Regulation of L-selectin-dependent hydrodynamic shear thresholding by leukocyte deformability and shear dependent bond number

Abstract

Background:

During inflammation leukocyte attachment to the blood vessel wall is augmented by capture of near-wall flowing leukocytes by previously adherent leukocytes. Adhesive interactions between flowing and adherent leukocytes are mediated by L-selectin and P-selectin Glycoprotein Ligand-1 (PSGL-1) co-expressed on the leukocyte surface and ultimately regulated by hydrodynamic shear thresholding.

Objective:

We hypothesized that leukocyte deformability is a significant contributory factor in shear thresholding and secondary capture.

Methods:

Cytochalasin D (CD) was used to increase neutrophil deformability and fixation was used to reduce deformability. Neutrophil rolling on PSGL-1 coated planar surfaces and collisions with PSGL-1 coated microbeads were analyzed using high-speed videomicroscopy (250 fps).

Results:

Increased deformability led to an increase in neutrophil rolling flux on PSGL-1 surfaces while fixation led to a decrease in rolling flux. Abrupt drops in flow below the shear threshold resulted in extended release times from the substrate for CD-treated neutrophils, suggesting increased bond number. In a cell-microbead collision assay lower flow rates were correlated with briefer adhesion lifetimes and smaller adhesive contact patches.

Conclusions:

Leukocyte deformation may control selectin bond number at the flow rates associated with hydrodynamic shear thresholding. Model analysis supported a requirement for both L-selectin catch-slip bond properties and multiple bond formation for shear thresholding.

Keywords

Selectin inflammation PSGL-1 neutrophil rolling mechanokinetics

1. Introduction

Rolling of leukocytes on the endothelial wall during an inflammatory response or normal immunological trafficking is initiated by specific interactions between P- or L-selectin and their common ligand, P-selectin Glycoprotein Ligand-1 (PSGL-1). While P-nselectin is found on the surface of endothelial cells, leukocytes co-constitutively express L-selectin with PSGL-1 on the tips of their microvilli [1–3]. Co-expression of selectin and ligand allows leukocytes to aggregate in suspension and also accumulate on vascular endothelium via cell–cell collisions [4–6]. In addition, leukocytes use L-selectin to make primary contacts and roll on the endothelium of peripheral lymph nodes [7].

A characteristic of L-selectin-dependent leukocyte rolling on endothelium is that it requires a minimum level of hydrodynamic flow [8]. Leukocyte L-selectin rolling flux drops to undetectable levels below a threshold level of flow of approximately 200 s⁻¹ in vivo and 50 s⁻¹ in flow chamber assays with reconstituted ligands [9,10]. A maximum in rolling flux occurs at approximately 450 s⁻¹ wall shear rate in vivo and at 100 s⁻¹ in flow chamber assays, while at higher flow rates the rolling flux falls off precipitously.

The physiologic role of the shear threshold phenomenon has been hypothesized to maximize leukocyte adhesion at the blood vessel wall, where shear stresses are greatest and prevent unwanted leukocyte aggregation in the bulk flow of the circulation [8,11,12]. Leukocyte collisions with previously adherent leukocytes on the vessel wall results in the formation of strings of aligned leukocytes in a process dependent on L-selectin dependent adhesive interactions. String formation has been observed in vivo and accounts for the majority of L-selectin dependent accumulation in vivo [5,6,8,13,14]. Hydrodynamic thresholding has been observed in GPIbα-dependent platelet binding to von Willebrand factor that may also exist to maximize platelet vessel wall adhesive interactions and minimize platelet aggregation in the bulk flow [15,16].

Unique lectin structure and chemistry of carbohydrate-protein bonds [17,18], selectin catch-slip bond mechanics, shear enhanced molecular transport, and cell and membrane deformation (reviewed in [19]) have been hypothesized to underlie the shear threshold phenomenon. In particular, the catch-slip bond behavior of selectins has been shown to be an important component of leukocyte shear thresholding [18,20,21]. Computational modeling approaches have further suggested that translational and rotational transport of selectin receptors into the rolling contact patch contributes to the shear threshold phenomenon [22–24]. In some modeling approaches, the shear threshold phenomenon has been be explained, in part, by an increase in molecular encounter frequency as a result of an increase in translational velocity of the flowing or rolling leukocyte [25].

Leukocyte rolling at shear stresses above the hydrodynamic threshold is strongly influenced by its ability to deform [6,26]. Deformation of the leukocyte may enhance rolling and adhesion by reducing hydrodynamic drag due to cell flattening [27,28] and by increasing the overall size of the contact patch between the cell and the substrate, thereby increasing the number of bonds available for adhesion [24,29]. Membrane deformation may further regulate adhesive dynamics, specifically through the ability of adhesion receptor decorated microvilli to stretch and thereby decrease the force experienced by the bonds at the rear of the contact zone [30–32]. However, leukocyte mechanical properties have not been explicitly linked to the hydrodynamic shear threshold phenomenon.

In this study, high-speed video microscopy was used to analyze the effect of changes in cell stiffness on L-selectin mediated leukocyte-surface contacts at flows above and below the hydrodynamic shear threshold. Similar approaches were originally developed by Goldsmith and colleagues [11,33]. We found that increasing cell deformability amplified rolling flux but did not alter low flow suppression of L-selectin adhesion efficiency. Model analysis suggested that selectin catch-slip bond characteristics and multiple bond loading were essential for the existence of a hydrodynamic shear threshold during adhesive encounters. The role of leukocyte deformation during hydrodynamic shear thresholding may be to permit rapid increases in contact area to indirectly regulate bond number and loading during L-selectin tethering events.

