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# Single-molecule force spectroscopy reveals the dynamic strength of the hair-cell tip-link connection

## Introduction

Our senses of hearing and balance rely on the extraordinarily sensitive molecular machinery of the inner ear to convert deflections as small as the width of a single carbon atom into electrical signals that the brain can process1,2,3. In humans and other vertebrates, these senses are mediated by hair cells, named for the bundle of hair-like stereocilia protruding from their apical surfaces (Fig. 1a). Deflection of this organelle during a mechanical stimulus tenses tip links, the thin, 170-nm-long protein filaments that connect the tip of each stereocilium to the lateral wall of its tallest neighboring stereocilium4,5. Tip links bind to and directly gate mechanotransduction channels at their lower ends (Fig. 1a)6,7,8,9.

The tip link is a double-stranded complex of the Ca2+-dependent extracellular adhesion proteins protocadherin-15 (PCDH15) and cadherin-23 (CDH23). A parallel dimer of CDH23 binds to a parallel dimer of PCDH15 at their N termini to form an antiparallel helical tetramer (Fig. 1a)10,11. CDH23 is a long atypical cadherin comprising the upper 2/3 of the tip link; it has 27 extracellular (EC) domains, a specialized membrane-adjacent domain, a single-pass transmembrane helix, and an intracellular domain12. The CDH23 intracellular domain binds to the scaffolding proteins harmonin (USH1C) and sans (USH1G), which in turn bind to myosin motors that move along the actin core filaments of stereocilia13,14. These myosin motors are likely responsible for the millisecond-timescale adaptation of transduction current and for maintaining the resting open probability of the transduction channel15,16,17. PCDH15 has a similar domain structure to CDH23 but contains only 11 EC domains18. PCDH15 binds to several components of the mechanotransduction apparatus at the lower end of the tip link, including the pore-forming subunits of the mechanotransduction channel TMC1 and TMC26. Exactly how tensile force from PCDH15 is transmitted to the mechanotransduction channel is unknown, but the N-terminal binding domains of PCDH15 and CDH23 must be connected in trans in order to convey mechanical information7,10,19.

While classic trans cadherin bonds are mediated by homophilic strand swapping of an N-terminal tryptophan residue into a hydrophobic pocket of its binding partner20, we previously demonstrated that the heterophilic trans tip-link bond has a far more extensive, amphiphilic “handshake” interface involving ~30 amino acids in the first two EC domains of each protein11. Yet, despite having a far more extensive interface, the equilibrium dissociation constant of a single tip-link bond is nearly the same as for classic cadherin trans bonds11,21,22,23,24,25. Mutations that occur in the bond interface of each protein are known to alter the equilibrium dissociation constant (KD) of the interaction11,26 and to cause deafness in humans and other animals27,28,29. However, dissociation constants provide little insight into how the tip link functions in response to dynamic force stimuli and how these mutations result in deafness. Tip links experience a ~10-piconewton (pN) resting tension exerted by myosin motors12,17,30, they may experience forces up to 100 pN31, and the force oscillates at over 100 kHz in some species32. Therefore, examining the behavior of the tip link under tension is critical for describing its function, especially in the context of disease-causing mutations.

The tip link’s double-stranded quaternary structure is also distinct from classic cadherins, which form clusters of tens or hundreds of monomeric proteins in a variety of tissues33 and which rely on the additive strength of many links to maintain their connection over hours, days, or weeks34,35. The tip link, with just two strands, must be strong enough to continuously convey mechanical information to the mechanotransduction channel under both the resting tension and the dynamic forces exerted by sound or head movement. However, since tip links are vulnerable to acoustic trauma in vivo36,37, they apparently release under a high-intensity stimulus. How does the tip link perform these dual functions?

## Results

### The mechanical strength of a single tip-link bond

To measure the mechanical strength of tip-link cadherins, we used optical tweezers to perform single-molecule dynamic force spectroscopy on engineered fusion proteins (Fig. 1b–d and Supplementary Fig. 1). Fusion proteins were expressed in and purified from mammalian cells; they included between 3 and 27 EC domains of PCDH15 or CDH23, fused to an antibody Fc-domain to promote dimerization. Paired Fc domains were then linked to one end of a DNA tether through a SNAPtag. DNA tethers were biotinylated at the other end and linked to streptavidin-coated silica microspheres of ~3-µm diameter, passivated with a polyethylene glycol (PEG) brush (Supplementary Fig. 1a–e). These beads, attached to either CDH23- or PCDH15-linked DNA–protein complexes and distinguishable via a fluorescent marker, were placed in a flow cell on the microscope stage, and manipulated with a dual-beam optical tweezers setup (see “Methods” section). They were brought close together, to allow a PCDH15–CDH23 bond to form, and then moved apart while recording extension and force. As the force built up the bond eventually ruptured, a transition that was easily identified by the abrupt drop to zero-force (Fig. 1d and Supplementary Fig. 1f). The use of long DNA tethers reduced non-specific interactions and enabled the identification of each tether as the desired single-molecule linkage based on force-extension curves (Supplementary Fig. 1g, h).

