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Molecular Bond Formation between Surfaces: Anchoring and Shearing Effects David Lebœuf and Nelly Henry* CNRS UMR 168/Institut Curie - 11, rue P. et M. Curie - 75 248 Paris CEDEX 05- France ReceiVed July 8, 2005. In Final Form: October 20, 2005 Specific molecular bonds between apposing surfaces play a central role in many biological structures and functions. They display a widely varying anchoring to the cell surface, and they are subject to forces that affect their binding characteristics due to their hydrodynamic environments. Here, we examine both anchoring and shearing aspects using simplified model systems aimed at gaining insight into the formation of a 2D bond collection under stress using two different surface anchors. The highly specific streptavidin-biotin molecular bond was chosen as the model receptorligand pair, and grafted colloids were used as model surfaces. To explore the role of the surface anchor, we grafted biotin onto the particle surface following two different approaches: first, the grafting was performed directly on the particle amine functions; second, a 35-nm-long PEG spacer was used. Hybrid particle classes were brought into contact in a homogeneous shear (between 200 s-1 and 1200 s-1) using a cone plate geometry. The bond association and dissociation kinetics were given by the time course assemblage of hybrid particles into doublets. We observed saturating kinetics profiles that we interpreted as a linkage-breakage equilibrium, which yielded the on and off rates. We found that the biotin-PEG spacer was needed in order to observe significant binding at any shear rate. We also showed that only the number of collisions per unit time, generated by the shear, affected the on rate of the binding. Neither the exerted forces nor the collision lifetime had any effect. The off rate decreased with shear, possibly because of the shortening of the force duration, which results from the increasing shear rate.
Introduction Formation and dissociation of collections of specific molecular links between apposing surfaces are omnipresent events in biosystems. They govern cell adhesion1-4 and intercellular communication, for example, in tissue formation5 or in immune responses.6,7 They take place in the complex and crowded environment of the cell surface and also in the highly dynamic conditions of the blood stream, where wall shear rates are believed to vary from 150 to 1600 s-1.8 Substantial efforts have therefore been made in order to make progress from the traditional threedimensional (3D) vision of molecular interactions to actual twodimensional (2D) experiments on surface-bound molecular bonds.9-16 Several different experimental approaches using flow chambers, micropipets, or atomic force microscopy (AFM) have yielded significant understanding of 2D bond breakage by observing the breakage under different forces. Bell17 in the 1970s *
[email protected]. Tel: 33 (0) 142 34 64 95. Fax: 33 (0) 140 51 06 36. (1) Pierres, A.; Benoliel, A. M.; Bongrand, P. Curr. Opin. Colloid Interface Sci. 1998, 3, 525. (2) Orsello, C. E.; Lauffenburger, D. A.; Hammer, D. A. Trends Biotechnol. 2001, 19, 31. (3) Hammer, D. A.; Tirrell, M. Annu. ReV. Sci. 1996, 26, 651. (4) Zhu, C. J. Biomech. 2000, 33, 23. (5) Gumbiner, B. M. Cell 1996, 84, 345. (6) Davis, S. J.; Ikemizu, S.; Evans, E. J.; Fugger, L.; Bakker, T. R.; van der Merwe, P. A. Nat. Immunol. 2003, 4, 217. (7) Krummel, M. F.; Davis, M. M. Curr. Opin. Immunol. 2002, 14, 66. (8) Gallik, S.; Usami, S.; Jan, K. M.; Chien, S. Biorheology 1989, 26, 823. (9) Pierres, A.; Benoliel, A. M.; Bongrand, P. Faraday Discuss. 1998, 111, 321. (10) Pierres, A.; Eymeric, P.; Baloche, E.; Touchard, D.; Benoliel, A. M.; Bongrand, P. Biophys. J. 2003, 84, 2058-70. (11) Dustin, M. L.; Ferguson, L. M.; Chan, P. Y.; Springer, T. A.; Golan, D. E. J. Cell Biol. 1996, 132, 465. (12) Chesla SE, Selvaraj P, Zhu C., Biophys. J. 1998, 75, 1553. (13) Cozens-Roberts, C.; Quinn, J. A.; Lauffenburger, D. A. Biophys. J. 1990, 58, 857. (14) Piper, J. W.; Swerlick, R. A.; Zhu, C. Biophys. J. 1998, 74, 492. (15) Evans, E.; Ritchie, K.; Merkel, R. Biophys. J. 1995, 68, 2580. (16) Evans, E. Annu. ReV. Biophys. Biomol. Struct. 2001, 30, 105. (17) Bell, G. I. Science 1978, 200, 618.