2. Materials and methods

2.1. Reagents and protein isolation

KPL-1, a function blocking monoclonal antibody (mAb) to PSGL-1, was developed as previously described [34]. DREG-56, a function blocking mAb to L-selectin, was purchased from BD Biosciences (San Jose, CA). All other reagents were purchased from Sigma (St. Louis, MO).

PSGL-1 was purified from harvested HL-60 cells lysed in detergent (1% octoglucoside (OG)) as previously described [30]. L-selectin was purified from human tonsil obtained from the Tissue Procurement Facility at the University of Virginia in accordance with the guidelines set forth by the Human Investigation Committee. The human tonsil was homogenized in a detergent solution and purified with 1% OG by passing over a column of 1H3 antibody (ATCC, Manassas, VA) specific for L-selectin.

2.2. Neutrophil isolation and cell lines

Human neutrophils were obtained from 60 ml of heparin (10 U/ml)-anti-coagulated whole blood. Blood was obtained from consented donors following the University of Virginia Human Investigation Committee approved protocol #10,671. The experiments were undertaken with the understanding and written or verbal consent of each subject according to the conditions set forth by a Human Subjects or Ethics Review Board, and that the study conforms with The Code of Ethics of the World Medical Association (Declaration of Helsinki). Neutrophils were isolated by density separation using 1-Step Polymorphs (Accurate Chemical, Westbury, NY), washed, and placed in calcium and magnesium-free buffer on ice. For flow chamber assays, neutrophils were taken from the reserve and resuspended in HBSS containing 2 mM CaCl₂, 10 mM HEPES, pH 7.4 at room temperature (RT).

As a model neutrophil, a PSGL-1 expressing murine pre-B lymphocytic cell line, 300.19, was used (a gift of Dr. K. Snapp, UIC, Chicago, Illinois). 300.19 cells were selected for proper core-2 expression and glycosylation and comparable PSGL-1 expression to neutrophils [35]. 300.19 cells were cultured in RPMI Medium 1640 with 10% fetal bovine serum (FBS) containing 2 mM L-Glutamine, 100 U/ml penicillin, 0.1 mg/ml streptomycin, and 10 mM 2-mercaptoethanol (GIBCO-BRL, Grand Island, NY). 300.19 cells were washed and resuspended in HBSS containing 2 mM CaCl₂, 10 mM HEPES, pH 7.4 at RT.

For cell deformability experiments, neutrophils or 300.19 cells were treated with 15 µM cytochalasin D (CD) for 15 min at RT under end-to-end rotation. For fixation, cells were treated with a mixture of 1% paraformaldehyde and 0.1% glutaraldehyde for 15 min. at RT. Both 300.19 and neutrophils were washed and resuspended in HBSS containing 2 mM CaCl₂, 10 mM HEPES, pH 7.4 at RT.

2.3. Micropipet experiments

Glass micropipets with an inner diameter of 5 µm were purchased from World Precision Instruments (Sarasota, FL). Neutrophils, suspended in PBS and untreated or treated with CD or a mixture of 1% paraformaldehyde/0.1% glutaraldehyde, were placed between two glass slides and mounted on an inverted Olympus phase contrast microscope (Olympus, Central Valley, PA). The micropipet was connected to a micromanipulator, which was hooked to a syringe pump (Harvard Apparatus, South Natick, MA) to apply a specified pressure. A Dwyer 490 digital manometer (Dwyer Instruments, Inc., Michigan City, IN) was used to measure the applied pressure. Images were taken with a CCD camera (Burle Security Products, Las Vegas, NV) and recorded on a VCR at 30 frames/s (JVC, Wayne, NJ).

2.4. Microbead preparation

Polystyrene microbeads (9.377 ± 0.354 µm) were purchased from Polysciences, Inc. (Warrington, PA). Beads were washed three times with 0.1 M borate buffer, pH 8.5, and incubated for 4 hours with L-selectin (2 µg/ml) in 0.1 M borate buffer at RT and blocked with 1% Tween-20 solution at 4°C. A site density of ∼100 sites/µm² of L-selectin on the microbeads was estimated using a europium assay. The microbeads were stored at 4°C in 0.1 M borate buffer containing 1% Tween-20. Before use in the laminar flow chamber assay, the microbeads were centrifuged and resuspended in assay media (HBSS, 10 mM HEPES, pH 7.4, and 2 mM CaCl₂) at a concentration of $5 \times 10^{5} beads/ml$ .

2.5. Flow chamber assay

Polystyrene slides were cut from bacteriological Petri dishes (Falcon 1058, Fisher Scientific, Pittsburgh, PA) and the diluted adhesion molecules were passively adsorbed to the slide and allowed to incubate at RT for 2 hours. Concentrations were adjusted to achieve a PSGL-1 (0.5 µg/ml) or L-selectin (2 µg/ml) density of ∼100 site/µm² based on a europium assay [36]. Slides were blocked for nonspecific adhesion overnight at 4°C with 1% Tween in HBSS. The wall shear stress of the parallel plate flow chamber (Glycotech, Rockville, MD) was determined by the gasket dimensions, which were 0.01 inches thick and 1 cm wide. Cell or bead suspensions were drawn into the chamber at RT using a syringe pump (Harvard Apparatus, South Natick, MA). The chamber was mounted over an inverted phase-contrast microscope (Diaphot-TMD; Nikon, Garden City, NY) at 40× magnification (1 pixel = 0.185 µm) unless otherwise noted.

