Fast Force Loading Disrupts Molecular Binding Stability in Human and Mouse Cell Adhesions

: Force plays critical roles in cell adhesion and mechano-signaling, partially by regulating the dissociation rate, i.e., off-rate, of receptor-ligand bonds. However, the mechanism of such regulation still remains elusive. As a controversial topic of the field, when measuring the “off-rate vs. force” relation of the same molecular system, different dynamic force spectroscopy (DFS) assays (namely, force-clamp and force-ramp assays) often yield contradictive results. Such discrepancies hurdled our further understanding of molecular binding, and casted doubt on the existing theoretical models. In this work, we used a live-cell DFS technique, biomembrane force probe, to measure the single-bond dissociation in three receptor-ligand systems which respectively have important functions in vascular and immune systems: human platelet G PIbα VWF, mouse T cell receptor-OVA peptide:MHC, and mouse platelet integrin α IIb β 3 -fibrinogen. Using force-clamp and force-ramp assays in parallel, we identified that the force loading disrupted the stability of molecular bonds in a rate-dependent manner. This disruptive effect was achieved by the transitioning of bonds between two dissociation states: faster force loading induces more bonds to adopt the fast-dissociating state (and less to adopt the slow-dissociating state). Based on this mechanism, a new biophysical model of bond dissociation was established which took into account the effects of both force magnitude and loading rate. Remarkably, this model reconciled the results from the two assays in all three molecular systems under study. Our discoveries provided a new paradigm for understanding how force regulates receptor-ligand interactions and a guideline for the proper use of DFS technologies. Furthermore, our work highlighted the opportunity of using different DFS assays to answer specific biological questions in the field of cell adhesion and mechano-signaling.


Introduction
Mechanical force plays a crucial role in cell-cell and cell-substrate communications. Force-regulated molecular interactions initiate many cellular activities such as adhesion, migration, and cytoskeleton restructuring. Dynamic force spectroscopy (DFS) [1] which includes atomic force microscopy (AFM), optical tweezer, and biomembrane force probe (BFP), currently serves as the mainstream technology to measure force-regulated molecular interactions at the single-molecule level. Combined with concurrent intracellular signaling readouts, DFS technologies enable direct correlation of molecular binding kinetics with mechano-signaling in real-time [2,3,4], demonstrating the importance of molecular binding kinetics on cellular functions.
Off-rate (koff, rate of bond dissociation) is an important attribute of receptor-ligand interaction that reflects bond stability: the higher the off-rate, the less stable the bond. Over the last few decades, two major DFS-based assays have emerged to obtain the koff of single molecular bonds: 1) force-clamp assay directly measures bond lifetimes (the reciprocal of koff) by clamping the bond at a constant force [5]; 2) force-ramp assay derives koff from the rupture force magnitudes by ramping the bond with constant force loading rate [6,7]. Both assays demonstrated koff as a function of force magnitude [5,[7][8][9][10][11][12][13]. However, as a controversial topic of the field, the "koff vs. force" relations derived from the above two assays were often in discrepancy, despite similar experimental setups/conditions. For instance, a catch bond behavior have been observed in the interactions of P-selectin-PSGL-1 [5], integrin α5β1-fibronectin [10], integrin αLβ2-ICAM-1 [8] and integrin α4β1-VCAM-1 [9] using the DFS force-clamp assay, where the bond lifetime increases (and therefore koff decreases) with force within a certain force regime. Yet, analysis of the same biological systems in DFS force-ramp assay resulted in slip bonds, where the koff monotonically increased with force [7,[11][12][13]. Even with the same AFM setup, koff was measured to be different for P-selectin-sPSGL-1 and P-selectin-G1 interactions, not only between force-clamp and -ramp assays, but also within the force-ramp assay amongst different force loading rates [14]. Such discrepancies casted doubt on the general applicability of existing theoretical models assuming koff to be a function of only force magnitude [15][16][17][18][19], and suggested that bond stability can be affected by other attributes of force application as well.
In this work, we measured the binding kinetics of three receptor-ligand systems using the forceclamp and force-ramp assays in parallel, and discovered that fast force loading can disrupt bond stability. By investigating the underlying mechanism, we established a new theoretical model that depicts the regulation of bond dissociation by both force magnitude and loading rate.

