Regulation of Catch Bonds by Rate of Force Application

Abstract

The current paradigm for receptor-ligand dissociation kinetics assumes off-rates as functions of instantaneous force without impact from its prior history. This a priori assumption is the foundation for predicting dissociation from a given initial state using kinetic equations. Here we have invalidated this assumption by demonstrating the impact of force history with single-bond kinetic experiments involving selectins and their ligands that mediate leukocyte tethering and rolling on vascular surfaces during inflammation. Dissociation of bonds between L-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) loaded at a constant ramp rate to a constant hold force behaved as catch-slip bonds at low ramp rates that transformed to slip-only bonds at high ramp rates. Strikingly, bonds between L-selectin and 6-sulfo-sialyl Lewis X were impervious to ramp rate changes. This ligand-specific force history effect resembled the effect of a point mutation at the L-selectin surface (L-selectinA108H) predicted to contact the former but not the latter ligand, suggesting that the high ramp rate induced similar structural changes as the mutation. Although the A108H substitution in L-selectin eliminated the ramp rate responsiveness of its dissociation from PSGL-1, the inverse mutation H108A in P-selectin acquired the ramp rate responsiveness. Our data are well explained by the sliding-rebinding model for catch-slip bonds extended to incorporate the additional force history dependence, with Ala-108 playing a pivotal role in this structural mechanism. These results call for a paradigm shift in modeling the mechanical regulation of receptor-ligand bond dissociation, which includes conformational coupling between binding pocket and remote regions of the interacting molecules.

Introduction

Receptor-ligand interactions are usually modeled by chemical reaction kinetics wherein force-dependent kinetic rates are key parameters (1). A typical example is the interactions between selectins and their ligands that mediate the tethering and rolling of circulating leukocytes on vascular surfaces during their recruitment to secondary lymphoid organs or inflammation sites (1). L-selectin is expressed on leukocytes and binds to P-selectin glycoprotein ligand-1 (PSGL-1),⁴ a leukocyte mucin, and to 6-sulfo-sialyl Lewis X (6-sulfo-sLe^x), a terminal component of glycans on a group of mucins expressed on endothelial cells in lymph nodes and some sites of inflammation (1). Selectin-ligand interactions provide adhesive forces for leukocytes to balance hemodynamic forces, and their kinetics have long been shown to depend on blood flow (2).

Since first modeled by Bell (3) and later by many others (4–11), the existing paradigm for the mechanical regulation of receptor-ligand dissociation assumes a priori that the kinetic rates depend only on the instantaneous, present level of force on the bond but not its prior history. A simple model is the first-order single-step irreversible dissociation of single monomeric bonds:

where p is the probability of having a bond at time t. The off-rate k₋₁ is assumed to be a single-valued function of force f, which may depend on time. Dynamic force spectroscopy (DFS) is the most common approach used to evaluate k₋₁(f) (6, 8, 12). Recognizing that force is loaded to a bond over time along an experimentally controlled path, e.g. constant rate of ramping, given by f(t) = r_ft, where r_f is ramp rate. DFS transforms the independent variable in Equation 1 from t to f and determines k₋₁(f) from the rupture force distributions p(f/r_f) or their peaks measured over a range of ramp rates (6, 8, 12). A much easier to interpret but far more time-consuming experiment is that of the force clamp assay, which determines k₋₁(f) from the lifetime distributions p(t) measured over a range of constant forces (13). Although a bond has to be loaded by a ramp force before the force is clamped, the lifetime is measured after clamping the force. This is equivalent to setting the initial time at the moment when ramping stops and solving Equation 1, with k₋₁ as a constant (because f is a constant) without variable transformation (13). It should be noted that the force clamp assay has been used exclusively in flow chamber experiments (4, 5, 9, 13–16). Under the present paradigm, k₋₁(f) for the same molecular interaction should be the same regardless of the assay (force ramp or force clamp) used for its measurement. Although this assertion is supported by studies of homophilic cadherin bonds (17), it is not consistent with data from several other systems.

Indeed, significant and extensive discrepancies in off-rate estimations from force clamp and DFS measurement methods have been reported that are not only quantitative but also qualitative. Force clamp measurements of dissociation of respective counter-molecules from P-selectin (13), L-selectin (9), E-selectin (18), integrin α₅β₁ (19), integrin α_Lβ₂ (20), and myosin (21) revealed catch bonds at certain force ranges. In sharp contrast, DFS measurements of the same interactions observed only slip bonds over the entire force ranges studied (7, 21–27). Even for unfolding of the von Willebrand factor A2 domain, force clamp measurements observed catch-slip bonds (28), and DFS measurements observed slip bonds (29). These discrepancies persisted even when the two types of measurements were made in the same laboratories by the same experimenters using the same instruments with the same reagents (21, 30).

To reconcile the discrepant off-rates for the interaction between P-selectin and PSGL-1, we had previously introduced the concept of force history-dependent off-rate, i.e. k₋₁ at t is a functional of all values of f in the past times up to the present time t, not just its present value at t (30). This new concept should not be confused with the concept of ramp rate-dependent rupture forces. In DFS, pulling bonds with different ramp rates results in different rupture force distributions, i.e. p(f/r_f) or its peak depends on the force history or the ramp rate r_f (31). However, the off-rate k₋₁ is still assumed to depend only on the present level of force f, not its prior history. This is the theoretical basis for using DFS to derive the same k₋₁(f) from rupture forces measured over a range of ramp rates (6, 8, 32). Furthermore, the new concept should not be confused with the concept of a bond transitioning among multiple stable states and dissociating along multiple pathways, which have been proposed to explain transition between catch and slip bonds (9–11, 14, 16, 33). The latter concept requires more involved models than Equation 1 and more kinetic rates than just a single k₋₁, but they are all assumed to be single-valued functions of force. Moreover, the new concept is different from that reported by Pincet and Husson (34), who suggested that the history of streptavidin-biotin bond formation might influence the distribution of initial subpopulations of bonds among multiple bound states and therefore might impact bond dissociation kinetics.