was the first to propose a theoretical framework for the intuitive idea that bond lifetime depended on the force applied. More recently, Evans and co-workers,18-21 using a single molecule force technique, the biomembrane force probe, provided higherresolution evidence that the strength of protein-ligand bonds depended not simply on the force applied but also on the loading rate. This revealed the internal bond energy landscape. Goldsmith’s group investigated shear-induced breakage of multiple bonds between apposing surfaces, which is what actually occurs at the cell surface.22-25 They approached the problem from both a theoretical and experimental point of view in addressing the stochastic character of the process. The question of the 2D bond formation itself, however, still remains poorly understood. Determination of on rates is largely unexplored, and what is known is primarily due to the work of Zhu and collaborators on the formation of bonds between several selectins and their ligands. These results support the concept of catch and slip bonds28-31 as the key mechanism for flow-enhanced adhesion and cell rolling, thus demonstrating the existence of a shear regime where (18) Merkel, R.; Nassoy, P.; Leung, A.; Ritchie, K.; Evans, E. Nature (London) 1999, 397, 50. (19) Evans, E. Faraday Discuss. 1998, 111, 1. (20) Evans, E. Biophys. Chem. 1999, 82, 83. (21) Evans, E.; Ritchie, K. Biophys. J. 1997, 72, 1541. (22) Long, M.; Goldsmith, H. L.; Tees, D. F.; Zhu, C. Biophys. J. 1999, 76, 1112. (23) Kwong, D.; Tees, D. F.; Goldsmith, H. L. Biophys. J. 1996, 71, 1115. (24) Tees, D. F.; Goldsmith, H. L. Biophys. J. 1996, 71, 1102. (25) Tees, D. F.; Coenen, O.; Goldsmith, H. L. Biophys. J. 1993, 65, 1318. (26) Marshall, B. T.; Long, M.; Piper, J. W.; Yago, T.; McEver, R. P.; Zhu, C. Nature (London) 2003, 423, 190. (27) Yago, T.; Wu, J.; Wey, C. D.; Klopocki, A. G.; Zhu, C.; McEver, R. P. J. Cell Biol. 2004, 166, 913. (28) Chang, K. C.; Tees, D. F.; Hammer, D. A. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 11262. (29) Pierres, A.; Touchard, D.; Benoliel, A. M.; Bongrand, P. Biophys. J. 2002, 82, 3214. (30) Goldsmith, H. L.; Quinn, T. A.; Drury, G.; Spanos, C.; McIntosh, F. A.; Simon, S. I. Biophys. J. 2001, 81, 2020. (31) Bonnefoy, A.; Liu, Q.; Legrand, C.; Frojmovic, M. M. Biophys. J. 2000, 78, 2834.
