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Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, Paris, France
Correspondence: Address reprint requests to Frédéric Pincet, Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France. Tel.: 33-144-32-2502; Fax: 33-144-32-3433; E-mail: pincet{at}lps.ens.fr.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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–6). In these experiments a microscopic but optically visible event, like the bending of a spring or the displacement of a bead, is detected in order to measure a force. The authors usually try to interpret their results at the molecular level in terms of intrinsic parameters of the bonds such as association and dissociation constants, binding energy, or energy landscape. Such interpretations in which the observation of a visible event is supposed to directly give information on properties at the nanometric level may sometimes be presumptuous. Subtle molecular mechanisms can render the problem much more complicated than expected and lead to erroneous conclusions with the usual analysis. Recent efforts have been made to refine this analysis (7–11).
Many measurements have been reported on the streptavidin-biotin bond (1,2,6,12). A comparative reading of these results shows that some of them, among the major ones, seem to be in complete contradiction: the force of the bond under given pulling conditions depends on the technique used. By doing an in-depth analysis of these measurements and conducting complementary experiments on functionalized DNA strands with a BFP, we show that this contradiction is due to the slow molecular rearrangement of the bond that takes time to reach its most stable state. This phenomenon had never been experimentally demonstrated at the single-molecule level before.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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) uses a force transducer made of a biotinylated red blood cell maintained by a glass micropipette and with a streptavidin-coated glass microbead attached on its top. The red blood cell is used as a spring of known stiffness k, which is tuned by the controlled aspiration pressure applied by the holding micropipette. The streptavidin-coated glass bead can be decorated with molecules of interest (here biotinylated DNA strands) which will be displayed on the tip of the force transducer (see Fig. 1). The glass bead also enables precise video tracking, because when observed with a slightly unfocused optical microscope, it displays a light spot with Gaussian intensity profile on its center.
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For BFP force-transducer and target latex-microbeads manipulations, micromanipulators were mounted on the stage of a Leica inverted microscope (DMIRB type, Leica, Solms, Germany). Glass micropipettes with inner diameter of 1.5–2.5 µm were attached and connected to homemade water manometers for pressure adjustment. The red blood cell membrane tension is set by the pipette aspiration pressure, and the spring constant of the cell is obtained at the beginning of each experiment for each cell by multiplying this pressure by a geometrical factor measured for each red blood cell with a calibrated program used with a video device coupled to the microscope (63x Leica objective with 1.5x supplementary lens, camera purchased from JAI, Yokohama, Japan). The micropipette holding the force transducer is coupled to a linear piezoelectric translator (Physik Instrumente, Karlsruhe, Germany) connected to a digital-analog converter connected to a personal computer. The DNA-coated bead on the top of the red blood cell is tracked by video processing with the camera connected to the microscope. The tracking procedure was kindly provided by V. Croquette and adapted to our device. Video tracking gives the bead position, whereas the piezoelectric translator provides the position of the extremity of the micropipette holding the red blood cell. The difference of these two positions gives the elongation of the red blood cell with an accuracy of a few nanometers. When multiplying it by the spring constant k of the red blood cell, the force exerted on the force transducer is obtained with an accuracy of a few picoNewtons. The desired loading rate is given by r = k x v, where v is the constant retraction speed set by the piezoelectric. This speed is adapted for each red blood cell. Effective loading rate was afterward verified on the force-extension curves.
Micropipettes were first obtained by elongating borosilicate glass capillaries (1-mm outer diameter, 0.78-mm inner diameter, Harvard Apparatus, Holliston, MA) with a micropipette puller (P-2000, Sutter Instrument, Novato, CA). Next, a custom-made microforge allowed opening the extremity of the micropipettes at the desired diameter.
Experiments were conducted in a chamber made of two glass coverslips facing each other where 
200 µL of fluid was held by capillary forces. Micropipettes could access to the chamber from its sides. Before red blood cells and beads introduction, the chamber was incubated for 1 h in phosphate-buffered saline (PBS 0.01 M, 150 mM NaCl, 290 mOsm, pH 7.4) with 5% bovine serum albumin (BSA, Sigma-Aldrich, Lyon, France). The chamber was next washed several times in PBS, and all experiments were conducted in PBS, pH 7.4, at room temperature.
