Selectin Catch–Slip Kinetics Encode Shear Threshold Adhesive Behavior of Rolling Leukocytes

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

Michael T. Bestea and Daniel A. Hammera,b,1

Departments of aChemical and Biomolecular Engineering and bBioengineering, University of Pennsylvania, Philadelphia, PA 19104

Edited by Shu Chien, University of California at San Diego, La Jolla, CA, and approved October 27, 2008 (received for review August 19, 2008) The selectin family of leukocyte adhesion receptors is principally bonds with their complementary ligand, P-selectin glycopro- recognized for mediating transient rolling interactions during the tein-1 (PSGL-1) (2, 13–15). Beyond this regime, unbinding inflammatory response. Recent studies using ultrasensitive force becomes accelerated by force. Such evidence for so-called probes to characterize the force–lifetime relationship between P- ‘‘catch–slip’’ kinetics has provided a compelling rationale for and L-selectin and their endogenous ligands have underscored the shear-dependent leukocyte adhesion; however, the molecular ability of increasing levels of force to initially extend the lifetime basis for variations among P-, L-, and E-selectin-mediated rolling of these complexes before disrupting bond integrity. This so-called dynamics remains unclear. Unlike L-selectin, a shear threshold ‘‘catch–slip’’ transition has provided an appealing explanation for is not consistently observed for leukocytes adhering to P- or shear threshold phenomena in which increasing levels of shear E-selectin (2–4), even though both share homologous structures stress stabilize leukocyte rolling under flow. We recently incorpo- with L-selectin, and P-selectin has been extensively characterized rated catch–slip kinetics into a mechanical model for cell adhesion as a bona fide catch bond (13, 16). Recent attempts to under- and corroborated this hypothesis for neutrophils adhering via stand these differences by using site-directed mutagenesis and L-selectin. Here, using adhesive dynamics simulations, we demon- selectin chimeras have revealed a role for allosteric regulation at strate that biomembrane force probe measurements of various P- the interdomain hinge linking the lectin headpiece to the EGF- and L-selectin catch bonds faithfully predict differences in cell like stalk (17, 18). Greater hinge flexibility appears to be adhesion patterns that have been described extensively in vitro. associated with a transition to the resilient molecular confor- Using phenomenological parameters to characterize the dominant mation at lower levels of shear stress and leads to an overall features of molecular force spectra, we construct a generalized enhancement in rolling adhesion. phase map that reveals that robust shear-threshold behavior is To unravel the complex link between catch–slip kinetics and possible only when an applied force very efficiently stabilizes the the shear threshold for leukocyte adhesion, we have coupled bound receptor complex. This criteria explains why only a subset experimental measurements of selectin–ligand force spectra of selectin catch bonds exhibit a shear threshold and leads to a with mechanochemical simulations of adhesion dynamics over a quantitative relationship that may be used to predict the magni- range of fluid shear stress. We demonstrate that precise knowl- tude of the shear threshold for families of catch–slip bonds directly edge of the catch–slip mechanism is not required to accurately from their force spectra. Collectively, our results extend the con- simulate shear threshold rolling dynamics and that features of ceptual framework of adhesive dynamics as a means to translate the force spectra can be appropriately coarse-grained by phe- complex single-molecule biophysics to macroscopic cell behavior. nomenological parameters characterizing the force scale and allosteric efficiency of the catch–slip transition. In turn, simu- force spectroscopy ͉ inflammation ͉ nanomechanics lating a wide spectrum of possible catch bond behaviors reveals empirical criteria that differentiate whether and to what extent y associating with cognate ligands on apposed surfaces, cells adhering through a given catch bond will exhibit a shear Bselectins expressed inducibly on the endothelial lumen (E- threshold. and P-selectin) and constitutively on the microvillar tips of Selectin–Ligand Kinetics peripheral blood leukocytes (L-selectin) mediate cell tethering and rolling adhesion (1). Stable rolling through L-selectin re- Although a variety of mechanisms and associated kinetic models quires a threshold level of fluid shear stress, an unexpected but have been postulated to explain the molecular basis for catch– important consequence that prevents homotypic aggregation slip transitions (16, 19–22), there remains little consensus re- and inappropriate adhesion in low-shear environments (2–4). garding which description is most appropriate for selectins. This Much attention has focused on the underlying molecular kinetics uncertainty is largely a consequence of the considerable number to understand this behavior, with particular emphasis on the role of theoretical parameters—4 or more—used to model low- of convective transport (5–8) and the molecular response to dimensional force–lifetime data. Illustrated conceptually in Fig. mechanical strain (9, 10). Several studies have now firmly 1, the most general mechanism considers 2 distinct, ligand- established that fluid shear rate controls the tethering rate at bound conformations that may reversibly interchange or disso- which cells initially adhere to the substrate (6–8). Although a ciate along independent pathways (19–21). This 2-state model rate-controlled model of rolling adhesion does account for has gained support from structural studies of P-selectin that observed changes in adherent cell flux to a surface above and suggest the existence of ‘‘bent’’ and ‘‘extended’’ molecular below the shear threshold, it does not provide a satisfactory