For cell-bead collision assays, glass slides (Fisher Scientific, Pittsburgh, PA) were incubated with 2 µg/ml DREG-56 for two hours at RT. Glass slides were blocked for nonspecific with 1% Tween and 1% HSA in HBSS at 4°C overnight. L-selectin coated beads were allowed to bind to the DREG-56 coated surface. Neutrophils or 300.19 cells were then drawn into the chamber and collisions were visualized on differential interference contrast microscope (Eclipse TE 300; Nikon, Garden City, NY) with a 60× oil immersion objective.

2.6. Data acquisition and high speed video analysis

Images from all experiments were recorded using the Photron PCI FastCam (Photron USA, Inc.; San Diego, CA). The digital images were stored in the PCI’s memory board and transferred directly to the hard drive of a Dell Dimension 8400 (Dell, Inc., Austin, TX) in AVI format. AVI movies were loaded on ImageJ and particles were identified and tracked using a normalized cross-correlation algorithm [37]. To resolve particle position and deformation from high spatio-temporal resolution images (250 frames/s), subpixel centroid interpolation was incorporated into the tracking program [38], similar to pioneering work by Goldsmith and colleagues [11,33].

2.7. Model design

We created a simple deterministic model of leukocyte shear thresholding that combined selectin molecular kinetics and the first order effect of cellular deformation: the control of bond number. Using site-density values and tether bond dissociation kinetics determined on the imaging, immobilized L-selectin substrates, and flow chamber apparatus [13,30,39], we computed the following equations for apparent bond formation rate for P-selectin and L-selectin based on microbead tethering data using a MatLab curve fitting routine [13]. The exponential curves fitted to experimental data using $F_{b}$ (units of pN) to represent the force on the model cell. With the suspending medium having a viscosity of 1 cP the force on the model cell at a wall shear rate of 100 s⁻¹ was calculated to be $F_{b} = 110 pN$ . The model was based on the following relationships between force on the model cell and bond formation frequency and dissociation kinetics, as indicated below in Eqs (1)–(4) [40]: $\begin{array}{rcl} (1) & k_{on, Psel} = 0.74 * exp (- 0.31 F_{b}), \\ (2) & k_{on, Lsel} = 0.029 * exp (0.011 F_{b}), \\ (3) & k_{off, Psel} = 1.1 * exp (0.026 F_{b}), \\ (4) & k_{off, Lsel} = (1.09 * 10^{4}) * exp (- 0.29 F_{b}) + 11.1 * exp (0.014 F_{b}) . \end{array}$

$k_{on, Psel}$ (Eq. (1)) and $k_{on, Lsel}$ (Eq. (2)) are bond formation rates on a per-site basis for P-selectin and L-selectin, respectively. To further simplify the model the area site density was converted to a linear site density to represent the number of possible binding events in the model cell’s trajectory. Binding sites were therefore represented as being in an evenly spaced rectangular grid (i.e., 100 sites/µm² has a linear site density of 10 sites/µm). The number of binding sites (sites/µm) per micrion was then multiplied by the reaction zone length and the appropriate bond formation frequency ( $k_{on}$ ). This calculation determined the number of bonding events per cell and therefore the total time bound to the chamber surface. $k_{off, Psel}$ (Eq. (3)) and $k_{off, Lsel}$ (Eq. (4)) are apparent off-rates for P-selectin and L-selectin, respectively. Both equations are a function of the force on the bond based on adhesion lifetime distributions in a previous study [40]. The force on the cell or bond cluster ( $F_{b}$ in the equations above) was estimated based on equations of near-wall hydrodynamics and is essentially a parameter linked to the flow rate [41,42]. In multibond interactions, the force is assumed to be evenly distributed.

We set up a material balance on a control volume of the flow chamber assuming steady-state conditions: $\begin{matrix} (5) & \frac{d N_{cell, b} (t)}{d t} = N_{in} (t) - N_{out} (t) + N_{cell, rxn} (t) . \end{matrix}$

In Eq. (5), $N_{cell, b}$ denotes “number of cells/time”. At steady state, $d N_{cell} / d t \Rightarrow 0$ , indicating the number of beads entering the control volume equals the number of beads exiting plus the number of beads reacting with the surface. The number of cell collisions was calculated based on a previously described model integrating sedimentation and axial transport of cells as a function of shear flow and is largely insensitive to wall shear stresses between 0.3 to 2 dyn/cm² at the bead and cell sizes modeled [42].

The model computes the average residence time of a model cell in the control volume, which defines the rolling flux. To determine the average residence time of a cell in the reaction zone it’s total time of flight (based on lubrication theory [41]) and total reaction time (sum of time spent bound to the substrate) are summed. The time of flight is the translational velocity between binding events and is a function of shear stress and distance from the surface (100 nm). Model cells are in either of two states: bound or flowing. The equation for total time in the non-reacting state ( $t_{non}$ ) can be written as the following: $\begin{matrix} (6) & t_{non} = \frac{L}{h s (\frac{0.7431}{0.6376 - 0.2 ln (\frac{δ}{r})})} . \end{matrix}$

In Eq. (6), L is the length of the control volume (2 cm), s is the shear rate, r is the particle radius, δ is the gap thickness (distance between the surface and the bottom of the particle) and $h = δ + r$ . The velocity equation (denominator of Eq. (6)) is derived from the lubrication approximation for velocity of a sphere translating in shear flow [40,41].

