Dimerization of Cell-Adhesion Molecules Can Increase Their Binding

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Dimerization of Cell-Adhesion Molecules Can Increase Their Binding Strength Wenmao Huang,† Meng Qin,† Ying Li,*,‡ Yi Cao,*,† and Wei Wang*,† †

Collaborative Innovation Center of Advanced Microstructures, National Laboratory of Solid State Microstructure and Department of Physics, Nanjing University, Nanjing 210093, China ‡ Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, School of Environmental Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China S Supporting Information *

ABSTRACT: Cell-adhesion molecules (CAMs) often exist as homodimers under physiological conditions. However, owing to steric hindrance, simultaneous binding of two ligands to the homodimers at the same location can hardly be satisfied, and the molecular mechanism underlying this natural design is still unknown. Here, we present a theoretical model to understand the rupture behavior of cell-adhesion bonds formed by multiple binding ligands with a single receptor. We found that the dissociation forces for the cell-adhesion bond could be greatly enhanced in comparison with the monomer case through a ligand rebinding and exchange mechanism. We also confirmed this prediction by measuring dimeric cRGD (cyclic Arg-Gly-Asp) unbinding from integrin (αvβ3) using atomic force microscopy-based single-molecule force spectroscopy. Our finding addresses the mechanism of increasing the binding strength of cell-adhesion bonds through dimerization at the single-molecule level, representing a key step toward the understanding of complicated cell-adhesion behaviors. Moreover, our results also highlight a wealth of opportunities to design mechanically stronger bioconjunctions for drug delivery, biolabeling, and surface modification.

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of 0.5−5 pN s−1, the bond rebinding changes the linear relationship between rupture forces and the logarithm of loading rates, leading to the saturation of bond strength.21,22 Such nonlinear force spectra can also be explained as the asynchronized rupture of multiple individual bonds.21,23 Nonetheless, these two kinds of mechanisms are not mutually exclusive. Instead, they can complementarily and collectively determine the stability of adhesion bonds. It has long been noticed that many CAMs, such as fibronectin, cadherin, and PSGL-1, exist as homodimers in their biological settings24−27 (Figure 1a). In addition, researchers have started constructing a dimer or even a trimer of artificial CAMs for biotechniques and medical research with a cyclic RGD (Arg-Gly-Asp, the integrin-binding site) dimer as a representative example.28−30 A rationale for such a design is that the binding affinity is increased by the number of binding sites. Although formation of multiple bonds could significantly increase the binding affinity, these CAM dimers can hardly form two bonds in the presence of steric hindrance and relatively low local concentrations of CAMs on the surface. Recent studies using surfaces with geometrically controlled RGD patterns revealed that when ligands are presented below a critical length of ∼60 nm, cell adhesion can be greatly

INTRODUCTION Cell-adhesion molecules (CAMs) are proteins involved in cell− cell or cell−extracellular matrix (ECM) adhesions. They are responsible for many cellular functions, including cell migration, growth, differentiation, and apoptosis.1−3 They also define cell shape and cell−cell/ECM contact, which are essential for tissue patterning and structure.4 Because CAMs are subjected to mechanical forces in biological settings, the mechanical stability of adhesion bonds formed between CAMs and their binding partners is obviously of great importance for functions. However, our current knowledge on the mechanics of cell adhesion is still limited. The mechanical strength of an individual adhesion bond can be directly measured using various single-molecule techniques, such as magnetic tweezers, optical tweezers, biomembrane force apparatus, and atomic force microscopy (AFM).5−13 Most of the measurements were recorded under nonequilibrium conditions. To obtain the free energy landscape underlying the mechanical dissociation (e.g., free energy barrier ΔG⧧u and the width of the potential well x⧧u ), dynamic force spectroscopy has been widely used.14−18 In typical force spectra, the rupture forces of a single bond are logarithmically proportional to the loading rate r (e.g., f ∝ ln r) as explained by Bell−Evans model,19,20 where r is defined as the rate of force change over time (e.g., r = df/dt). Recently, it has been found that such a relationship is valid only at high loading rates for slip bonds. Under physiological conditions with much lower loading rates © XXXX American Chemical Society

Received: December 7, 2016 Revised: January 19, 2017 Published: January 22, 2017 A

