolling becoming progressively interrupted by intervals of no adhesion. Within these limits, cell velocity varied inversely with substrate density and consistently exhibited a minimum near a shear stress of 0.8 dynes/cm^{2}, in good agreement with experimental measurements of the shear threshold for neutrophils adhering to PSGL1. In a similar manner, we confirmed that dimerization of adhesion receptors promoted more robust rolling while leaving the magnitude of the shear threshold unaltered (34). Much like a doubling in substrate density, dimerizing Lselectin in our simulations resulted in slower cell rolling but an identical shear threshold at 0.8 dynes/cm^{2} (Fig. S1).
Prediction of Shear Threshold Adhesion Among Selectins and Their Ligands
Given the ability to accurately simulate the motion of adherent neutrophils, we asked whether adhesive dynamics could be used to identify criteria that would estimate characteristics of the shear threshold directly from molecular force spectra. Because mapping adhesion dynamics to mechanistic features of a presumed energy landscape would simply reflect an arbitrary choice of one kinetic model over another, we opted instead to express our results in terms of f_{cr} and ε, universal parameters that are modelindependent. When assessing the accuracy of our predictions, we relied solely upon BFP force spectra reported in refs. 16 and 17 for 7 distinct catch bonds to avoid problematic comparisons between dissimilar force probe measurements of f_{cr}, t_{min}, and t_{max}(Fig. 4 A and B). Corresponding adhesion dynamics—rolling velocity as a function of shear stress—for microspheres adhering via these 7 receptor/ligand pairs were analyzed from refs. 15, 17, and 35.
To quantify the magnitude of shearenhanced adhesion, we considered the decrease in rolling velocity observed with increasing shear stress, leading up to the shear threshold. For example, the velocity of unfixed neutrophils in Fig. 3A drops from 45 μm/s at 0.2 dyne/cm^{2} to 15 μm/s at 0.8 dyne/cm^{2}, a net decrease of 30 μm/s. In published reports of microspheres adhering via Pselectin, this characteristic inflection in rolling velocity was conspicuously absent; that is, Pselectin catch bonds did not manifest any measurable stabilization in rolling velocity. In contrast, microspheres adhering through wildtype and mutant Lselectin displayed varying degrees of shear stabilization between ≈10 and 35 μm/s. This disparity highlights an important aspect of catch bond adhesion, namely that catch–slip kinetics do not necessarily confer cells or particles with adhesive behavior that exhibits a shear threshold.
To decipher this complex relationship between kinetics and adhesion, we performed a multiplexed series of simulations with catch bonds characterized by variable phenomenological parameters and calculated the expected stabilization in rolling velocity leading up to the shear threshold. Regression analysis (Fig. 4C) revealed that selectin bonds were primarily distinguished by their values of t_{min}, with t_{max} being approximately constant (≈0.2 s). This allowed us to exclusively consider variations in t_{min}, which could be manipulated to achieve a desired level of kinetic efficiency within the simulations. To fully span the set of phenomenological parameters derived from experimental force spectra (Fig. 4 C and D), we varied critical force linearly from 0 to 100 pN and efficiency logarithmically from 1 to 100. At every (f_{cr}, ε) permutation, rolling dynamics were quantified at 0.1 dyne/cm^{2} intervals from 0 to 3 dynes/cm^{2} to identify the magnitude of shear stabilization. Our results are illustrated as a gradient map in Fig. 4E, with darker contours indicating a greater enhancement of slow rolling adhesion at the shear threshold (i.e., a more pronounced shear threshold effect). We find that high f_{cr}, high ε catch bonds exhibit the greatest decrease in rolling velocity, whereas low f_{cr}, low ε catch bonds exhibit no stabilization. The intermediate regime is characterized by a stabilization boundary that suggests a tradeoff between critical force and efficiency. In fact, as f_{cr} approaches zero, the efficiency required to mediate any reduction in rolling velocity diverges to infinity.
Superposing the regressed (f_{cr}, ε) catch bond data onto the calculated results reveals good agreement between the predicted and observed magnitudes of shear stabilization. For every molecular pair in Fig. 4E, symbol shading and size reflect the magnitude of the experimentally observed decrease in rolling velocity. Consistent with experiments, Pselectin bonds with PSGL1, GP1, SGP3, and sLe^{x} fall within the regime in which a decrease in rolling velocity is predicted to be absent. In contrast, wildtype and mutant Lselectin catch bonds with PSGL1 and 6sulfosLe^{x} all fall within the predicted shear threshold regime with relative stabilization magnitudes consistent with the predicted gradient. Together, the regression and simulation analyses confirm that catch bonds with a combination of a large critical force and high kinetic efficiency are most effective at enhancing adhesion at the shear threshold.