Biocytin (Sigma-Aldrich) at a final concentration of 0.1 mg/ml was used to block the empty streptavidin sites.
Red blood cells were covalently linked with PEG-biotin polymers, following the protocol kindly provided by E. Evans. More details about this protocol can be read in Merkel et al. (2).
DNA-coated silica and latex microbeads (Fig. 2)
Amino silane groups (n-(2-Aminoethyl)-3-aminopropylmethydimethoxysilane, ABCR GmbH, Karlsruhe, Germany) were covalently bound to glass microbeads (uniform silica microspheres, mean diameter 3 µm, Bangs Laboratories, Fishers, IN). A mixture of Amine-reactive polyethylene oxide polyethylene glycol with biotin (NHS-PEG3400-biotin, Interchim, Montluçon, France) and Sulfo-MBS (Pierce, c/o Touzard et Matignon, Les Ullis, France) was then covalently bound to the silanized microbeads. The biotinylated microbeads were finally incubated in a 2 mg/mL streptavidin solution (Jackson Immunoresearch Laboratories, West Grove, PA). Beads were finally washed several times in PBS and stored in PBS at 4°C. J.-F. Allemand kindly provided 15-kb DNA strands that were biotinylated at one end with a single biotin (biotinylated ends were purchased from Roche, Nutley, NJ). The day before each experiment, streptavidin-coated silica beads previously prepared were incubated in a 48 µL of PBS + 2 µL of 0.8 ng/µL DNA solution overnight at 4°C under low agitation. It can be noted that the attachment between these DNA-coated beads and the biotinylated red blood cells was possible because the DNA beads still exhibited free streptavidin sites on their surface.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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,15) and widely studied (see for instance (1,2,6,16,17)). It is also often used to couple molecules. For instance, DNA stretching has been studied by grafting each extremity of the double strand to latex beads through a single streptavidin-biotin bond (18,19). After attachment to the beads, the DNA is stretched with a controlled pulling force. Up to 80 pN, the bonds are stable over 1 min, whereas, when the pulling force exceeds 100 pN, one of the bonds often breaks after a few seconds. This strongly contradicts another work where the rupture force of the bond was measured with a BFP (2). In the latter experiments, two glass beads, one coated with ligand (biotin) and the other one with receptor (streptavidin), are brought into contact to allow a single bond to form. An increasing traction is then immediately applied on the bond until separation of the molecules. The rate at which the traction is applied (variation of the force with time, df/dt) is called the loading rate. Because thermal fluctuations will ultimately be responsible for bond breakage when traction is applied, two rupture force measurements on the same bond will give different results. A consequence of this nonreproducibility is that the strength of the bond is not characterized by a given force but by a distribution of the rupture force that depends on the loading rate. In the BFP experiments, rupture force distribution of the streptavidin-biotin complex was obtained for several loading rates. A convenient way of visualizing the robustness of the bond is to plot the most likely rupture force as a function of the loading rate (Fig. 3). From the BFP measurements, it can be deduced that for a pulling force of 75 pN, an upper bound for the lifespan of the bond is 75 ms, which is at least two orders-of-magnitude smaller than the one obtained with the DNA experiment. Hence, one has to reach the senseless conclusion that for a given constant pulling force, the lifespan of the bond will depend on the technique used to apply the force. This is the streptavidin-biotin paradox. The rest of the article is devoted to understanding its origin.
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). From this trajectory, they approximated the neighborhood of the minima in the energy landscape (Fig. 4). This study indicates that there are three minima. The two intermediate metastable states can be found at 0.3 nm and 1.0 nm from the deepest one. The presence of three minima indicates that there are also three barriers in the energy landscape. Their positions cannot be accurately defined from molecular dynamics simulations since they correspond to locations that are only transiently visited by the biotin during the extraction process. Even though these are not actual simulations of the extraction of a biotin from a streptavidin pocket, it can be used to approximate it for several reasons. Firstly, streptavidin and avidin structures are very similar and have very close affinities with biotin (20,21). Secondly, the presence and positions of the three barriers seems to be confirmed by Grubmüller et al. (16), who have conducted simulations on streptavidin without deriving an approximate energy landscape.