explanation for why rolling cells in continuous contact with the Author contributions: M.T.B. and D.A.H. designed research; M.T.B. and D.A.H. performed surface roll progressively slower as the optimal level of fluid research; M.T.B. analyzed data; and M.T.B. and D.A.H. wrote the paper. shear is approached. Rather, the favored hypothesis for the shear The authors declare no conﬂict of interest. threshold postulates that the fluid force, translated through This article is a PNAS Direct Submission. molecular linkages, regulates the lifetime and stability of adhe- 1To whom correspondence should be addressed at: Department of Chemical and Biomo- sive contacts at the trailing edge of the rolling cell (6, 11). lecular Engineering, University of Pennsylvania, 240 Skirkanich Hall, 210 South 33rd Street, Although initial experiments suggested that the rate of ligand Philadelphia, PA 19104. E-mail: [email protected]. dissociation increased exponentially with applied tension (9, 12), This article contains supporting information online at www.pnas.org/cgi/content/full/ a number of studies have since demonstrated that low levels of 0808213105/DCSupplemental. force (Ͻ100 pN) initially prolong the lifetime of P- and L-selectin © 2008 by The National Academy of Sciences of the USA

20716–20721 ͉ PNAS ͉ December 30, 2008 ͉ vol. 105 ͉ no. 52 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0808213105 Downloaded by guest on September 27, 2021 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 fcr and kinetic efficiency ␧—that characterize the most important features of the catch-bond regime independent of the underlying mechanism. Consistent with the definition given in (22), fcr corresponds to the force at which bond lifetime exhibits a maximum (Fig. 1B). Here, we define ␧ as the ratio of maximum lifetime tmax ϭ t(fcr)tothe minimum lifetime tmin below the critical force. We favor this definition of the efficiency as opposed to t(fcr)/t(f ϭ 0) (27) because it excludes the assumption that bond lifetime decreases Fig. 1. Generalized 2-state model and force–lifetime behavior. (A) Crystal monotonically as force approaches zero. Indeed, the general structures for P-selectin—unligated and complexed with SGP-3 (23)—suggest dynamic equilibrium between ‘‘bent’’ and ‘‘extended’’ conformations. Me- 2-state model predicts the intriguing possibility of 2-fold ‘‘slip– chanical force tilts the underlying energy landscape, shifting equilibrium away catch–slip’’ transitions if the bent dissociation pathway displays from the bent conformation and accelerating dissociation from the extended a strong force dependence. In this case, bond lifetime exhibits a state (faded contour). (B) The resulting force–lifetime relationship exhibits a local minimum at a nonzero force before reaching tmax (Fig. 1C). biphasic increase and decrease with increasing levels of force. The ‘‘catch’’ Importantly, the critical force and kinetic efficiency may be regime (shaded) is characterized by the lifetime minimum (tmin) at low force obtained by numerical differentiation for any of the aforemen- and lifetime maximum (t ) at the critical force (f ). (C) When a high level of max cr tioned kinetic models, regardless of the complexity of the energy force is required to shift conformational equilibrium, the general model Ͼ predicts a lifetime minimum at nonzero force. landscape. For catch–slip and slip–catch–slip bonds, fcr 0 and ␧ Ͼ 1, whereas fcr ϭ 0 and ␧ ϭ 1 for a perfect slip bond. In this respect, fcr and ␧ represent a minimal parameterization of conformations of the lectin headpiece relative to the EGF-like catch-bond properties that will greatly simplify our subsequent domain (23). At intermediate levels of force, dynamic equilib- analyses. rium between states allows mechanical tension to progressively Because distinct mechanochemistry among selectins is favor the extended conformation, which is assumed to exhibit a thought to underlie differences in shear-promoted leukocyte greater resistance to failure. rolling, we