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Figure 1. Effect of CAM homodimers on bond strength. (a) Illustration of some typical CAM homodimers. (b) For CAM monomer (single ligand) unbinding from a receptor at force f, the bond ruptures with the force-dependent dissociation rate constant ku = k0u exp(βf x⧧u ) and rebinds with the association rate constant kb = k0b exp(−βf x⧧b ), β = 1/kbT. For CAM homodimer (dimeric ligand), the bound one has the same ku and k1b as the single ligand and the other one contributes additional force-independent association rate constant k2b = k0b. (c) Unbinding rate ku (solid blue line), rebinding rates of the first and second ligands (k1b, dashed red line; k2b, dashed green line), and the overall rebinding rate kb (solid black line) were numerically simulated using typical parameters of k0u = 0.1 s−1, x⧧u = x⧧b = 0.01 nm, and k0b = 104 s−1.

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enhanced.31,32 It is still perplexing how dimerization or high local concentrations increase the binding strength of celladhesion bonds. Here, we provided a new theoretical framework that can explain the advantage of CAM dimers for cell adhesion. We showed that the cell-adhesion bonds formed by CAM dimers can have much higher dissociation energies than those formed by monomers under physiological conditions because the unbound CAM in the dimer can exchange with the bound one to greatly increase the rebinding rate; especially, the saturation forces (equilibrium forces) in the dimer cases can be reached at much higher loading rates, covering the full physiologically relevant range, as compared with the monomer cases. To validate these predictions, we studied the unbinding of RGD peptide with integrin (αvβ3) using AFM-based force spectroscopy. Our results indicated that the saturation force for the RGD dimer can be as high as ∼120 pN and ∼80% higher than the saturation force for the RGD monomer. On the basis of the theoretical framework, we found that to achieve the same equilibrium adhesion force, the rebinding rate in the dimeric RGD case can be 2-fold slower than that in the monomeric RGD case, which is equivalent to a decrease in the binding energy by ∼12 kJ/mol. Our theoretical framework also predicted that dimers provide the optimum case for high mechanical stability of adhesion bonds. The equilibrium adhesion force does not further increase with the increase in the CAM number for a single-binding site, which is consistent with the natural situation.

EXPERIMENTS AND METHODS

Materials. Integrin αvβ3 was purchased from R&D. Mal-PEG-NHS (MW 3400) was purchased from NanoCS. Diisopropylethylamine, 2(1H-benzotriazol-1-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate, and (3-mercaptopropyl) trimethoxysilane (MPTMS) were purchased from Sigma-Aldrich. Fmoc-Gly-OH, Fmoc-Arg(Pbf)-OH, Fmoc-Lys(Boc)-OH, Fmoc-DPhe-OH, Fmoc-Asp(OtBu)-OH, and Boc-Glu(ONHS)-ONHS were purchased from GL Biochem. Synthesis of Peptides. Synthesis of peptides cRGD and biscRGD followed a previously published procedure.33 The peptide structures and detailed synthetic procedures of cRGD and bis-cRGD can be found in Figure S1. Functionalization of Substrates and Cantilevers. Glass substrates were washed with water several times, soaked in chromic mixture overnight, thoroughly washed with Milli-Q water, acetone, and ethanol, and then dried under a steam of nitrogen to produce a hydroxyl-exposed surface. These substrates were immersed into a dimethyl sulfoxide (DMSO) solution containing 1% (v/v) of MPTMS for 1 h, cleaned, heated in an 80 °C oven for another 1 h, rinsed with dichloromethane several times, and dried under a nitrogen flow. Then, the substrates were immersed in a toluene solution containing 0.5 mM Mal-PEG-NHS/Mal-PEG-CH3 (MW: 3400 Da) (1:10) for 1 h. After being rinsed with toluene, ethanol, and Milli-Q water, the substrates were dried under nitrogen and then put into 0.1 μM integrin αvβ3 1× PBS buffer for half an hour at room temperature. The integrin-coated substrates were washed with 1× PBS several times and then stored in phosphate-buffered saline (PBS) at 4 °C before use. Standard silicon nitride (Si3N4) cantilevers were purchased from Bruker (type: MLCT). The cantilevers were first cleaned with Milli-Q water, then placed in an O3 generator under UV illumination at 95 °C B