Finally, we addressed whether we might develop a similar criterion to predict the magnitude of the threshold shear stress for cells or microparticles adhering through an arbitrary catch bond. For a stationary sphere adhering through a single molecular tether, the force acting on the bond may be directly related to the fluid shear stress by a force balance if the angle at which the tether meets the substrate, θ is known (12). For a sphere of radius r, this conversion reduces to where τ is the fluid shear stress, f the force on the bond, and α = 1.7005·6π is a dimensionless coefficient for the viscous drag on a sphere near a plane wall (15). Although Eq. 1 is strictly an approximation of the adhesive force experienced by a rolling cell or particle due to dynamic loading of adherent tethers, it does suggest that the critical force at which bond lifetime is maximum will correspond exactly to the shear stress at which rolling velocity is minimum. Yago et al. (15) previously demonstrated that this relation was sufficient to model the scaling of the shear threshold for Lselectin coated microspheres of variable radii. To further validate Eq. 1 as a heuristic relationship between bond mechanics and rolling dynamics, we confirmed by simulation that the critical shear stress τ_{cr} required to minimize cell rolling velocity increased linearly with f_{cr} and was largely independent of the choice of ε (Fig. 5Inset). This calculation implies that precise knowledge of θ, r, and f_{cr} is sufficient to estimate the shear threshold for any catch–slip bond.
To test this assertion, we again considered the 4 catch–slip interactions between Lselectin or LselectinN138G and PSGL1 or 6sulfosLe^{x}. Assuming that a single residue substitution preserves the physical length of the selectin, any difference in tether orientation among these bonds will be attributed to variations in ligand rather than receptor size. Indeed, because PSGL1 is >20 times the length of the 6sulfosLe^{x} construct described in ref. 15 (≈50 nm versus ≈2 nm), the variation in tether inclination between these ligands is expected to be significant. Although individual measures of θ have not been reported, estimates for 1 molecular pair can be obtained from independent measurement of the remaining variables in Eq. 1 for a distinct molecular pair expected to have an identical orientation. For example, the observed f_{cr} (61.8 pN) and τ_{cr} (1 dyne/cm^{2}) for wildtype Lselectin/PSGL1 suggests a contact angle of 62.2° for 3μm microbeads. Using θ = 62.2° with f_{cr} (47.9 pN) for the N138G mutant predicts a shear threshold of 0.77 dyne/cm^{2} that compares well with the observed threshold at 0.75 dync/cm^{2}. Fig. 5 illustrates the accuracy of this technique for all 4 Lselectin–ligand pairs. For each data point, the predicted shear threshold was calculated by using the angle of inclination determined from the complementary selectin and the indicated ligand (or for neutrophils, directly from the most frequent angle of bond rupture reported from simulations). As expected, wildtype and mutant Lselectin tethers to PSGL1 approached the surface at a shallower angle of inclination than those to 6sulfosLe^{x} (≈62.7° versus ≈74.7°, respectively) due to the longer length of PSGL1. By comparison, simulated neutrophil tethers exhibited a tether inclination of 54.0°, reflecting the additional extension provided by microvilli. In each case, the predictive capacity of Eq. 1 is excellent, demonstrating that the static force balance can be extended as a reasonable approximation to predict dynamic features of rolling adhesion such as the shear threshold.
Discussion
We have extensively canvassed the literature to identify force spectra for all leukocyte adhesion complexes known to act as catch bonds and embedded these spectra into adhesive dynamics to understand the origin of the shear threshold effect. Our attempts to regress multiple kinetic models derived for complex energy landscapes lead us to conclude that there remains insufficient resolution in the available force spectra to definitively ascertain the response of the energy landscape to force; hence, a precise mechanism for a given catch–slip bond remains elusive. Despite this ambiguity, characterizing the phenomenological features of selectin–ligand bonds proves sufficient to map the relationship between catch–slip kinetics and shearpromoted adhesion. These phenomenological parameters—the critical force, f_{cr} and kinetic efficiency, ε—are physical properties that are encoded by the energy landscape of the selectin–ligand interaction and represent the most important determinants of shearthreshold behavior for rolling leukocytes.
We anticipate that the phenomenological criteria may provide an understanding of why other biological molecules known to act as catch bonds do not exhibit a pronounced shearinduced stabilization. Much like selectins, the bacterial adhesin FimH is a wellstudied catch bond that selectively exhibits a shear threshold for its monomannose but not trimannose ligand (36). Because both bonds transition to the catch regime at similar levels of force, it is likely that the absent shear threshold for trimannose adhesion reflects an underlying variation in kinetic efficiency. This selective modulation of forcesensitivity represents another example of a natural strategy that might be exploited in the rational design and engineering of novel adhesion molecules.
Methods
Parameter Regression and Analysis.