Because the a priori assumption that kinetic rates depend only on force still serves as the theoretical basis for conceptualizing how applied force could alter bond dissociation, we set out to test this fundamental assumption and to exemplify force history regulation of selectin-ligand dissociation. We characterized their bond lifetimes under controlled histories of force application using atomic force microscopy (AFM) and biomembrane force probe (BFP) experiments (see Fig. 1, A and B). Bonds were loaded along multiple families of “ramp and hold” force histories, each consisting of two line segments on the force-time plane: an ascending segment representing the ramp phase and a plateau segment representing the hold phase. These segments were chosen so as to simplify the path of force application to two parameters only: the slope of the segment during the ramp phase (i.e. ramp rate) and the force during the hold phase (see Fig. 1C). The bond lifetime was measured on the hold phase only, i.e. after the end of ramp phase. We asked whether different ramp rates (that represent different prior force histories) affected the lifetimes of the bonds between L-selectin and their ligands (as shown in Figs. 4–8) and if so, how. These experiments revealed that L-selectin off-rates exhibit ligand-specific “memory” for the past history of force applied on the bonds, which is distinct from those previously reported (see Fig. 9). More importantly, we could trace the structural basis for this unusual kinetic property to a single residue in L-selectin (Ala-108), suggesting that the observed force history effect was probably related to changes in molecular conformation. These findings call for a paradigm shift in modeling receptor-ligand dissociation kinetics. Therefore, we extended the sliding-rebinding model previously proposed for catch-slip bonds (11, 14, 16) to incorporate this additional regulation by force history (see Figs. 10 and 11). Like catch-slip bonds that are found in many molecular systems, a similar force history regulation mechanism may be operative in the interaction kinetics of other molecular systems such as integrins.

FIGURE 1.

Experimental setup and measurement of bond lifetimes. AFM (A) and BFP (B) setup depicting all of the molecules used. sPSGL-1, PSGL-1, 2-GSP-6, and 6-sulfo-sLe^x were captured by PL2 or streptavidin coated on AFM tips or BFP probe beads. Membrane L-selectin was reconstituted into supported bilayers. L-selectinA108H, P-selectinH108A-Ig, and L-selectin-Ig were respectively captured by HPC4, GG-7, and anti-Fc polyclonal antibody coated on polystyrene dishes and BFP target beads. C, force-time curves illustrating bonds ramped (blue) at two rates (left and right) to two forces (top and bottom) to measure lifetime (green) until rupture (red). Cantilever bending at different times is shown.

FIGURE 4.

Dual dependence of l-selectin-PSGL-1 bond lifetime on hold force and ramp rate. Bond lifetimes were measured (cf. Fig. 1C) using AFM (A–F) or BFP (G–I). The average (± S.E.) of several tens of lifetimes per force bin (circles) is plotted versus hold force loaded at the indicated ramp rate and fitted by the modified sliding-rebinding model (curves). The data at low ramp rates are biphasic because force initially prolongs (catch) and then shortens (slip) lifetime. Increasing ramp rate shifts the curve leftward, progressively reducing the catch-slip transition force (where lifetime peaks) until the catch bond regime vanishes. However, changes in peak lifetimes are mild.

FIGURE 5.

Dual dependence of l-selectin-2-GSP-6 bond lifetime on hold force and ramp rate. Bond lifetimes were measured as shown in Fig. 1C using AFM. The average (± S.E.) of several tens of lifetimes per force bin (circles) is plotted versus hold force loaded at the indicated ramp rate and fitted by the modified sliding-rebinding model (curves). The data and model predictions are similar to Fig. 4. At a low ramp rate, a biphasic trend is observed with force initially prolonging (catch bond) and then shortening (slip bond) lifetime (A). At an intermediate ramp rate, the biphasic curve is shifted leftward with a reduced catch-slip transition force (where the lifetime peaks) but with a similar peak lifetime (B). At a high ramp rate, the catch bond regime vanishes completely, leaving a slip-only bond (C).

FIGURE 6.

Dependence of l-selectin-6-sulfo-sLe^x bond lifetime on hold force but not on ramp rate. A, model of L-selectin-PSGL-1 complex (based on the co-crystal structure of the P-selectin-PSGL-1 complex (43). Different contacts of L-selectin (green) with PSGL-1 glycan (pink) and peptide (purple) are shown. The dashed box indicates a region that has been magnified in Fig. 8A. The golden sphere represents a Ca²⁺ ion. The Ala-108 residue in L-selectin is marked. B–F, bond lifetimes were measured (cf. Fig. 1C) using BFP (B and C) or AFM (D–F). Average (± S.E.) of several tens of lifetimes per force bin is plotted versus hold force loaded at the indicated ramp rate. The data in all panels show similar biphasic trend of catch-slip bonds that are indifferent to ramp rate increases of one or two logs.

FIGURE 7.

AFM lifetime distributions. The natural log (number of measurements with a lifetime ≥ t) versus t plots measured at the indicated forces for interactions of membrane L-selectin with sPSGL-1 (A–C) and 6-sulfo-sLe^x (D and E) are shown. The 95% confidence intervals of the slopes are shown by the paired, color-matched lines (R² > 0.95 for most of the cases). With sPSGL-1 interactions, the switch from catch-slip bonds to slip-only bonds with increasing ramp rate (Fig. 4) is evident from the change in the slopes of the distributions. In contrast, for 6-sulfo-sLe^x interactions, there is no such switch in the slopes, corroborating the conservation of the catch-slip bond behavior at all ramp rates tested (Fig. 6).

FIGURE 8.

Elimination and generation of ramp rate dependence by point mutations. A, crystal structure (43) (lower left) and models (all other panels) of wild-type (left column) or mutant (right column) L-selectin (top row) or P-selectin (bottom row) complexed with PSGL-1, highlighting the change in residue 108. The same color codes are used as in Fig. 6A (showing only the boxed region). B–F, bond lifetimes were measured (cf. Fig. 1C) using AFM for PSGL-1 interacting with L-selectinA108H (B and C) or P-selectinH108A (D–F). The average (± S.E.) of several tens of lifetimes per force bin (circles) is plotted versus hold force loaded at the indicated ramp rate and fitted by the modified sliding-rebinding model (curves). Replacing L-selectin Ala-108 by His converted the catch-slip bond to a slip-only bond even at low ramp rate, thereby eliminating the ramp rate dependence. Compared with wild-type P-selectin (13), replacing P-selectin His-108 by Ala generated a broader catch bond regime at low ramp rate that progressively left-shifted with increasing ramp rate.