Total reaction time is a combination of how frequently bond events occur and their lifetimes. For single bond interactions total bond events within the control volume were computed by multiplying the total number of sites in the control volume by the bond formation frequency. Average bond lifetime was be estimated by calculating the inverse of the off-rate. For multiple bond interactions, the stress was equally shared between all bonds and the model of Tees and co-workers was used [43]. Total reaction time was then computed by multiplying the total number of adhesive events by each event’s average duration. Finally, total time within the volume, or residence time, was found by adding total non-reaction time to total reaction time.

3. Results

3.1. Neutrophil rolling flux measurements indicate hydrodynamic shear thresholding

We set out to probe how a change in global cell deformability would modify leukocyte hydrodynamic shear thresholding. Cytochalasin D (CD) depolymerizes actin and has been shown to increase resistance to detachment and decrease rolling velocity on P-selectin [44–47]. However, it is not known how actin depolymerization might affect L-selectin mediated leukocyte rolling or shear thresholding. To assess the effects of actin depolymerization on shear thresholding through L-selectin, we treated neutrophils (Fig. 1(A)) with 15 µM CD and compared to untreated neutrophils and fixative treated neutrophils. Treatment with CD significantly magnified neutrophil rolling flux on L-selectin relative to untreated controls at every shear stress, but did not produce a shift in the peak rolling flux (Fig. 1(A)). In contrast, fixation dramatically suppressed neutrophil rolling flux, shifting the location of peak flux to ∼0.4–0.5 dyn/cm² wall shear stress and attenuated rolling at wall shear stresses of 1 dyn/cm² and above, especially in neutrophils (Fig. 1(A)). Virtually identical results were observed with 300.19 cells expressing human PSGL-1 in terms of the effects of CD treatment and fixation (Fig. 1(B)). We have previously shown that fixation does not affect the mechanokinetics of PSGL-1 [30].

Fig. 1.

Neutrophil and 300.19 cell rolling flux on L-selectin. (A) Neutrophils or (B) 300.19 cells treated with CD or fixative were flowed over an L-selectin substrate and the number of cells was counted. The shear threshold can be clearly seen in both types of cells as the rolling flux increases up to a maximum at 1 dyn/cm² wall shear stress. (C) Pressure required to pull treated or untreated neutrophil into micropipet in a set time. A minimum of 20 cells were used for each treatment and only cells that were pulled completely into the pipet in <1 s were counted. (D) A neutrophil visualized on the tip of the micropipette was drawn into the micropipette (panel D1). The second panel (panel D2) was imaged 0.033 s later. The line illustrates that approximately half of the cell was pulled into the pipet in 0.033 s.

3.2. Micropipet measurement of neutrophil deformability

To validate the impact of CD and fixation on the biomechanical properties of neutrophils, we measured the force required to pull the cell into a micropipet of 5 µm diameter (Fig. 1(C)). As shown in Fig. 1(C), the pressure required to pull the neutrophil into the pipet for each cell treatment was measured. Cells treated with 15 µM CD needed approximately four-fold less pressure to be drawn into the micropipet compared to controls, whereas fixed cells necessitated a four-fold greater pressure compared to controls ( $p < 0.01$ , paired two-tailed t-test). The micropipet experiment binned cells based on “squishiness” and provided an estimate for the degree of cell deformability that each of the treatments imparted. It appeared that CD reduced resistance to deformation while fixation increased resistance to deformation.

3.3. Effect of L-selectin-PSGL-1 bond number on hydrodynamic shear thresholding

While alterations in cell deformability significantly modified cell rolling flux, it is unclear how deformability might influence the avidity or number of L-selectin-PSGL-1 interactions during cell tethering and rolling. To first determine the effects of modifying bond number on adhesion dynamics independent of changes in deformability, we measured neutrophil rolling flux on immobilized PSGL-1 (Fig. 2(A)) or L-selectin (Fig. 2(B)) with addition of subsaturating concentrations of blocking mAb. Addition of subsaturating concentrations of DREG-56, a function blocking mAb for L-selectin, reduced neutrophil rolling flux on PSGL-1 over all shear stresses tested in a dose-dependent manner (Fig. 2(A)). Similarly, KPL-1, a function blocking mAb for PSGL-1, suppressed neutrophil rolling on L-selectin in a dose dependent manner as increasing concentrations of mAb were added (Fig. 2(B)). The addition of blocking mAb to either receptor to lower the available ligands for bonding decreased neutrophil rolling flux at every shear stress tested. The reduction in allowable bond number at each flow rate did not shift the location of the peak in rolling flux. Whether L-selectin or PSGL-1 was immobilized on the wall of the flow chamber had no significant effect on the observations.

Fig. 2.

Neutrophil rolling flux on L-selectin and PSGL-1. (A) Neutrophils were incubated with a range of concentrations of L-selectin mAb DREG-56 and flowed over a PSGL-1 coated surface. The shear threshold phenomenon is easily discernible as the rolling flux reaches a maximum at 1 dyn/cm² wall shear stress. (B) Similarly, neutrophils were incubated with a range of concentrations of PSGL-1 mAb KPL-1 and flowed over an L-selectin coated surface. Sub-saturating concentrations of mAb in both cases reduced the shear threshold pattern, but did not shift it.

3.4. Bond number appears to be influenced by neutrophil deformability

The shear threshold not only manifests itself as a peak in cell rolling flux, but also can be demonstrated on individual leukocyte rolling dynamics. For example, as shear stress is dropped below the threshold, a rolling leukocyte will detach from the surface and start moving at the hydrodynamic velocity [10]. The process can be seen in reverse; that is, an increase in shear from below to above the shear threshold converts transient leukocyte tethers on a peripheral node addressing or PSGL-1 surface to steady rolling. We took advantage of this phenomenon to further investigate the link between deformability and bond number. In essence, the time required for a rolling leukocyte on an L-selectin ligand to release from the surface following a flow stoppage is hypothesized to depend on the number of bonds supporting rolling [26]. Any treatment that leads to an increase in the number of bonds during rolling would be expected to lead to a longer release time following an abrupt drop in the flow [26].