proceeded to compile a complete set of kinetic and From kinetic theory, the mean lifetime of the selectin–ligand phenomenological parameters for published catch bond inter- bond (or equivalently, the inverse dissociation rate, kr) may be actions. Listed in Table S1, we analyzed 48 selectin dissociation estimated if a free energy landscape of the bound complex is experiments reporting force–lifetime data from flow chamber constructed a priori. For the general 2-state model, the assumed assays, atomic force microscopy (AFM), or biomembrane force energy landscape contains 2 minima corresponding to the bent probe (BFP) experiments (10, 13–17). For each dataset, we and extended molecular conformations separated by a small performed nonlinear least-squares regression to extract kinetic energetic barrier (see Fig. 1A). The ensemble average lifetime parameters for the 8-, 5-, and 4-parameter models as outlined in may be computed as the weighted contribution of escape events

Methods. When available, we used published parameter values to BIOPHYSICS from each conformation. Transitions across putative barriers initialize the regression routine. The resulting parameter esti- separating bound and unbound states are, in general, accelerated mates and goodness-of-fit statistics may be found in Tables by mechanical force f, as predicted by Bell’s model; i.e., k ( f) ϭ i S2–S4. Consistent with previous reports, each model was capable k0exp(␥f/k T), where the force dependent transition rate, k ( f) i B i of fitting the experimental data with comparable degrees of is related to the intrinsic rate in the absence of force, k0, the i accuracy (22). reactive compliance characterizing the force sensitivity, ␥, and As demonstrated in Fig. 2 for L-selectin/PSGL-1, our analysis the thermal energy scale, kBT (24). Eight kinetic parameters are therefore required to fully specify the force dependence of the revealed good agreement among datasets obtained by using a 4 possible transition events and the overall dissociation rate, common experimental technique but considerable discrepancies k ( f) for the generalized 2-state model (19). Importantly, not all between data obtained from distinct force probes. BFP data r Ͻ 2-state landscape variations give rise to catch–slip behavior. For collected at the highest temporal resolution ( 1 ms) consistently a catch–slip transition to exist, the dissociation pathway of least reported shorter bond lifetimes at low levels of force, indicating resistance must become progressively inaccessible at higher that temporal aliasing limits accuracy at slower acquisition rates. forces (25). Furthermore, bond lifetimes peaked at relatively higher forces in Given the complexity of an 8-parameter model, several groups tethering experiments, suggesting an underlying bias in the force have proposed mechanistic simplifications to the 2-state formal- calibration. Although AFM and BFP force measurements may ism that reduce the parameterization of the free energy land- be calibrated to high precision (Ϯ1 pN), the force resolution of scape. By assuming that (i) bound conformations rapidly equil- flow chamber measurements (Ϯ10 pN) is fixed by the optical ibrate and (ii) the fast dissociating pathway is insensitive to determination of the lever arm length of the bound tether (9, 15). applied force, Evans and coworkers (16) formulated a special Given these limitations, we concluded that BFP experiments case of the general model requiring only 5 parameters. Alter- provide the most accurate measure of force–lifetime behavior natively, if the bound states are energetically indistinguishable, for P- and L-selectin and their respective ligands. Differentiating the rates describing conformational transitions can be elimi- the regressed kinetic models for these data yielded the corre- nated, reducing the kinetic model to 4 parameters (22). The sponding phenomenological parameters fcr and ␧, which are corresponding mathematical formulations of ␶( f) predicted by given in Table S5.