Published force spectra for P and Lselectin were compiled according to the mode of force application (i.e., flow chamber, AFM, or BFP) (10, 13–17) (Table S1). All Lselectin lifetime measurements were interpreted as monomeric binding events (14). Assuming equal load distribution and random failure, the lifetime data reported in ref. 13 for dimeric Pselectin–PSGL1 interactions, was transformed to the equivalent monomeric lifetime (22). Parameters for the 2state (19), 2state/rapid equilibrium (16), and 1state (22) kinetic models were obtained by fitting each dataset by using Levenberg–Marquardt nonlinear leastsquares minimization in IGOR Pro (WaveMetrics). Maximumlikelihood parameter estimates ± SD. (Tables S2–S4) were determined by assuming that lifetime measurement error for each dataset was normally distributed with zero mean and constant variance. The goodness of fit, reported as the χ^{2} value, is estimated from the calculated variance in the residuals.
Adhesive Dynamics.
Adhesive interactions between leukocytes and complementary substrates are modeled by using adhesive dynamics (37). Monomeric P and Lselectin are treated as linear springs with elasticities 1 pN/nm and 4 pN/nm, respectively (38). The corresponding equilibrium bond lengths with PSGL1 are estimated from electron micrograph measurements to be ≈88 nm (38 + 50) for Pselectin/PSGL1 and ≈62 nm (12 + 50) for Lselectin/PSGL1 (39). Consistent with experimental observation, receptors are locally clustered to the tips of microvilli. The deformation of bound microvilli is modeled by using the viscoelastic rheology reported by Shao and coworkers (40). Additional parameters describing cellular geometry, microvillus distribution, and molecular densities are taken from literature reports on human neutrophils (Table S6).
The forward binding rate k_{f} of unbound receptors is calculated as a function of both separation distance and relative motion between the microvilli and substrate as described in ref. 5. The catch–slip lifetime, τ(f) for each bound complex is calculated from Eqs. S9, S10, or S11 given in SI Text, depending on the choice of kinetic model. Simulations proceed by (i) testing unbound molecules in the contact area for formation with probability P_{f} = 1 − exp(−k_{f}·δt); (ii) testing existing bonds for dissociation with probability P_{r} = 1 − exp(−k_{r}·δt); (iii) summing all adhesive, hydrodynamic, and repulsive forces/torques acting on the cell; and (iv) updating the positions of the cell and all bound tethers based on the instantaneous velocity determined from the hydrodynamic mobility calculation. Rolling dynamics—velocity and pause time distributions—are quantified over 30 s by using a time interval of δt = 1 μs.
Acknowledgments
We thank Kelly Caputo and Andrew Trister for helpful discussions. This work was supported by National Institutes of Health Grant HL18208.
Footnotes
 ^{1}To whom correspondence should be addressed at: Department of Chemical and Biomolecular Engineering, University of Pennsylvania, 240 Skirkanich Hall, 210 South 33rd Street, Philadelphia, PA 19104. Email: hammer{at}seas.upenn.edu

Author contributions: M.T.B. and D.A.H. designed research; M.T.B. and D.A.H. performed research; M.T.B. analyzed data; and M.T.B. and D.A.H. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0808213105/DCSupplemental.
 © 2008 by The National Academy of Sciences of the USA
References
 ↵
 Kansas GS
 ↵
 ↵
 Lawrence MB,
 Kansas GS,
 Kunkel EJ,
 Ley K
 ↵
 Ramachandran V,
 et al.
 ↵
 ↵
 Chen S,
 Springer TA
 ↵
 ↵
 ↵
 Alon R,
 Chen S,
 Puri KD,
 Finger EB,
 Springer TA
 ↵
 Dwir O,
 et al.
 ↵
 ↵
 ↵
 ↵
 Sarangapani KK,
 et al.
 ↵
 Yago T,
 et al.
 ↵
 Evans E,
 Leung A,
 Heinrich V,
 Zhu C
 ↵
 Lou J,
 et al.
 ↵
 ↵
 Bartolo D,
 Derenyi I,
 Ajdari A
 ↵
 Barsegov V,
 Thirumalai D
 ↵
 ↵
 ↵
 ↵
 Bell GI
 ↵
 ↵
 ↵
 Pereverzev YV,
 Prezhdo OV,
 Thomas WE,
 Sokurenko EV
 ↵
 Chang KC,
 Tees DF,
 Hammer DA
 ↵
 ↵
 Caputo K,
 Lee D,
 King M,
 Hammer DA
 ↵
 ↵
 ↵
 ↵
 Dwir O,
 et al.
 ↵
 ↵
 Nilsson LM,
 Thomas WE,
 Trintchina E,
 Vogel V,
 Sokurenko EV
 ↵
 ↵
 ↵
 Li F,
 et al.
 ↵
 Shao JY,
 TingBeall HP,
 Hochmuth RM
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