The tip-link bond is destabilized by very low [Ca2+]11,19, so we measured unbinding in a Ca2+ concentration near that of the endolymph fluid that bathes tip links in the cochlea. However, we found that the mean lifetime of a single tip-link bond at zero-force is reduced by only 50% in 50 µM Ca2+ (Fig. 1g). This insensitivity to low [Ca2+] is in stark contrast with classic cadherins, for which half-maximal adhesion of even the relatively Ca2+-insensitive N-cadherin is observed at 720 µM Ca2+ 40. Thus, the tip-link bond is less sensitive to the Ca2+-poor cochlear and vestibular endolymph, which enables the tip link to reliably convey mechanical stimuli in the inner ear.

### The dynamics of the double-stranded tip-link connection

Why is the tip link double-stranded? Avidity is the cumulative strength that results from multiple bonds, and one important contribution to avidity is the division of externally applied force among the individual components41. Force-sharing among bonds can result in dramatic increases in lifetime because the off-rate of a single bond has an exponential dependence on force. Another contribution comes from the ability of individual components to rebind after they rupture, dynamically maintaining the overall connection. Since CDH23 and PCDH15 both form strong cis-dimers in vitro and in vivo, facilitated by bonds along their ectodomains5,10,42,43,44,45, we hypothesized that the tip link could dramatically increase its lifetime through rebinding of unbound PCDH15 and CDH23 EC1-2 domains.

The tip-link connection may be described by a kinetic model (Fig. 2b and see “Methods” section) in which a transition from the double-bound (B2) to unbound (U) state requires an intermediate single-bound (B1) state. If opposing PCDH15 and CDH23 EC1-2 domains are spatially constrained by cis-dimerization interfaces42, the effective concentration might be sufficiently high and the concentration-dependent binding rate Ceff kon of an unbound pair might then be sufficiently fast, relative to the single bond off-rate koff, to allow the bond to transition back to the B2 state rather than moving to the U state where complete rupture occurs. One approximation of the effective local concentration Ceff can be obtained by calculating the volume of a sphere with a radius equal to the length of an individual EC1-2 binding domain (~10 nm)11, yielding Ceff ~400 µM (see “Methods” section). Although N terminal cis-dimerization interfaces for CDH23 are not yet solved, a cis-dimerization interface is present at PCDH15 EC342, consistent with our estimate of sphere size. Using a single-bond kon of 6.2 ± 2.8 ×104 M−1 s−1 46 and a zero-force single-bond koff0 of 0.5 s−1 (Fig. 1g), we estimated the zero-force rebinding rate (B1 → B2) to be ~25 ± 14 s−1 and the overall zero-force lifetime of the connection to be 22–63 s (see “Methods” section), much longer than the single-bond zero-force lifetime, which we determined to be 1.9 ± 0.4 s.

To test the hypothesis that rebinding results in a substantially increased lifetime at zero-force, we used biolayer interferometry47,48 and fusion proteins containing the entire dimerized extracellular domains of PCDH15 and CDH23 to measure the zero-force kinetics of the double-bond tip link connection (Fig. 2a, c, d and Supplementary Fig. 2). We found the effective on-rate to be 3.5 ± 0.7 × 105 M−1 s−1, in reasonable agreement with published single-bond on-rates46, and the mean lifetime of the connection to be 63.3 ± 3.8 s (SEM, n = 18), in good agreement with the lifetime estimated from force spectroscopy. These values provide an empirical means of determining the effective concentration Ceff in the B1 state, yielding Ceff = 650 ± 200 µM. This is three orders of magnitude more concentrated than the equilibrium KD of a single-bond interaction11,26, consistent with our estimates and sufficient for promoting rapid rebinding to the B2 state. Thus, our data suggest that at zero-force the lifetime of the tip-link connection is substantially increased by rebinding, and rebinding is likely facilitated by cis-dimerization domains which keep binding domains in close proximity and the effective concentration high.

### The strength of the tip-link connection under force

To determine the dynamics of the tip-link connection under force, we used optical tweezers to measure the unbinding kinetics of the double-stranded tip link containing the entire cadherin ectodomains (Figs. 2a and 3a–c and Supplementary Table 1) (see “Methods” section). We found a large increase in strength (Fig. 3a, black circles) relative to the single bond (magenta squares). From single-bond data (Fig. 1f), we can independently predict the rupture force in the case of simple load sharing between two bonds41 (Fig. 3a, “No Rebinding”, and “Methods” section). This line represents dimer strength with perfect load sharing between the two strands, and with a unidirectional unbinding transition through the states B2 → B1 → U; it is the maximum strength achievable from two independent slip bonds without rebinding.