Beste and Hammer PNAS ͉ December 30, 2008 ͉ vol. 105 ͉ no. 52 ͉ 20717 Downloaded by guest on September 27, 2021 Fig. 2. Comparison of force–lifetime measurements and model regressions obtained for L-selectin/PSGL-1 interactions. Previously reported bond lifetimes were obtained via ﬂow chamber assay, AFM, or BFP as a function of constant tensile force at the indicated temporal resolution (14, 15, 17). The standard deviations and negative inverse slopes of linearized survival histo- grams—auxiliary measurements of bond lifetime—were reported in the ﬂow chamber and AFM analyses. Binding to soluble PSGL-1 monomers (sPSGL-1) and membrane-derived PSGL-1 dimers (mPSGL-1) was assumed to be monomeric. Solid blue lines represent the least-squares regression to the generalized 2-state model described in the text (Selectin-Ligand Kinetics).

Predicting Selectin-Mediated Adhesion Dynamics Fig. 3. Comparison between experimental and simulated neutrophil rolling Provided with quantitative models for complex dissociation dynamics at low shear. (A and B) Rolling velocities (A) and mean stop times (B) for fixed and unfixed neutrophils reported in ref. 15 were measured via flow kinetics, we wished to elucidate how differences in the molecular chamber assay on substrates bearing 140 sites per ␮m2 sPSGL-1. Density- behavior among selectin catch bonds relate to the dynamics of matched adhesive dynamics simulations were performed by using kinetic cell motion under flow by using adhesive dynamics simulations. parameters for L-selectin/sPSGL-1 regressed from BFP lifetime measurements. Adhesive dynamics has been used extensively to investigate the (C) Shear-induced stabilization disappears at low (Ͻ10 ␮mϪ2) and high (Ͼ300 biophysics of cell adhesion (28, 29), and we recently demon- ␮mϪ2) substrate density. At intermediate levels of adhesiveness, the shear strated that integrating catch–slip mechanochemistry can ac- optimum (Ϸ0.8 dyne/cm2) is independent of ligand density. Data represent count for shear-promoted rolling behavior (30). We first eval- the mean Ϯ SD of 5 experiments/simulations. uated the ability of each parameter set to accurately predict the rolling dynamics of human neutrophils on a PSGL-1 substrate When embedded in adhesive dynamics, we found that kinetic observed from 0 to 2 dynes/cm2 wall shear stress. Leukocyte data obtained from BFP experiments yielded the most accurate rolling in vitro is frequently quantified by the total flux of adherent or rolling cells in the frame of view (cells per area per prediction of cell motion. By comparison, parameters derived time). Although this simple metric clearly highlights the shear from flow chamber and AFM lifetime data consistently pre- threshold required to promote robust rolling, accumulation is dicted faster rolling velocities and lower overall pause times directly related to the concentration of flowing cells near the relative to those observed experimentally (Fig. S1). To confirm substrate (31), which is difficult to measure and not generally that we could predict more general features of the shear reported. We rely instead on more precise measurements of cell threshold using this dataset, we also performed simulations over kinematics that may be obtained from high-speed video micros- a variable range of substrate adhesiveness. Multiple studies have copy, namely cell velocity and stop-time distributions. For demonstrated that the shear threshold for adhesion is evident validation, we compared our predictions to the rolling dynamics only when the density of substrate ligand is low, and absent at reported by Yago and coworkers (15) for neutrophils rolling on high ligand density (3, 33). Consistent with these reports, cells Ͼ ␮ Ϫ2 soluble, monomeric PSGL-1 (sPSGL-1) substrates