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Endothelial Surface Protrusion by a Point Force
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Biophysical Journal
Volume 110
March 2016
1150–1157
Article Endothelial Surface Protrusion by a Point Force Yong Chen,1 Lan Lu,1 and Jin-Yu Shao1,* 1
Department of Biomedical Engineering, Washington University, Saint Louis, Missouri
ABSTRACT During leukocyte rolling on the endothelium, surface protrusion and membrane tether extraction occur consecutively on leukocytes. Both surface protrusion and tether extraction of leukocytes stabilize leukocyte rolling. Tethers can also be extracted from endothelial cells (ECs), but surface protrusion of ECs has never been confirmed to exist. In this study, we examined EC surface protrusion with the micropipette aspiration technique. We found that, like leukocytes, surface protrusion on an EC did exist when a point force was imposed. Both the protrusional stiffness and the crossover force of EC surface protrusion were dependent on the force loading rate and the cytoskeletal integrity, but neither of them was dependent on tumor necrosis factor a stimulation. Temperature (37 C) affected the protrusional stiffness only at small force loading rates. When a neutrophil was employed to directly impose the pulling force on the EC, simultaneous surface protrusion from both cells occurred, and it can be modeled as two springs connected in series, although the spring constants should be adjusted according to the force loading rate. Therefore, EC surface protrusion is an important aspect of leukocyte rolling, and it should not be ignored when leukocyte rolling stability is studied systematically.
INTRODUCTION During the inflammatory response, leukocytes roll on the endothelium on the inside of the blood vessel. This process has been recognized as a key initial step for leukocyte migration to sites of injury or inflammation (1,2). Leukocyte rolling is regulated by many factors, including shear stress, chemotactic cytokines, adhesion molecules, and mechanical properties of both leukocytes and endothelial cells (ECs). Because of shear stress, point forces are imposed on leukocytes and ECs through adherent membrane receptors and ligands. As a result, two types of subcellular deformation are produced consecutively, surface protrusion and tether extraction, both of which contribute to mechanically stabilizing leukocyte rolling (3–12). Tethers are membrane nanotubes that are extracted from cells due to membrane flow induced by pulling forces (5,13). A constant pulling force (F) yields a constant tether extraction velocity (Ut), whereas larger F yields larger Ut. When Ut approaches zero, F should approach a nonzero value called the threshold force (F0) (14). Tethers can be extracted from both leukocytes and ECs, as well as from many other types of cells (11,14,15). For human neutrophils and ECs, F0 values are ~45 and 50 pN, respectively (3,5). During leukocyte rolling, tether extraction has been shown experimentally and numerically to decrease the pulling force applied to the adhesive bonds between leukocytes and ECs, thereby stabilizing rolling (3,7,9,10,12,16). In addition, tethers from ECs contribute more to leukocyte rolling stabilization than tethers from neutrophils (5,17).
Submitted August 12, 2015, and accepted for publication January 12, 2016. *Correspondence: [email protected]
More recently, tethers from leukocytes were shown to act as slings to facilitate their rolling in high shear (18). In contrast to fluid-like tether extraction, surface protrusion, which is a local tent-like deformation, behaves more like a solid. When an increasing pulling force is imposed on a cell surface, surface protrusion occurs first, followed by tether extraction. The force at which surface protrusion makes the transition to tether extraction is defined as the crossover force (Fc). Fc is generally larger than F0, because F0 is mainly determined by membrane mechanics and its interaction with the cytoskeleton, whereas Fc also includes the contribution from the interaction between the pulled receptor and the cytoskeleton. During surface protrusion, the surface stiffness is defined as the protrusional stiffness (kp). Surface protrusion of neutrophils was first studied using the micropipette aspiration technique (MAT), and a value of 43 pN/mm was found for kp at very small force loading rates (10). Afterward, surface protrusion of neutrophils was studied using the biomembrane force probe (4) and the optical trap (19) with larger force loading rates. These studies showed clearly that both Fc and kp depended on the force loading rate. Like leukocytes, ECs play an active role during the inflammatory response (20). However, surface protrusion of ECs has never been studied in detail, although surface protrusion and tether extraction of neutrophils, as well as tether extraction of ECs, have been well characterized. In this study, using either latex beads or human neutrophils as the force transducer of the MAT, we examined surface protrusion of ECs and illustrated its role in leukocyte rolling.
Editor: Andrew McCulloch. Ó 2016 by the Biophysical Society 0006-3495/16/03/1150/8
http://dx.doi.org/10.1016/j.bpj.2016.01.007
Surface Protrusion of ECs
MATERIALS AND METHODS EC culture and treatment Human umbilical vein ECs (HUVECs) were obtained from Cambrex Bioscience (Walkersville, MD) and cultured in six-well plates with EC growth medium 2 (Cambrex Bioscience). The cells were grown to confluence at 37 C in a humidified 5% carbon dioxide atmosphere and then detached with 0.05% trypsin-EDTA. A cell-culture-treated coverslip (Fisher Scientific, Hampton, NH) was prepared and mounted in advance on the inner side wall of our experimental chamber. After the coverslip was firmly attached, HUVECs were plated on the small coverslip and the whole chamber was kept in the incubator for at least 12 h for the cells to attach completely (the evidence used to assess the health of these cells is provided in the Supporting Material). To stimulate endothelial cells, 10 ng/mL tumor necrosis factor a (TNF-a; R&D Systems, Minneapolis, MN) was added to the cell culture 4 h before the experiment.
Neutrophil isolation
1151 possible to apply constant and variable aspiration pressure. In this study, three sets of experiments were performed. In the first set, spherical beads were used as the force transducer (Fig. 1, A and B) and increasing pressure was applied. In the second set, the setup was the same as shown in Fig. 1, A and B, but constant pressure was applied. In the third set, neutrophils were used as the force transducer (Fig. 1 C) and increasing pressure was applied. In a typical contact event in all three sets of experiments, the force transducer (the bead or the neutrophil in Fig. 1) first moved toward the EC on the left and made a brief contact. Then an aspiration pressure was applied in the micropipette and the force transducer either adhered or immediately moved freely away from the cell. When the aspiration pressure was increased at rates %2 pN/mm2/s, the experiments were recorded with an analog camera (30 frames/s) and a 5-V voltage stamp was used to indicate the instant when the pressure started to increase (Fig. 1 A). When the aspiration pressure was increased at rates >2 pN/mm2/s, a high-speed digital camera (Vision Research, Wayne, NJ) was needed for image acquisition (Figs. 1, B and C). At the start of the pressure increase, a voltage signal was used to trigger the recording and a sampling rate of between 100 and 500 frames/s was chosen based on the rate of pressure increase.
