# Variation in the Velocity, Deformation, and Adhesion Energy Density of Leukocytes Rolling Within Venules

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## Abstract

Leukocyte rolling along the endothelium in inflammation is caused by continuous formation and breakage of bonds between selectin adhesion molecules and their ligands. We investigated trauma-induced leukocyte rolling in venules (diameter, 23 to 58 μm; wall shear stress, 1.2 to 35 dyne/cm^{2}) of the exteriorized rat mesentery using high-resolution intravital microscopy. While rolling, the leukocytes deformed into a teardroplike shape. Deformation continued to increase with shear stress up to the highest values observed (35 dyne/cm^{2}). Successive leukocytes had similar rolling velocities at the same axial positions along each vessel, suggesting that heterogeneity of endothelial adhesiveness is responsible for velocity variation. Adhesion energy density varied inversely with instantaneous rolling velocity and directly with instantaneous deformation. Adhesion energy density reached a maximum of 0.36 dyne/cm, similar to values found for lymphocyte function–associated antigen-1–dependent adhesion of stimulated T cells to isolated intercellular adhesion molecule-1. We conclude that selectin-mediated adhesion during rolling produces adhesion energy densities comparable to those observed for integrin-mediated adhesion events in other experimental systems.

Near-wall encounters of marginated leukocytes with the venular endothelium provide opportunity for transient adhesive bond interactions to arise between leukocytes and endothelial cells. During inflammation, these interactions give rise to leukocyte rolling, which is mediated by continuous formation and breakage of bonds between selectin adhesion molecules and their ligands.^{1} ^{2} E- and P-selectin expression is induced on endothelial cells by proinflammatory mediators and cytokines,^{3} ^{4} whereas L-selectin is constitutively expressed on circulating leukocytes.^{5} In the presence of appropriate stimuli, rolling is followed by firm adhesion of leukocytes, mediated by the integrin family of adhesion molecules and, ultimately, migration of leukocytes into the extracellular matrix through a process of transendothelial extravasation.^{6} Leukocyte capture and rolling are associated with the first steps in inflammatory response.^{1} ^{2} The first quantitative investigations into leukocyte rolling were conducted by Atherton and Born^{7} ^{8} in hamster cheek pouch venules. Since that time, a number of in vivo and in vitro studies have characterized rolling dynamics by measuring quantities such as leukocyte rolling velocity, deformation, and flux.^{9} ^{10} ^{11} ^{12} ^{13}

Of particular interest is the manner in which these quantities vary with respect to the imposed shear stress. Previous studies^{8} ^{9} ^{11} have reported data up to wall shear rates of 1000 s^{−1}. In the present study, we present data that extend this range using a more accurate estimate for wall shear rate than has previously been used.^{14} In addition, the present study is aimed at exploring another aspect of leukocyte rolling associated with the instantaneous variation of rolling velocity around the mean. Although it has not been closely examined in vivo, Goetz et al^{12} have studied instantaneous velocity patterns in vitro for bovine neutrophils rolling over stimulated bovine aortic endothelial cells in a radial flow chamber at four distinct shear stresses. They found large variations in rolling velocity and attributed their results to a number of factors, including heterogeneity of adhesion receptor expression on both the endothelial substrate and neutrophil surfaces and the possibility of stochastic binding behavior between the ligand and receptor. In an effort to better understand these variations in vivo, we investigate the instantaneous velocity patterns of individual leukocytes rolling along the endothelium of postcapillary mesenteric venules in the rat.

In addition to the kinematic quantities mentioned above (ie, the velocity and deformation), an analysis of the strength of adhesion provides further insight into the mechanics of leukocyte rolling. The adhesion energy density, defined as the work done by the cell membrane tension in detaching a unit area of membrane from the substrate, is a continuum-based quantity that characterizes the strength of the adhesive interaction. In rolling leukocytes, most of the work is assumed to be expended in the process of breaking selectin bonds at the trailing edge of the leukocyte.^{15} At sufficiently high shear rates, a rolling leukocyte will deform significantly from its undeformed spherical shape. Under these conditions, the adhesion energy density becomes a useful means of characterizing the strength of the adhesion process.^{16} ^{17} The adhesion energy density is therefore related to the site density of load-bearing bonds, a fundamental parameter that cannot be measured directly.