10.1021/la0518501 CCC: $33.50 © 2006 American Chemical Society Published on Web 11/25/2005
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increasing the force strengthens the bond. Nevertheless, the question of whether and how force affects the on rate remains unclear. Moreover, the case of L-selectin bonding with its ligand seems unique, and the observations made with different molecular pairs display different behaviors28-31 suggesting that increasing shear induces a decreasing on rate. In the present work, we undertook the characterization of the major effects resulting from the application of a mechanical stress on the net interaction of an assembly of surface-bound protein-ligand pairs. The purpose is to elucidate, on a statistical basis, the intrinsic role of the shear forces on the molecular bond formation step. We therefore sheared receptor or ligand-grafted colloidal particles and analyzed the kinetics of net doublet formation for several different shear values. For the sake of simplicity, we chose to work with a very well characterized receptor-ligand pair, the streptavidin-biotin molecular couple, for which there is a huge amount of structural and thermodynamical data available.32-34 The molecules were grafted onto colloidal particles using two different types of anchor. Indeed, the way the molecules are attached to the substrate is expected to affect the characteristics of surface-bound receptor-ligand interactions. Evans and Ritchie35 have shown that flexible polymer linkage of the molecules to the substrate led to major distortion of the bond strength spectrum when compared to a bond rigidly linked to the substrate. Other authors also showed, using a surface forces apparatus and polymer theory,36,37 that the kinetics and spatial range of the interaction of the surface-tethered receptor and ligand are highly dependent on the linking polymer chain dynamics. In this paper, the streptavidin-biotin interactions under controlled shear stress will be described for (1) biotin directly attached to the particle amine surface functions and for (2) a spaced out biotin connected to the particle via a flexible poly(ethylene glycol) (PEG) polymer. This polymer has often been used in biomimetic systems either to create a steric hindrance against nonspecific adsorption of unwanted proteins38-41 or to mimic the cell glycocalix42 or as a cross-linker for various receptors or ligands.43 It has also been shown to help bond formation between surface-anchored and soluble molecules.44 We examine here the situation where both receptor and ligand are bound to the surface.
Experimental Section Materials. (a) Beads. Amine and streptavidin polystyrene magnetic beads, 2.8 µm in diameter, were purchased from Dynal France (Compie`gne). Their magnetic load greatly facilitated washing steps in the surface-modification procedures. (b) Molecules. D-Biotin was from Sigma-Aldrich. The Nhydrosuccinimide PEGylated biotin derivative (NHS-PEG3400(32) Schief, W. R.; Edwards, T.; Frey, W.; Koppenol, S.; Stayton, P. S.; Vogel, V. Biomol. Eng. 1999, 16, 29. (33) Chilkoti, A.; Stayton, P. S J. Am. Chem. Soc. 1995, 117, 10622. (34) Green, N. M. AdV. Protein Chem. 1975, 29, 85. (35) Evans, E.; Ritchie, K. Biophys. J. 1999, 76, 2439. (36) Jeppesen, C.; Wong, J. Y.; Kuhl, T. L.; Israelachvili, J. N.; Mullah, N.; Zalipsky, S.; Marques, C. M. Science 2001, 293, 465. (37) Wong, J. Y.; Kuhl, T. L.; Israelachvili, J. N.; Mullah, N.; Zalipsky, S. Science 1997, 275, 820. (38) Kirpotin, D.; Park, J. W.; Hong, K.; Zalipsky, S.; Li, W. L.; Carter, P.; Benz, C. C.; Papahadjopoulos, D. Biochemistry 1997, 36, 66-75. (39) Meyer, O.; Kirpotin, D.; Hong, K.; Sternberg, B.; Park, J. W.; Woodle, M. C.; Papahadjopoulos, D. J. Biol. Chem. 1998, 273, 15621. (40) Blume, G.; Cevc, G. Biochim. Biophys. Acta 1993, 1146, 157. (41) Gref, R.; Luck, M.; Quellec, P.; Marchand, M.; Dellacherie, E.; Harnisch, S.; Blunk, T.; Muller, R. H. Colloids Surf., B 2000, 18, 301. (42) Boulbitch, A.; Guttenberg, Z.; Sackmann, E. Biophys. J. 2001, 81, 2743. (43) Perret, E.; Leung, A.; Morel, A.; Feracci, H.; Nassoy, P. Langmuir 2002, 18, 846. (44) Ebato, H.; Gentry, C. A.; Herron, J. N.; Mueller, W.; Okahata, Y.; Ringsdorf, H.; Suci, P. A. Anal. Chem. 1994, 66, 1683.