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for 20 min. After that, the cantilevers were immersed in 1% (v/v) MPTMS methylbenzene for 1 h for sulfhydrylation. Next, they were rinsed with Milli-Q water, dried under nitrogen, and immersed in a DMSO solution containing 0.5 mM Mal-PEG-NHS (MW: 3400 Da) for 1 h. Then, the cantilevers were washed with DMSO and ethanol, dried under nitrogen, and immersed into PBS buffer containing 0.01 mM peptides for 0.5 h. The resultant peptide-coated cantilevers were ready for single-molecule experiments. Single-Molecule AFM Experiment and Data Analysis. Singlemolecule AFM experiments were carried out on a commercial AFM (JPK Force Robot 300) at room temperature (∼22 °C). The D cantilevers (spring constant ∼0.05 N/m) were used in all experiments, and the spring constant was calibrated using equipartition theorem for each experiment. The experiments were undertaken in 1× PBS buffer at pH 7.4. During each single-molecule force spectroscopy (SMFS) experiment, the cantilever was brought into contact with the surface at a contact force of ∼500 pN for ∼0.5 s to bind the RGD peptide at the end of the cantilever tip to the integrin surface and pulled back to obtain the force−extension curves. Furthermore, all pulling-speed experiments were carried out using 50, 100, 200, 400, 1000, 1600, 3200, 6400, and 10 000 nm s−1. All force curves were collected using commercial software from JPK and analyzed using a custom-written protocol in Igor 6.0 (WaveMetrics, Inc.). We converted pulling speeds to loading rates following a published procedure.34 We first converted force−extension curves to force−time curves. Then, the average slope (k) of the force−time curves right before the rupture event was taken to estimate the average loading rate for the nonequilibrium constant-speed pulling. In this way, the contribution of the stiffness of the whole mechanical linkage, such as the cantilever, the PEG linker, and the ligand−receptor, to the loading rates was considered together.

dPb/dt = −k u(t )Pb +

(2)

i=1 i

i

where kb (t) and Pu are the instantaneous binding rate constant and unbinding probability of the ith CAM. Note that Σin= 1Pu i = 1 − Pb and the binding probability for each CAM are proportional to the binding rate constant

Pbi:Pb j = μk bi:k b j

(3)

In the simple case that CAMs form homomultimers, μ = 1. Therefore, the probability density of forming the cell-adhesion bond can be expressed as n

n

dPb/dt = −k u(t )Pb + [∑ k bi(t )2 /∑ k b j(t )](1 − Pb) i=1

j=1

(4)

Compared with eq 1, the overall rebinding rate constant depends on all CAMs at the binding site, not just on the single CAM that forms adhesion bond with the binding partner. In other words, the increased “local concentration” of ligands in the vicinity of the receptor site leads to the increase in the rebinding rate constant. The transition rate constants kb(t) and ku(t) are dependent on the force applied to the bond at time t, describing the dynamics of bonds under increasing force. To simplify the derivation, they are replaced by kb( f) and ku(f) hereafter. Because the pulling potential varies with displacement, force constantly modifies the shape of the free energy landscape (barrier height and position). However, as pointed out by Evans,38 the intrinsic bond potential is highly curved, and thus the position of the barrier remains approximately unchanged during pulling and the barrier height is lowered proportionally to a fixed transition distance. The potential for rebinding is dependent on the stiffness of the pulling device and can also be assumed to be unchanged if the stiffness of the pulling device is high.12 Therefore

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RESULTS AND DISCUSSION Theoretical Model. In real cell-adhesion bonds, force is transduced to the CAMs through the elastic deformation of the cell or ECM.35,36 In SMFS experiments, force is transduced to the CAMs through a polymer connecting to an AFM cantilever, a biomembrane force probe, a magnetic bead, or an optical trap.7 Because the real cell adhesion is analogous to the singlemolecule pulling experiments, we use the single-molecule AFM experiments as a representative example for the development of our theoretical framework (Figure 1b). In all of these conditions, the energy landscape is the sum of the bond potential and the pulling potential (i.e., the elastic energy stored by the molecular linker and the spring of the pulling apparatus). As pointed out by Noy and Friddle, pulling creates a second minimum when the loading rate is higher than a certain threshold, which is typically satisfied in single-molecule AFM experiments.21 Therefore, the whole bond system comprises two states divided by a single energy barrier: the bound state “b” describing the formed bond and the unbound state “u” describing the broken bond where the system fluctuates in the parabolic well of the transducer. The barrier crossing is mainly driven by thermal fluctuation, and the effect of external force is mainly to modify the shape of the potential surface. The probability of the bond residing in the bound state Pb can be described by the Markov equation of a two-state process37 dPb/dt = −k u(t )Pb + k b(t )Pu