Human neutrophils were isolated from finger-prick blood donated by healthy volunteers (the protocol for obtaining blood was approved by the Washington University Institutional Review Board). Briefly, 200 mL of blood was collected in a heparinized capillary glass tube (Fisher Scientific) and then carefully overlaid on 300 mL Mono-Poly Resolving Medium (ICN Biomedicals, Aurora, OH) in a tube. The tube was centrifuged at 300 g for 15 min and the top layer with plasma and platelets was aspirated out. The remaining top layer above the red blood cells was carefully collected and mixed with 200 mL of phosphate-buffered saline (PBS) containing 0.1% human serum albumin (HSA). After it was centrifuged again at 250 g for 5 min, the supernatant enriched with lymphocytes was discarded and the remaining neutrophils were mixed in Hank’s balanced salt solution with 0.5% HSA (1 mM calcium) and 5 mg/mL anti-ICAM1 antibodies (Sigma, Saint Louis, MO) and then transferred to the chamber for the experiment.
Bead preparation Spherical latex beads (~8 mm in diameter; Sigma) coated with goat antimouse IgG antibodies were washed twice with 1 mL PBS and then coated with mouse anti-human antibodies (5 mg/mL) at 37 C for 1 h. Two different mouse anti-human antibodies, anti-CD31 (R&D Systems) and anti-CD62E (BD Pharmingen, San Diego, CA), were used in the experiments. After the incubation with antibodies, the beads were stored in PBS at 4 C. Before use, 20 mL of beads were taken out and washed twice with PBS.
Micropipette preparation The micropipette preparation and manipulation have been described in detail previously (13,15). A glass micropipette (~8 mm in diameter) was made to hold the force transducer in the experiment. The first 10 mm of the micropipette was filled with 1% bovine serum albumin (with latex beads as the force transducer) or 5% HSA (with neutrophils as the force transducer), and the rest of it was backfilled with PBS. The diameter of the micropipette was determined with differential interference contrast microscopy and divided by a correction factor (15).
Characterization of surface protrusion Our experiments were conducted with a modified version of the MAT, the details of which were described previously (14,21). Using a motorized manometer in place of the manual one in the traditional MAT made it
FIGURE 1 Three video micrographs showing three different experimental setups of the MAT. (A) An attached HUVEC grown on the side wall of the experimental chamber was studied. (B) A suspended HUVEC held by another micropipette was studied. In both (A) and (B), an antibody-coated bead was used as the force transducer of the MAT. (C) An attached HUVEC was studied with a spherical neutrophil as the force transducer of the MAT. In all experiments, when the pressure was increased at rates %2 pN/mm2/s, the video was recorded with an analog camera (30 frames/s) and a voltage stamp, þ05.06, as shown in (A), was used to indicate the instant when the pressure started to increase. When the pressure was increased at rates >2 pN/mm2/s, as shown in (B) and (C), a high-speed digital camera (100–500 frames/s) was used for video acquisition. Biophysical Journal 110(5) 1150–1157
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Data analysis The details of our data analysis were described previously (14,21). Briefly, each contact event was recorded as a separate movie in TIF format. The displacement of the force transducer was tracked with a method modified from Gelles et al. (22). In our experiments, the deformation is approximately a linear function of time, the force applied on the transducer (F) is calculated from (13,15,21)
F ¼
pR2p Dp
4 Ut 1 ε 1 ; 3 Uf
(1)
where Dp is the suction pressure, Rp is the radius of the micropipette, Uf is the bead velocity when it is moving freely under Dp, and
ε ¼ Rp Rb
Rp ;
(2)
where Rb is the radius of the bead. The bead diameter was determined with bright-field microscopy and divided by its correction factor (15). The accuracy of Eq. 1 when part of the transducer is outside the micropipette was verified using finite-element analysis (Fig. S1).
RESULTS Surface protrusion of suspended or attached HUVECs Using anti-CD31-coated beads as the force transducer in the MAT, we pulled either suspended or attached HUVECs with increasing force. Before the final adhesion rupture (as shown in Fig. 2 A), two different phases of cellular deformation can be identified: slow surface protrusion and fast tether extraction. Tether extraction of ECs was studied in detail (5,14,17,23), so we focused on surface protrusion in this work. To calculate F during surface protrusion with Eq. 1, we need to calculate Dp, Ut , and Uf at each time point. Dp was determined from its increasing rate and time. Uf was obtained in the cases where no adhesion occurred between the bead and the cell. During surface protrusion (as shown from 1.3 s to 1.9 s in the inset of Fig. 2 A), the bead moved at a constant velocity, so Ut was calculated by linear regression. We found that F increased linearly with time during surface protrusion (Fig. S2), i.e., the force loading rate was constant. Since EC surface protrusion also increased linearly with time (Fig. 2 A), a linear relationship was found between F and EC surface protrusion, as shown in Fig. 2 B. The protrusional stiffness was found by linear regression to be ~260 pN/mm. The cell surface deformed for ~900 nm until the crossover force reached ~230 pN, after which surface protrusion terminated and tether extraction started. Using increasing pressure at different rates (0.1–50 pN/ mm2/s), we studied EC surface protrusion at 11 different force loading rates. Low adhesion frequency (<20%) was achieved by reducing the contact time between the bead and the cell (24–27), so it was expected that F was very likely imposed on one receptor in any adhesion event. Both surface protrusion and tether extraction were produced Biophysical Journal 110(5) 1150–1157
FIGURE 2 (A) A typical bead displacement curve acquired at an increasing pressure of 10 pN/mm2/s and an attached HUVEC. Two consecutive phases of cellular deformation, surface protrusion and tether extraction, can be identified. (B) The relationship between the pulling force (F) and the cellular deformation during surface protrusion. The protrusional stiffness was calculated by linear regression to be ~260 pN/mm.
by this point force alone. Fig. 3, A and B, shows the protrusional stiffness and crossover force, respectively, measured at the 11 different force loading rates. Each point represents an average of 8–29 adhesion events obtained from 3–13 cells. When the force loading rate increased from 5 to 2500 pN/s, the stiffness increased from 100 to 500 pN/mm and the crossover force increased from 50 pN to 200 pN. No difference was found regardless of whether suspended or attached cells were pulled, indicating that surface protrusion was a local deformation. It is worth noting that the amount of EC surface protrusion at the crossover force (0.40 5 0.09 mm; mean 5 SD) did not depend on the force loading rate (Fig. S3), indicating a common structural basis for the transition from surface protrusion to tether extraction.