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Figure 1. Biotin particles. Magnetic latex particles bearing amine functions are grafted with biotin according to two different approaches: one class of particles is grafted with D-biotin directly onto the amine function via a nucleophilic substitution activated by carbodiimide; the other class couples an N-hydroxysuccinimide active ester PEG-biotin onto the particle amine function. The poly(ethylene glycol) spacer is MW 3400. This tether is composed of N (N ≈ 95) ethylene oxide monomer units of size a ) 3.5 Å, which yield a fully extended length close to 35 nm and an average distance from the surface of the tether’s end of De ≈ 6 nm (Flory radius ≈ aN0,64).
biotin) was obtained from NEKTAR Therapeutics. Ethyl dimethylaminopropyl carbodiimide (EDAC), FITC-labeled biotin, and streptavidin were supplied by Molecular Probes (Port Gebow, Netherlands). Phosphate buffer saline (PBS), made of 10 mM sodium phosphate (pH 7.4) added to 150 mM NaCl, was from Invitrogen (Les Ulis, France). Bead Grafting. The amine magnetic latex was grafted with biotin derivatives according to two different approaches in order to obtain two different sets of biotinylated beads: one with a biotin closely anchored to the surface (D-biotin grafted beads) and another with a remote biotin attached to the surface through a longer spacer (PEG-biotin grafted beads) as shown in Figure 1. The first approach consists of direct coupling of the D-biotin carboxyl group with the amine group of the cell surface according to the nucleophilic substitution that occurs after carboxyl activation by EDAC. Briefly, 5 mg/mL D-biotin in 10mM Na2HPO4 buffer (pH 4.7) was added to 50 mg/mL EDAC and gently vortexed for 15 min at room temperature. Amine beads previously washed in phosphate buffer were then added to a final concentration of 3 × 108 beads/mL. The mixture was vortexed one additional hour at room temperature before settling overnight at 4 °C. The particles were then concentrated using a magnet and washed twice in phosphate buffer. The second class of beads was prepared by grafting biotin derivatized with an N-hydrosuccinimide polymeric linker (NHS-PEG-biotin) that allowed conjugation of the tethered biotin with amine groups. Detailed procedures can be found in Merkel et al.18 Briefly, 2 mg of NHS-PEG-biotin were dissolved in 150 µL of 0.1 M bicarbonate buffer (pH 8.5) and added with amine beads to a final concentration of 3 × 108 particles/mL. The mixture was vortexed during 1 h at room temperature and left to settle overnight at 4 °C. The particles were then washed twice in phosphate buffer as previously described (first route). In both cases, particle counts were checked using a hemocymeter. Grafting efficiency was measured by flow cytometry titrating biotin molecules present on the bead surface with fluorescent streptavidin (FITC-labeled). Shearing Experiments. A uniform shear stress was applied to the bead suspension using the cone-plate geometry described in Figure 2. The volume of the suspension to be sheared (135 µL) was calculated exactly to fill the gap between the plate and
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Figure 2. Schematic representation of the cone-plate shearing device. Sample volume was adjusted to 135 µL to exactly fit the gap between the plate and the cone. The whole volume was then submitted to a homogeneous shear stress before being collected for flow cytometry analysis or microscope observation.