Within the loading-rate range of 0.39 to 22.5 pN s−1, the measured unbinding forces were significantly higher than predicted by perfect load sharing (Fig. 3a). We wondered whether atypical single-bond properties might explain this increase in most likely rupture force. Although we were unable to make reliable single-bond optical tweezer measurements at loading rates below 22.7 pN s−1, an alternative method to calculate bond lifetimes at constant forces fit well with our single-bond model and showed no deviation from slip bond behavior, even at very low forces (Supplementary Fig. 3a)49,50. Importantly, each method predicts a bond lifetime at zero-force of ~2 s, consistent with independent zero-force measurements26. Another possible explanation for an increased dimeric lifetime is bond cooperativity; however, full cooperativity predicts an unreasonably low energy barrier for a single-bond and a loading-rate dependence for bond rupture that is incompatible with our force spectroscopy data41.

A rebinding model, based on single-bond kinetics and a constant Ceff that was determined from biolayer interferometry, successfully predicts higher unbinding forces relative to no rebinding, but it predicts forces even higher than observed (Fig. 3a, “Ceff = Constant”). What can account for this? Recent studies using optical tweezers and molecular dynamics simulations suggest that tip link proteins are far more elastic than initially thought51,52. Elasticity would allow unbound domains in the B1 state (Fig. 2a) to separate as force increases, decreasing Ceff and reducing rebinding. A three-state kinetic model, in which Ceff decreases with a Gaussian decay dependent on the compliance parameter fc (see “Methods” section)50, fits the data well (Fig. 3a, “Ceff = Ceff (F)”), yielding fc = 10.0 ± 1.8 pN and an effective concentration at zero-force of Ceff0 = 465 ± 100 µM (Supplementary Fig. 3c). This model predicts a zero-force mean lifetime of 62 ± 17 s, in excellent agreement with both our biolayer interferometry measurements and our estimates based on extrapolating the effect of avidity from single-bond measurements. The model also indicates that protein elasticity can be an important factor in determining the dynamics of the tip-link connection within the physiological range of forces.

Importantly, these measurements enable the prediction of mean tip-link connection lifetimes as a function of force (Fig. 3b and Supplementary Fig. 3a) for different force histories. At a constant resting tension of 10 pN53, the double-bond interaction lasts ~9 s, an order of magnitude longer than a single-bond interaction of 0.9 s. Yet at very high forces of 50–60 pN the predicted lifetime is much less than a second. The tip link has apparently evolved to use avidity to stabilize the connection at the normally low operating forces but releases exponentially faster at higher forces.

### Cis-dimerization stabilizes avidity of the tip-link connection under force

Our model predicts that the mechanical and structural properties of tip-link cadherins significantly affect rebinding and overall avidity. One contributor to these mechanical properties is the cis-dimerization that links dimers of PCDH15 and of CDH23 laterally at several points along their extracellular domains5,10,43,44,45; indeed, disruption of a cis-dimerization domain at EC3 of PCDH15 disrupts mechanotransduction42. For a full-length tip-link protein, unbinding of one PCDH15–CDH23 bond in the tip-link connection would redistribute tension to the strand with the remaining bond (Fig. 2b, Supplementary Fig. 3c). If the two strands were essentially independent, the loaded strand would stretch more than the unloaded strand, causing shearing between the strands. In the B1 state, strand shearing is likely to result in an increased distance between the unbound EC1–EC2 domains of PCDH15 and CDH23, reducing Ceff, decreasing the rebinding rate Ceffkon under force loads, and consequently decreasing the lifetime of the connection overall. However, cis-dimerization at multiple points could reduce shearing and facilitate rebinding to prolong bond lifetime. These shearing and force distribution phenomena are well described for DNA, actin, and other biopolymer filaments containing multiple dimerization domains54,55,56,57.

To disrupt full cis-dimerization and explore this effect, we truncated PCDH15 and CDH23 to their first five N-terminal EC domains and used single-molecule force spectroscopy to determine their strength (Fig. 4a). At higher loading rates where rebinding is not expected to be significant (>20 pN s−1), truncated EC1-5 dimers still displayed an enhanced binding strength relative to the single-bond interaction, very similar to the full dimer proteins. This indicates that truncation did not disrupt the attachment of both EC1-2 binding domains. However, at slower loading rates where rebinding is expected to significantly impact kinetics, the truncated EC1-5 dimer ruptured at lower forces than the full dimer, exhibiting a lifetime similar to that predicted by a no-rebinding model with perfect force sharing (Fig. 4a, pink dashed line). A fit of our force-dependent concentration rebinding model to the EC1-5 data (Fig. 4a, blue line) was not different from the no-rebinding model and the predicted zero-force lifetime had a high error (Supplementary Table 1). Therefore, we conclude that although the truncated EC1-5 dimer binds with both EC1-2 binding domains, rebinding does not appear to occur at forces above 6 pN over the range of loading rates we tested. But what happens under conditions of low-to-zero stress?