Surface Protrusion of ECs
FIGURE 3 Effect of the force loading rate on the protrusional stiffness (A) and the crossover force (B) of unstimulated HUVECs, either suspended in the experimental chamber or attached to the chamber wall. Each point represents the mean value of 5–22 adhesion events obtained from 3–10 cells. The error bars represent the standard deviations.
Effects of TNF-a, latrunculin, and temperature In vivo, cytokine stimulation of ECs is required for stable leukocyte rolling (2,28), so we stimulated both attached and suspended HUVECs with 10 ng/mL TNF-a and studied their surface protrusion using anti-CD62E-coated beads as the force transducer. Again, almost identical results were obtained from attached and suspended HUVECs (Fig. S4). To examine whether receptor types affect EC surface protrusion, we also used anti-CD31-coated beads as the force transducer. As shown in Fig. 4, for five different force loading rates, no significant difference in the protrusional stiffness or the crossover force was found among the three groups at any force loading rate (p > 0.05). The average amount of EC surface protrusion at the crossover force was found to be 0.41 mm, which is almost the same as before, and it did not depend on the force loading rate (Fig. S5). After HUVECs were treated with 5 mM latrunculin A, surface protrusion was no longer clearly visible in the
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FIGURE 4 Protrusional stiffness (A) and crossover force (B) of TNF-astimulated HUVECs measured with either anti-CD31-coated or antiCD62E-coated beads as force transducers. Each point represents the mean of 18–41 adhesion events obtained from 6–15 cells.
bead displacement curve (Fig. S6) and tethers were extracted almost immediately after pulling forces were imposed. Tether diameters were clearly larger and they became easily visible under the light microscope, consistent with what was found for tether extraction from neutrophils (19,29). All the previous experiments were carried out at room temperature around 20 C. Previous studies in our lab have shown that temperature affects both surface protrusion and tether extraction of neutrophils (22). Whether temperature affects surface protrusion from ECs is still unknown. To address this issue, we measured surface protrusion of HUVECs at 37 C using a custom-made temperature-controlled chamber (22). Five different force loading rates were selected and anti-CD62E-coated beads were used as the force transducer to interact with stimulated attached cells. As shown in Fig. 5, after temperature increased from 20 C to 37 C, the stiffness at two smaller force loading rates decreased by ~50%. Statistical analysis using Student’s ttest showed that the stiffness values from the two groups Biophysical Journal 110(5) 1150–1157
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FIGURE 5 Protrusional stiffness of TNF-a-stimulated HUVECs measured with anti-CD62E-coated beads at 20 C and 37 C. The error bars in the vertical direction represent the standard deviations of the corresponding measurements. Asterisks indicate a significant difference between the two groups.
were significantly different at both force loading rates, but no statistical difference was found at the three larger force loading rates. To confirm this observation, we also measured surface protrusion of individual cells first at 20 C and then again at 37 C to guarantee that the same cells were studied at both temperatures. A similar level of decrease was always found in the stiffness at smaller force loading rates, but not at larger loading rates (Fig. S7). At 37 C, adhesion was often ruptured before tether extraction. Because of insufficient data, no definitive conclusion could be drawn about how temperature affects the crossover force. Simultaneous surface protrusion from both neutrophils and HUVECs Previous studies have shown that surface protrusion also occurred when a neutrophil was pulled by a point force (4,19), so simultaneous surface protrusion should occur during neutrophil rolling when both neutrophils and ECs are pulled. Compared with other piconewton force methods, the MAT is advantageous for studying cell-cell interactions, because a spherical cell can be used directly as the force transducer. Therefore, we used spherical neutrophils as the force transducer of the MAT and pulled them after their adhesion to TNF-a-stimulated HUVECs. As shown in Fig. 6 A, a different pattern of bead displacement was observed during surface protrusion, i.e., the deformation is not linear anymore, especially at the beginning (cf. Fig. 2 A). Our analysis in the Appendix showed that this nonlinear deformation was due to the smaller protrusional stiffness when two cells were pulled in series. In this case, Eq. A5 should be used for calculating the overall protrusional stiffness. By fitting the inset curve in Fig. 6 A to Eq. A5, we obtained an overall protrusional stiffness of 145 pN/mm, which is much smaller than the average protrusional stiffness of Biophysical Journal 110(5) 1150–1157
FIGURE 6 (A) A typical bead displacement curve acquired at an increasing pressure of 10 pN/mm2/s when a TNF-a-stimulated HUVEC was pulled by a spherical neutrophil. Two different phases, surface protrusion and tether extraction, can be identified before adhesion rupture. The initial surface protrusion phase is enlarged in the inset, where the solid line represents fitting of Eq. A5 to the data. (B) Effect of the force loading rate on the stiffness of simultaneous surface protrusion of neutrophils and HUVECs (diamonds). The results measured from ECs (squares; data from Fig. 4) and neutrophils (crosses), as well as those estimated for neutrophils (triangles), are also plotted here for comparison.