in a parallel- rolled slowly on densities 300 m but ceased to exhibit a plate flow chamber. The surface densities of L-selectin and minimum in rolling velocity (Fig. 3C). By contrast, cell adhesion Ͻ ␮ Ϫ2 PSGL-1 on simulated neutrophils and substrates were specified became saltatory at densities 10 m , with continuous peri- to match the corresponding estimates provided by the authors ods of rolling becoming progressively interrupted by intervals of (251 L-selectin per ␮m2, 140 sPSGL-1 per ␮m2). no adhesion. Within these limits, cell velocity varied inversely Fig. 3 illustrates the comparison between experimental rolling with substrate density and consistently exhibited a minimum dynamics of fixed and unfixed neutrophils from (15) and those near a shear stress of 0.8 dynes/cm2, in good agreement with simulated by using kinetic parameters obtained from BFP experimental measurements of the shear threshold for neutro- experiments. Predicted cell velocity initially increases rapidly phils adhering to PSGL-1. In a similar manner, we confirmed with increasing shear stress before reaching a maximum, then that dimerization of adhesion receptors promoted more robust falls and exhibits a more gradual increase with rising shear stress, rolling while leaving the magnitude of the shear threshold mirroring the experimental measurements (Fig. 3A). Agreement unaltered (34). Much like a doubling in substrate density, between simulation and experiment is excellent except at the dimerizing L-selectin in our simulations resulted in slower cell lowest reported shear stress of 0.1 dyne/cm2. Similarly, the rolling but an identical shear threshold at 0.8 dynes/cm2 (Fig. S1). calculated mean stop time transitions through a maximum with rising shear between 0.5 and 1.0 dyne/cm2, showing good agree- Prediction of Shear Threshold Adhesion Among Selectins and ment with experiment Ͼ0.1 dyne/cm2 (Fig. 3B). Below this level Their Ligands of shear, Brownian fluctuations reduce the signal-to-noise ratio Given the ability to accurately simulate the motion of adherent of detected rolling steps and, although filtered, contribute to an neutrophils, we asked whether adhesive dynamics could be used overestimation in the observed cell velocity and pause times (32). to identify criteria that would estimate characteristics of the Our predictions of cell velocity and pause time faithfully predict shear threshold directly from molecular force spectra. Because a shear threshold in neutrophil adhesion at a shear optimum of mapping adhesion dynamics to mechanistic features of a pre- Ϸ0.8 dyne/cm2 for L-selectin/PSGL-1 interactions. sumed energy landscape would simply reflect an arbitrary choice

20718 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0808213105 Beste and Hammer Downloaded by guest on September 27, 2021 Fig. 4. Selectin phenomenological parameters and prediction of shear-threshold behavior. (A and B) Regression analysis of experimental L-selectin/PSGL-1 force spectra from refs. 10 and 13–17. Measurements of tmin, tmax, and fmax show good consistency among data obtained from the same force probe, but less agreement between techniques. (C and D) Systematic variation in tmin, tmax, and fmax is observed among 7 distinct catch bonds probed via BFP. (E) Magnitude of shear-stabilized rolling as a function of critical force fcr and kinetic efﬁciency ␧ as predicted by adhesive dynamics. Symbols reﬂect regressed kinetic parameters for interactions between P-selectin, L-selectin, or L-selectinN138G and the indicated ligands obtained from BFP lifetime data. The magnitude of the rolling velocity decrease observed experimentally for microbeads adhering through the corresponding selectin–ligand pairs (15, 17, 35) is indicated by symbol size and shading.