FIGURE 9.

Lack of effect of ramp in previous test cycles on bond lifetimes. Shown is a comparison of bond lifetime versus hold force curves for P-selectinH108A-PSGL-1 interactions when the lifetime events were (filled triangles) and were not (open squares) immediately preceded by an adhesion event in the previous test cycle. The two curves are indistinguishable from each other and from the curve plotted using the pooled data (gray circles and gray line; replotted from Fig. 8D), suggesting that kinetic memory is confined to within a single adhesion event and wears off once the molecular bond dissociates. The average (± S.E.) of several tens of lifetimes per force bin is plotted versus hold force loaded at the indicated ramp rate.

FIGURE 10.

Modified sliding-rebinding model for the dual dependence of bond lifetimes on hold force and ramp rate. A, conceptual energy landscape for the interaction between L-selectin (and P-selectinH108A) and PSGL-1 with one or two dissociation pathways that respond in different ways to changes in ramp rate and hold force, as modeled by the master equations of the modified sliding-rebinding model (“Experimental Procedures”). At low ramp rates, high hold force (upper right) applied to the Lec domain unbends the hinge (depicted by a coiled spring) with the EGF domain, causing the selectin ligand (SL) to tangentially slide along the inclined binding interface (state (1,0)). From here, formation of new interaction(s) with the Lec domain is energetically more favorable than dissociation along pathway 1 (indicated by the relative height between the two energy barriers besides state (1,1), upper right), which dominates at low forces caused by the unopened hinge (upper left). Sliding into a new interaction energy well (state (0,1)) and rebinding back to the initial bound state (state (1,1)) would strengthen binding and prolong lifetime, resulting in catch-slip bond behavior. In contrast, high loading rates during ramp phase would open the interdomain hinge angle even at low hold forces (lower left), allowing the selectin-PSGL-1 complex to slide into state (0,1) and rebind back to state (1,1). Higher hold forces cannot further enhance the already maxed out sliding-rebinding, but would accelerate dissociation from state (0,1) (lower right). Key parameters that govern the ramp rate regulation of lifetimes, viz. the force scale, f₀, above which the Lec-EGF interdomain angle would be fully opened, and the rebinding rate from state (0,1) to state (1,1), k₊₂, would be inversely correlated to the ramp rate, as reflected by the differences in the Lec-EGF hinge angle and the energy barrier level from state (0,1) to (1,1), respectively. The indicated difference in energy barrier height for all the scenarios, i.e. dissociation pathways 1 and 2 and transitions between states (1,1) and (0,1), is qualitatively consistent with the master equations. The relative magnitude of sliding and rebinding rates is reflected by the size and thickness of the respective arrows for the interstate transitions. B, the Ala to His substitution in L-selectin changes residue 108 from not contacting to contacting the PSGL-1 peptide (cf. Fig. 8A) abolishes the sliding-rebinding mechanism and reduces the two-dimensional energy landscape to one of a single dimension, resulting in slip bond behavior.

FIGURE 11.

Modified sliding-rebinding model parameters. A and B, the best fit model parameters, f₀ (A) and k₊₂ (B) are plotted versus the ramp rates for the indicated interactions studied by AFM or BFP (indicated). C, summary of the best fit ramp rate-independent model parameters (k₋₁⁰, k_BT/a, and k₊₁) for the indicated interactions studied by AFM or BFP (indicated).

EXPERIMENTAL PROCEDURES

Proteins and Antibodies

Membrane L-selectin (35), L-selectin-Ig, P-selectinH108A-Ig, and L-selectinA108H with a C-terminal HPC4-tag (15) have been described. Soluble recombinant monomeric PSGL-1 without (sPSGL-1) (9, 13) or with (PSGL-1) (36) a C-terminal biotin tag as well as biotinylated 6-sulfo-sLe^x and 2-GSP-6 (15) have been described. PSGL-1 blocking (PL1) and capturing (PL2) (13, 30) as well as L-selectin blocking (DREG-56) mAbs (9) have been described. Human Fc capturing mouse mAb (GG-7) and goat polyclonal antibody were from Sigma-Aldrich and Chemicon, respectively. HPC4 mAb was from Roche Applied Science.

AFM and BFP Setup

To exclude differences in spring constants of the force probe, differences in dissociation between the selectin and ligand constructs other than at their binding sites, and differences in methods of molecular immobilization as possible causes for the observed force history effect, we varied these parameters and tested the interactions using both AFM and BFP. Our previously described AFM system (9, 13) used commercial cantilevers with nominal spring constants between 6 and 100 piconewton (pN)/nm (Veeco), each of which was calibrated in situ using the thermal fluctuations method in all experiments (9, 13). Cantilevers were incubated overnight at 4 °C with 10 μl of 10 μg/ml PL2 (or streptavidin) solution and functionalized on the following day with either 10 μl of 0.1–1 μg/ml sPSGL-1 (captured by PL2) or biotinylated 6-sulfo-sLe^x (or PSGL-1 or 2-GSP-6) (captured by streptavidin) (see Fig. 1A). The preparation of selectin-incorporated vesicle solutions has been described (9, 13). Bilayers were formed by vesicle fusion. A 3–5-μl drop of the lipid vesicle solution was placed on the surface of a 100-ppm polyethyleneimine-coated coverslip, incubated for 20 min under damp conditions, and covered with 10 ml of Dulbecco's phosphate buffered saline (Fisher) containing Ca²⁺, Mg²⁺, and 1% BSA. The bilayers had low molecular densities, which ensured their infrequent binding (15–20%) to the ligand-coated AFM tips (see Figs. 1A and 2A) and were used immediately. In other experiments, the polystyrene surface was incubated with 20 μl of 50 μg/ml GG-7 or HPC4 mAb overnight at 4 °C. Following two washes with buffer, the polystyrene surface was incubated with 15 μl of 50 μg/ml P-selectinH108A-Ig (or L-selectinA108H) for 30 min at room temperature (see Fig. 1A).