From micropipette aspiration studies, Tözeren et al^{18} estimated the adhesion energy density associated with LFA-1–dependent adhesion of stimulated T cells to isolated ICAM-1. Using shell equations of equilibrium together with geometric data gathered from their micromanipulations, they obtained estimates of the adhesion energy density on the order of 0.1 to 0.2 dyne/cm at the initiation of detachment. The magnitude of this quantity in selectin-mediated adhesive events, however, has never been quantified. In the present study, we relate the membrane tension of rolling leukocytes to the flow conditions in postcapillary venules and measure the resulting cell deformations in an attempt to obtain an estimate for the adhesion energy density of selectin-dependent adhesive interactions in vivo. Using high-resolution intravital microscopy, we measure and analyze the instantaneous velocity and deformation patterns of leukocytes rolling along venules of the exteriorized rat mesentery and study their relationship to the estimated wall shear rate and the adhesion energy density. The rat mesenteric preparation offers superior optical resolution because the tissue is very thin. Thus, it provides favorable conditions for precise measurements of the shape of rolling cells. Furthermore, this model is well characterized, and the molecular mechanisms underlying leukocyte rolling have been defined in previous studies.^{19} ^{20} ^{21} ^{22} ^{23} In this model, rolling is initially dependent on P-selectin, which is expressed in response to tissue trauma associated with exteriorization via a mast cell–dependent process^{19} ^{22} ^{23} ; however, L-selectin is also known to be involved.^{20} ^{21}

## Materials and Methods

Experiments were performed using female Sprague-Dawley rats (250 to 300 g) anesthetized with ketamine and pentobarbital (75 mg/kg Ketavet and 20 mg/kg IM Nembutal, respectively) after premedication with atropine (0.1 mg/kg IM). Surgery and instrumentation were as described previously.^{19} Briefly, the trachea, right carotid artery, and jugular vein were cannulated to record arterial blood pressure, heart rate, and systemic leukocyte counts and to infuse saline containing pentobarbital to maintain anesthesia and a neutral fluid balance. The peritoneal cavity was opened by a midline incision. The terminal ileum was exteriorized onto a lucite stage and superfused with bicarbonate-buffered saline equilibrated with 5% CO_{2} in N_{2} at 37°C. A Leitz intravital microscope modified for telescopic imaging^{24} was used with a high-resolution salt water immersion objective (SW 50/1.0 numerical aperture) and a 1.6× projection eyepiece. Venules of intermediate size (diameter, 20 to 50 μm) were selected on the basis of optimal clarity and resolution of the video image. Only leukocytes rolling along the lateral vessel walls in the central axial plane of each microvessel were used for analysis. Video recordings were made on S-VHS videotape via a multidiode camera (RCA).

### Mean Rolling Velocity, Flux, and Deformation Experiments

A series of experiments were aimed at studying how mean leukocyte rolling velocity, flux, and deformation vary with wall shear rate. In particular, these experiments were designed to extend across a broad range of physiologically relevant shear rates (up to 3100 s^{−1}). In some of these experiments, the flow rate in the investigated venules was manipulated using a blunt microprobe to occlude appropriate side branches.

The mean rolling velocity corresponding to a given shear rate was determined from the average time (typically between 2 and 3 seconds) required for ≈20 cells to roll across the same segment of a vessel spanning a length of ≈100 μm. Approximately 50 vessels in all, each having known centerline velocity and diameter, were considered over the range of shear rates investigated. The vessel diameter (*D*) was measured by positioning a line perpendicular to the vessel axis on a still video frame produced using custom digital-imaging software.^{25} The centerline blood velocity (*v _{cl}*) was measured using a dual phototransistor linked to an automatic tracking correlator

^{26}(model 102B, Instrumentation for Physiology and Medicine). Mean blood velocity (

*v*) was determined from the centerline velocity using the empirically derived relationship given by

_{b}*v*=0.625

_{b}*v*.

_{cl}^{27}

^{28}

Assuming a velocity gradient consistent with empirically derived profiles measured in vivo,^{14} ^{29} wall shear rate was estimated as follows:The factor of 2.1 appearing in Equation 1 is the median ratio of the measured wall shear rate obtained in rabbit mesenteric microvessels in vivo to the corresponding Poiseuille value.^{29} It accounts for the fact that velocity gradients near the vessel wall are much steeper than in a Poiseuille flow by virtue of the axial concentration of red blood cells that is known to occur in the microcirculation.

The wall shear stress (τ* _{w}*) was calculated from the wall shear rate, given by Equation 1, whereand μ is the plasma viscosity, taken to be 1.1 cp. Use of the plasma viscosity in calculating the wall shear stress is reasonable in light of the plasma-rich zone that arises in near-wall regions of microvessels coupled with our accounting for the increased shear rate in these regions by using Equation 1.