∑ k bi(t )Pui

⎛ fx ⧧ ⎞ k u(f ) = k u0 exp⎜⎜ u ⎟⎟ ⎝ k bT ⎠

(5)

⎛ −fx ⧧ ⎞ b ⎟⎟ k b(f ) = k b0 exp⎜⎜ ⎝ k bT ⎠

(6)

where k0u and k0b are the intrinsic unbinding and binding rate constants of the cell-adhesion bond, respectively, kbT is Boltzmann’s constant times the absolute temperature as the scale of energy, and x⧧u and x⧧b are the distances from the freeenergy minima of the bound and unbound states, respectively, to the barrier along the direction of force. Although the shape of the free-energy landscape in our model is slightly different from that in Noy’s21 and Li’s22 models, it can adequately reproduce the logarithmic increase in the unbinding force at high loading rates and saturation unbinding force at low loading rates from experiments. In our model, we assumed that the rebinding of the free ligands is not diffusion-controlled to simplify the calculation. Chen and co-workers have provided an excellent theoretical model to consider diffusion on the rebinding rate,39,40 which can be incorporated in our model in the future. It is worth mentioning that the force-independent transition distance based on Bell’s model is valid only for the rebinding events with a very short rebinding distance. Recent

(1)

where kb(t) and ku(t) are the instantaneous binding and unbinding rate constants, respectively, and Pu is the probability of the bond residing in the unbound state. Considering the scenario that a cell-adhesion bond is formed by a multimer comprising n CAMs and a single-binding partner, the probability density of forming the cell-adhesion bond dPb/dt is represented by the differential equation C

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Figure 2. SMFS experiment of RGD unbinding from integrin αvβ3. (a) PEG linker was used to attach the RGD peptides and integrin, respectively, to the AFM tip and substrate. (b) Typical curves of approaching (gray line) and retraction (green line) traces for cRGD unbinding at a pulling speed of 200 nm s−1. Red lines are the wormlike chain fittings with a persistence length of 0.4 nm and a contour length of ∼50 nm, based on the physical properties of PEG. (c) Force curves for bis-cRGD under the same conditions, and wormlike chain fittings are shown in black. (d) Histogram of cRGD (red) and bis-cRGD (black) unbinding forces at 200 nm s−1. The solid lines are calculation-fitted dynamic force spectra, showing an average force increase from 103.83 ± 2.7 to 124.45 ± 4.4 pN when ligands unbind from integrin αvβ3 (mean ± SEM). (e) Mean rupture forces of two RGD peptides at different loading rates. Numerical simulation fitting was at k0u = 0.5 s−1, k0b = 700 s−1, x⧧u = 0.25 nm, and x⧧b = 0.3 nm.

affinity.43,44 cRGD is well-known for its high binding affinity to integrin αvβ3 (one member of the integrin family),45 and it has been reported that dimeric cRGD in the vicinity of the receptor-binding site could lead to enhanced binding strength.46 Two different ligands cRGD and bis-cRGD were linked through the amino group to N-hydroxysuccinimide (NHS)−polyethylene glycol (PEG)-functionalized cantilevers, respectively, and integrin αvβ3 was anchored on the substrate surface using molar excess monofunctional PEG to compete with bifunctional PEG to reduce labeling concentration and to avoid nonspecific interactions (Figure 2a). Because the two cRGD rings in bis-cRGD are very close to each other and the size of integrin on the substrate is quite bulky, it is impossible for bis-cRGD to form two adhesion bonds with a single integrin. The single-molecule unbinding experiments were conducted at room temperature in 1× PBS buffer at pH 7.2. A negative control experiment without integrin αvβ3 coated on the surface showed clean force traces without any force peaks (Figure S2). The force extension traces were analyzed using the wormlike chain fitting (Figure 2b,c). The histogram of single force peaks showed the total length of the linkers ∼50 nm with a persistence length of ∼0.38 nm (Figure S3). Such a mechanical feature is consistent with that for a single PEG chain, confirming that a single bond is ruptured in the pulling experiments in which we observed a higher rupture force for bis-cRGD at a pulling speed of 200 nm s−1 (103 ± 2.7 vs 124 ± 4.4 pN; mean ± SEM, Figure 2d). If there was no rebinding from the free cRGD to integrin, we would have observed the same rupture forces for cRGD and bis-cRGD. Therefore, our results strongly suggest that the rebinding from the neighboring