FIGURE 2.

Binding specificity and capture strength controls. A, L-selectin-bilayer (AFM, left) and L-selectin-coated target bead (BFP, right) were tested, respectively, by AFM tip and BFP probe bead, with sequentially changing treatments: nonspecific binding of PL2-coated AFM tip or streptavidin-coated probe bead (open bars); increased binding after capturing PSGL-1 (closed bars); reduced binding upon adding indicated mAbs or EDTA (hatched bars); and restored binding by removing EDTA and adding Ca²⁺ to medium (spotted bar). Binding frequency was measured from 150 to 300 contacts/bilayer tip pair per condition and presented as the means ± S.E. of three different bilayer tip pairs (AFM) or pooled from three to five bead pairs with 50 contacts/bead pair per condition (BFP). B, simplified AFM setup depicting only a set of serial linkages that consist of four molecules: streptavidin, biotinylated PSGL-1, P-selectinH108A-Ig, and GG-7, all shown as color-matched springs (with the exception of P-selectinH108A-Ig, which is depicted as a black spring) and three noncovalent molecular bonds in series: streptavidin-biotin bond; P-selectinH108A-PSGL-1 bond, and IgG Fc-GG-7 bond. During hold phase (lifetime measurement), any of these three bonds could have broken (depicted by red lightning symbols), thereby causing the cantilever to snap back to the zero mean force position (cf. Fig. 1C). C–E, comparison of averages (± S.E.) of several tens of lifetimes at indicated hold forces of capture bonds (open bars) and serial bonds (solid and gray bars) involving L-selectin-2-GSP-6 (or 6-sulfo-sLe^x)-biotin-streptavidin (C) HPC4-L-selectinA108H (D) and GG-7-P-selectinH108A-Ig (E) interactions. The capture strengths of biotin-streptavidin and antibody-antigen bonds are much greater than those of the selectin-ligand bonds because the former have far longer lifetimes than the serial bonds that include the latter. Note that the y axis is in log scale.

Our previously described BFP system used an online image processing and analysis software to track red blood cell deflection with 0.7-ms temporal and ± 3 nm (standard deviation) spatial precision (14, 37, 38). L-selectin-Ig was captured by an anti-Fc covalently precoupled to 3-μm-diameter target beads as previously described (14, 37, 38) (see Fig. 1B). The same protocol (but without linking the proteins with PEG polymer) was used to couple streptavidin-maleimide (Sigma-Aldrich) to 2-μm-diameter probe beads, which captured biotinylated PSGL-1 or 6-sulfo-sLe^x (14) (see Fig. 1B). A streptavidin-coated probe bead was attached to the apex of a biotinylated red blood cell, which, after pressurization by micropipette aspiration, served as an ultrasensitive force transducer with spring constant ranging from 0.3 to 0.69 pN/nm (to apply different ramp rates) (see Fig. 1B).

Measurements of Bond Lifetimes along Defined Loading Histories

Lifetimes of single selectin-ligand bonds were measured along different families of ramp and hold force histories. Depending on the selectin constructs used, two test cycles were used in the AFM experiments to minimize nonspecific binding that differed in the bond formation step (9, 15). For L-selectinA108H or P-selectinH108A-Ig, the Piezo translator drove the AFM cantilever to first contact the polystyrene surface for ∼0.03 s, immediately retract ∼15 nm, and hold for 1 s to allow bond formation. For membrane L-selectin, the cantilever contacted the bilayer for 2 s with a ∼30 pN compressive force to allow bond formation. Following bond formation, the cantilever was retracted at 0.2–20 μm/s to load the bonds with 2 × 10² to 1 × 10⁵ pN/s ramp rates directly measured from the linear ascending segment of the force-time scan curves (blue segments in Fig. 1C). The Piezo translator finally stopped to hold the cantilever at different distances to set 5–200 pN of constant forces on the bonds, if one resulted from contact and survived ramping. Lifetimes were measured from the instant the Piezo translator stopped to the instant of bond rupture (green segments in Fig. 1C). The data were collected at 2–5 kHz to ensure detection of short-lived events while also enabling measurement of forces comparable with the level of thermal fluctuations. Hundreds of lifetimes were collected at each ramp rate and used to generate the lifetime versus hold force curves (see Figs. 4, A–F; 5; 6, D–F; and 8, B–F) as well as the lifetime distribution plots (see Fig. 7).

The test cycle used in the BFP experiments with L-selectin-Ig was similar to that used in the AFM experiments with membrane L-selectin except for the parameter values. The target bead was driven by the computer-controlled Piezo translator to approach at 0.5 μm/s and contact the probe bead for ∼0.1 s with a ∼20 pN compressive force to allow bond formation, retracted at 4–10 μm/s to load the bonds at 10³–10⁴ pN/s ramp rates and stopped at different distances to subject the bonds to 5–100 pN of constant forces, if bonds formed and survived ramping. Hundreds of lifetimes were collected in the same way as the AFM experiments at different ramp rates to generate the lifetime versus hold force curves (see Figs. 4, G–I, and 6, B and C).

Modified Sliding-rebinding Model and Monte Carlo Simulations

We modified a previously described sliding-rebinding model (11, 14) to fit the ramp rate-dependent bond lifetime data in Figs. 4, 5 and 8 (D–F). The atomic level interactions that mediate the molecular bonds between PSGL-1 and L-selectin or P-selectinH108A were simplified as two identical pseudo-atomic interactions. The molecular bond has three possible internal states depending on whether the two interacting molecules are bound by: (a) both pairs of pseudo-atoms (state (1,1), probability p₁₁), (b) either pseudo-atom pair (the other pair has dissociated) in its original position without sliding (state (1,0), probability p₁₀), or (c) the newly formed interaction between a switched pseudo-atomic pairing after sliding (state (0,1), probability p₀₁), as depicted by the energy landscapes in Fig. 10A. The rates of changes in the probabilities of these states are described by the following master equations (11),

where p₀₀ (= 1 − p₁₁ − p₁₀ − p₀₁) is the probability of dissociation, k₊₁ and k₋₁ denote the respective on and off-rates for each pseudo-atomic interaction, and k₊₂ is the rebinding rate. k₊₁ is assumed to be a constant, but k₋₁ is assumed to obey the Bell equation,

where k₋₁⁰ is the force-free dissociation rate, a is the width of the energy well, f is the instantaneous level of applied force, k_B is the Boltzmann constant, and T is the absolute temperature. k₋₂ = k₋₁(f/2). p_n is the probability of forming a new interaction after sliding, given by the following.