Mean rolling leukocyte flux was determined by counting the number of cells passing a fixed line perpendicular to the axis of each vessel over a period of 1 minute. The flux percentage of rolling leukocytes was estimated as the ratio of the rolling leukocyte flux (φ_{roll}) to the total flux (φ_{tot}) of all leukocytes passing through the vessel during the same time interval. The total leukocyte flux per unit time was estimated from the total volume flow of leukocytes through the vessel and is given bywhere *C _{L}* is the systemic concentration of leukocytes obtained from 20-μL blood samples using a Coulter counter after red blood cell lysis with saponin.

Geometric parameters corresponding to the length and height of rolling leukocytes were also collected in these experiments and are shown in Fig 1⇓. Measurements of these quantities were performed by an interactive image processing system. Leukocyte deformation was characterized by a deformation index defined as the ratio *l*/*h*, where *h* is the maximum height of the cell and *l* is the length of the cell measured at a height *h*/2 above the endothelium. These quantities were measured only once for each leukocyte, and measurements were strictly limited to rolling cells that did not remain stationary for more than one or two video frames. The deformation index represents an average value of *l*/*h* for many cells interacting with the same segment of the vessel. This index was determined under flow conditions extending across a large range of shear rates within many different venules.

### Instantaneous Rolling Velocity Experiments

Another series of experiments were conducted to investigate how the instantaneous rolling velocity of individual leukocytes varies along a segment of venule. For these experiments, the axial positions of rolling leukocytes were determined repeatedly (typically ≈50 times) by measuring the displacement of the leukocyte's leading edge from a designated reference point along the vessel every 40 milliseconds (two video frames [PAL Standard]). From these data, the instantaneous leukocyte rolling velocity was estimated as the change in position divided by the 40-millisecond time interval. Instantaneous rolling velocity patterns typically spanned a distance along the venular endothelium, which ranged between 10 and 12 leukocyte diameters (80 to 100 μm). Individual velocity patterns were obtained for several leukocytes rolling along the same venular segment. These data were collected at a variety of shear rates within different venules.

### β_{2} Integrin–Blocking Experiments

In order to examine the influence of β_{2} integrins on these rolling interactions, a series of experiments was conducted in rats that had received 2 mg/kg IV of the mouse anti-rat CD18 mAb CL26,^{30} which recognizes and functionally blocks rat β_{2} integrins. In these experiments, the magnitude and variation of leukocyte rolling velocity was measured and compared with untreated rats. To assess the efficiency of the antibody treatment, firm leukocyte adhesion and transendothelial migration were investigated after local microinjection of the chemoattractant fMLP.

### Adhesion Energy Density Experiments

A final series of experiments was designed to study the magnitude and variation of the instantaneous adhesion energy density of leukocytes rolling within a segment of venule and how that quantity correlates with instantaneous deformation and rolling velocity. In addition to estimating the wall shear stress in the vessel and instantaneous leukocyte rolling velocity as described earlier, geometric measurements characterizing the instantaneous deformation of the leukocyte as it rolled along the venule were also made. In particular, measurements of the deformation parameters *l* and *h* were made as described previously; however, in these experiments, the data were collected at 40-millisecond intervals rather than at only one point along the vessel. In addition to the deformation index, other geometric quantities that were measured included the contact length (*l _{c}*) over which the leukocyte appears to be in contact with the endothelium and the exterior macroscopic peeling angle (θ) subtended by the surface of the endothelium and the surface of the leukocyte's trailing end (see Fig 1⇑). This peeling angle was measured by aligning two video lines with the contact surface and the free surface at the trailing end of the cell. In addition to these parameters, the circumference (

*C*) of each leukocyte was measured by placing a polygon around the cell. The results that were obtained are consistent with those obtained from modeling the deformed cells as hemisphere-cone combinations or ellipsoids using cell volumes measured by microscopy of peripheral blood leukocytes (data not shown). From the measurement of the cell circumference, the free-membrane length (

*l*=

_{f}*C*−

*l*) was determined. The free-membrane length and the macroscopic peeling angle were used in estimating the instantaneous peeling tension and adhesion energy density, respectively.