studies have shown that for rebinding or refolding involving a large conformational change, a more general Arrhenius law could provide better estimation of force-dependent rebinding rates.41,42 Nonetheless, the simplification did not change the physical picture of our model in any important ways. The presence of a second unbound CAM at the same celladhesion bond could greatly increase the effective rebinding rate. Once the adhesion bond is broken, either the CAM that is subjected to force or the neighboring CAM that is free in solution can rebind back to the binding partner (Figure 1b). However, because the second CAM is not subjected to force, its rebinding rate is force-independent and is constantly higher than that for the one bearing force based on eq 4 (Figure 1c). Therefore, it has a higher chance to rebind to the binding partner, leading to the ligand exchange. Certainly, CAM dimers could greatly increase the overall rebinding rates, leading to a higher saturation force and longer lifetime of the bond, which is confirmed by the numerical simulation (Figure 1c). SMFS. We then verify this prediction experimentally using AFM-based SMFS. We used cyclic RGD (cRGD) and cRGD (bis-cRGD) dimers as the model of the CAM monomer and CAM dimer. The structure and detailed synthetic procedure of cRGD and bis-cRGD can be found in Figure S1. It is worth mentioning that bis-cRGD is not a perfect analog of natural CAM dimer because the space between RGD is shorter than that in the natural fibronectin dimer. However, we chose biscRGD in this study because it provides a simple system to verify our theoretical model and avoids some potential complexity of natural fibronectin, such as bulky size, multiplemodular structure, and force-dependent integrin-binding D

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Figure 3. Predictions of the intrinsic properties for bis-cRGD based on our model. (a) Relationship between rebinding rate constant k0b and the increase in the rupture force f 0 and the saturation force f ′0 with the rebinding rate constant k0b. (b) Δ saturation force Δf = f ′0 − f 0 increases with k0b with a logarithmic relationship. (c) Theoretically predicted unbound state probability and (d) histogram probability of cRGD, bis-cRGD, and cRGDn at a pulling speed of 400 nm s−1. The lifetime and saturation unbinding force do not further increase with further increase in the number of ligands to 100.

appreciated that the activated integrin has higher affinity.48 For inactivated integrin, the ligand-binding pocket is oriented backward to the pulling direction, which impedes ligand engagement.49,50 The chances to rupture the inactivated and activated integrin−RGD complexes should follow the Boltzmann distribution based on their differential binding affinity. Because the activated conformation has much higher affinity, we believed that most of the events we measured were originated from the activated conformation. Therefore, in all rupture force histograms, we observed only a single force distribution instead of two. Nonetheless, the different binding affinities between activated and inactivated integrin will not change the ligand-exchange mechanism in our model and the major conclusion of this study. Theoretical Predictions. Our model also allows us to make a few predictions using numerical simulation. First, the increase in saturation force by dimerization depends on the intrinsic rebinding rate. As shown in Figure 3a,b, the saturation forces increase monotonically with the rebinding rate constant k0b with a logarithmic relationship. The loading rate at which the saturation force can be reached also increases by more than 1 order of amplitude when a dimer is used. A similar prediction was shown in Li and Ji’s paper: the bond strength at an ultralow loading rate (saturation force) significantly increased with an increasing rebinding rate. However, in their model, the forcedependent rebinding behavior was modeled by a different energy landscape shape with different parameter sets. It is difficult to quantitatively compare the saturation forces predicted by their model and ours.51 Second, dimers provide the optimum situation for the high binding force without wasting too many free ligands. As shown in Figure 3c,d, the