ECs at similar force loading rates. We further measured the overall protrusional stiffness during simultaneous surface protrusion of neutrophils and ECs at four other force loading rates, and these results are shown in Fig. 6 B. Using these overall protrusional stiffness values and our results shown in Figs. 3 A and 4 A, we can estimate the protrusional stiffness of neutrophils by modeling simultaneous surface protrusion simply as two springs pulled in series. As shown in Fig. 6 B, the estimated protrusional stiffness of neutrophils agrees very well with the stiffness measured or estimated with the optical trap (unpublished data) (19), the biomembrane force probe (4), and total internal reflectance fluorescence microscopy (30). This shows that although simultaneous surface protrusion occurs during leukocyte
Surface Protrusion of ECs
rolling, most of the cellular deformation would come from neutrophils. DISCUSSION In this study, we examined the mechanical properties of surface protrusion of HUVECs and simultaneous surface protrusion of neutrophils and ECs. As observed in neutrophils, surface protrusion also exists before tether extraction of ECs. In contrast to the fluid-like extraction of membrane tethers, surface protrusion behaves like a linear spring when pulled at a constant force loading rate (Fig. 2 B). For surface protrusion of HUVECs, both the stiffness and the crossover force increased as the force loading rate increased, but neither of them was dependent on TNF-a stimulation, although both were dependent on cytoskeletal integrity. Compared to the typical tether length of several micrometers to tens of micrometers (9), the average length of surface protrusions of ECs were always ~400– 500 nm. This length was the same at different force loading rates, and it was not dependent on TNF-a stimulation. At the same force loading rate, ECs appear to be stiffer than neutrophils and have a larger crossover force (4,19). When pulled at a constant force loading rate, surface protrusion behaves like a linear spring. For simultaneous surface protrusion of leukocytes and ECs, it can be treated like two springs in series. In either case, the deformation can be described by Eq. A5, as shown in Fig. 6 A. For a stiff spring such as EC surface protrusion, Eq. A5 can be further simplified and the displacement of the force transducer can be fit very well with a linear equation (Fig. 2 A). Not surprisingly, this displacement can be also fit pretty well with Eq. A5. For example, the stiffness obtained from fitting the curve in Fig. 2 A to Eq. A5 was ~250 pN/mm, which is very close to the value obtained using linear regression. To simplify data processing, we only used linear regression to obtain Ut and calculate F when we studied surface protrusion of ECs. Previous studies have shown that temperature affects both surface protrusion and tether extraction of human neutrophils (31). In this study, we found that temperature affected surface protrusion of ECs, but only at small force loading rates (Fig. 5). Cellular surface protrusion can be described by a three-parameter solid model, which consists of a spring element connected in series to a Kelvin-Voigt element (19). The spring represents the fast elastic response, which is generally not sensitive to temperature; on the other hand, the Kelvin-Voigt element represents the slow elongation of the cell body, which is more sensitive to temperature because this element includes a viscous damper. The fact that surface protrusion of ECs only changed significantly at small force loading rates indicates that temperature only has a major effect on the slow viscous response of ECs. At larger force loading rates, the contri-
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bution from the Kelvin-Voigt element to the overall cellular protrusion is smaller due to a shorter pulling time, yielding less effect. It appears that both the protrusional stiffness and the crossover force made a transition around the force loading rate of 100 pN/s (Figs. 3 and 4). When the force loading rate increased from ~5 to 100 pN/s, the protrusional stiffness and the crossover force only increased slightly; in contrast, when the force loading rate increased from ~100 to 2600 pN/s, the protrusional stiffness and the crossover force increased sharply and depended linearly on the logarithm of the force loading rate. Interestingly, Evans et al. showed that when P-selectin on human neutrophils was pulled from ~200 to 40,000 pN/s, the crossover force also depended linearly on the logarithm of the force loading rate, a signature of rupturing molecular bonds by force (4). This indicates that surface protrusion of ECs was dominated by rupture of molecular interactions at large force loading rates. At small force loading rates, the off rates of these molecular interactions were fast enough to render the cellular membrane as the major determinant of the protrusional stiffness and the crossover force. This may also be the reason why temperature only affected the protrusional stiffness at small force loading rates (Fig. 5), because the mechanical properties of lipid membranes are very sensitive to temperature change (32). Our findings about surface protrusion of ECs in this work provide valuable data for simulating leukocyte rolling on the endothelium. In all previous modeling efforts, surface protrusion of ECs was ignored, because it was never characterized. Surface protrusion was not observed before tether extraction of ECs in previous studies (5,17,23). One likely reason for this is the large pulling force used in those tether studies. When constant pressure was applied with the MAT as in previous studies, since the force transducer was almost stationary at the beginning, the force was very large and the crossover force was probably overcome quickly without being noticed by the analog camera. Likely for the same reason, simultaneous tether extraction without surface protrusion was observed from both neutrophils and ECs (6). In reality, what happens in vivo is very likely simultaneous surface protrusion followed by tether extraction from one cell and then from the other, reducing the force on the adhesive bonds along the way. By exploiting their mechanical properties in such a manner, leukocytes and ECs work concertedly to stabilize leukocyte rolling, which leads to successful leukocyte firm adhesion and emigration. Fig. 6 B indicates that with their large stiffness, ECs play a negligible role during surface protrusion compared to neutrophils, especially at small force loading rates. However, at the later stage of tether extraction, their levels of importance will reverse, with ECs contributing more to the overall tether length (5,6). Besides, it is the crossover force that dictates whether tether extraction can occur. Therefore, during leukocyte rolling, surface Biophysical Journal 110(5) 1150–1157
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protrusion of ECs is an important precursor of tether extraction that should not be overlooked. APPENDIX A: CELLULAR SURFACE PROTRUSION WITH THE MAT When an increasing pressure was applied in the micropipette of the MAT, the total pressure drop ðDpÞ is determined by the speed of the motorized manometer ðVm Þ according to
Dp ¼ rgVm t :
(A1)
Because of the linear nature of low-Reynolds-number flow, the free motion velocity ðUf Þ is linearly dependent on the total pressure drop (13), so Uf can be expressed as
Uf ¼ at;
(A2)
where a is the acceleration of the force transducer during its free motion. If we assume a spring with stiffness k is stretched with the MAT, a first-order ordinary differential equation can be obtained for the spring extension (x, which also represents the bead displacement of the MAT) by balancing the force on the spring and the force on the force transducer of the MAT (13,21),
b dx kx ¼ at ; a dt
where
b ¼ pR2p rgVm
4 1 ε : 3
(A3)
(A4)
At t ¼ 0, x ¼ 0 and Ut ¼ dx=dt ¼ 0, so Eq. A3 can be solved and
ak b b t b x ¼ t 1e : k ak
(A5)
This work was supported by grants from the American Heart Association and the National Institutes of Health to J.Y.S.
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Hence, ak dx b ¼ Ut ¼ 1 e b t dt k
ACKNOWLEDGMENTS
(A6)
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When akt=b[1, x is a linear function of t and we have Ut yb=k, which is a constant. When akt=b[1 does not hold, x is a nonlinear function of t and Eq. A5 can be used for calculating k, where a can be calculated from the free motion of the force transducer and b can be calculated using Eq. A4 where all the parameters are known. When akt=b 1, if Eq. A5 is approximated by linear regression with b=k as the slope, k will be significantly overestimated.
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SUPPORTING MATERIAL Supporting Materials and Methods and seven figures are available at http:// www.biophysj.org/biophysj/supplemental/S0006-3495(16)00051-5.
AUTHOR CONTRIBUTIONS Y.C. and J.Y.S. designed the research; Y.C., L.L., and J.Y.S. performed the research and analyzed the data; and Y.C. and J.Y.S. wrote the article. Biophysical Journal 110(5) 1150–1157
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31. Liu, B., C. J. Goergen, and J. Y. Shao. 2007. Effect of temperature on tether extraction, surface protrusion, and cortical tension of human neutrophils. Biophys. J. 93:2923–2933.
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32. Waugh, R. E., and R. M. Hochmuth. 1995. Mechanics and deformability of hematocytes. In Biomedical Engineering Handbook. J. D. Bronzino, editor. CRC Press, Boca Raton, FL, pp. 474–486.