As an example, Fig. 3(A) shows velocity tracing of a neutrophil rolling on L-selectin before and after flow was dropped. Images were taken at 250 frames/s and the frame-to-frame displacement was computed to determine the rolling velocity. Up to the 2.5 s mark, the cell is rolling under 1 dyn/cm² wall shear stress. When shear was dropped to 0.2 dyn/cm², the neutrophil began to lift off the surface and traverse at hydrodynamic velocity (∼116 µm/s). The response to step decrease in shear is shown in the red box (Fig. 3(A)). The velocity tracing in the red box of Fig. 3(A) is zoomed for analytical purposes in Fig. 3(B). The initiation time of the release was determined by tracking the surrounding cells in the free stream.

Fig. 3.

Neutrophil shear-drop release experiment. (A) Velocity tracing of neutrophil rolling on L-selectin at 1 dyn/cm² as shear is dropped to 0.2 dyn/cm² at 2.5 seconds. The cell lifts off the surface and flows at hydrodynamic velocity (rectangle). (B) The portion of (A) in the rectangle is zoomed for clarity and to show how velocity after release, $V_{f}$ , and τ are calculated. $V_{f}$ , and τ are computed by fitting an exponential to the velocity profile after a decrease in shear stress. (C) No statistically significant differences were found in average velocity after release for all experimental conditions. (D) Release time, τ, was computed for a variety of experimental conditions. Release time decreases for perturbations to decrease bond number and increases when conditions act to increase bond number or deformability. ∗ denotes control, $* *$ indicates $p < 0.05$ compared to appropriate control.

The neutrophil release was modeled as a first order step response that can be described by the following equation: $\begin{matrix} (7) & V = V_{f} (1 - exp (\frac{- t}{τ})) . \end{matrix}$

In Eq. (7), V is the velocity at any given time point, t is time, $V_{f}$ is the final velocity reached and is equivalent to the hydrodynamic velocity, and τ is the characteristic time constant of the response and is determined by computing the time at which the value of $0.63$ $V_{f}$ is achieved. A MATLAB program was written to find the best fit of parameters $V_{f}$ and τ to the response by minimizing the sum of the squared error between the actual data and the predicted response.

The velocity after release, $V_{f}$ , and time constant, τ, were plotted for a variety of experimental conditions in Fig. 3(C) and Fig. 3(D). For the table of conditions, a (+) in the L-selectin row indicates that L-selectin was the substrate and likewise for PSGL-1. A (+) in the DREG-56 or KPL-1 row signifies that 6 pM of that mAb was added to the neutrophils before the experiment to reduce the number of potential bonds. All tests were performed dropping the shear from 1 dyn/cm² to 0.2 dyn/cm² except experiments indicated by a (+) in the 3 dyn/cm² row. In these experiments, shear was dropped from 3 dyn/cm² to 0.2 dyn/cm² to see if increased cell deformation due to higher shear forces could induce larger bond numbers. Finally, a (+) in the row for CD denotes its addition before the run. The effects of fixation were not measured because sustainable rolling could not be obtained above 1 dyn/cm² wall shear stress.

We found no statistically significant differences in the final velocity after release ( $V_{f}$ ), indicating that all neutrophils were unbound and moving at the velocity of an unencumbered cell (Fig. 3(C), $n = 20$ each condition). However, release times, τ, were dramatically altered by changes in experimental conditions (Fig. 3(D)). Addition of 6 pM KPL-1 reduced τ from 0.052 s to 0.022 s on L-selectin while 6 pM DREG-56 lowered τ from 0.043 s to 0.014 s on PSGL-1. Neutrophil rolling at 3 dyn/cm² wall shear stress resulted in an increase in τ to 0.073 s on L-selectin and 0.070 s on PSGL-1, suggesting that more bonds existed at 3 dyn/cm² wall shear stress compared to 1 dyn/cm². Treatment with CD raised τ to 0.11 on L-selectin and 0.10 on PSGL-1 for neutrophils previously rolling at 1 dyn/cm² wall shear stress. All of these changes meet the requirements for statistical significance using a paired, two-tailed t-test ( $p < 0.02$ ). The reduction in the number of available bonds via addition of subsaturating concentrations of monoclonal antibodies lowered the time required for the cell to release from the surface. At the same time, an increase in deformability raised the required time to release from the surface, consistent with the hypothesis that more bonds existed.

3.5. Cell-bead collision assay

To establish a link between cell deformability and contact patch size, we modified a microbead collision assay previously used to study P-selectin-PSGL-1 mediated membrane tether dynamics [6,46]. Immediately before, during, and after the collision the flowing cell was tracked to determine its trajectory in an approach based on previous work by Goldsmith and co-workers [33]. The modification we introduced was to use cell-sized microbeads as targets to simulate secondary capture/tethering geometries and facilitate measurement of the 2-D projection of the contact patch formed L-selectin mediated tethers [46]. Microbeads (10 µm) were coated with purified L-selectin (2.5 µg/ml) and adhered to a glass surface via immobilized an L-selectin antibody (DREG-56). In this way, L-selectin was only presented on the microbead surface and not on the wall of the flow chamber. The immobilized L-selectin antibody used to tack the microbeads to the wall did not support neutrophil tethering at wall shear stresses examined (greater than 0.2 dyn/cm²), allowing us to isolate interactions solely between the neutrophil and the L-selectin-presenting microbead.