Blood Collection and Platelet Isolation and Preparation
All procedures involving the collection of blood from healthy human donors were approved by the Institutional Review Board of the Georgia Institute of Technology (protocol number H12354). All human donor blood samples were obtained with written informed consent. Human blood was slowly drawn from the vein of a healthy volunteer to fill in a 3 ml syringe preloaded with 0.43 ml ACD buffer (85 mM sodium citrate, 72.9 mM citric acid anhidrous, 110 mM D-glucose and 70 mM Theophylline, pH 4.6). Whole blood was transferred into a 15 ml tube pre-loaded with apyrase (0.005 U mL -1 ) and Clexane (20 U mL -1 ). After resting for 15 min at 37ºC, whole blood was centrifuged at 200 g for 10 min without brake. Platelet-rich plasma was extracted, allowed to rest for 10 min at 37ºC and centrifuged at 1,700 g for another 5 min. The platelet pellet was resuspended into platelet washing buffer (4.3 mM K2HPO4, 4.3 mM Na2HPO4, 24.3 mM NaH2PO4, 113 mM NaCl, 5.5 mM D-Glucose, 10 mM theophylline and 1% BSA, pH 6.5) pre-added with Clexane (20 U mL -1 ) and apyrase (0.01 U mL -1 ), rested for 10 min and centrifuged again at 1,500 g for 5 min. The platelet pellet was resuspended into Hepes-Tyrode buffer (134 mM NaCl, 12 mM NaHCO3, 2.9 mM KCl, 0.34 mM sodium phosphate monobasic, 5 mM HEPES, and 5 mM glucose, 1% BSA, pH 7.4) pre-added with apyrase (0.02 U mL -1 ) with a platelet count at 3 × 10 8 mL -1 , and placed in a 37°C water bath for 30 min before use.
All procedures involving the collection of blood from mice were approved by the Institutional Animal Care and Use Committee (IACUC). The mouse was anesthetized with ketamine/xylazine mix during the terminal blood collection via inferior vena cava; anticoagulant (Clexane, 40 U mL -1 ) was preloaded in syringe. After the blood collection (0.8-1 mL), a final concentration of 1X ACD buffer was added to the blood. Whole blood that was transferred to a small separation tube was centrifuged at 250 g for 2.5 min with soft brake. Platelet-rich plasma was obtained and centrifuged at 1950 g for 1 min. The platelet pellet was resuspended into platelet washing buffer pre-added with Clexane (20 U mL -1 ) and apyrase (0.01 U mL -1 ), then centrifuged again at 1950 g for 1 min. The platelet pellet was resuspended with Hepes-Tyrode buffer pre-added with apyrase (0.02 U mL -1 ), and placed in a 37°C water bath for 30 min before use.

Mouse T Cell Collection
All procedures involving the collection of T cells from mice were approved by IACUC. T cell purification from mouse spleen was performed using the Stemcell kit, cat. # 19853. Briefly, the mouse was euthanized first with CO2; spleen was collected into culture medium R10 (purchased RPMI 1640 1X w/L-glutamine, Corning 10-4-CM; adding 100 ml FBS, 10 ml P/S, 10 ml Hepes and 10 ml Sodium Pyruvate per 1 L). Spleen was then grinded with 3 ml R10 through a 70 um cell strainer placed on top of a 6-cm Petri dish using a 3 ml syringe plunger end, and RBCs lysed using the Mouse Erythrocyte Lysing Kit (#WL2000, R&D Systems). CD8 T cells were then negatively purified with Mouse CD8+ T Cell Enrichment Kit (cat#19853, Stemcell Technologies), following the EasySep protocol.

RBC and Glass Bead Preparation for BFP Experiments
8-10 μL of human blood was collected from finger prick and centrifuged to isolate RBCs. RBCs were biotinylated by incubating with Biotin-PEG3500-NHS (JenKem) solution [21] and partially swollen for BFP assembly by incubating with nystatin (Sigma-Aldrich).
The protocol of beads functionalization was described before [21]. Glass beads (Distrilab Particle Technology, Leusden, Netherlands) were first thiolated. To make OVA beads, the thiolated glass beads were incubated first with SA-MAL overnight, then with biotinylated OVA for 3 h. To make Fg and VWF-A1 beads, the protein was first mixed and incubated with MAL-PEG3500-NHS (JenKem) for 30 min [22,23]. The mixture was then incubated with the thiolated glass beads overnight. Beads were washed with and resuspended in phosphate buffer (27.6 g/L NaH2PO4 • H2O, 28.4 g/L Na2HPO4).