Here, f₀ is a characteristic force above which the Lec-EGF interdomain hinge would be fully open (11).

Our extension to the above model is based on the hypothetical dual dependence of the conformational coupling between the hinge angle and the ligand-binding interface (39) on force and ramp rate, such that increasing ramp rate would reduce the stiffness of the interdomain hinge, allowing it to fully open at a lower force while also shortening the sliding time (see Fig. 10A). This is equivalent to assuming the force scale f₀ and the rebinding rate k₊₂ to be decreasing functions of the ramp rate. Equations 2–4 were solved by Monte Carlo simulations as described previously (11).

Molecular Modeling

Using previously described methods (15), the coordinates of the crystal structures of human L-selectin (Protein Data Bank entry 3CFW) and of human P-selectin bound to PSGL-1 (Protein Data Bank entry 1G1S) were used to generate the molecular models in Figs. 6A and 8A. Models of the lectin domains of L-selectinA108H and P-selectinH108A were derived from their respective parent structures by in silico replacement of residue 108 using InsightII (Accelrys Inc., San Diego, CA). The images in Figs. 6A and 8A were generated using InsightII.

Measuring Ramp Rates during Tethering of Flowing Neutrophils

The methods for measuring tethering of flowing neutrophils to selectin ligands have been described (14, 40). Briefly, neutrophils (10⁶/ml in Hanks' balanced saline solution with 0.5% human serum albumin) were perfused over 180 sites/μm² PSGL-1 at given flow rates in a parallel flow chamber placed on an inverted microscope. Events of freely flowing neutrophils that tethered to PSGL-1 for the first time were recorded at 500 frames/s by a FASTCAM-Super 10 K high speed digital video camera (Photron) mounted on the microscope. Tethering events were identified by observing the abrupt drops from the time courses of instantaneous velocity (40). The instantaneous velocity was calculated from the frame-by-frame x and y coordinates of the mass center of each individual neutrophil determined using the tracking software Nanotrack (Isee program). The ramp time (i.e. the time required to arrest the cells) was calculated by multiplying 2 ms to the number of frames required to reduce the instantaneous velocity of freely flowing neutrophil to 0. The tether force was calculated by multiplying the wall shear stress by the conversion factor (36), 125 pN/(dyn/cm²). The ramp rate was calculated by dividing the tether force by the ramp time (see Fig. 3).

FIGURE 3.

Ramp rate estimates from flow chamber experiments. Ramp time (i.e. the time required to arrest a free-flowing neutrophil) is plotted against shear rate (bottom) and the corresponding tether force (top). Neutrophils were perfused over a surface coated with PSGL-1 in a parallel flow chamber, and the times required to arrest them were recorded at multiple shear rates. The ramp rate (at a given shear rate) would be given by the tether force (at that shear rate) divided by the ramp time (see text for details).

RESULTS

To measure dissociation kinetics, AFM and BFP were functionalized using molecules and immobilization methods depicted in Fig. 1, A and B, respectively (see also “Experimental Procedures”). Selectins and their ligands were brought into contact to allow bond formation, retracted at a constant rate, and held at a given position, thereby subjecting the bonds to a well defined force history described by two independent parameters: ramp rate and hold force (Fig. 1C). Lifetimes were measured during the force hold phase from the instant ramping stopped to the instant the bonds dissociated (Fig. 1C).

Binding Specificity Controls and Capture Strengths of Streptavidin, GG-7, and HPC4

For each of the selectin-ligand systems studied, controls were performed in both AFM and BFP experiments to ensure that nonspecific binding did not exceed 5% in repeated test cycles, as exemplified in Fig. 2A. Densities of selectins and ligands were adjusted to yield 15–20% binding frequencies in repeated test cycles, at which the majority of specific interactions were expected. This ensured that the measured lifetimes were dominated by specific selectin-ligand interactions.

Captured molecules were used to ensure proper orientations of selectins and ligands (Fig. 1A), resulting in two or more molecular bonds in series, an example of which is shown in Fig. 2B. The reciprocal lifetime of the serial bond system would equal the sum of the reciprocal lifetimes of the bonds in the series because rupture can result from dissociation of any of them (19). To ensure that the measured lifetimes reflected that of the selectin-ligand bonds, biotin-streptavidin and antigen-antibody interactions were used for capturing because their strength, much greater than those of the selectin-ligand interactions, was expected to prevent them from dissociating. To confirm that the capturing bonds were indeed substantially longer-lived than the selectin-ligand bonds, the lifetimes at comparable hold forces of bonds between biotin and streptavidin, between HPC4 antibody and its antigenic epitope tagged at the C-terminal of L-selectinA108H, and between P-selectinH108A-Ig and anti-Fc GG-7 mAb were measured and respectively compared with those of L-selectin-2-GSP-6-biotin-streptavidin and L-selectin-6-sulfo-sLe^x-biotin-streptavidin, HPC4-L-selectinA108H-PSGL-1-biotin-streptavidin, and GG-7-P-selectinH108A-Ig-PSGL-1-biotin-streptavidin serial bonds (Fig. 2, C–E).

To measure the lifetimes of antigen-antibody bonds, we incubated the AFM tips with HPC4 or P-selectinH108A-Ig and respectively tested them against L-selectinA108H or GG-7 adsorbed on the polystyrene surface. To measure the lifetimes of biotin-streptavidin bonds, biotinylated BSA was adsorbed on both the AFM tip and Petri dish. The Petri dish was then incubated with streptavidin and tested against the functionalized AFM tip. It has been shown that adsorption of proteins to glass or plastic surface is far stronger than specific molecular bonds between proteins (19). At hold forces between 15 and 50 pN, the lifetimes of the capture bonds alone were several- to several hundred-fold longer than the lifetimes of selectin-ligand bonds in series with the capture bonds (Fig. 2, C–E). This indicated that the lifetimes of the serial bonds predominantly reflected those of the selectin-ligand bonds, because they are far more short-lived than the capture bonds.