_{c}For deformed leukocytes that are significantly elongated along the direction of flow, the adhesion energy density (γ) was defined by Tözeren et al^{18} as follows:where *T* is the peeling tension in the membrane at the edge of conjugation. The adhesion energy density defined in this way is a measure of the work done by the cell membrane tension in detaching a unit area of membrane from the substrate. Since elongated “liquid drop–shaped” cells emerge only in vessels having high flow rates, our consideration of adhesion energy density is restricted to venules having wall shear rates above 400 s^{−1} (corresponding to a deformation index, *l*/*h* >1.2). Under such conditions, where the cell deforms significantly enough to adhere over a large contact region on the substrate and not only with a few microvilli, the adhesion energy density defined by Equation 4 is meaningful and may play an important role in leukocyte adhesion and rolling. Note that when the macroscopic peeling angle, θ, is equal to 90°, γ corresponds to the tension required to peel the membrane from the substrate. This peeling tension is, in general, greater than the minimum tension required to prevent the tendency of the membrane to spread over the substrate and may be dependent upon the peeling velocity.^{31}

The approximation for the cell membrane tension, *T*, can be obtained by assuming that its magnitude in the direction perpendicular to the flow is negligible in comparison with its magnitude in the direction of flow. In essence, this is equivalent to assuming that the curvature in the direction perpendicular to the flow at the trailing edge of the leukocyte is small compared with the curvature in the direction of flow, which is consistent with what we observe in our photomicrographs. This approximation was made in earlier models of leukocyte deformation.^{18} The validity of this assumption is discussed in detail in Tözeren et al.^{18} Under this condition, using the equilibrium equation for the peeling of a one-dimensional tape, the membrane tension, *T*, is estimated by the following:where *l _{f}* is the free membrane length of the leukocyte and τ

_{cell}is the mean shear stress acting on the cell membrane. We assume that τ

_{cell}is proportional to τ

*, given by Equation 2, such that τ*

_{w}_{cell}=ατ

*, where the factor α has been determined to be ≈3 on the basis of a computational analysis of a Stokes flow past an array of adherent cells in a parallel-plate flow chamber having shapes of the form shown in Fig 1⇑.*

_{w}^{32}For more spherically shaped cells, the factor α can be as large as 4 when the ratio of cell diameter to plate-separation distance is equivalent to the cell-to-vessel diameter ratios measured in these studies. The estimate of the fluid force acting on a sphere near a planar boundary in the presence of a Couette flow, as predicted by Goldman and colleagues,

^{33}

^{34}is ≈50% greater than the estimate used here for a cell-to-vessel diameter ratio of 20%.

^{32}It should be noted, however, that the estimate of α used here for determining the average shear stress acting on the cell surface does not account for the cylindrical geometry of the vessel nor does it account for the effect of transient encounters with passing red blood cells that occasionally invade the plasma-rich zone, which may result in intermittent increases in the instantaneous shear stress experienced by adherent leukocytes.

^{35}

^{36}Based on these considerations, our estimate for the shear stress acting on the cell therefore represents a lower bound on the stress that a rolling leukocyte is likely to experience in 30- to 40-μm venules in vivo. With the exception of the parameter α and the empirical correction factors used in estimating the wall shear rate and mean blood velocity, the estimate of the membrane tension given by Equation 5 is otherwise consistent with the expression Dembo et al

^{37}used (see Equation 35 in Reference 37) in estimating this quantity in which they assumed a Poiseuille flow to exist in the vessel.

In addition to the shear stress acting on the cell membrane, the membrane tension, given by Equation 5, also depends on the measurement of the free membrane length of the leukocyte. However, because of certain limitations in intravital microscopy,^{38} our measurement of the free membrane length may also slightly underestimate the true value of this quantity in vivo. Using optical sectioning microscopy, Shen and Lipowsky^{38} found that the length, *l _{c}*, of the leukocyte-endothelial contact zone is ≈35% smaller than the value obtained from intravital microscopy measurements. Thus, the free membrane length, which is the difference in the cell circumference and the contact length, might actually be as much as 15% larger than the values reported here. Since the membrane tension is estimated from the product of the free membrane length and the mean shear stress acting on the cell membrane and since our measurements of these quantities are likely to represent lower bound estimates of their true values, our estimate of membrane tension is also likely to be somewhat less than the actual value. According to Equation 4 then, the results reported here for the adhesion energy density can also be regarded as a lower-bound estimate of the actual value that this quantity assumes in vivo.