BFP Setups, Experiment Modes and Related Assays
BFP setup and operation has been described [21]. Briefly, in an experimental chamber filled with Hepes-Tyrode buffer (for platelet experiments) or L15 buffer (for T cell experiments), a biotinylated RBC was aspirated by a micropipette with a SA-coated probe bead attached to its apex, which altogether forms a force transducer ( Fig. 1(A)). The bead was co-functionalized with proteins of interest to interact with the platelet aspirated by an opposing micropipette ( Fig. 1(B)) driven by a piezoelectric translator (Physik Instrumente, Karlsruhe Germany). The horizontal position of the probe bead was tracked by a high-speed camera to signify the RBC axial deformation and, by calculation, the platelet-bead force. For force clamp experiments, the BFP spring constant k, determined using Evans' model [24], was set to 0.3 or 0.25 pN nm -1 for clamping forces higher or lower than 10 pN, respectively, by adjusting the aspirating pressure.
For force ramp experiments, k was set to 0.3 or 0.4 pN nm -1 for ramping rates lower or higher than 1000 pN s -1 , respectively. Experimental data were collected and analyzed by LabView (National Instrument, Austin, TX). Apyrase with a final concentration of 0.02 U mL -1 was added into the experimental chamber to chelate ADP released from the platelets.

Force-Clamp Mode and Bond Lifetime Assay
Force-clamp mode was used to measure single receptor-ligand bond lifetimes under a range of constant forces. The probe bead ligand coating density was adjusted to keep the adhesion infrequent (~20%) to satisfy the necessary condition for most of the adhesions (> 89%) to be single bond events [25]. The platelet was driven to contact and impinge the probe bead, and then retracted at 3 µm s -1 . If no adhesion occurs between the two surfaces, the force signal will return to zero during the retraction ( Fig.  1(C)). When binding was detected during retraction, the target pipette was held at a pre-set distance to wait for bond dissociation, which then returned to the original position to start a new cycle ( Fig. 1(D)). Lifetime was defined as the duration of the clamping phase before bond dissociation ( Fig. 1(D)). Lifetime data were binned according to the clamp forces; the forces and lifetimes in each bin were then averaged to plot the lifetime vs. force curve.

Fitting Lifetime Distributions by Two-State Model
Within each clamp force bin, "survival frequency" was defined for each lifetime event as the fraction of lifetime events that lasted longer than it. The survival frequency was then plotted against lifetime, and fitted by a two-state model [8] that assumes superposition of two exponential decays in Eq. (1): (1) in which t is the lifetime, and ki and ωi are respectively the off-rate and fraction of the ith state. The sum of the two fractions always equals 1.
The off-rate of each state as a function of force was then fitted to the Bell's equation [15] depicted in Eq. (2): (2) in which ki0 is the zero-force off-rate of the ith state, f is force, and fai is defined as fai = kBT/ai where ai is the reactive compliance of the ith state, kB is Boltzmann constant, and T is absolute temperature.

Force-Ramp Mode and Rupture Force Measurement
In a test cycle of force-ramp mode [25], the platelet approached and contacted the probe bead and retracted. A tensile force signal following retraction reports an adhesion event ( Fig. 1(E)) between the platelet and the bead. The force loading rate was calculated based on the slope of the force-ramp phase, and the peak force right before bond dissociation was recorded as the rupture force ( Fig. 1(E)).

Deriving Off-Rates by Fitting Rupture Force Distribution
The rupture force distribution under a constant loading rate can be used to calculate the effective offrate (kE) under different forces (f) using a previously described theoretical model which assumes no functional form of kE against f [14]: where rf is the force loading rate, and pd and Pc are respectively the probability density and cumulative probability of the distribution.
If only one dissociation state exists for the receptor-ligand pair, the kE equals the off-rate of this dissociation state. If two or more dissociation states co-exist, kE equals the reciprocal of the average lifetime of all states.