Biophysical Journal 110(5) 1150–1157
Biophysical Journal
Volume 110
March 2016
1150–1157
Article Endothelial Surface Protrusion by a Point Force Yong Chen,1 Lan Lu,1 and Jin-Yu Shao1,* 1
Department of Biomedical Engineering, Washington University, Saint Louis, Missouri
ABSTRACT During leukocyte rolling on the endothelium, surface protrusion and membrane tether extraction occur consecutively on leukocytes. Both surface protrusion and tether extraction of leukocytes stabilize leukocyte rolling. Tethers can also be extracted from endothelial cells (ECs), but surface protrusion of ECs has never been confirmed to exist. In this study, we examined EC surface protrusion with the micropipette aspiration technique. We found that, like leukocytes, surface protrusion on an EC did exist when a point force was imposed. Both the protrusional stiffness and the crossover force of EC surface protrusion were dependent on the force loading rate and the cytoskeletal integrity, but neither of them was dependent on tumor necrosis factor a stimulation. Temperature (37 C) affected the protrusional stiffness only at small force loading rates. When a neutrophil was employed to directly impose the pulling force on the EC, simultaneous surface protrusion from both cells occurred, and it can be modeled as two springs connected in series, although the spring constants should be adjusted according to the force loading rate. Therefore, EC surface protrusion is an important aspect of leukocyte rolling, and it should not be ignored when leukocyte rolling stability is studied systematically.
INTRODUCTION During the inflammatory response, leukocytes roll on the endothelium on the inside of the blood vessel. This process has been recognized as a key initial step for leukocyte migration to sites of injury or inflammation (1,2). Leukocyte rolling is regulated by many factors, including shear stress, chemotactic cytokines, adhesion molecules, and mechanical properties of both leukocytes and endothelial cells (ECs). Because of shear stress, point forces are imposed on leukocytes and ECs through adherent membrane receptors and ligands. As a result, two types of subcellular deformation are produced consecutively, surface protrusion and tether extraction, both of which contribute to mechanically stabilizing leukocyte rolling (3–12). Tethers are membrane nanotubes that are extracted from cells due to membrane flow induced by pulling forces (5,13). A constant pulling force (F) yields a constant tether extraction velocity (Ut), whereas larger F yields larger Ut. When Ut approaches zero, F should approach a nonzero value called the threshold force (F0) (14). Tethers can be extracted from both leukocytes and ECs, as well as from many other types of cells (11,14,15). For human neutrophils and ECs, F0 values are ~45 and 50 pN, respectively (3,5). During leukocyte rolling, tether extraction has been shown experimentally and numerically to decrease the pulling force applied to the adhesive bonds between leukocytes and ECs, thereby stabilizing rolling (3,7,9,10,12,16). In addition, tethers from ECs contribute more to leukocyte rolling stabilization than tethers from neutrophils (5,17).
Submitted August 12, 2015, and accepted for publication January 12, 2016. *Correspondence: [email protected]
More recently, tethers from leukocytes were shown to act as slings to facilitate their rolling in high shear (18). In contrast to fluid-like tether extraction, surface protrusion, which is a local tent-like deformation, behaves more like a solid. When an increasing pulling force is imposed on a cell surface, surface protrusion occurs first, followed by tether extraction. The force at which surface protrusion makes the transition to tether extraction is defined as the crossover force (Fc). Fc is generally larger than F0, because F0 is mainly determined by membrane mechanics and its interaction with the cytoskeleton, whereas Fc also includes the contribution from the interaction between the pulled receptor and the cytoskeleton. During surface protrusion, the surface stiffness is defined as the protrusional stiffness (kp). Surface protrusion of neutrophils was first studied using the micropipette aspiration technique (MAT), and a value of 43 pN/mm was found for kp at very small force loading rates (10). Afterward, surface protrusion of neutrophils was studied using the biomembrane force probe (4) and the optical trap (19) with larger force loading rates. These studies showed clearly that both Fc and kp depended on the force loading rate. Like leukocytes, ECs play an active role during the inflammatory response (20). However, surface protrusion of ECs has never been studied in detail, although surface protrusion and tether extraction of neutrophils, as well as tether extraction of ECs, have been well characterized. In this study, using either latex beads or human neutrophils as the force transducer of the MAT, we examined surface protrusion of ECs and illustrated its role in leukocyte rolling.
Editor: Andrew McCulloch. Ó 2016 by the Biophysical Society 0006-3495/16/03/1150/8
http://dx.doi.org/10.1016/j.bpj.2016.01.007
Surface Protrusion of ECs
MATERIALS AND METHODS EC culture and treatment Human umbilical vein ECs (HUVECs) were obtained from Cambrex Bioscience (Walkersville, MD) and cultured in six-well plates with EC growth medium 2 (Cambrex Bioscience). The cells were grown to confluence at 37 C in a humidified 5% carbon dioxide atmosphere and then detached with 0.05% trypsin-EDTA. A cell-culture-treated coverslip (Fisher Scientific, Hampton, NH) was prepared and mounted in advance on the inner side wall of our experimental chamber. After the coverslip was firmly attached, HUVECs were plated on the small coverslip and the whole chamber was kept in the incubator for at least 12 h for the cells to attach completely (the evidence used to assess the health of these cells is provided in the Supporting Material). To stimulate endothelial cells, 10 ng/mL tumor necrosis factor a (TNF-a; R&D Systems, Minneapolis, MN) was added to the cell culture 4 h before the experiment.
Neutrophil isolation
1151 possible to apply constant and variable aspiration pressure. In this study, three sets of experiments were performed. In the first set, spherical beads were used as the force transducer (Fig. 1, A and B) and increasing pressure was applied. In the second set, the setup was the same as shown in Fig. 1, A and B, but constant pressure was applied. In the third set, neutrophils were used as the force transducer (Fig. 1 C) and increasing pressure was applied. In a typical contact event in all three sets of experiments, the force transducer (the bead or the neutrophil in Fig. 1) first moved toward the EC on the left and made a brief contact. Then an aspiration pressure was applied in the micropipette and the force transducer either adhered or immediately moved freely away from the cell. When the aspiration pressure was increased at rates %2 pN/mm2/s, the experiments were recorded with an analog camera (30 frames/s) and a 5-V voltage stamp was used to indicate the instant when the pressure started to increase (Fig. 1 A). When the aspiration pressure was increased at rates >2 pN/mm2/s, a high-speed digital camera (Vision Research, Wayne, NJ) was needed for image acquisition (Figs. 1, B and C). At the start of the pressure increase, a voltage signal was used to trigger the recording and a sampling rate of between 100 and 500 frames/s was chosen based on the rate of pressure increase.