the spindle. The desired shear rate was obtained by varying the angular velocity of the conic spindle. The torque required to rotate the cone above the plate was measured using a Brookfield viscometer (model DV-III). It allowed the accuracy of the operation to be checked. For each run, a few seconds were necessary from the onset of the spindle rotation to the steady flow. This lapse was systematically subtracted from the total shear time. After shearing, the sample was carefully recovered with a large open-tip pipet and analyzed either by flow cytometry or by microscopy. For flow cytometry experiments, the sample (135 µL) was immediately added to 100 µL of PBS in a measurement tube and set to collect cytometric data. The whole operation took less than 20 s from the end of shearing to the end of flow cytometry recording. Flow Cytometry Analysis. (a) Aggregation. The different populations of beads and bead aggregates generated by the shearing were analyzed using a Becton Dickinson flow cytometer (Facscalibur) equipped with an air-cooled 488-nm argon-ion laser. In this setup, the sample is injected at the center of a coaxial laminar flow in order to produce a single object line through the laser-beam waist. No significant shear stress is experienced by the particles on the stream except at the outlet of this hydrodynamic focusing system where velocity gradients are high and may in some cases generate shear stresses as high as 400 s-1, according to a previous theoretical model.45 However, this effect is balanced by the very short flight time (>0.5 ms) of the particles in this region. In our system, recordings performed at various flow rates provided identical results, and microscope observations corroborated flow cytometry data, ruling out any significant flow effects during the measurements. Fluorescence was measured using dichroı¨c mirrors and filter sets: a 530/30 nm band-pass on the FL1 channel. Low-angle and side-scattered beams were also collected for each event (single bead or aggregate). Usually, 5 000 events were collected. Data were analyzed using the multivariate analysis software CellQuest (BDIS), except in a few cases where more detailed analysis was performed on listmode data files stored in FCS format. (b) Fluorescence Calibration. The flow cytometer provided an arbitrary fluorescence signal which depended on the gain and amplification sets chosen for the experiment. A calibration was needed to convert this arbitrary fluorescence per bead into molecules per bead. We used an autocalibration method already described in Sarda et al.46 It simply requires that free ligand may be neglected in the initial phase of the titration, i.e., low ligand and high receptor concentrations together with an affinity constant higher than 106 M-1 are needed. Consequently, bound ligand may be approximated to total ligand. By knowing the number of particles in each sample, the number of molecules per bead may be easily calculated, and the calibration coefficient is then (45) Amblard, F.; Auffray, C.; Sekaly, R.; Fischer, A. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 3628. (46) Sarda, S.; Pointu, D.; Pincet, F.; Henry, N. Biophys. J. 2004, 86, 3291.
Figure 3. Streptavidin binding site titration: Mean fluorescence (channel FL1) per particle was recorded with samples of increasing FITC-labeled streptavidin concentrations to determine the number of binding sites per particle. Particle concentration was equal to 1.5 × 105 particle/mL. Experiments were performed in PBS buffer, and sample equilibration was carried out for ca. 30 min before fluorescence acquisition. Saturating concentrations of 6 × 106 and 7.5 × 106 streptavidin molecules per particle were obtained for pD-biot and pPEG-biot, respectively.
obtained from the titration curve slope in the linear range (low ligand concentration). This approach was very well adapted to the case of the streptavidin-biotin pair because of its particularly high affinity constant (Ka ≈ 1014 M-1).47
Results Biotin Surface Density and Binding Capacity of Closely Grafted and Tethered Particles. The grafting efficiency was measured for the two particle classes by titrating the surface residues with fluorescent streptavidin. D-Biotin and PEG-biotin particle samples containing 1.5 × 106 beads/mL were incubated during 30 min with a range of increasing streptavidin-FITC concentrations. The data displayed in Figure 3 show that very similar results were obtained for the two classes of particles. In both cases, the curve sharply shifted from a linear increase to a plateau as expected because of the strong affinity of the streptavidin-biotin pair. Quantitative interpretation of the results was based on the assumption of a one-to-one streptavidin/biotin binding ratio. Indeed, biotin was restrained at the bead surface, and the formation of the streptavidin-biotin complex requires a precise orientation. The simultaneous binding of several biotin molecules by one streptavidin was thus unlikely. On this basis, according to the autocalibration method explained in the previous section, we obtained a number of streptavidin binding sites per bead for each class of particle. For D-biotin particles (pD-biot), the saturating concentration was found to be equal to 1.4 nM for a particle concentration of 1.5 × 105 particle/mL, which means approximately 6 × 106 streptavidin molecules per bead. Slightly higher values were obtained for PEG-biotin particles (pPEGbiot) that went up to 7.5 × 106 molecules per bead, meaning at least this amount of grafted biotins. This represents a dense coverage of the particle surface: ca. one site per 5 nm2 for pDbiot and one per 4 nm2 for pPEG-biot, which is even more dense than a compact streptavidin monolayer if we refer to physical surface (28 µm2 per bead). It should be noted, however, that the supplier indicated a surface area of more than twice the physical surface, which could explain the high binding densities. These results demonstrate the high efficiency of the grafting procedures and indicate that similar amounts of streptavidin are bound to pD-biot and pPEG-biot (although pPEG-biot was able to accommodate a few more binding sites). It should be (47) Livnah, O.; Bayer, E. A.; Wilchek, M.; Sussman, J. L. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 5076.