Fitting Force-Ramp Off-Rates with an Upgraded State Transition Model
Evans' equation [17] first described a state transition model that describes how force shifts bonds to the dissociating state in the force-ramp assay, with the assumption of rapid inner conversion (at every moment, the transition of bonds between the two states rapid reaches equilibrium): where S1 and S2 are respectively the probability of bonds in State 1 (fast-dissociating) and 2 (slowdissociating) surviving at time t (meaning not yet ruptured), and P is the probabilities of all bonds surviving at time t. kB is the Boltzmann constant, T is temperature, and k12 and k21 are respectively the conversion rate from State 1 to State 2 and vice versa. ΔE21 is the energy difference between the two states at zero force, and Δx12 is the movement distance in the direction of force f when a bond transits from State 1 to State 2 (which explains why a tensile force shifts more bonds to State 2).
The above model only considers the impact of force magnitude to the bond state. To add force loading rate rf as a second factor, a new function U21(rf) (which equals zero when rf = 0), the energy difference contributed by rf, was added to Eq. (5): Combing Eqs. (4) and (6), we have: (7) in which f12 = kBT /Δx12. The expression equations of k1 and k2 as a function of force have already been derived from force-clamp assay ( Fig. 2(C)), and is in fact the effective off-rate kE (Eq. (3)).

Statistical Analysis
Statistical significance was assessed by two-tailed Student's t-test.

Deriving Two Dissociation States from Directly Measured Platelet GPIbα-VWF-A1 Lifetimes
Platelet tethering via GPIbα binding to VWF-A1 initiates both hemostasis and thrombosis under high shear stress [26] in the arteries and arterioles. To examine the binding kinetics that governs the physiological and pathological platelet functions, we performed the BFP experiments to measure this interaction under controlled tensile force. Briefly, the VWF-A1 domain and streptavidin were coimmobilized on a glass bead (Figs. 1(A), 1(B)), which was then attached to the apex of a micropipetteaspirated biotinylated red blood cell (RBC). On the opposing side, a micropipette-aspirated human platelet was driven by a piezo to repeated touch the bead and retract, allowing adhesion events to happen in a stochastic manner (Figs. 1(A), 1(B)). Force was determined by the RBC deformation, which was monitored in real-time (Methods). Upon the retraction of the platelet, force returning to zero would indicate no adhesion ( Fig. 1(C)), whereas a tensile force would signify an adhesion event (Fig. 1D). As a control, the addition of an VWF-A1 blocking antibody 6G1 [27] eliminated most of the adhesion events ( Fig. 2(A)), confirming the binding specificity. To directly measure bond lifetimes, the VWF-A1 coating density was titrated to achieve ~ 20% adhesion frequency, so that most (> 89%) adhesion events were mediated by single GPIbα-A1 bonds [25]. By clamping the bond and waiting for its dissociation, lifetimes were collected under different clamp forces ( Fig. 1(D)). The "lifetime vs. force" manifested a tri-phasic "slip-catch-slip" pattern agreeing with previous studies [23,28]: the average lifetime first decreased with incrementing force when force is < 15 pN, but increased with force in the range of 15-25 pN with a peak value of ~ 2.5 s, beyond which it decreased again (Fig. 2(B)).
Based on Bell's equation [15], the off-rate (reciprocal of lifetime) of a receptor-ligand bond should increase exponentially with force if the bond only adopts a single dissociating state; accordingly, its lifetime curve exponentially decays with force. The 'catch' behavior in the GPIbα-A1 lifetime curve suggested that the sampled single bonds were a mixture of at least two subpopulations in terms of dissociation state, and the fractions of the subpopulations shifted with force magnitude [8,23]. In order to delineate these dissociation states, we adopted a biophysical model that assumes the superposition of two states (fast-and slow-dissociating; Methods) [23], which fitted well with the experimental data (R 2 ≥ 0.8 under all forces). The calculated off-rates of the slow-dissociating state (k2) were approximately one order of magnitude less than those of the fast-dissociating state (k1) under all forces, while the fraction of the slow-dissociating subpopulation (ω2) gradually increased with force, agreeing with the catch bond behavior and indicating a force-induced bond activation (Figs. 2(C), 2(D)). Importantly, the off-rates of both bond states respectively fitted nicely to Bell's equation, demonstrating that both states followed the first-order dissociation kinetics [8] (Fig. 2(C), fitting parameters annotated).