Human neutrophils were isolated from finger-prick blood donated by healthy volunteers (the protocol for obtaining blood was approved by the Washington University Institutional Review Board). Briefly, 200 mL of blood was collected in a heparinized capillary glass tube (Fisher Scientific) and then carefully overlaid on 300 mL Mono-Poly Resolving Medium (ICN Biomedicals, Aurora, OH) in a tube. The tube was centrifuged at 300 g for 15 min and the top layer with plasma and platelets was aspirated out. The remaining top layer above the red blood cells was carefully collected and mixed with 200 mL of phosphate-buffered saline (PBS) containing 0.1% human serum albumin (HSA). After it was centrifuged again at 250 g for 5 min, the supernatant enriched with lymphocytes was discarded and the remaining neutrophils were mixed in Hank’s balanced salt solution with 0.5% HSA (1 mM calcium) and 5 mg/mL anti-ICAM1 antibodies (Sigma, Saint Louis, MO) and then transferred to the chamber for the experiment.
Bead preparation Spherical latex beads (~8 mm in diameter; Sigma) coated with goat antimouse IgG antibodies were washed twice with 1 mL PBS and then coated with mouse anti-human antibodies (5 mg/mL) at 37 C for 1 h. Two different mouse anti-human antibodies, anti-CD31 (R&D Systems) and anti-CD62E (BD Pharmingen, San Diego, CA), were used in the experiments. After the incubation with antibodies, the beads were stored in PBS at 4 C. Before use, 20 mL of beads were taken out and washed twice with PBS.
Micropipette preparation The micropipette preparation and manipulation have been described in detail previously (13,15). A glass micropipette (~8 mm in diameter) was made to hold the force transducer in the experiment. The first 10 mm of the micropipette was filled with 1% bovine serum albumin (with latex beads as the force transducer) or 5% HSA (with neutrophils as the force transducer), and the rest of it was backfilled with PBS. The diameter of the micropipette was determined with differential interference contrast microscopy and divided by a correction factor (15).
Characterization of surface protrusion Our experiments were conducted with a modified version of the MAT, the details of which were described previously (14,21). Using a motorized manometer in place of the manual one in the traditional MAT made it
FIGURE 1 Three video micrographs showing three different experimental setups of the MAT. (A) An attached HUVEC grown on the side wall of the experimental chamber was studied. (B) A suspended HUVEC held by another micropipette was studied. In both (A) and (B), an antibody-coated bead was used as the force transducer of the MAT. (C) An attached HUVEC was studied with a spherical neutrophil as the force transducer of the MAT. In all experiments, when the pressure was increased at rates %2 pN/mm2/s, the video was recorded with an analog camera (30 frames/s) and a voltage stamp, þ05.06, as shown in (A), was used to indicate the instant when the pressure started to increase. When the pressure was increased at rates >2 pN/mm2/s, as shown in (B) and (C), a high-speed digital camera (100–500 frames/s) was used for video acquisition. Biophysical Journal 110(5) 1150–1157
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Data analysis The details of our data analysis were described previously (14,21). Briefly, each contact event was recorded as a separate movie in TIF format. The displacement of the force transducer was tracked with a method modified from Gelles et al. (22). In our experiments, the deformation is approximately a linear function of time, the force applied on the transducer (F) is calculated from (13,15,21)
F ¼
pR2p Dp
4 Ut 1 ε 1 ; 3 Uf
(1)
where Dp is the suction pressure, Rp is the radius of the micropipette, Uf is the bead velocity when it is moving freely under Dp, and
ε ¼ Rp Rb
Rp ;
(2)
where Rb is the radius of the bead. The bead diameter was determined with bright-field microscopy and divided by its correction factor (15). The accuracy of Eq. 1 when part of the transducer is outside the micropipette was verified using finite-element analysis (Fig. S1).
RESULTS Surface protrusion of suspended or attached HUVECs Using anti-CD31-coated beads as the force transducer in the MAT, we pulled either suspended or attached HUVECs with increasing force. Before the final adhesion rupture (as shown in Fig. 2 A), two different phases of cellular deformation can be identified: slow surface protrusion and fast tether extraction. Tether extraction of ECs was studied in detail (5,14,17,23), so we focused on surface protrusion in this work. To calculate F during surface protrusion with Eq. 1, we need to calculate Dp, Ut , and Uf at each time point. Dp was determined from its increasing rate and time. Uf was obtained in the cases where no adhesion occurred between the bead and the cell. During surface protrusion (as shown from 1.3 s to 1.9 s in the inset of Fig. 2 A), the bead moved at a constant velocity, so Ut was calculated by linear regression. We found that F increased linearly with time during surface protrusion (Fig. S2), i.e., the force loading rate was constant. Since EC surface protrusion also increased linearly with time (Fig. 2 A), a linear relationship was found between F and EC surface protrusion, as shown in Fig. 2 B. The protrusional stiffness was found by linear regression to be ~260 pN/mm. The cell surface deformed for ~900 nm until the crossover force reached ~230 pN, after which surface protrusion terminated and tether extraction started. Using increasing pressure at different rates (0.1–50 pN/ mm2/s), we studied EC surface protrusion at 11 different force loading rates. Low adhesion frequency (<20%) was achieved by reducing the contact time between the bead and the cell (24–27), so it was expected that F was very likely imposed on one receptor in any adhesion event. Both surface protrusion and tether extraction were produced Biophysical Journal 110(5) 1150–1157
FIGURE 2 (A) A typical bead displacement curve acquired at an increasing pressure of 10 pN/mm2/s and an attached HUVEC. Two consecutive phases of cellular deformation, surface protrusion and tether extraction, can be identified. (B) The relationship between the pulling force (F) and the cellular deformation during surface protrusion. The protrusional stiffness was calculated by linear regression to be ~260 pN/mm.
by this point force alone. Fig. 3, A and B, shows the protrusional stiffness and crossover force, respectively, measured at the 11 different force loading rates. Each point represents an average of 8–29 adhesion events obtained from 3–13 cells. When the force loading rate increased from 5 to 2500 pN/s, the stiffness increased from 100 to 500 pN/mm and the crossover force increased from 50 pN to 200 pN. No difference was found regardless of whether suspended or attached cells were pulled, indicating that surface protrusion was a local deformation. It is worth noting that the amount of EC surface protrusion at the crossover force (0.40 5 0.09 mm; mean 5 SD) did not depend on the force loading rate (Fig. S3), indicating a common structural basis for the transition from surface protrusion to tether extraction.