of one kinetic model over another, we opted instead to express greater enhancement of slow rolling adhesion at the shear our results in terms of fcr and ␧, universal parameters that are threshold (i.e., a more pronounced shear threshold effect). We model-independent. When assessing the accuracy of our predic- find that high fcr, high ␧ catch bonds exhibit the greatest decrease tions, we relied solely upon BFP force spectra reported in refs. in rolling velocity, whereas low fcr, low ␧ catch bonds exhibit no 16 and 17 for 7 distinct catch bonds to avoid problematic stabilization. The intermediate regime is characterized by a comparisons between dissimilar force probe measurements of fcr, stabilization boundary that suggests a tradeoff between critical tmin, and tmax(Fig. 4 A and B). Corresponding adhesion dynam- force and efficiency. In fact, as fcr approaches zero, the efficiency ics—rolling velocity as a function of shear stress—for micro- required to mediate any reduction in rolling velocity diverges to spheres adhering via these 7 receptor/ligand pairs were analyzed infinity. from refs. 15, 17, and 35. Superposing the regressed (fcr, ␧) catch bond data onto the To quantify the magnitude of shear-enhanced adhesion, we calculated results reveals good agreement between the predicted considered the decrease in rolling velocity observed with in- and observed magnitudes of shear stabilization. For every creasing shear stress, leading up to the shear threshold. For molecular pair in Fig. 4E, symbol shading and size reflect the example, the velocity of unfixed neutrophils in Fig. 3A drops magnitude of the experimentally observed decrease in rolling from 45 ␮m/s at 0.2 dyne/cm2 to 15 ␮m/s at 0.8 dyne/cm2, a net velocity. Consistent with experiments, P-selectin bonds with decrease of 30 ␮m/s. In published reports of microspheres PSGL-1, GP-1, SGP-3, and sLex fall within the regime in which

adhering via P-selectin, this characteristic inflection in rolling a decrease in rolling velocity is predicted to be absent. In BIOPHYSICS velocity was conspicuously absent; that is, P-selectin catch bonds contrast, wild-type and mutant L-selectin catch bonds with did not manifest any measurable stabilization in rolling velocity. PSGL-1 and 6-sulfo-sLex all fall within the predicted shear In contrast, microspheres adhering through wild-type and mu- threshold regime with relative stabilization magnitudes consis- tant L-selectin displayed varying degrees of shear stabilization tent with the predicted gradient. Together, the regression and between Ϸ10 and 35 ␮m/s. This disparity highlights an important simulation analyses confirm that catch bonds with a combination aspect of catch bond adhesion, namely that catch–slip kinetics do of a large critical force and high kinetic efficiency are most not necessarily confer cells or particles with adhesive behavior effective at enhancing adhesion at the shear threshold. that exhibits a shear threshold. Finally, we addressed whether we might develop a similar To decipher this complex relationship between kinetics and criterion to predict the magnitude of the threshold shear stress adhesion, we performed a multiplexed series of simulations with for cells or microparticles adhering through an arbitrary catch catch bonds characterized by variable phenomenological param- bond. For a stationary sphere adhering through a single molec- eters and calculated the expected stabilization in rolling velocity ular tether, the force acting on the bond may be directly related leading up to the shear threshold. Regression analysis (Fig. 4C) to the fluid shear stress by a force balance if the angle at which revealed that selectin bonds were primarily distinguished by their the tether meets the substrate, ␪ is known (12). For a sphere of values of tmin, with tmax being approximately constant (Ϸ0.2 s). radius r, this conversion reduces to This allowed us to exclusively consider variations in tmin, which could be manipulated to achieve a desired level of kinetic cos ␪ ␶ ϭ f, [1] efficiency within the simulations. To fully span the set of ␣r2 phenomenological parameters derived from experimental force spectra (Fig. 4 C and D), we varied critical force linearly from 0 where ␶ is the fluid shear stress, f the force on the bond, and ␣ ϭ to 100 pN and efficiency logarithmically from 1 to 100. At every 1.7005⅐6␲ is a dimensionless coefficient for the viscous drag on (fcr, ␧) permutation, rolling dynamics were quantified at 0.1 a sphere near a plane wall (15). Although Eq. 1 is strictly an dyne/cm2 intervals from 0 to 3 dynes/cm2 to identify the mag- approximation of the adhesive force experienced by a rolling cell nitude of shear stabilization. Our results are illustrated as a or particle due to dynamic loading of adherent tethers, it does gradient map in Fig. 4E, with darker contours indicating a suggest that the critical force at which bond lifetime is maximum