## Results

The flux of leukocytes rolling along mesentery venules of rats, measured as a fraction of the total flux of leukocytes in the vessel, was found to vary between 3% and 88% (averaging 23±21%) over shear rates ranging between 160 and 3100 s^{−1}. The top panel in Fig 2⇓ shows leukocyte rolling flux fraction as a function of wall shear rate. Rolling flux is seen to be negatively correlated with wall shear rate. The rolling flux ranges from ≈60% at shear rates below 600 s^{−1} to ≈5% to 10% above 1500 s^{−1} (16.5 dyne/cm^{2}). The mean velocity of rolling leukocytes, shown in the middle panel in Fig 2⇓, varies approximately linearly over the range of shear rates reported above. Over this range, mean rolling velocity varied between 9.9 and 57.3 μm/s, with an average value of 28.5±9.4 μm/s. Results for leukocyte flux and rolling velocity are consistent with previously published data^{9} ^{11} and extend to higher shear rates. The bottom panel in Fig 2⇓ shows leukocyte deformation (defined in terms of the deformation index *l*/*h*; see Fig 1⇑) relative to wall shear rate. The deformation index varied from 1.09 to 1.69 over the entire range of wall shear rates, with an average value of 1.36±0.15. Deformation, characterized in this way, is seen to increase approximately linearly with increasing shear rate. This trend is observed even beyond previously reported values of shear rate.^{9} Thus, within the physiologically relevant range, rolling leukocytes continue to deform with increasing wall shear rates.

To investigate the possible source(s) of the heterogeneity in leukocyte rolling velocity, we analyzed particle trajectories and the variation in the instantaneous velocities of 29 individual leukocytes rolling along the endothelium of three different venules. The top two graphs of Fig 3⇓ show the time-dependent positions, or particle trajectories, of individual leukocytes rolling along a fixed segment of venule in vessels A and B. It is interesting to note that these patterns are similar to those found by Alon et al^{39} for neutrophils rolling in a parallel-plate flow chamber over purified P-selectin reconstituted in lipid bilayers at a density of 30 sites/μm^{2}. The rolling-velocity patterns associated with three of the particle trajectories from each vessel appearing in the top two graphs of Fig 3⇓ are shown in the bottom two graphs corresponding to the same segment of endothelium. The rolling velocity data are low pass–filtered by averaging each point with the two nearest neighboring points. Selected tracings that emphasize the rolling-velocity pattern are shown. These velocity patterns are seen to be strongly dependent on position within the venule, suggesting that the venular endothelium is a major source of the heterogeneity in rolling velocity. Striking similarities in the velocity patterns were evident between most of the cells studied. However, no periodicity at or around 25 μm (the approximate circumference of a leukocyte) was observed over a length of nearly four cell circumferences.

Leukocyte rolling velocity was investigated in rats treated with mAb CL26, a function-blocking anti-CD18 antibody, to study the possible contributions of β_{2} integrins in these rolling interactions.^{40} ^{41} Tables 1⇓ and 2 summarize these results. For untreated rats, 573 measurements were made in 26 venules having an average diameter of 31 μm (24 to 46 μm) and having an average shear rate of 523 s^{−1} (143 to 1459 s^{−1}). For treated rats, 410 measurements were made in 16 venules with an average diameter of 35 μm (23 to 57 μm) and an average shear rate of 429 s^{−1} (172 to 1097 s^{−1}). As illustrated in Table 1⇓, blocking β_{2} integrin function had no influence on rolling velocity or on the variation in rolling velocity when individual cells were tracked. This was also true in vessels with shear rates below 250 s^{−1} (data not shown). Furthermore, as a control to test the effectiveness of the antibody at blocking β_{2} integrin function, we examined the number of adherent and emigrated cells in both treated and untreated rats at fixed intervals. We found that rats treated with the antibody showed no emigration and almost no firm adhesion 15 minutes after microinjection of the chemoattractant fMLP next to the venule, whereas untreated rats had, on average, 49 adherent leukocytes and eight emigrated cells after 15 minutes (see Table 2⇓).

Fig 4a⇓ shows the pattern of rolling velocity and adhesion energy density of a single leukocyte as it rolls along a venule. The adhesion energy density, γ, is calculated from measurements of centerline velocity and cell deformation using Equations 4 and 5. Leukocyte rolling velocity is seen to vary inversely with adhesion energy density. At areas of high adhesion energy density, rolling velocity is lower than at areas of low adhesion energy density. The relationship between instantaneous rolling velocity and adhesion energy density of two leukocytes rolling in two similar venules is shown in Fig 4b⇓. For both leukocytes shown in panel b, a negative correlation between adhesion energy density and leukocyte rolling velocity is observed. The correlation coefficients were .32 (open symbols) and .15 (closed symbols) in vessels having shear rates of 626 and 463 s^{−1}, respectively. This negative correlation was found to be significant in venules with low to moderate wall shear rates, such as in this example, corresponding to calculated adhesion energy densities that are <0.06 dyne/cm. Correlation of leukocyte deformation with adhesion energy density in these venules was not significant. The associated correlation coefficients were only .11 (open symbols) and .09 (closed symbols).