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). Transitions from the deepest metastable state (i.e., the second deepest energy minimum) outward to the second metastable state as well as forward to the deepest energy minimum were observed, indicating the presence of three energy barriers. The transfer rates were 5.3 s–1 and 1.3 s–1, respectively. From these two studies, it is clear that three main energy barriers can be observed during the rupture of the streptavidin-biotin complex.
Can the history of the bond be at the origin of the paradox?
It is commonly admitted that each linear regime in the curve of the most likely rupture force as a function of the logarithm of the loading rate corresponds to a given barrier in the energy landscape (3–5,22,23). Even though this assumption has been somewhat shaken recently (7,24), it can be claimed that n different regimes correspond at most to n different barriers (8). Two linear regimes can be found in Fig. 3. Thus, in the BFP experiments, only two barriers are observed in the energy landscape of the streptavidin-biotin bond. As molecular dynamics simulations and flow chamber data showed that three barriers are present, one of these barriers is missing in the BFP measurements. To determine which one, we have reanalyzed in details the distributions of rupture forces for all the loading rates. These distributions can be theoretically predicted by applying reaction-rate theory, also known as Kramers' theory (25–27), to the energy landscape of the bond. To proceed with the analysis, it is necessary to describe this theory in the case where there are two barriers in a one-dimensional energy landscape. The probabilities of being in each of the two energy minima are given by
 | (1a) |
 | (1b) |
if(f) indicates the transition rates from a minimum i to a neighbor minimum j, 3 referring to the unbound state. When the landscape is locally approximated by an harmonic potential around each minimum and each maximum, ij(f) can be written as
 | (2a) |
 | (2b) |
is a damping coefficient, the subscripts mi and bi refer, respectively, to the ith metastable state and to the ith barrier, the 
-values are the local curvatures of the landscape, and E(x,f) the energy of the potential tilted by the force—i.e., E(x,0) – x x f. It is important to note that the local curvatures are necessary to predict the positions xmi(f) and xbi(f) and therefore the associated energies Emi(xmi(f),f) and Ebi(xbi(f),f). The diffusive microscopic times are usually written
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 | (3b) |
To suppress any further reference to time, the set of master equations, Eqs. 1a and 1b, can equivalently be rewritten as
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 | (4b) |
The overall evolution will be fully determined by the knowledge of the initial values of the probabilities, P1(0) and P2(0). The force distribution is then given by
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From Eqs. 2a, 2b, 4a, 4b, and 5, it is clear that the complete knowledge of the energy landscape is sufficient to predict the theoretical rupture force distribution. Since the measurements are not infinitely accurate, an experimental error has to be added, which will slightly widen the force distribution. For our purpose, we have chosen a Gaussian error with a reasonable width (see Fig. 5). We have tried to apply Kramers' theory to each possible pair of barriers of the energy landscape. In each case, we have varied the different parameters (i.e., height, position, and curvature for each minimum and each barrier) with the constraint that they should remain consistent with the molecular dynamics simulations. The only way by which the experimental rupture force distributions obtained by Merkel and co-workers (2) could be fitted was by keeping the two outer barriers from the molecular dynamics and assuming that the bond is in the second deepest minimum at the start of the separation process (values of the parameters are given in Table 1). The predicted rupture force distributions are given in Fig. 5. The agreement with the experimental histograms is almost perfect for all the loading rates. Such a good prediction could not have been achieved otherwise. Therefore, in the BFP experiment the streptavidin-biotin bond did not reach its deepest minimum. This may be the difference between these measurements and the DNA stretching technique. Intuitively, it can be understood that, in the BFP, the bond is given a fraction of second to form, whereas for the study of DNA stretching, the DNA strand has been attached to the streptavidin-coated beads for several minutes before any pulling force was applied. Hence, we can assume that the history of the bond is at the origin of the streptavidin-biotin paradox.