Neutrophils were treated with fixative, CD or left untreated, and then flowed over the immobilized microbeads. Collisions were analyzed on a DIC microscope with high speed video (250 frames/s). A sample collision is provided in Fig. 4(A) and (B). In Fig. 4(A) the neutrophil collides with a 10 µm L-selectin microbead that fails to form a bond. As shown, the displacements between frames are evenly spaced for a non-interacting cell, and the approach and exit velocity are approximately equal, indicative of no adhesive interaction with the microbead [40]. By contrast, an interacting cell is displayed in Fig. 4(B) where the displacements decrease following an adhesive (L-selectin mediated) interaction and the rings of the multiplied image overlap each other, indicating that the exit velocity has decreased compared to the approach velocity. This alteration of cell trajectory is indicative of an adhesive interaction [40].

Fig. 4.

Images of cell-bead collisions. Neutrophil colliding with 10 µm L-selectin coated bead with no bond formation (A) and bond formation (B). The images were taken at 60× and 250 fps. (C) Visualization of measurement of size of the contact angle between a cell and a bead. Angle lines indicate that this collision generated a projected contact angle of 25°.

Figure 4(C) exemplifies the quantification of the contact patch area between the neutrophil and microbead during collision. Using the centroid of the stationary bead as an anchor point, an angle was measured corresponding to the part of the circumference of the bead in contact with the cell. Contact angles were binned in 10° increments. Neutrophils with highly offset collisions were not in a favorable orientation to produce quantifiable contact patches and consequently were not measured.

From cell-bead collision data, we measured residence times, or the time a cell remained in contact with the bead, and sought to quantify a relationship between shear stress, contact angle, and residence time. Residence time was measured similar to our protocol for quantification of release time. A drop of 50% in the neutrophil’s velocity was used to mark the initiation of a tether bond [17]. To determine the end of the tether, the time to reach 50% of the departure velocity ( $V_{f}$ ) was quantified. Residence times were plotted as a function of wall shear stress and contact angle for neutrophils on 10 µm beads (Fig. 5(A)–(D)).

Fig. 5.

Contour plots of residence time of neutrophils on bead as a function of wall shear stress and contact angle. Two-dimensional plots illustrating the history of neutrophil collisions with stationary L-selectin-coated 10 µm diameter microbeads. Neutrophils encounters with 10 µm were binned according to maximum contact angle (degrees, x-axis) during cell-bead interaction and flow conditions (wall shear stress, y-axis). The legend groups interactions in bins of 0 ms, 20 ms, 40 ms, 60 ms, 80 ms, and 100 ms or greater as indicated by the appropriate grey level. Panel (A) depicts resting, untreated neutrophil-bead collisions, panel (B) depicts fixed neutrophil-bead collisions, and panel (C) depicts CD-treated neutrophil-bead collisions. Gray-scale gradients are scaled by the maximum residence time of a particular data set.

For all shear stresses, the residence time increased as the contact angle increased (Fig. 5). The magnitude of contact angle did not correlate strongly with shear stress, possibly due to contributions of off-center encounters that became more numerous at higher flow rates. The shear threshold phenomenon was evident for the large majority of contact angles measured (Fig. 5). As an example, looking at the 40°–49° bin of Fig. 5(A), the shear threshold is easily distinguished by the fact that the residence time is very low at the lowest wall shear stress, increases up to a maximum at 1 dyn/cm² and subsequently decreases as shear is further increased. For neutrophils that collided at 0.4 dyn/cm² wall shear stress, even the much briefer interactions display a peak in residence time that correlated well with the measured contact angle. The data imply that residence time on the target microbead is closely aligned with cell deformation and the peak of cell rolling flux.

The contributions of changes in deformability were also examined by fixation (Fig. 5(B)) and treatment with CD (Fig. 5(C)). For fixed cells, residence time and contact angle were not significantly different from control cells at wall shear stress at 0.3 dyn/cm². We could not detect measurable interactions of fixed neutrophils above 0.5 dyn/cm², hence, the zero residence times at those shear stresses. As with control cells, the larger contact angles correlated with longer residence times. For cells treated with CD, the residence times for cells with greater than 49 degree contact angles were greater than controls ( $p < 0.25$ ). CD treatment appeared to facilitate neutrophil deformation at low shear stresses sufficiently that many collisions could be classified in the larger contact angle bins. This reveals an important component of the shear threshold phenomenon in that an increase in deformability on subsecond time scales augments a cell’s ability to adhere in an L-selectin-PSGL-1 dependent manner. The maximum in residence time and contact angle correlated well with the peak in leukocyte rolling fluxes typically observed for L-selectin mediate neutrophil rolling.