At higher wall shear rates, an increase in the deformation of rolling leukocytes, defined as the ratio *l*/*h*, accompanies increased adhesion energy density. Fig 4c⇑ shows the instantaneous variation in rolling leukocyte deformation and adhesion energy density of a single leukocyte as it rolls along a venule. Leukocyte deformation is seen to increase with adhesion energy density. The relationship between instantaneous leukocyte deformation and adhesion energy density of two leukocytes rolling in the same venule is shown in Fig 4d⇑. The leukocyte represented by the closed symbols corresponds to the one shown in panel c. For both leukocytes shown in panel d, a strong positive correlation between adhesion energy density and rolling leukocyte deformation is observed. The correlation coefficients were .46 (open symbols) and .59 (closed symbols) in a vessel having a shear rate of 1343 s^{−1}. This positive correlation was found to be significant in venules with high wall shear rates, such as in this example, corresponding to calculated adhesion energy densities that range between 0.09 and 0.15 dyne/cm. Interestingly, rolling velocity did not correlate with adhesion energy density in these venules. The associated correlation coefficients were only .05 (open symbols) and .10 (closed symbols).

## Discussion

We have studied how rolling leukocyte flux, mean leukocyte rolling velocity, and leukocyte deformation vary with wall shear rate over the physiologically relevant range (up to 3100 s^{−1}). We found no limit to leukocyte deformation over this range. Both leukocyte deformation and mean rolling velocity are seen to increase approximately linearly with increasing shear rate. In studying the dependence of mean rolling velocity on wall shear rate, the frame-by-frame analysis of rolling velocity was carried out for at least 10 leukocyte diameters along the endothelium. According to Zhao et al,^{42} the variance in rolling velocity, not its mean value, is sensitive to the value of the time window used in the computations of rolling velocity.

The instantaneous velocity patterns of individual leukocytes rolling in both vessels A and B (Fig 3⇑) reveal regions along the vessel over which the leukocytes all appear to roll at nearly the same average velocity and other regions where they consistently appear to skip rather than roll across the vessel. Perhaps the most striking feature about these velocity patterns is the consistency with which this skipping seems to occur over the same segment of the vessel. The strong similarity in these patterns suggests that the venular endothelium significantly contributes to the heterogeneity in leukocyte rolling velocity. The stochastic behavior of these rolling events may also be due to heterogeneity within the rolling leukocyte population as well as to nonuniform distributions of adhesion receptors and irregular leukocyte surface morphology. Although these results do not rule out these other sources of variation in rolling velocity, they do suggest that the heterogeneity inherent to the substrate is a fundamental determinant of instantaneous leukocyte rolling velocity, which may have important physiological consequences.

Of the possible sources of heterogeneity on the venular endothelium, one might be associated with a nonuniform distribution of adhesion molecules. Regions of high receptor density would lead to low rolling velocities, whereas low-density regions would allow for faster rolling.^{15} Another source of heterogeneity on the endothelium may be that because of irregularities in endothelial surface geometry, some adhesion receptors might be physically inaccessible to ligands expressed on passing leukocytes. Regions of the endothelium that are out of reach to leukocyte adhesion molecules might be manifested as an “unsticky patch” over which the leukocytes would skip rather than roll. At the optical resolution possible with intravital microscopy, this cannot be distinguished from the effect of a locally low receptor density. A further consequence of a nonuniform surface topology might be associated with the development of locally nonuniform shear stress distributions.^{43} However, because of the relative insensitivity of mean rolling velocity to shear stress, over the range of 5 to 35 dyne/cm^{2} (see Fig 2⇑), it is not expected that surface irregularities on the endothelium would lead to variations in local flow conditions large enough to account for the level of heterogeneity in instantaneous rolling velocity reported here. Goetz et al^{12} point to the possibility of stochastic binding interactions as an explanation for the large variances found in the velocity of neutrophils rolling over stimulated endothelium. Results of the present study suggest that much of the variation of in vivo rolling velocity, which is comparable to that found by Goetz et al, might be due to heterogeneity on the endothelium, either in terms of geometric variations in surface topology, nonuniform distributions of receptor site density, or as combinations thereof. Since Goetz et al conducted their experiments over stimulated endothelium, a similar level of heterogeneity is likely to be present in their assay, which in turn might account for a significant fraction of the variation in rolling velocity that was reported. Although all of the above-mentioned sources of these variations in rolling velocity are likely to play a role, the common nonperiodic pattern that emerged from cell to cell strongly suggests that endothelial heterogeneity largely determines instantaneous leukocyte rolling velocity.