Surface Protrusion of ECs
FIGURE 3 Effect of the force loading rate on the protrusional stiffness (A) and the crossover force (B) of unstimulated HUVECs, either suspended in the experimental chamber or attached to the chamber wall. Each point represents the mean value of 5–22 adhesion events obtained from 3–10 cells. The error bars represent the standard deviations.
Effects of TNF-a, latrunculin, and temperature In vivo, cytokine stimulation of ECs is required for stable leukocyte rolling (2,28), so we stimulated both attached and suspended HUVECs with 10 ng/mL TNF-a and studied their surface protrusion using anti-CD62E-coated beads as the force transducer. Again, almost identical results were obtained from attached and suspended HUVECs (Fig. S4). To examine whether receptor types affect EC surface protrusion, we also used anti-CD31-coated beads as the force transducer. As shown in Fig. 4, for five different force loading rates, no significant difference in the protrusional stiffness or the crossover force was found among the three groups at any force loading rate (p > 0.05). The average amount of EC surface protrusion at the crossover force was found to be 0.41 mm, which is almost the same as before, and it did not depend on the force loading rate (Fig. S5). After HUVECs were treated with 5 mM latrunculin A, surface protrusion was no longer clearly visible in the
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FIGURE 4 Protrusional stiffness (A) and crossover force (B) of TNF-astimulated HUVECs measured with either anti-CD31-coated or antiCD62E-coated beads as force transducers. Each point represents the mean of 18–41 adhesion events obtained from 6–15 cells.
bead displacement curve (Fig. S6) and tethers were extracted almost immediately after pulling forces were imposed. Tether diameters were clearly larger and they became easily visible under the light microscope, consistent with what was found for tether extraction from neutrophils (19,29). All the previous experiments were carried out at room temperature around 20 C. Previous studies in our lab have shown that temperature affects both surface protrusion and tether extraction of neutrophils (22). Whether temperature affects surface protrusion from ECs is still unknown. To address this issue, we measured surface protrusion of HUVECs at 37 C using a custom-made temperature-controlled chamber (22). Five different force loading rates were selected and anti-CD62E-coated beads were used as the force transducer to interact with stimulated attached cells. As shown in Fig. 5, after temperature increased from 20 C to 37 C, the stiffness at two smaller force loading rates decreased by ~50%. Statistical analysis using Student’s ttest showed that the stiffness values from the two groups Biophysical Journal 110(5) 1150–1157
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FIGURE 5 Protrusional stiffness of TNF-a-stimulated HUVECs measured with anti-CD62E-coated beads at 20 C and 37 C. The error bars in the vertical direction represent the standard deviations of the corresponding measurements. Asterisks indicate a significant difference between the two groups.
were significantly different at both force loading rates, but no statistical difference was found at the three larger force loading rates. To confirm this observation, we also measured surface protrusion of individual cells first at 20 C and then again at 37 C to guarantee that the same cells were studied at both temperatures. A similar level of decrease was always found in the stiffness at smaller force loading rates, but not at larger loading rates (Fig. S7). At 37 C, adhesion was often ruptured before tether extraction. Because of insufficient data, no definitive conclusion could be drawn about how temperature affects the crossover force. Simultaneous surface protrusion from both neutrophils and HUVECs Previous studies have shown that surface protrusion also occurred when a neutrophil was pulled by a point force (4,19), so simultaneous surface protrusion should occur during neutrophil rolling when both neutrophils and ECs are pulled. Compared with other piconewton force methods, the MAT is advantageous for studying cell-cell interactions, because a spherical cell can be used directly as the force transducer. Therefore, we used spherical neutrophils as the force transducer of the MAT and pulled them after their adhesion to TNF-a-stimulated HUVECs. As shown in Fig. 6 A, a different pattern of bead displacement was observed during surface protrusion, i.e., the deformation is not linear anymore, especially at the beginning (cf. Fig. 2 A). Our analysis in the Appendix showed that this nonlinear deformation was due to the smaller protrusional stiffness when two cells were pulled in series. In this case, Eq. A5 should be used for calculating the overall protrusional stiffness. By fitting the inset curve in Fig. 6 A to Eq. A5, we obtained an overall protrusional stiffness of 145 pN/mm, which is much smaller than the average protrusional stiffness of Biophysical Journal 110(5) 1150–1157
FIGURE 6 (A) A typical bead displacement curve acquired at an increasing pressure of 10 pN/mm2/s when a TNF-a-stimulated HUVEC was pulled by a spherical neutrophil. Two different phases, surface protrusion and tether extraction, can be identified before adhesion rupture. The initial surface protrusion phase is enlarged in the inset, where the solid line represents fitting of Eq. A5 to the data. (B) Effect of the force loading rate on the stiffness of simultaneous surface protrusion of neutrophils and HUVECs (diamonds). The results measured from ECs (squares; data from Fig. 4) and neutrophils (crosses), as well as those estimated for neutrophils (triangles), are also plotted here for comparison.