Determining the Physiological Ramp Rate Range

To select a physiologically relevant range for ramp rates, we used high speed video microscopy to directly measure the time required for freely flowing neutrophils to be arrested in a flow chamber. It was found that 2–6 ms were required for neutrophils to tether to PSGL-1 on the floor of a flow chamber at wall shear rates of 10–40 s⁻¹ (Fig. 3). This translates to ramp rates of 3,000–10,000 pN/s loaded on L-selectin-PSGL-1-mediated tethers to hold forces of 12–60 pN.

Dual Dependence of L-selectin-PSGL-1 Bond Lifetime on Hold Force and Ramp Rate

Fig. 1C illustrates the unusual dual dependence of L-selectin-PSGL-1 bond lifetime on both hold force (green segments) and ramp rate (blue segments). At low hold force (top row), bond lifetime was longer when loaded by high than low ramp rate. However, this trend was reversed at high hold force (bottom row): bond lifetime was shorter when loaded by high than low ramp rate. To systematically quantify this dual dependence, we analyzed the lifetimes by their averages (Figs. 4–6; see also Fig. 8) and distributions (Fig. 7) over a range of hold forces at multiple ramp rates, which are relevant to what these bonds experienced in flow chamber experiments (Fig. 3).

When ramped at a low rate of ∼1000 pN/s, L-selectin dissociated from PSGL-1 as a catch bond at hold forces <50 pN that transitioned to a slip bond at hold forces >50 pN (Fig. 4, A and G) as previously shown (9, 14, 15). Surprisingly, this biphasic bond lifetime versus hold force curve changed with increasing ramp rate (Fig. 4). The catch-slip transition force (where lifetime is maximum) progressively left-shifted toward smaller forces with little change in the peak lifetime (Fig. 4, A–C, G, and H). At a ramp rate of ∼7000 pN/s, the catch bond regime vanished as the transition force went below the lowest force tested, leaving only slip bonds, which remained unchanged with further ramp rate increase (Fig. 4, D–F and I). Furthermore, consistent results were obtained by AFM using soluble PSGL-1 (sPSGL-1) (Fig. 4, A–F) and BFP using PSGL-1 (Fig. 4, G–I), immobilized via different protocols (Fig. 1, A and B; see also “Experimental Procedures”). These results excluded differences in the molecular constructs, their immobilization protocols, the experimental techniques, and the force probe stiffness as possible causes for the observed effect (41, 42). Also, the single exponential distributions of bond lifetimes suggest that a single population of bonds with the same dissociation characteristics were tested (Fig. 7). Thus, we have demonstrated a dependence of lifetimes measured during the hold phase on the loading rate during the ramp phase. This invalidates the aforementioned a priori assumption, because theory based on this assumption predicts that the average lifetime measured from force clamp experiments (equals reciprocal off-rate) should be a function of only the hold force and not the prior ramping history used to reach that force.

Force History Regulation of L-selectin-2-GSP-6 Bond Lifetimes

Previously, we have shown that the A108H substitution of L-selectin dramatically altered the force-dependent kinetics of its interaction with streptavidin-captured biotinylated 2-GSP-6 but not 6-sulfo-sLe^x (15). Here we observed ligand-specific force history regulation of L-selectin bond lifetimes using PL2-captured sPSGL-1 (Fig. 4). As a further confirmation, we tested the interaction of membrane L-selectin with streptavidin-captured biotinylated-2-GSP-6, a short synthetic glycosulfopeptide mimicking the selectin binding site at the N terminus of PSGL-1 (15) (Fig. 1A). As expected, we observed ramp rate-dependent lifetime versus hold force behavior (Fig. 5) similar to those obtained using PL2-captured sPSGL-1 (Fig. 4). Catch-slip bonds were observed at low ramp rate (Fig. 5A) with the transition force left shifting with increasing ramp rate (Fig. 4B) until only slip bonds were observed at high ramp rate (Fig. 5C). Thus, the dissociation kinetics of L-selectin from 2-GSP-6 and sPSGL-1 are identical. These results also excluded the different methods of immobilizing L-selectin and ligands as possible causes for the observed force history effect.

Lack of Dependence of L-selectin-6-sulfo-sLe^x Bond Lifetime on Ramp Rate

L-selectin also forms catch-slip bonds with 6-sulfo-sLe^x (14). The structural bases for L-selectin bonds with PSGL-1 and 6-sulfo-sLe^x differ (15). The lectin domain of L-selectin binds to the N-terminal region of PSGL-1. The interacting residues on PSGL-1 include sulfated tyrosines and other amino acids, plus fucose, sialic acid, and galactose on sLe^x (NeuAcα2–3Galβ1–4[Fucα1–3]GlcNAcβ1-) capping a core 2 O-glycan. The orientation of these residues can be modeled using the crystal structure of P-selectin bound to PSGL-1 (43) (Fig. 6A). 6-Sulfo-sLe^x, a modification of sLe^x with a sulfate ester attached to the C6 position of GlcNAc, has no peptide components. The 6-sulfo-sLe^x glycan can be modeled to dock to L-selectin in the same orientation as the sLe^x moiety on the N-terminal PSGL-1 glycosulfopeptide. Regardless of where the 6-O-sulfate ester might dock, 6-sulfo-sLe^x is not predicted to interact with the L-selectin residues that bind to the peptide components of PSGL-1 (Fig. 6A). We therefore tested whether ramp rate changes also impacted L-selectin-6-sulfo-sLe^x catch-slip bonds. In sharp contrast to the L-selectin-PSGL-1 bonds, the biphasic L-selectin-6-sulfo-sLe^x bond lifetime versus hold force curve did not change over a ramp rate increase of up to two logs, as measured by both BFP (Fig. 6, B and C) and AFM (Fig. 6, D–F). These data demonstrate that the force history dependence of L-selectin dissociation kinetics is ligand-specific, which serves as a control to exclude potential artifacts (e.g. detachment of L-selectin constructs and ligands from their surface attachments) as possible causes of the unusual effect. More importantly, this ligand specificity isolates the structural basis of the ramp rate dependence of bond lifetime to the L-selectin residues that contact the peptide, but not the glycan, of PSGL-1 (15).