We have loosely referred to the velocity patterns shown in Fig 3⇑ as the instantaneous velocity of the cell. However, it is clear that the data sets shown in Fig 3⇑ merely provide a discrete representation of the continuous variation in instantaneous rolling velocity. Discrete representations of continuous signals in general depend upon the time resolution dictated by the sampling rate. For the data reported here, the sampling rate corresponded to 40 milliseconds (every two PAL video frames), whereas Goetz et al^{12} analyzed images once every 2 seconds. Alon et al^{39} determined the instantaneous displacement of T lymphocytes rolling on VCAM-1 every 0.25 second and reported the resulting particle paths as a function of time. The sampling rate used here affords the highest resolution that was technically feasible and represents the best approximation that has yet been reported of the continuous variation in instantaneous rolling velocity by a discrete data set.

The continuum approximation for the adhesion energy density used in the present study represents a good approximation of the energy required to separate a unit area of membrane if the bond density is sufficiently high.^{16} ^{17} Since the adhesion receptors involved in leukocyte rolling are concentrated at the tips of the microvilli, it seems likely that for nearly spherical cells rolling on a substrate, only a small number of bond clusters might interact with the ligands on the substrate at any given time. In this case, models that take into account the discrete nature of these molecular interactions and their associated stochastic behavior are perhaps more appropriate.^{17} ^{42} Under large deformations the contact region increases relative to spherical cells and the possibility for a greater number of bond interactions increases. As the deformation increases and the discrete distribution of crossbridges approaches a continuous distribution, the applicability of a continuum model along the lines of Dembo et al^{37} becomes reasonable. Since the deformation has been shown to increase without limit in proportion to wall shear rate (refer to the bottom panel of Fig 2⇑), so too should the number of bond interactions increase. Thus, we restrict our discussions of adhesion energy density in this analysis to deformation indexes in excess of 1.2.

Both deformation and rolling velocity are seen to correlate with adhesion energy density. These correlations, however, are strongly dependent on shear rate. At moderate shear rates, adhesion energy density modulates instantaneous rolling velocity. Under these flow conditions, membrane tension and leukocyte deformation remain small (deformation index between 1.2 and 1.3) and are accompanied by low adhesion energy densities and high instantaneous rolling velocities. Regions of high adhesion energy density, corresponding to “sticky patches” on the endothelium, tend to retard instantaneous rolling velocities. At high rates of shear, elevated adhesion energy density leads to enhanced deformation of rolling leukocytes. The adhesion energy density of the (fewer) cells rolling in these vessels ranges above 0.09 dyne/cm. This suggests that in these venules, the wall shear stress is sufficient to substantially deform the leukocyte when it is retarded by a sticky patch on the endothelium.

These results also suggest that firmly and loosely adherent cells exist in distinct populations among rolling leukocytes. At moderate shear rates, both types roll, but the loosely adherent ones do so more rapidly. At high rates of shear, only those cells from the firmly attached population are able to roll; the more loosely adherent cells are whisked away in the flow. For those cells that do roll, the adhesiveness is sufficient to produce significant deformation, whereas the more loosely adherent cells may never form enough crossbridges to sustain rolling at high shear rates.

We have shown that β_{2} integrin function was effectively blocked by injection of the anti-CD18 antibody, mAb CL26 (see Table 2⇑). Blocking CD18 function had no effect on the mean rolling velocity or its variation under the prevailing flow conditions (see Table 1⇑). In previous studies, CD18 has been shown to contribute to leukocyte rolling at low shear.^{40} ^{41} In the acutely exteriorized rat mesentery, expression of ICAM-1 (an important endothelial ligand for CD18 integrins) is likely to be low, which may explain the lack of an effect of the mAb CL26 treatment on rolling. Furthermore, neutrophils, which make up >90% of leukocytes rolling in the mesentery,^{44} do not express the β_{1} integrin VLA-4 on their surface.^{45} ^{46} Therefore, VLA-4–VCAM-1 interactions are not likely to be significantly involved in leukocyte rolling in postcapillary mesenteric venules. With minimal contributions from integrins, the rolling interactions reported here are predominantly governed by the selectin family of adhesion molecules. It is interesting to note that over the range of shear stresses considered, the adhesion energy density reached a maximum of 0.36 dyne/cm, which is similar in magnitude to values reported by Tözeren et al^{18} for LFA-1 integrin–dependent adhesion of stimulated T cells to isolated ICAM-1. Thus, it seems that the strength of selectin-mediated adhesive interactions in vivo is comparable to integrin-mediated adhesion events measured in vitro. However, the more transient nature of selectin-mediated adhesion^{18} ^{45} enables leukocyte rolling rather than firm adhesion.