force-free ligand can greatly affect the dissociation force at low loading rates. The rupture force distributions can be reproduced using eq 4 with an unbinding rate constant k0u = 0.5 s−1, binding rate constant k0b = 700 s−1, unbinding distance x⧧u = 0.25 nm, and binding distance x⧧b = 0.3 nm. Those parameters were close to some previous reports on the rate constant and binding distance of RGD.43,47 The dynamic force spectra for both cRGD and bis-cRGD are shown in Figure 2e. In all experimentally accessible loading rates (>100 pN s−1), the average rupture forces for cRGD increase logarithmically with the increase in the loading rates, indicating that the saturation force is not reached at these loading rates. For bis-cRGD, the slope of average rupture forces versus ln r is similar to that for cRGD, indicating that at high loading rates, the effect of rebinding is neglectable. However, at low loading rates of less than 2 × 104 pN s−1, we clearly observed the nonlinearity of the force−ln v relationship. The rupture forces do not change much at low loading rates and gradually get saturated at an asymptotic value. Although such a saturation force was predicted by a few models previously, we provide the first theoretical model and experimental evidence that the presence of a neighboring free ligand can greatly increase the saturation force and make it reachable at higher loading rates. Moreover, we can use the same fitting parameters for reproducing the rupture force distributions in Figure 2d to numerically fit the dynamic force spectra for both cRGD and bis-cRGD using our model. This again provides strong support to our theoretical model. In our single-molecule force experiment, we used untreated integrin for our experiments. Therefore, there should be both activated and inactivated integrin in our experiment. It has been E

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Migration Speed Through Cell-Substratum Adhesiveness. Nature 1997, 385, 537−540. (2) Springer, T. A. Adhesion Receptors of the Immune System. Nature 1990, 346, 425−434. (3) Takeichi, M. Cadherin Cell Adhesion Receptors as a Morphogenetic Regulator. Science 1991, 251, 1451−1455. (4) Gumbiner, B. M. Cell Adhesion: The Molecular Basis of Tissue Architecture and Morphogenesis. Cell 1996, 84, 345−357. (5) Bao, G.; Suresh, S. Cell and Molecular Mechanics of Biological Materials. Nat. Mater. 2003, 2, 715−725. (6) Zhu, C.; Bao, G.; Wang, N. Cell Mechanics: Mechanical Response, Cell Adhesion, and Molecular Deformation. Annu. Rev. Biomed. Eng. 2000, 2, 189−226. (7) Neuman, K. C.; Nagy, A. Single-Molecule Force Spectroscopy: Optical Tweezers, Magnetic Tweezers and Atomic Force Microscopy. Nat. Methods 2008, 5, 491−505. (8) Matthews, B. D.; Overby, D. R.; Alenghat, F. J.; Karavitis, J.; Numaguchi, Y.; Allen, P. G.; Ingber, D. E. Mechanical Properties of Individual Focal Adhesions Probed with a Magnetic Microneedle. Biochem. Biophys. Res. Commun. 2004, 313, 758−764. (9) Mehta, A. D.; Rief, M.; Spudich, J. A.; Smith, D. A.; Simmons, R. M. Single-Molecule Biomechanics with Optical Methods. Science 1999, 283, 1689−1695. (10) Evans, E.; Ritchie, K.; Merkel, R. Sensitive Force Technique to Probe Molecular Adhesion and Structural Linkages at Biological Interfaces. Biophys. J. 1995, 68, 2580−2587. (11) Benoit, M.; Gabriel, D.; Gerisch, G.; Gaub, H. E. Discrete Interactions in Cell Adhesion Measured by Single-Molecule Force Spectroscopy. Nat. Cell Biol. 2000, 2, 313−317. (12) Evans, E. Probing the Relation between ForceLifetimeand Chemistry in Single Molecular Bonds. Annu. Rev. Biophys. Biomol. Struct. 2001, 30, 105−128. (13) Litvinov, R. I.; Shuman, H.; Bennett, J. S.; Weisel, J. W. Binding Strength and Activation State of Single Fibrinogen-Integrin Pairs on Living Cells. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 7426−7431. (14) Merkel, R.; Nassoy, P.; Leung, A.; Ritchie, K.; Evans, E. Energy Landscapes of Receptor−Ligand Bonds Explored with Dynamic Force Spectroscopy. Nature 1999, 397, 50−53. (15) Cui, S. Single-molecule Force Spectroscopy of Biomacromolecules: Comparative Studies in Aqueous Solution and Nonpolar Solvents. Acta Polym. Sin. 2016, 0, 1160−1165. (16) Zhang, Y.; Liu, C.; Shi, W.; Wang, Z.; Dai, L.; Zhang, X. Direct Measurements of the Interaction between Pyrene and Graphite in Aqueous Media by Single Molecule Force Spectroscopy: Understanding the π−π Interactions. Langmuir 2007, 23, 7911−7915. (17) Shi, W.; Zhang, Y.; Liu, C.; Wang, Z.; Zhang, X. Interaction between Dendrons Directly Studied by Single-Molecule Force Spectroscopy. Langmuir 2008, 24, 1318−1323. (18) Tan, X.; Litau, S.; Zhang, X.; Müller, J. Single-Molecule Force Spectroscopy of an Artificial DNA Duplex Comprising a Silver(I)Mediated Base Pair. Langmuir 2015, 31, 11305−11310. (19) Bell, G. I. Models for the Specific Adhesion of Cells to Cells. Science 1978, 200, 618−627. (20) Evans, E.; Ritchie, K. Dynamic Strength of Molecular Adhesion Bonds. Biophys. J. 1997, 72, 1541−1555. (21) Friddle, R. W.; Noy, A.; De Yoreo, J. J. Interpreting the Widespread Nonlinear Force Spectra of Intermolecular Bonds. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 13573−13578. (22) Li, D.; Ji, B. Predicted Rupture Force of a Single Molecular Bond Becomes Rate Independent at Ultralow Loading Rates. Phys. Rev. Lett. 2014, 112, 078302. (23) Seifert, U. Rupture of Multiple Parallel Molecular Bonds under Dynamic Loading. Phys. Rev. Lett. 2000, 84, 2750−2753. (24) Singh, P.; Carraher, C.; Schwarzbauer, J. E. Assembly of Fibronectin Extracellular Matrix. Annu. Rev. Cell Dev. Biol. 2010, 26, 397−419. (25) Nagar, B.; Overduin, M.; Ikura, M.; Rini, J. M. Structural Basis of Calcium-Induced E-Cadherin Rigidification and Dimerization. Nature 1996, 380, 360−364.