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Figure 4. Soluble streptavidin binding on surface-bound biotin kinetics: FITC-labeled strepatvidin, 8 × 10-9 M, was added at t ) 0 with 1.5 × 105 particles/mL. Time course fluorescence increase per particle was recorded by sequential short-flow cytometry acquisitions. The curves were adjusted to a monoexponential expression, F(t) ) F∞(1 - exp(-bt)). Characteristic times (t1/2 ) (Ln2/b)) of 160 s and 100 s were obtained for pD-biot and pPEGbiot, respectively.
noted that we measured a binding capacity, and not the amount of bound biotin molecules, since the binding may be restricted by the steric hindrance between the strepatvidin-FITC complex. To complete characterization of the grafting, we compared the kinetics of soluble fluorescent streptavidin binding onto the surface of each class of particle. Suspensions of 1.5 × 105 particle/ mL were brought into contact with an excess of strepatvidinFITC (8 × 10-9 M) at t ) 0, and binding to the particle surface was measured owing to the increase in particle fluorescence. The data displayed in Figure 4, were fitted using a pseudofirst-order kinetics equation of the form F(t) ) F∞(1 exp(-bt)), where F∞ stands for the saturating concentration, which corresponded to the total number of binding sites per bead, and a characteristic constant, b, proportional to the on rate of the association of the soluble streptavidin with the surface-bound biotin. D-Biotin and PEG-biotin grafted surfaces exhibited an apparent on rate of 5.4 × 105 s-1 M-1 and 8.4 × 105 s-1 M-1, respectively. Very good correlation coefficients (χ2 > 0.99) were obtained for the adjustments, but high relative standard deviations (around 50%) were obtained over independent experiments. These results confirmed that the two classes of surfaces behaved very similarly with respect to soluble streptavidin, except pPEGbiot displayed, as expected, a slightly higher binding rate. 2D Molecular Bond Formation. The capacity of the pD-biot and pPEG-biot beads to form specific bonds with streptavidingrafted particles (pSA) was evaluated next. Particle suspensions were adjusted to 1.5 × 106 beads/mL in PBS. The flow cytometry scattering profile (side vs forward scattering) of each sample was recorded as well as fluorescence (FL1 channel, i.e., excitation wavelength of 488 nm and emission wavelength of 520 ( 15 nm) versus forward scattering in the presence of 10-8 M FITClabeled biotin added to every sample tube prior to analysis. Figure 5 shows the obtained dot plots. Singlets and doublets were clearly identified on the cytograms owing to the scattering parameters (FSC and SSC) that in both cases scaled linearly with the number of particles in the aggregate. Homotypic (with only one type of particle) suspensions displayed background levels of doublets ranging from 0.8% for pSA to 2% for pPEG-biotspD-biot suspensions usually had usually doublet levels around 1%. Triplets were very rare. The fluorescence plot of pSA showed an expected significant fluorescence increase (FL1 ) 195 au) in the presence of fluorescent biotin, whereas pD-biot and pPEG-biot fluorescence remained at background levels (around 7 au). This will allow additional clear discrimination between heterotypic doublets and background. To acquire the data at t ) 0, equal volumes of pSA
Figure 5. Particle scattering and fluorescence flow cytometry profiles. D-biotin-, PEG-biotin-, and streptavidin-grafted particles were recorded separately in the presence of 10-8 M FITC-labeled biotin. 5000 events were acquired. Side scattering (upper graphs) and fluorescence (FL1 channel) are shown versus forward scattering. Singlets (S) represented the major population (>98%) and are clearly distinguishable from doublets (D) and triplets (T), which appeared at double and triple scattering. The fluorescence parameter evidently differentiates streptavidin from biotin-grafted particles.