Force Loading Disrupts Bond Stability
To investigate whether the force-ramp off-rates can predict force-clamp lifetime results, the BFP was set to pull each bond with a pre-set loading rate until the bond was ruptured (Fig. 1(E); Methods). The rupture force data were collected under a wide range of force loading rates (Fig. 3(A)), and segregated based on the loading rate to acquire distribution histograms (Fig. 3(B)) [14,29]. The distributions were then fitted to derive the effective off-rates (kE) (Methods).  Fig. 2(D); black squares) was also plotted Intriguingly, the derived lifetime (1/kE) curves manifested a slip-bond behavior under all force loading rates (Fig. 3(C), curves) and were generally lower than the tri-phasic lifetime curve directly measured from the force-clamp assay (Fig. 3(C), open circles). Moreover, the average lifetimes across forces became shorter as loading rate increased (Fig. 3(C)). Considering that the force-clamp assay holds the bond still with rf = 0, these results indicated that the molecular interaction was disrupted by force loading in a rate-dependent fashion. Notably, a similar phenomenon has previously been observed in Pselectin-sPSGL-1 and P-selectin-G1 interactions [14].

Reconciling the Off-Rate Discrepancy Using an Upgraded State Transition Model
Force can activate bonds by decreasing the energy of the slow-dissociating state relative to the fastdissociating state, thereby transiting bonds from fast-to slow-dissociating state, which underlies the 'catch bond' behavior [8,17] (Fig. 2(D)). We hypothesize that force loading may affect bond dissociation by conversely shifting more bonds to the fast-dissociating state (Fig. 3(D)). A biophysical model was previously created to describe the transition of bonds between dissociation states [17], which only considered the effect of force magnitude. Here, we introduced a new parameter, U21(rf), to depict the energy difference between the two dissociation states contributed by force loading rate rf (Methods; Eq. (7)). A higher U21 value indicates an increase of the energy level of the slow-dissociating state relative to the fast-dissociating state, which should drive bonds to transition to the more stable, fast-dissociating state.
Our new model fitted nicely with the "kE vs. force" data under all force loading rates (Fig. 3(E)). Importantly, the derived values of (ΔE21 + U21) manifested an obvious positive trend against rf (Fig. 3(F); ΔE21 is a constant that represents the default energy difference between two states in the absence of force and force loading), which agreed with our hypothesis. The fractions of slow-dissociating bonds (w2) were then calculated, which demonstrated a concurrent regulation by both force magnitude and loading rate that counteracted with each other (Fig. 3(G)). Under the same force, the fractions of slow-dissociating bonds in force-ramp were all lower than those in the force-clamp condition, and exhibited a negative correlation to rf, confirming the bond state transitioning triggered by force loading (Fig. 3(G)). By using the derived parameters to back-calculate the rupture force distributions, we found that the model could predict our experimental data acquired under all force loading rates (Fig. 3(B), curves). Overall, these results demonstrated the robustness of our new state transition model.

Force Loading Shifts Bonds to Fast-Dissociating State in Two Mouse Molecular Systems
To test if the model is also applicable to other molecular systems, we investigated the bond dissociation in mouse T cell receptor (TCR)-OVA peptide:MHC and mouse platelet integrin αIIbβ3fibrinogen (Fg). The former interaction initiates T cell activation in adaptive immune responses [4,30], while the latter plays a key role in platelet aggregation and thrombus growth [26]. Both interactions manifested a catch bond in force-clamp assay [4], indicating the mixture of two dissociation states. In contrast, the force-ramp assay yielded a slip bond with generally shorter lifetimes, similar to that of the GPIbα-VWF-A1 binding (Fig. 4(A)), suggesting that force loading takes effect again. However, these lifetimes did not show a correlation with rf ( Fig. 4(A), curves); accordingly, the derived kE under different rf also overlapped with one another (Fig. 4(B), points), which suggested insensitivity of bond stability to force loading rate [6,16].
To understand these seemingly contradicting results, we considered the possibility that in these two systems the effect of force loading was so strong that even the lowest rf used (250 pN/s for αIIbβ3-Fg and 150 pN/s for TCR-OVA) already transited all of the bonds to the fast-dissociating state (i.e., none in the slow-dissociation state). To test this hypothesis, force-clamp lifetimes were used to derive the parameters of fast-and slow-dissociating states in the two systems (Figs. 4(C), 4(D)). Remarkably, the calculated fast-dissociating state off-rates of both systems (Fig. 4(B), solid curves) aligned well with their corresponding force-ramp kE data ( Fig. 4(B), points) under all forces, suggesting that the bonds in the force-ramp assay were indeed all in the fast-dissociating state. In the context of the new state transition model, the results suggested that the U21 of these two molecular systems increased steeply with rf, so that a relatively small rf already resulted in a very large U21. To study the "U21 vs. rf" relation in these two molecular systems would require other DFS techniques, e.g., the optical tweezer [31], that have a much softer force transducer than that of BFP to achieve much slower force loading.