ECs at similar force loading rates. We further measured the overall protrusional stiffness during simultaneous surface protrusion of neutrophils and ECs at four other force loading rates, and these results are shown in Fig. 6 B. Using these overall protrusional stiffness values and our results shown in Figs. 3 A and 4 A, we can estimate the protrusional stiffness of neutrophils by modeling simultaneous surface protrusion simply as two springs pulled in series. As shown in Fig. 6 B, the estimated protrusional stiffness of neutrophils agrees very well with the stiffness measured or estimated with the optical trap (unpublished data) (19), the biomembrane force probe (4), and total internal reflectance fluorescence microscopy (30). This shows that although simultaneous surface protrusion occurs during leukocyte
Surface Protrusion of ECs
rolling, most of the cellular deformation would come from neutrophils. DISCUSSION In this study, we examined the mechanical properties of surface protrusion of HUVECs and simultaneous surface protrusion of neutrophils and ECs. As observed in neutrophils, surface protrusion also exists before tether extraction of ECs. In contrast to the fluid-like extraction of membrane tethers, surface protrusion behaves like a linear spring when pulled at a constant force loading rate (Fig. 2 B). For surface protrusion of HUVECs, both the stiffness and the crossover force increased as the force loading rate increased, but neither of them was dependent on TNF-a stimulation, although both were dependent on cytoskeletal integrity. Compared to the typical tether length of several micrometers to tens of micrometers (9), the average length of surface protrusions of ECs were always ~400– 500 nm. This length was the same at different force loading rates, and it was not dependent on TNF-a stimulation. At the same force loading rate, ECs appear to be stiffer than neutrophils and have a larger crossover force (4,19). When pulled at a constant force loading rate, surface protrusion behaves like a linear spring. For simultaneous surface protrusion of leukocytes and ECs, it can be treated like two springs in series. In either case, the deformation can be described by Eq. A5, as shown in Fig. 6 A. For a stiff spring such as EC surface protrusion, Eq. A5 can be further simplified and the displacement of the force transducer can be fit very well with a linear equation (Fig. 2 A). Not surprisingly, this displacement can be also fit pretty well with Eq. A5. For example, the stiffness obtained from fitting the curve in Fig. 2 A to Eq. A5 was ~250 pN/mm, which is very close to the value obtained using linear regression. To simplify data processing, we only used linear regression to obtain Ut and calculate F when we studied surface protrusion of ECs. Previous studies have shown that temperature affects both surface protrusion and tether extraction of human neutrophils (31). In this study, we found that temperature affected surface protrusion of ECs, but only at small force loading rates (Fig. 5). Cellular surface protrusion can be described by a three-parameter solid model, which consists of a spring element connected in series to a Kelvin-Voigt element (19). The spring represents the fast elastic response, which is generally not sensitive to temperature; on the other hand, the Kelvin-Voigt element represents the slow elongation of the cell body, which is more sensitive to temperature because this element includes a viscous damper. The fact that surface protrusion of ECs only changed significantly at small force loading rates indicates that temperature only has a major effect on the slow viscous response of ECs. At larger force loading rates, the contri-
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bution from the Kelvin-Voigt element to the overall cellular protrusion is smaller due to a shorter pulling time, yielding less effect. It appears that both the protrusional stiffness and the crossover force made a transition around the force loading rate of 100 pN/s (Figs. 3 and 4). When the force loading rate increased from ~5 to 100 pN/s, the protrusional stiffness and the crossover force only increased slightly; in contrast, when the force loading rate increased from ~100 to 2600 pN/s, the protrusional stiffness and the crossover force increased sharply and depended linearly on the logarithm of the force loading rate. Interestingly, Evans et al. showed that when P-selectin on human neutrophils was pulled from ~200 to 40,000 pN/s, the crossover force also depended linearly on the logarithm of the force loading rate, a signature of rupturing molecular bonds by force (4). This indicates that surface protrusion of ECs was dominated by rupture of molecular interactions at large force loading rates. At small force loading rates, the off rates of these molecular interactions were fast enough to render the cellular membrane as the major determinant of the protrusional stiffness and the crossover force. This may also be the reason why temperature only affected the protrusional stiffness at small force loading rates (Fig. 5), because the mechanical properties of lipid membranes are very sensitive to temperature change (32). Our findings about surface protrusion of ECs in this work provide valuable data for simulating leukocyte rolling on the endothelium. In all previous modeling efforts, surface protrusion of ECs was ignored, because it was never characterized. Surface protrusion was not observed before tether extraction of ECs in previous studies (5,17,23). One likely reason for this is the large pulling force used in those tether studies. When constant pressure was applied with the MAT as in previous studies, since the force transducer was almost stationary at the beginning, the force was very large and the crossover force was probably overcome quickly without being noticed by the analog camera. Likely for the same reason, simultaneous tether extraction without surface protrusion was observed from both neutrophils and ECs (6). In reality, what happens in vivo is very likely simultaneous surface protrusion followed by tether extraction from one cell and then from the other, reducing the force on the adhesive bonds along the way. By exploiting their mechanical properties in such a manner, leukocytes and ECs work concertedly to stabilize leukocyte rolling, which leads to successful leukocyte firm adhesion and emigration. Fig. 6 B indicates that with their large stiffness, ECs play a negligible role during surface protrusion compared to neutrophils, especially at small force loading rates. However, at the later stage of tether extraction, their levels of importance will reverse, with ECs contributing more to the overall tether length (5,6). Besides, it is the crossover force that dictates whether tether extraction can occur. Therefore, during leukocyte rolling, surface Biophysical Journal 110(5) 1150–1157
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protrusion of ECs is an important precursor of tether extraction that should not be overlooked. APPENDIX A: CELLULAR SURFACE PROTRUSION WITH THE MAT When an increasing pressure was applied in the micropipette of the MAT, the total pressure drop ðDpÞ is determined by the speed of the motorized manometer ðVm Þ according to
Dp ¼ rgVm t :
(A1)
Because of the linear nature of low-Reynolds-number flow, the free motion velocity ðUf Þ is linearly dependent on the total pressure drop (13), so Uf can be expressed as
Uf ¼ at;
(A2)
where a is the acceleration of the force transducer during its free motion. If we assume a spring with stiffness k is stretched with the MAT, a first-order ordinary differential equation can be obtained for the spring extension (x, which also represents the bead displacement of the MAT) by balancing the force on the spring and the force on the force transducer of the MAT (13,21),
b dx kx ¼ at ; a dt
where
b ¼ pR2p rgVm
4 1 ε : 3
(A3)
(A4)
At t ¼ 0, x ¼ 0 and Ut ¼ dx=dt ¼ 0, so Eq. A3 can be solved and
ak b b t b x ¼ t 1e : k ak
(A5)
This work was supported by grants from the American Heart Association and the National Institutes of Health to J.Y.S.
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Hence, ak dx b ¼ Ut ¼ 1 e b t dt k
ACKNOWLEDGMENTS
(A6)
12. Yu, Y., and J. Y. Shao. 2007. Simultaneous tether extraction contributes to neutrophil rolling stabilization: a model study. Biophys. J. 92:418–429.
When akt=b[1, x is a linear function of t and we have Ut yb=k, which is a constant. When akt=b[1 does not hold, x is a nonlinear function of t and Eq. A5 can be used for calculating k, where a can be calculated from the free motion of the force transducer and b can be calculated using Eq. A4 where all the parameters are known. When akt=b 1, if Eq. A5 is approximated by linear regression with b=k as the slope, k will be significantly overestimated.
13. Shao, J. Y., and R. M. Hochmuth. 1996. Micropipette suction for measuring piconewton forces of adhesion and tether formation from neutrophil membranes. Biophys. J. 71:2892–2901.
SUPPORTING MATERIAL Supporting Materials and Methods and seven figures are available at http:// www.biophysj.org/biophysj/supplemental/S0006-3495(16)00051-5.
AUTHOR CONTRIBUTIONS Y.C. and J.Y.S. designed the research; Y.C., L.L., and J.Y.S. performed the research and analyzed the data; and Y.C. and J.Y.S. wrote the article. Biophysical Journal 110(5) 1150–1157
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