and pD-biot or pPEG-biot were carefully deposited in a sample tube at a particle concentration equal to 1.5 × 106 particles/mL with 10-8 M FITC-labeled biotin for immediate recording of the flow cytometry profiles (Figure 6). Next, pSA and pPEG-biot or pD-biot were sheared together in the cone-plate sample cell for a fixed time at a final concentration of 1.5 × 106 particle/mL (total particle concentration). The formation of molecular links between heterotypic particles was evaluated using the parameter ×c4, defined as the fraction of single beads in aggregates, or in other words, the fraction of missing singlets compared to the number of particles initially brought into contact. ×c4, regarded as a linkage index, was calculated from the biparametric flow cytometry dot plots (see Figure 6) giving the fluorescence per particle as a function of forward scattering as follows:
f)1-
N1F + N1W (N1F + N1W) + 2(N2F) + 3(N3F) + 4(N4F)
where F and W index fluorescent and “white” (nonfluorescent) regions defined according to their mean FL1 value (averaged over all events contained in the considered region). n ) 1, 2, 3, or 4 refers to the mean FSC value, which gives the size of the object, i.e., the number of particles in the aggregate. NnF (or NnW) is then the number of events contained in the indexed region. Figure 7 shows the time course plot of the fraction of aggregated singlets after application of a shear rate G ) 1200 s-1. The formation of true hybrid doublets was confirmed using epifluorescence microscopy. Sample images can be seen in Figure 8. The fraction of aggregates formed with the particles bearing a PEG-tethered biotin was markedly greater than that of the
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Figure 6. Fluorescence versus forward scattering dot plots to probe aggregate formation. pSA and pPEG-biot were mixed at 1.5 × 106 particle/mL (total concentration) and submitted to a shear stress at t ) 0 for various time periods. Here, dot plots are displayed before mixing (left plots), at t ) 0 just before shearing (middle plot), and after 1 min shearing at 1200 s-1 (right plot). Flow cytometry acquisitions were all performed in the presence of 10-8 M FITC-labeled biotin to reveal relevant hybrid aggregates.
Figure 7. Kinetics of 2D streptavidin-biotin bond formation. pDbiot or pPEG-biot were sheared in PBS buffer with pSA at 1200 s-1 for increasing time periods. Total particle concentration was equal to 1.5 × 106 particle/mL. The fraction of aggregated singlets for each time point was determined from the flow cytometry recordings as in Figure 6 and plotted as a function of shear time. Standard deviation was calculated from 4 to 8 independent experiments.
closely grafted biotin. The latter remained very low, around 0.1, only slightly above the aggregated fraction obtained with the rough, uncontrolled mixing (data not shown). In contrast, when pSA were sheared with the pPEG-biot, the fraction of hybrid aggregates increased, displaying an asymptotical behavior around ×c4 ) 0.65 after 2 or 3 min of shearing. In the meantime, no significant aggregate formation was observed when only one type of particle was subjected to this shear rate for any of the particles sampled. This demonstrates that the formed aggregates genuinely resulted from the formation of specific molecular links. The results clearly showed that the ligand tether played a crucial role in the establishment of stable links between two surfaces and that only the surface spaced out ligand allowed significant numbers of particles to assemble. The experiments were extended to shear rates ranging from 200 to 1200 s-1 to better understand the role of the applied force (stress) on the profile obtained. The curves depicting the kinetics of aggregate formation in Figures 7 and 9 show that, with pD-
Figure 8. Optical micrographs of pSA and pPEG-biot sheared together at 1200 s-1 for 1 min and added with fluorescent biotin. Bright field (A) and fluorescence (B) images were recorded. pSA are labeled with FITC-biotin. These micrographs show that doublets were actually hybrid doubletssonly one particle was labeled per doublet.