Elimination and Generation of Ramp Rate Dependence by Point Mutations

We previously characterized a mutant of L-selectin, L-selectinA108H, with Ala replaced by His at position 108 of the lectin domain (15). This substitution prolonged the lifetimes of L-selectinA108H bonds with 2-GSP-6 at low forces, converting catch bonds to slip bonds even at a ramp rate of ∼1000 pN/s. This closely resembles the effects of high ramp rates (≥7000 pN/s) on L-selectin bonds with PSGL-1 (Fig. 4, D–F and I) and 2-GSP-6 (Fig. 5C). In addition, the A108H substitution did not alter L-selectin-6-sulfo-sLe^x catch bonds, similar to the lack of response of this interaction to changing ramp rate (Fig. 6). Importantly, a structural model of the L-selectin-PSGL-1 complex predicts that this Ala-to-His substitution changes residue 108 from not contacting to contacting the PSGL-1 peptide (15) (Fig. 8A). The similarities between the effects of high ramp rate and the A108H substitution suggest that a high ramp rate induces a conformational change in L-selectin closely resembling the change caused by the mutation, which affects interactions with PSGL-1 but not with 6-sulfo-sLe^x. This hypothesis predicts that the L-selectinA108H-PSGL-1 bond lifetime versus hold force curve is impervious to ramp rate changes, which was indeed observed (Fig. 8, B and C).

Our hypothesis also predicts that the reverse substitution in P-selectin (H108A) should reduce contact with the peptide component of the PSGL-1-binding site (Fig. 8A), making the P-selectinH108A-PSGL-1 dissociation responsive to changes in ramp rate. This prediction was also observed: the P-selectinH108A-PSGL-1 bond lifetime versus hold force curves were biphasic with lifetime initially prolonged and then shortened by force at a low ramp rate of 300 pN/s (Fig. 8D). The catch-slip transition force gradually left-shifted with increasing ramp rate toward lower forces until only slip bonds were observed (Fig. 8, E and F).

Lack of Effect of Ramp in Previous Test Cycles on Bond Lifetimes

Our data show a ligand-specific force history dependence of dissociation from selectins, revealing that the off-rate has memory for the past history of force applied to selectin via PSGL-1 (but not via 6-sulfo-sLe^x). Two related questions may be asked immediately: (a) How long would this memory last? and (b) Would the memory effect persist after ligand dissociation?

It should be noted that our lifetime data were collected from repeated ramp and hold test cycles. As an initial step toward addressing the above questions, we tested whether the ramp phase in previous test cycles would impact the lifetimes in future events. To do so, we segregated the data from Fig. 8D into two groups: one group contained lifetimes measured from adhesion tests whose immediate past tests had also resulted in adhesion (and hence, an associated ramp phase) and the other group contained the rest of the lifetime events, i.e. those measured from adhesion tests whose immediate past tests had resulted in no adhesion. Interestingly, the lifetime versus hold force curves of the two groups were indistinguishable, suggesting that the ramp phase in the preceding cycles had no effect on future measurements (Fig. 9).

Modified Sliding-Rebinding Model for Dual Dependence of Bond Lifetime on Hold Force and Ramp Rate

The finding of force history-dependent bond lifetime contradicts existing dogma and calls for a new paradigm for modeling receptor-ligand dissociation kinetics. We therefore extended a previous sliding-rebinding model for selectin-ligand catch-slip bonds (11, 14) to account for the additional ramp rate dependence in interactions of L-selectin and P-selectinH108A with PSGL-1 (Fig. 10A) as well as for the lack of ramp rate dependence in the case of L-selectinA108H mutant that also eliminates catch bonds with PSGL-1 (Fig. 10B). In the original form of our model, force applied to the selectin lectin (Lec) domain unbends its hinge with the EGF domain, causing the ligand to tangentially slide along the binding interface during dissociation rather than normally breaking away, which allows formation of new atomic level interactions and rebinding of partly dissociated interactions to strengthen the molecular bond (11, 14). Using pseudo-atom representation, this model has been formulated by Equations 2–4 with five parameters (11) (“Experimental Procedures”). The present extension keeps three constant but allows two of them: the rebinding rate, k₊₂, and the force scale, f₀, above which the Lec-EGF interdomain angle would be fully opened (11), to vary with the ramp rate changes (Fig. 10A). Their values (Fig. 11) were determined by using Monte Carlo simulations to best fit the model predictions (curves) to the experimental measurements (points) (Figs. 4, 5, and 8, D–F). Indeed, this structurally based model is supported by its ability to globally fit a wide range of data exhibiting dual dependence of bond lifetimes on ramp rate and hold force despite the limited parameters.

The ramp rate dependence of k₊₂ and f₀ reveals inverse correlations (Fig. 11, A and B). This is intuitive because higher ramp rate would accelerate the sliding of the binding interface, which reduces the time for rebinding of broken interactions, thereby lowering k₊₂. In addition, a higher ramp rate would also make the interdomain hinge more flexible by reducing rebinding of the atomic level interactions that maintain the bent hinge angle, thereby lowering f₀ (11).

The modified sliding-rebinding model also explains the pivotal role of residue 108 (Fig. 8). The ground-state interactions for L-selectin (and P-selectinH108A) may be suboptimal because Ala-108 cannot contact PSGL-1 (Fig. 8A). At a low ramp rate, increased force in the holding phase may be required to induce a conformational change at this position to stabilize the interaction before destabilizing it, thereby producing catch-slip bonds (Fig. 10A). Rapid ramping may induce a similar conformational change before reaching the force hold phase even at low forces, thereby lengthening the lifetimes at low forces and left shifting the bond lifetime versus hold force curve (Fig. 10A). The A108H substitution in L-selectin (and P-selectin) may improve the interaction at very low forces with little ramping and hence eliminate the ramp rate dependence (Fig. 10B). Because 6-sulfo-sLe^x is not predicted to contact Ala-108, its replacement with His is not expected to affect the L-selectin-6-sulfo-sLe^x catch-slip bond, which may have a different structural mechanism.