At moderate shear rates, the rolling leukocytes deform significantly less than at high shear rates, as shown in Fig 2⇑. Selectin-mediated rolling is determined by bond formation, breakage, and the site density of adhesion molecules expressed per unit surface area. In the present study, we show that local variation in adhesion energy density (bond density) along a microvessel results in reciprocal variation of rolling velocity at moderate wall shear rates. This suggests that rolling velocity under these conditions is dominated by the selectin-selectin ligand site density so that a local increase in bond density can slow the cell down. An alternative explanation might be that there exist other selectin-independent mechanisms that contribute to rolling at moderate shear rates but might not be operative at high shear rates. The most likely candidates for a selectin-independent adhesion process contributing to leukocyte adhesion under the prevailing experimental conditions are the β_{2} integrins. Our results obtained using a blocking CD18 mAb, however, do not support a major role for β_{2} integrins. Furthermore, rolling in the rat mesentery in this model is known to be entirely dependent on the function of P- and L-selectin.^{19} ^{20} ^{21} ^{22} ^{23}

At high shear rates, considerably fewer leukocytes were seen to roll along the walls of venules than at lower shear rates. Those that did roll under these conditions traveled at velocities that were only slightly greater than those observed at lower shear rates. Since the fluid forces prevailing at high wall shear rates are sufficient to significantly deform rolling cells, the contact length was found to be longer than at lower shear rates. This suggests that local variations in adhesion energy density have less impact on rolling velocity because, at any given time, the increased adhesion region offers a greater number of bond interactions than would be available at lower shear rates. At high shear rates, therefore, the rolling velocity appears to be dominated by the rate of bond breakage at the trailing edge of the cells rather than by the bond density, which is reflected by the adhesion energy density.

The mean leukocyte rolling velocity of 28 μm/s is similar to in vivo rolling velocities reported previously.^{8} ^{9} ^{11} Similar velocities have also been reported for neutrophil rolling on purified P-selectin in vitro,^{10} whereas rolling on E-selectin results in much lower velocities both in vitro^{47} and in vivo.^{48} However, trauma-induced leukocyte rolling has been shown to be largely P-selectin dependent in the rat mesentery^{19} ^{22} ^{23} and in other preparations.^{49} ^{50} Therefore, in light of these findings, we propose that heterogeneity in P-selectin expression on the venular endothelium is likely to play an important role in the variation in instantaneous rolling velocity reported in the present study.

We have investigated leukocyte rolling velocity, deformation, and adhesion energy density and concluded that the venular endothelium accounts for a significant part of the heterogeneity seen in the instantaneous velocity of rolling leukocytes. Furthermore, we found that at moderate shear rates, adhesion energy density is negatively correlated with leukocyte rolling velocity but not with deformation, whereas at high rates of shear, adhesion energy density correlates positively with leukocyte deformation but not with rolling velocity. Finally, we have shown that selectin-mediated adhesion during rolling in vivo results in adhesion energy densities comparable to those observed for integrin-mediated adhesive interactions observed in vitro.

## Selected Abbreviations and Acronyms

fMLP | = | formyl-Met-Leu-Phe |

ICAM-1 | = | intercellular adhesion molecule-1 |

LFA-1 | = | lymphocyte function–associated antigen-1 |

mAb | = | monoclonal antibody |

VCAM-1 | = | vascular cell adhesion molecule-1 |

VLA-4 | = | very late antigen-4 |

## Acknowledgments

This study was supported by the National Institutes of Health grants HL-07284 and HL-54136 and Deutsche Forschungsgemeinschaft Le573/3-2. We thank C. Wayne Smith, Baylor College of Medicine, Houston, Texas, for providing us with the mAb CL26.

- Received July 18, 1996.
- Accepted September 11, 1996.

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- Variation in the Velocity, Deformation, and Adhesion Energy Density of Leukocytes Rolling Within VenulesE.R. Damiano, J. Westheider, A. Tözeren and K. LeyCirculation Research. 1996;79:1122-1130, originally published December 1, 1996https://doi.org/10.1161/01.RES.79.6.1122
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