3.6. Computational model analysis of varying bond number and selectin mechanokinetics

We wanted to test the hypothesis that the combination of molecular kinetics and cellular deformation would act collectively to produce shear thresholding. Therefore, we created a model to analyze the effects on shear thresholding of the unique biomechanical properties of the L-selectin-PSGL-1 interaction coupled with deformation-induced modulation of bond number. Central to the model hypothesis is that the first order effect of cell deformation is that there is an increase in the number of bonds. We computed equations for apparent bond formation rate of P-selectin (Eq. (1)) and L-selectin (Eq. (2)) and apparent dissociation rates for P-selectin (Eq. (3)) and L-selectin (Eq. (4)) (see Methods). The bond formation rates ( $k_{on, Psel}$ and $k_{on, Lsel}$ ) and apparent off-rates ( $k_{off, P}$ and $k_{off, L}$ ) for P-selectin and L-selectin were determined by fitting a simple exponential to previously published stop-time distributions [40]. In the case of L-selectin, a two exponential form of the off-rate equation was used to account for the catch slip bond transition that occurred at the experimental flow rates used. While P-selectin also displays catch-slip bond behavior, its transition force is below the range explored in our experimental assays [48], hence the simpler exponential form that captures the slip bond kinetics was appropriate for the model application [40]. Each equation is a function of the force on the bond estimated from the hydrodynamic stress on a hard sphere approximately the same size as a neutrophil (3 µm radius, 100 nm separation distance).

We set up a material balance on a control volume of the flow chamber such that the accumulation was equal to the number of cells coming in minus the number flowing out of the volume plus the number binding (See Methods, Eq. (5)).

In Eq. (5), $N_{b}$ denotes “number of cells” so that steady state, $d N_{b} / d t \Rightarrow 0$ , and the number of cells entering the control volume equals the number of cells exiting plus the number of cells reacting with the surface. The longest residence times (time in non-interaction state (Eq. (6))) plus the adhesion time, which consisted of the bond formation frequency (Eqs (1) and (2), P-selectin and L-selectin, respectively) multiplied by the median adhesion lifetimes (Eq. (3) or (4), P-selectin or L-selectin, respectively), should correlate with the highest rolling fluxes and are a function of the total time of flight and total reaction time. Multiple bonds shared the stress equally and breakage times calculated as described in the Methods.

Contributions of bond number and cell deformation were introduced into the model in a simple fashion. Leukocyte residence times were calculated for possible bond numbers that could form during a transient tethering interaction. The model calculates the leukocyte residence time for 1, 5, 10, or 15 bonds forming during each tethering interaction. Higher bond numbers were indicative of a larger contact patch. It was assumed that the total stress on the cell was distributed over the appropriate number of bonds, a reasonable assumption underlying many modeling approaches [43]. The off-rates for L-selectin-PSGL-1 bonds were modeled as catch-slip bonds. Since the flow rates in the model put the PSGL-1-P-selectin bond about the transition force, they were modeled as slip bonds only.

Residence times calculated as a function of shear stress are shown in Fig. 6. Model results at linear site-densities of 20, 50, and 75 sites/µm, are shown in Fig. 6(A), (B), and (C), respectively. Each curve represents the residence time given a number of bonds over which the load is distributed. For example, in Fig. 6(A), the black dotted line is the residence time as a function of shear stress if the load is distributed over 15 bonds at each stress. Figure 6(D) is a plot to illustrate the effects of site-density on residence time, assuming 15 bonds (i.e. the black dotted line in Fig. 6(A), (B), and (C) is plotted together for comparison). By changing only the site-density we were able to reproduce our findings from Fig. 2.

Fig. 6.

Model results for residence time as a function of shear stress. Residence times are calculated at a linear site-density of 20 (A), 50 (B), or 75 (C) sites/µm of L-selectin. The bond number in (A)–(C) denotes the number of bonds over which the load on the particle is distributed. (D) Data for 15 bonds at each site-density is plotted to demonstrate how site-density affects residence time.

To illustrate the critical elements of the model, we adjusted the off-rate and bond formation rate of the particle and recalculated the residence times. In Fig. 7(A), a particle has been given L-selectin bond formation rate kinetics (Eq. (2)) and P-selectin off-rate kinetics (Eq. (3)). With this combination, the residence time increases as a function of wall shear stress for all bond numbers. Giving the particle P-selectin bond formation kinetics (Eq. (1)) and L-selectin slip bond only off-rate kinetics (Eq. (4)), residence times become exponentially small as wall shear stress increases (Fig. 7(B)). Similar results to Fig. 7(B) are found if the particle is given P-selectin kinetics only (not shown). Limiting L-selectin to slip bond characteristics failed to recapitulate shear thresholding for all conditions examined (Fig. 7(B) and (C) compared to Fig. 6), suggesting the critical importance of catch-bond characteristics for L-selectin mediated hydrodynamic shear thresholding.

Fig. 7.

Model results with alternate bond formation and off-rate kinetics. (A) A cell is given L-selectin bond formation kinetics and P-selectin dissociation rate kinetics. The residence time increases exponentially with wall shear stress. (B) A cell is given P-selectin bond formation kinetics (non-force dependent) and L-selectin slip bond only dissociation kinetics. The residence time decreases exponentially with flow. (C) Cells given L-selectin bond formation kinetics and L-selectin slip bond only dissociation kinetics. Bond number appears to have little influence on the residence time with the simulated kinetics.

At wall shear stresses of 0.8–1.0 dyn/cm² L-selectin bonds are in the slip regime and interaction times are 2–10 fold briefer than P-selectin bond cluster lifetimes, depending on site density [40].

4. Discussion

Leukocyte adhesion through selectins has an unusual property of requiring a threshold level of shear to stabilize and promote rolling. This is most evident in L-selectin mediated rolling, where a pronounced peak, or optimum in rolling flux exists as a function of shear stress while adhesion is actually suppressed at flow rates lower flow rates. Below the optimum flow rate, L-selectin mediated interactions between leukocytes and natural ligand bearing surfaces become infrequent and highly transient, reducing rolling to a series of infrequent and highly transient tether bonds. As bond forces drop below 25 pN, L-selectin bond lifetimes shorten precipitously, to as brief as 30 milliseconds [18,49,50].