Experimental validation and complete description of the energy landscape
To test this assumption we have conducted experiments in which both experimental approaches were combined: we have used the BFP technique with streptavidin-coated beads that had previously been incubated with DNA strands biotinylated on one end (see Materials and Methods and Fig. 1). As the streptavidin-biotin bonds have been formed a long time before the pulling process starts, the rupture forces should be larger than the ones obtained previously with the BFP. However, as it is important to make a large number of measurements (a least 100 per loading rate) to obtain good statistics and smooth distributions, it is necessary to keep the same bead over several approaching-separation cycles. Thus, it can happen that a DNA strand that had previously been detached from the bead reattaches through a newly formed streptavidin-biotin bond. Consequently, the expected distribution should present two peaks: one corresponding to the old bonds, like in the DNA stretching studies, and one corresponding to the new bonds, like in the previous BFP measurements. This is exactly what we have observed (Fig. 6). By adding biocytin (0.1 mg/ml) in the solution to block all the available streptavidin sites, the first peak disappears, confirming that it was due to the formation of new streptavidin/biotin bonds during the measurements (Fig. 7). The experimental distributions of Fig. 6 can be predicted using the complete energy landscape of Fig. 4 with initial conditions in which the probability to be in the deepest minimum is 0.5. These predictions are obtained using Kramers' theory with an extra minimum and the corresponding probability P3(f) in Eqs. 4a and 4b,
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| (6a) |
 | (6b) |
 | (6c) |
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–c) to the energy landscape with the initial conditions P1(0) = P2(0) = 0 and P3(0) = 1. The corresponding curves are given in Fig. 8. They show that it takes >10 s to fill up the deepest state. This result confirms that in the BFP, when the bonds are just formed, they are only in the second deepest minimum. However, we are not able to understand one subtle detail at small loading rates (typically <100 pN/s). In these cases, the potential is not tilted too quickly by the pulling force, which is applied sufficiently slowly. Then, the bond still has a chance to reach the deepest minimum even after the separation process has started. One explanation can be suggested to understand this problem. It is related to the geometry of the system, in which both the streptavidin and the biotin were grafted on glass beads. It is possible that because of geometrical constraints, such as lever effects (28), random pulling forces were applied to the bond. The time required to reach the deepest minimum was then increased, preventing the bond from reaching the deepest minimum during the pulling phase.
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).
Finally, rupture forces stronger than the ones observed in Merkel et al. (2) have been measured with an AFM (12). In this latter case, their values are comparable to the ones we obtained for the second peaks in Fig. 6 (see Fig. 11 for a comparison of the forces). Therefore, in these AFM experiments they seem to have reached the deepest minimum. As we do not know their precise experimental protocol, we cannot explain how they managed to reach it.
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,30). Here, we show that the history of the bond during the bond formation phase is also crucial. Our results also indicate that the time a system takes to reach equilibrium can be relevant on experimental timescales and may be too often neglected in many fields such as chemistry or biology where association constants are commonly used. Therefore, there should be not just one association constant per molecular complex, but one per metastable state, relevant in the timescales of the considered process. Of course, the higher the barriers, the longer it takes to fill up the minima. |
ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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This work was partly funded by a University Paris 7 BQR contract.
Submitted on June 2, 2005; accepted for publication August 22, 2005.
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REFERENCES |
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2. Merkel, R., P. Nassoy, A. Leung, K. Ritchie, and E. Evans. 1999. Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy. Nature. 397:50–53.[CrossRef][Medline]
3. Chen, S. Q., and T. A. Springer. 2001. Selectin receptor-ligand bonds: formation limited by shear rate and dissociation governed by the Bell model. Proc. Natl. Acad. Sci. USA. 98:950–955.
4. Hanley, W., O. McCarty, S. Jadhav, Y. Tseng, D. Wirtz, and K. Konstantopoulos. 2003. Single molecule characterization of P-selectin/ligand binding. J. Biol. Chem. 278:10556–10561.
5. Li, F. Y., S. D. Redick, H. P. Erickson, and V. T. Moy. 2003. Force measurements of the 
5ß1 integrin-fibronectin interaction. Biophys. J. 84:1252–1262.
6. Pierres, A., D. Touchard, A.-M. Benoliel, and P. Bongrand. 2002. Dissecting streptavidin-biotin interaction with a laminar flow chamber. Biophys. J. 82:3214–3223.
7. Hummer, G., and A. Szabo. 2003. Kinetics from nonequilibrium single-molecule pulling experiments. Biophys. J. 85:5–15.
8. Derenyi, I., D. Bartolo, and A. Ajdari. 2004. Effects of intermediate bound states in dynamic force spectroscopy. Biophys. J. 86:1263–1269.