DISCUSSION

In the present study, we have observed an unusual ligand-specific force history dependence of L-selectin bond dissociation kinetics. Our data invalidate the widely accepted (but not proven) assumption that kinetic rates are single-valued functions of force. This assumption may require the interacting molecules to be quite stiff, such that applied force merely induces relative displacements at the interface to affect the interaction energy and in turn, kinetic rates. However, selectins are deformable (11), and applied force is not limited to the binding pocket. A force applied to the entire molecule may induce conformational changes in other regions and propagate to the binding interface to regulate kinetic rates. The interfacial displacements may respond to force quickly, resulting in kinetic rates to depend on the instantaneous level of force. But coupled conformational changes between the binding pocket and remote regions may accumulate in time because propagation of conformational changes over distance requires time, giving rise to force history-dependent kinetic rates. This may be thought of as kinetic rates exhibiting memory. The reasonable agreement between our data and model predictions suggests that force history-sensitive conformational changes (e.g. opening of the Lec-EGF interdomain angle) in a molecule may allosterically affect the kinetic rate of its interaction with another molecule.

There are several other biological systems wherein effects of kinetic rate memory have been demonstrated. However, the concept of kinetic rate memory has been used by different authors to describe different phenomena, which are also different from the one reported here. Previously, we have reported a form of memory in receptor-ligand interaction where the likelihood of bond formation in the next contact is affected by the outcome of the previous contact (44). Lu et al. (45) showed that enzymatic turnover of cholesterol oxidase was dependent on previous turnovers, a non-Markovian molecular memory attributed to a slow fluctuation of protein conformation. Non-Markovian emission fluctuations of horseradish peroxidase during catalysis were also observed by Edman and Rigler (46). Two other related examples were reported by Ha et al. (47), who observed conformational fluctuations in catalytic reactions of staphylococcal nuclease enzyme, and by Yang et al. (48), who observed correlation between structural fluctuations of flavin-enzyme complex and its conformation-based kinetics. Zhuang et al. (49) reported that the hairpin ribozyme has four docked conformations of distinct kinetic rates to undocked conformation, and individual ribozyme molecules memorize and tend to repeat their initial docked-to-undocked kinetics in successive turnovers. Memory effects were also observed in unfolding of globular protein domains wherein intermediate states in native to unfolded state transitions were detected, and interestingly, the reaction forces in the two sequential steps are correlated (50). In these cases, the kinetic measurements were made in repeated tests. If the time elapse between two consecutive tests is shorter than the relaxation time, the state immediately after one test may not return completely to the state immediately before that test. In such a case, the next test may start from a different state with a different kinetic rate, manifesting as kinetic rate memory.

The effects of kinetic rate memory in the work here refer to a different observation. Lifetimes were measured from the moment when a receptor-ligand bond was loaded to a clamped force. However, this initial state depends not only on that force but also on the loading rate used to ramp the force to that level. To test whether this is a new kind of kinetic rate memory or it is related to the previous observations, we looked at the effect (if any) of the presence of an adhesion in the immediate past test on bond lifetime versus hold force curves (Fig. 9) but detected no impact. These data show that, upon ligand dissociation, the selectin had sufficient time to relax to the same initial state before the next test, thereby exhibiting no memory of the previous kinds. To elicit memory in the kinetic rate of a selectin requires engagement with PSGL-1 (but not 6-sulfo-sLe^x). It is the path by which the present bond is loaded to the current force that is memorized and not whether or not a bond was formed in the immediate past test.

Thus, force history effects are related to the intrinsic kinetics of the interactions tested, whose origin may lie in the force induced conformational changes, as suggested by the structural mechanism proposed herein (Fig. 10). In this aspect, our work is conceptually related to but fundamentally different from the above reports. Our work is also distinct from DFS. DFS analyzes the rupture force “spectra,” i.e. rupture forces measured via a force ramp assay over a range of ramp rates, to evaluate off-rate as a function of force but not ramp rate (6, 8, 12). In our experiments, by comparison, force-dependent off-rates can be derived from the bond lifetimes measured in a range of constant forces after the ramp rates become zero. However, off-rates so evaluated also depend on the prior ramp rate used to reach the level of clamp forces, giving rise to a dual dependence of kinetic rates on two independent variables: force and ramp rate.

As a first step toward developing a new modeling framework to account for force history-dependent molecular dissociation, we extended our previous sliding-rebinding model for selectin ligand catch-slip bonds. This model is capable of capturing the key features of the data, viz. the catch-slip transitional behavior and, more importantly, the structural role played by residue Ala-108 in the interactions (Fig. 10). However, it is only the simplest possible model, with many aspects idealized or neglected, which may explain why its predictions do not fit all of the quantitative experimental data for some of the force ranges in Figs. 4 and 5. Some of the possible oversimplifications may include the phenomenological description in Equation 4 to model the probability of rebinding after sliding, and the assumption of a quasi-static dependence of the two key parameters that govern the force history regulation (f₀ and k₊₂) on ramp rate, without considering possible dynamic effects. Besides the sliding-rebinding model, other models for catch-slip bonds (10, 33) can also be modified to include dependence on force history. All of these factors are worthy of further study in the future, which would lead to more sophisticated models.

Applying force via different histories to receptor-ligand bonds may affect their biological functions. For example, ramp rates may differ markedly for selectin-ligand bonds formed at the leading and trailing edge of a rolling leukocyte. Ramp rates may also be affected by local variations in fluid dynamics, as when a flowing leukocyte uses L-selectin-PSGL-1 bonds to tether to and roll on a leukocyte already arrested on the vascular surface. This might explain in part why force history affects L-selectin interactions with PSGL-1 that is expressed on leukocytes, but not with 6-sulfo-sLe^x on mucins that are expressed on endothelial cells. Similar force history regulatory mechanisms may be operative in the interaction kinetics of other molecular systems such as integrins. Elucidating how the history of force application regulates receptor-ligand bond-mediated biological functions will be an interesting area of future research.