Discussion
In this work, we defined the role of force loading rate in regulating molecular binding kinetics. The newly developed model provided a theoretical foundation for using different DFS assays in combination to comprehensively characterize molecular binding.
The off-rate discrepancy between force-clamp and force-ramp assays was first reported in early 2000s when single-molecule DFS technologies started to prevail [5,18]. Meanwhile, some force-ramp assays noticed that the average rupture force of molecular bonds can be independent to or even negatively correlated with rf, which cannot be explained by models assuming that koff is only a function of force [20,22]. By performing AFM experiments, a study on purified P-selectin [14] demonstrated that koff is affected by how force is applied over time, denoted as "force history." Here, we identified force loading rate as the dominating factor in force history and showed that fast force loading disrupts the bond stability by transiting bonds into the fast-dissociating state. By incorporating an energy parameter associated with force loading rate, we established a new bond dissociation model which reconciled the unsolved off-rate discrepancy between the two mainstream DFS assays. Notably, this disruptive effect of force loading should be distinguished from another "force history" effect specific to P-selectin-PSGL-1 interaction [32], where fast force loading activates, instead of inactivates, the bond via a "sliding-rebinding mechanism". This effect is also to be distinguished from the reinforcement of stem cell integrin binding over a threshold loading rate, which requires myosin-dependent stiffness sensing and mechano-signaling of the cell [33].
The biophysics underlying how force loading changes the energy difference between the two dissociation states still remains elusive. We postulate that the force-induced bond activation is a "maturation process" that requires time; fast force loading may rupture the bonds before state transition takes place, thereby locking the bonds in the fast-dissociating state. Obviously, the disruptive effect of force loading does not occur ubiquitously: under circumstances where the molecular interaction only adopts a single dissociation state [34], the off-rates derived from force-clamp and force-ramp assays should be in agreement. It should also be noted that the state transition model established here is only applicable to systems with two dissociation states. In the cases where three or more states co-exist [8], a more complicated theory would be required.
In physiological contexts, the mechanical environment experienced by cells is highly dynamic and complex. DFS allows the observation of one bond at a time while precisely controlling the force waveform [35] on the bond, which is advantageous for mechanistic studies. However, the applied forces on cells are "simplified", and such simplification may affect the binding kinetics, as exemplified by the off-rate discrepancies between DFS assays. The force waveform affects cell mechano-signaling as well, as exemplified by the physiological and pathological cyclic stretch which differentially regulated glucocorticoid receptor nuclear translocation and mitochondrial remodeling in endothelial cells [36,37]. Also, in DFS experiments it has been observed that platelet GPIb and T cell surface TCR can only initiate intracellular calcium signaling following sustained, but not quickly ruptured, ligand binding [3,4]. Therefore, better characterization of cell adhesion and mechano-signaling requires the appropriate selection of DFS assays to mimic the mechanical stimulations cells physiologically experience while interacting with their environment. For instance, platelets and neutrophils adhered to the vascular wall experience nearly constant shear force from the bloodstream [38], and therefore it is more reasonable to select the DFS force-clamp assay to study their adhesion and mechano-signaling [3]. In contrast, platelets aggregating in disturbed blood flow [2,39] and cells forming focal adhesions on a substrate [40,41,42] are subjected to highly dynamic forces, which can be better recapitulated by the force-ramp assay.