lifetime and the saturation unbinding force do not further increase with an increasing number of ligands. The increasing unbinding force comes from the ligand-exchange mechanism. When the number of ligands increases from 1 to 2, the rebinding rate increases exponentially, according to eqs 4 and 6. The overall rebinding rate is mainly contributed by the forcefree ligand. Further increasing the number of ligands leads only to a slight increase in the overall rebinding rate, according to eq 4 and as illustrated in Figure S4. Therefore, the increased number of neighboring free ligands does not cause a significant increase in the saturation unbinding force. This prediction is a little counterintuitive but agrees well with the fact that most CAMs in nature exist as protein dimers.

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CONCLUSIONS In summary, we have provided a new theoretical model for the understanding of rupture forces of cell-adhesion bonds formed by multiple binding ligands with a single receptor. We discovered that in the presence of a CAM dimer, the dissociation forces for the cell-adhesion bond could be greatly enhanced in comparison with the monomer case through a ligand-exchange mechanism. Moreover, dimerization can also make the saturation force accessible at more physiologically related loading rates. Our finding addresses how dimerization increases binding strength of cell-adhesion bonds at the singlemolecule level, representing a key step toward the understanding of complicated cell-adhesion behaviors. Moreover, our results also highlight a wealth of opportunities to design mechanically stronger bioconjunctions for drug delivery, biolabeling, and surface modification.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b04396. Details of the synthesis of bis-cRGD and cRGD peptides, control experiment, analysis of contour length and persistence length, and prediction of rebinding rates (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Y.L.). *E-mail: [email protected] (Y.C.). *E-mail: [email protected] (W.W.). ORCID

Wenmao Huang: 0000-0002-5044-588X Yi Cao: 0000-0003-1493-7868 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the National Natural Science Foundation of China (nos. 21522402, 11674153, 11374148, 81421091, and 11334004) and the 973 Program of China (no. 2013CB834100).

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REFERENCES

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DOI: 10.1021/acs.langmuir.6b04396 Langmuir XXXX, XXX, XXX−XXX