Shear thresholding is hypothesized to be important in the regulation of L-selectin-dependent aggregation of leukocytes on the blood vessel wall, a process that contributes to secondary capture and leukocyte string formation. Away from the vessel wall, shear stress is reduced and therefore L-selectin-dependent aggregation is suppressed in the bulk flow of the circulation. The tuning of adhesion through variable shear stress has a parallel with platelet rolling on vWF, which is also inhibited when shear stresses drop below an optimum. It is possible that shear thresholding may similarly exist to direct platelet adhesion and aggregation to the vessel wall.

In light of the limitations of rigid particle systems in fully recapitulating shear thresholding [17,21,40,50], it is perhaps not so surprising that we observed significant effects of modulation of leukocyte deformability on L-selectin mediated tethering and rolling. A number of investigations have suggested that the ability of the leukocyte to deform can strengthen E-selectin and P-selectin rolling adhesions [26,44]. What our work adds to previous studies on the role of deformability on adhesion is the observation that increased deformability amplified leukocyte L-selectin dependent adhesion in flow. This pattern carried over to analysis of leukocyte collisions with L-selectin coated microbeads, where longer adhesion times strongly correlated with increasing size of the area of contact between the cell and bead.

Similar to the pattern of L-selectin-mediated rolling flux on planar surfaces, the duration of neutrophil adhesions to L-selectin-coated microbeads were brief below the shear threshold and hit a maximum at approximately the same wall shear stress at which the peak rolling flux would be observed. The geometry of the neutrophil-microbead collision not only simulated secondary tethering interactions that lead to leukocyte string formation; but also had the benefit of creating a side-view of the formation of a cell-microbead contact patch. By this means, we could correlate time of interaction with the projected size of the contact patch. Particularly with the high-speed video, it was strikingly evident that contact patches of 10% of the neutrophil’s surface area could form in a few ten’s of milliseconds, providing a mechanism for rapid increases in L-selectin molecules available for binding. Deformation-induced increases in available bond number would potentially provide a mechanism of adhesion stabilization on very short time frames relative to diffusive transport in the plane of the cell membrane [29].

To determine if deformation might control bond number, we analyzed leukocyte rolling and release from an L-selectin ligand substrates following a drop in shear. The release times as rolling was destabilized were longer both when the neutrophil was made more deformable by CD and when it was rolling at a higher initial level of shear stress, suggesting that increased deformation lead to more bonds during rolling. Rapid formation of relatively large contact patches, as directly visualized in projection during neutrophil-microbead collisions, would increase the number of adhesion receptors available for bond formation, and is consistent with the effects predicted by either softening or stiffening the leukocyte’s global mechanical properties.

Deformation on the short time scales critical for shear thresholding likely requires a relatively low cell viscosity as well. For the neutrophil to respond quickly enough on the time scale of a selectin interaction, viscosity would likely be towards the low end of the range of published values (12 cP to 60,000 cP) [51–54]. As leukocyte deformation appeared to regulate the number of selectin bonds, both pathological and therapeutically directed alterations in cell mechanics may have significant effects on adhesion.

To capture the complex interrelationships suggested by our experimental data and previous work characterizing L-selectin mechanokinetics on shear thresholding, we developed a very simple mathematical model that linked bond mechanics and bond number that is described in the supplemental data section. L-selectin’s unique shear enhanced formation rate was also incorporated into the model, as were its catch-slip bond characteristics as has been done in previous work modeling shear thresholding [55]. The modeling structure we developed minimized assumptions regarding the intricate micromechanics of cell structure by parameterization of the relevant outcome of cell deformation – the ultimate increase in bond number. Consequently, we could test for hydrodynamic shear thresholding as a function of P-selectin and L-selectin bond properties, allowing for different numbers of bonds and even examining the effect of changing catch-slip bond mechanics to slip bond mechanics for L-selectin. While the model is highly simplified, it allowed us to examine hypotheses regarding the interplay of bond number and bond mechanics during rolling interactions at a conceptual level.

The most striking inference from the model was that shear thresholding was dependent on leukocyte binding interactions being mediated by multiple catch-slip bonds. When the model analyzed the rolling flux of cells interacting through single bonds, it was unable to recapitulate shear thresholding over a wide range of site densities of ligand, consistent with some but not all previously published work [17,40,50]. This suggests that L-selectin catch-slip bond characteristics are a necessary for shear thresholding, in agreement with work of Yago and co-workers [50] and adhesive dynamics simulations [55]. What our model analysis and experiment adds to previous work is in underscoring the critical need for multiple bond formation events on time scales approaching the bond lifetime of L-selectin. Rapid formation of contact patches and commensurate increases in bond number during leukocyte-surface encounters may be a factor in how L-selectin bonds could be collectively driven into the catch regime by multiple-bond load sharing.

While selectin catch bond characteristics are clearly important for shear thresholding and leukocyte string formation, our experiments and modeling study also emphasize the importance of multiple bond formation at the cellular level. It is in this respect that cell deformation becomes an important regulatory element controlling leukocyte adhesion through L-selectin, as increases in bond number are dependent on the number of available receptors for binding and the degree of membrane-surface contact. Leukocyte deformability has long been thought to be an important modulator of rolling and firm adhesion [24,56–58]. Our studies here suggested that deformation also exerts a primary regulatory role in leukocyte accumulation through hydrodynamic shear thresholding.

Footnotes

Acknowledgements

We would like to acknowledge valuable discussions with Dr. Brian Schmidt. We would also like to acknowledge support from the NIH (BRP EB 02185-MBL).

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