Figure 9. Kinetics of 2D streptavidin-biotin bond formation under several shear stresses for pPEG-biot. Same conditions as in Figure 7.
biot, there was no significant variation in the fraction of singlets in aggregated doublets with increasing shear rate: f remained low, from 0.06 to 0.09. In contrast, the curves with samples sheared with pPEG-biot all displayed the same behavior: an initial rapid linear rise in the fraction of singlets in aggregates,
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followed by a slower increase leading to a plateau at >3 min of shearing (Figure 9). Considering the shape of the aggregation-time curves, we hypothesized that the observed kinetics describe an equilibrium between bond formation and bond breakage. This was supported by reversibility tests performed by shearing sample first at 900 s-1 for 3 min and then at 200 s-1 for 5 min. Mean aggregated singlet fraction was found equal to 0.35, which is close to the value obtained by shearing the sample at 200 s-1 for 5 min only. We thus analyzed the data according to a very simple model where only the formation of doublets was taken into account. Indeed, in all experiments, only a small fraction of higher-order aggregates were present. An analytical equation was written which described the appearance of DAB doublets formed by the association of two different singlets, SA and SB, according to the following equilibrium, where kon and koff are the linkage and breakage rates, respectively kon
SA + SB 98 DAB 9 8 k
(1)
off
We wrote the special case where SA and SB concentrations are the same and equal to S0. It follows then that the rate of doublets appearing is equal to
dx ) kon(S0 - x)2 - koffx dt
(2)
where x is the doublet concentration. After integration, one obtains
x(t) ) x1
1 - e-kon(x2 - x1)t x1 1 - e-kon(x2 - x1)t x2
(3)
where x1 and x2 (0 < x1 < x2) are the solutions of the following quadratic equation:
(
)
koff x - x 2S0 + + S02 ) 0 kon 2
(4)
and may therefore be written as functions of kon and koff. Taking into account that x(t) ) f(t)S0 , we may fit the experimental data shown in Figure 9 to eq 3 in order to retrieve the kon and koff values. However, because x1 and x2 are themselves nonlinear functions of kon and koff, we decided on the simplest approach, which consists of determining kon and koff values from the initial binding phase and plateau values. We assumed that at the initial time the number of formed doublets is small, and the initial rate of doublet formation could be approximated as
dx ) kon‚S02 dt
(5)
kon is then given by the slope of ×c4(t), which is equal to kon‚S0. Next, we considered the plateau value of f(t), ×c4∞, which is equal to x∞S0, where x∞ is the plateau doublets’ concentration. We found x∞ by setting the left-hand side of eq 2 equal to zero and rearranged the result to solve for (koff/kon)
S02 koff ) x‚2S0 + kon x
(6)
which allowed, by knowing kon from the previous determination, calculation of the koff value.
Figure 10. Apparent on and off rate constants obtained from singlet pSA and pPEG-biot aggregation kinetics at various shear rates. A simple equilibrium model was used in order to extract the constants from the experimental data (see text for details).
The results are shown in Figure 10. kon values increased linearly with shear rate up to 1000 s-1 with a divergence to the higher values appearing at 1200 s-1. This deviation was low but statistically significant and may be due to secondary flows which affect the value of the shear rate. The evolution of koff was at first sight rather unexpected, since it appeared to decrease when shear rate increased. This behavior, discussed later, was ascertained experimentally from 8 to 10 independent measurements for each shear time and shear rate value.
Discussion We describe here a simple approach allowing for the evaluation of the kinetics of formation and breakage of a collection of specific molecular links bound to apposing surfaces under shear. We first demonstrated the clear-cut role of the flexible polymer tether in the ability to form linking bonds between apposing complementary surfaces at any tested shear rate. When biotin molecules were directly grafted onto the surface amine functions, the fraction of aggregated singlets remained low (