Beste and Hammer PNAS ͉ December 30, 2008 ͉ vol. 105 ͉ no. 52 ͉ 20719 Downloaded by guest on September 27, 2021 rupture reported from simulations). As expected, wild-type and mutant L-selectin tethers to PSGL-1 approached the surface at a shallower angle of inclination than those to 6-sulfo-sLex (Ϸ62.7° versus Ϸ74.7°, respectively) due to the longer length of PSGL-1. 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 defini- tively 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 phenomeno- Fig. 5. Prediction of the shear threshold. Adhesive dynamics simulations of logical features of selectin–ligand bonds proves sufficient to map Ͻ Ͻ Ͻ ␧ Ͻ catch bonds spanning 0 fcr 100 and 1 100 reveal that the critical shear the relationship between catch–slip kinetics and shear-promoted stress, ␶cr required to minimize rolling velocity scales linearly with fcr and is sufficiently independent of variations in ␧ (shaded region, Inset). Thus, when adhesion. These phenomenological parameters—the critical force, f and kinetic efficiency, ␧—are physical properties that the shear threshold and fcr are known for 1 molecular pair, the angle of tether cr inclination, ␪ can be calculated directly from a static force balance (Eq. 1). The are encoded by the energy landscape of the selectin–ligand indicated values for ␪ were obtained in this manner (or from direct simulation interaction and represent the most important determinants of for neutrophils) and used to predict the shear threshold for complementary shear-threshold behavior for rolling leukocytes. molecular pairs expected to have identical angles of inclination. Error bars We anticipate that the phenomenological criteria may provide represent the uncertainty as determined by measurement resolution de- an understanding of why other biological molecules known to act scribed in refs. 15 and 17. as catch bonds do not exhibit a pronounced shear-induced stabilization. Much like selectins, the bacterial adhesin FimH is will correspond exactly to the shear stress at which rolling a well-studied catch bond that selectively exhibits a shear thresh- velocity is minimum. Yago et al. (15) previously demonstrated old for its monomannose but not trimannose ligand (36). Be- that this relation was sufficient to model the scaling of the shear cause both bonds transition to the catch regime at similar levels threshold for L-selectin coated microspheres of variable radii. To of force, it is likely that the absent shear threshold for trimannose further validate Eq. 1 as a heuristic relationship between bond adhesion reflects an underlying variation in kinetic efficiency. mechanics and rolling dynamics, we confirmed by simulation This selective modulation of force-sensitivity represents another that the critical shear stress ␶ required to minimize cell rolling example of a natural strategy that might be exploited in the cr rational design and engineering of novel adhesion molecules. velocity increased linearly with fcr and was largely independent ␧ of the choice of (Fig. 5 Inset). This calculation implies that Methods precise knowledge of ␪, r, and f is sufficient to estimate the shear cr Parameter Regression and Analysis. Published force spectra for P- and L- threshold for any catch–slip bond. selectin were compiled according to the mode of force application (i.e., flow To test this assertion, we again considered the 4 catch–slip chamber, AFM, or BFP) (10, 13–17) (Table S1). All L-selectin lifetime measure- interactions between L-selectin or L-selectinN138G and PSGL-1 ments were interpreted as monomeric binding events (14). Assuming equal or 6-sulfo-sLex. Assuming that a single residue substitution load distribution and random failure, the lifetime data reported in ref. 13 for preserves the physical length of the selectin, any difference in dimeric P-selectin–PSGL-1 interactions, was transformed