9. Raible, M., M. Evstigneev, P. Reimann, F. W. Bartels, and R. Ros. 2004. Theoretical analysis of dynamic force spectroscopy experiments on ligand-receptor complexes. J. Biotechnol. 112:13–23.[CrossRef][Medline]
10. Friedsam, C., A. K. Wehle, F. Kuhner, and H. E. Gaub. 2003. Dynamic single-molecule force spectroscopy: bond rupture analysis with variable spacer length. J. Phys. Condens. Mat. 15:S1709–S1723.[CrossRef]
11. Kuhner, F., L. T. Costa, P. M. Bisch, S. Thalhammer, W. M. Heckl, and H. E. Gaub. 2004. LexA-DNA bond strength by single molecule force spectroscopy. Biophys. J. 87:2683–2690.
12. Yuan, C. B., A. Chen, P. Kolb, and V. T. Moy. 2000. Energy landscape of streptavidin-biotin complexes measured by atomic force microscopy. Biochemistry. 39:10219–10223.[CrossRef][Medline]
13. Evans, E., K. Ritchie, and R. Merkel. 1995. Sensitive force technique to probe molecular adhesion and structural linkages at biological interfaces. Biophys. J. 68:2580–2587.
14. Green, N. M. 1975. Avidin. Adv. Protein Chem. 29:85–133.[Medline]
15. Chilkoti, A., and P. S. Stayton. 1995. Molecular origins of the slow streptavidin-biotin dissociation kinetics. J. Am. Chem. Soc. 117:10622–10628.[CrossRef]
16. Grubmüller, H., B. Heymann, and P. Tavan. 1996. Ligand binding: molecular mechanics calculation of the streptavidin-biotin rupture force. Science. 271:997–999.[Abstract]
17. Izrailev, S., S. Stepaniants, M. Balsera, Y. Oono, and K. Schulten. 1997. Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys. J. 72:1568–1581.
18. Smith, S. B., Y. J. Cui, and C. Bustamante. 1996. Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules. Science. 271:795–799.[Abstract]
19. Baumann, C. G., S. B. Smith, V. A. Bloomfield, and C. Bustamante. 1997. Ionic effects on the elasticity of single DNA molecules. Proc. Natl. Acad. Sci. USA. 94:6185–6190.
20. Livnah, O., E. A. Bayer, M. Wilchek, and J. L. Sussman. 1993. Three-dimensional structures of avidin and the avidin-biotin complex. Proc. Natl. Acad. Sci. USA. 90:5076–5080.
21. Freitag, S., I. LeTrong, L. Klumb, P. S. Stayton, and R. E. Stenkamp. 1997. Structural studies of the streptavidin binding loop. Protein Sci. 6:1157–1166.[Abstract]
22. Evans, E., and P. M. Williams. 2002. Dynamic force spectroscopy. In Physics of Bio-Molecules and Cells. F. Julicher, P. Ormos, F. David, and H. Flyvbjerg, editors. Springer Verlag, Berlin, Germany. 145–204.
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25. Kramers, H. A. 1940. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica (Utrecht). 7:284–304.[CrossRef]
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29. Evans, E., A. Leung, V. Heinrich, and C. Zhu. 2004. Mechanical switching and coupling between two dissociation pathways in a P-selectin adhesion bond. Proc. Natl. Acad. Sci. USA. 101:11281–11286.
30. Marshall, B. T., K. K. Sarangapani, J. Lou, R. P. McEver, and C. Zhu. 2005. Force history dependence of receptor-ligand dissociation. Biophys. J. 88:1458–1466.
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where the Gaussian error has a width 
(f), which is inspired by the experiments. Briefly, the force f is equal to kx, where k is the spring constant and x the spring extension. Therefore, df = kdx + xdk = kdx + fdk/k. The value dx is a constant due to the thermal fluctuations and the accuracy on the detection of the position of the bead in the BFP experiments; thus kdx is of the order of 100 pN/µm x 10 nm = 1 pN. The error on k is mainly due to the poor accuracy on various length measurements (inner diameter of the pipette, diameter of the red blood cell, and diameter of the contact between the red cell and the bead, all of the order of 1 µm); it can be estimated to be between 10 and 30%. Following these constraints, we chose 
, P2(0) = 1–