to the equivalent tether orientation among these bonds will be attributed to monomeric lifetime (22). Parameters for the 2-state (19), 2-state/rapid equi- variations in ligand rather than receptor size. Indeed, because librium (16), and 1-state (22) kinetic models were obtained by fitting each PSGL-1 is Ͼ20 times the length of the 6-sulfo-sLex construct dataset by using Levenberg–Marquardt nonlinear least-squares minimization Ϯ described in ref. 15 (Ϸ50 nm versus Ϸ2 nm), the variation in in IGOR Pro (WaveMetrics). Maximum-likelihood parameter estimates SD. (Tables S2–S4) were determined by assuming that lifetime measurement error tether inclination between these ligands is expected to be ␪ for each dataset was normally distributed with zero mean and constant significant. Although individual measures of have not been variance. The goodness of fit, reported as the ␹2 value, is estimated from the reported, estimates for 1 molecular pair can be obtained from calculated variance in the residuals. independent measurement of the remaining variables in Eq. 1 for a distinct molecular pair expected to have an identical orienta- Adhesive Dynamics. Adhesive interactions between leukocytes and comple- 2 tion. For example, the observed fcr (61.8 pN) and ␶cr (1 dyne/cm ) mentary substrates are modeled by using adhesive dynamics (37). Monomeric for wild-type L-selectin/PSGL-1 suggests a contact angle of 62.2° P- and L-selectin are treated as linear springs with elasticities 1 pN/nm and 4 pN/nm, respectively (38). The corresponding equilibrium bond lengths with for 3-␮m microbeads. Using ␪ ϭ 62.2° with fcr (47.9 pN) for the N138G mutant predicts a shear threshold of 0.77 dyne/cm2 that PSGL-1 are estimated from electron micrograph measurements to be Ϸ88 nm ϩ Ϸ ϩ compares well with the observed threshold at 0.75 dync/cm2. Fig. (38 50) for P-selectin/PSGL-1 and 62 nm (12 50) for L-selectin/PSGL-1 (39). Consistent with experimental observation, receptors are locally clustered to the 5 illustrates the accuracy of this technique for all 4 L-selectin– tips of microvilli. The deformation of bound microvilli is modeled by using the ligand pairs. For each data point, the predicted shear threshold viscoelastic rheology reported by Shao and coworkers (40). Additional parame- was calculated by using the angle of inclination determined from ters describing cellular geometry, microvillus distribution, and molecular densi- the complementary selectin and the indicated ligand (or for ties are taken from literature reports on human neutrophils (Table S6). neutrophils, directly from the most frequent angle of bond The forward binding rate kf of unbound receptors is calculated as a

20720 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0808213105 Beste and Hammer Downloaded by guest on September 27, 2021 function of both separation distance and relative motion between the positions of the cell and all bound tethers based on the instantaneous microvilli and substrate as described in ref. 5. The catch–slip lifetime, ␶( f ) velocity determined from the hydrodynamic mobility calculation. Rolling for each bound complex is calculated from Eqs. S9, S10,orS11 given in SI dynamics—velocity and pause time distributions—are quantiﬁed over 30 s Text, depending on the choice of kinetic model. Simulations proceed by (i) by using a time interval of ␦t ϭ 1 ␮s. testing unbound molecules in the contact area for formation with proba- ϭ Ϫ Ϫ ⅐␦ bility Pf 1 exp( kf t); (ii) testing existing bonds for dissociation with ACKNOWLEDGMENTS. We thank Kelly Caputo and Andrew Trister for helpful probability Pr ϭ 1 Ϫ exp(Ϫkr⅐␦t); (iii) summing all adhesive, hydrodynamic, discussions. This work was supported by National Institutes of Health Grant and repulsive forces/torques acting on the cell; and (iv) updating the HL-18208.

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