To measure the lifetime of the EC1-5 tip-link connection at zero-force and the potential influence of rebinding under these conditions, we used biolayer interferometry as before. We found the lifetime to be 27.1 ± 3.7 s (SEM, n = 11) (Fig. 4c), approximately half as long as the full-length tip-link connection (63.3 ± 3.8 s, Fig. 2d), but still over an order of magnitude longer than a single bond (1.9 ± 0.4 s, Fig. 1g), indicating rebinding is still occurring but to a lesser extent. We calculated that unbound strands of EC1-5 tip-link connection have an effective concentration for rebinding Ceff of ~170 µM at zero-force (see “Methods” section), compared with ~650 µM for the full-length tip-link connection. From the force spectroscopy data, we calculate that at forces as low as 6 pN, Ceff drops to essentially zero for the EC1-5 dimer but is maintained at ~350 µM for the full-length tip-link connection (Supplementary Fig. 3b). This is consistent with the idea that the loss of cis-dimerization domains in the truncated EC1-5 protein allows for more shearing under force and represents a likely explanation for the observed increase in force sensitivity fc of the EC1-5 dimer. These data highlight the importance of full cis-dimerization in enhancing the strength and lifetime of the tip-link connection relative to a single tip-link bond.

Ca2+ ions link the EC domains in each tip-link protein11,58, and act to maintain its structural integrity51. Chelation of extracellular Ca2+ disrupts tip links in intact hair cells and destabilizes the CDH23–PCDH15 interaction (Figs. 1g and 4c)11,19. Molecular dynamics simulations suggest that as the concentration of Ca2+ bathing the tip link decreases and there is decreased occupancy of Ca2+-binding sites, the junctions between each EC-domain become more flexible and the series elasticity of EC domains is increased52,58. Because protein elasticity is important in determining the extent of avidity under force (Figs. 3a and 4a), increased compliance in low Ca2+ should cause unbound EC domains in the B1 state (Fig. 2b) to separate more rapidly as force increases, decreasing Ceff and reducing rebinding.

We, therefore, measured unbinding forces in low [Ca2+] (Fig. 4b). In 30 µM Ca2+, the concentration found in bulk cochlear endolymph59,60, the lifetime of the tip-link connection at all forces was not significantly altered relative to 2 mM Ca2+, again demonstrating that the tip link is well equipped to convey mechanical stimuli in a physiological environment. Consistent with these results, tip-link lifetime at zero-force was not significantly decreased in 50 or 30 µM Ca2+ when measured with biolayer interferometry (Fig. 4c). However, at the sub-endolymphatic level of 10 µM Ca2+, the tip-link connection was severely weakened under force when measured with force spectroscopy (Fig. 4b) and significantly destabilized when measured with biolayer interferometry (Fig. 4c). Based on model fits to our force spectroscopy data, the single-bond off-rate at this calcium concentration is accelerated ~4 fold and the protein stiffness is decreased ~10 fold (Supplementary Table 1), causing Ceff to decrease rapidly with force. Thus, depletion of extracellular Ca2+ modifies the lifetime of the tip-link connection through two distinct mechanisms: the intrinsic single-bond off rate, and the stiffness-dependent decrease in Ceff.

### The mechanical phenotype of a hereditary deafness mutation

Hearing loss is one of the most common congenital disorders, and more than half of all cases are due to genetic causes61. A broad spectrum of Usher syndrome mutations disrupts tip-link integrity in hair cells62,63, including the human R113G mutation in PCDH15, which causes hearing loss without a vestibular or visual phenotype28. The R113 residue participates in the binding interface (Fig. 5b), and the R113G mutation reduces bond affinity in vitro11,46. To determine how this mutation disrupts function, we used polarized Fc-domain dimerization (see “Methods” section) to introduce this mutation either heterozygously (R113G+/) or homozygously (R113G+/+) into full-ectodomain mouse PCDH15 proteins and measured their strength with force spectroscopy. We found that the heterozygous R113G+/− tip-link bond (brown circles) is weaker than the wild-type, and the homozygous R113G+/+ bond (purple circles) is much weaker at all forces (Fig. 5c, d). The exceptional reduction in strength by a single amino acid substitution is additional confirmation that our measurements are specific to the tip-link bond.

To understand how this mutation disrupts function, we performed a simultaneous fit of R113G+/− and R113G+/+ unbinding forces, using modified three- and four-state force-dependent models (Fig. 5a and see “Methods” section). Most strikingly, the R113G mutation causes the single-bond off-rate to be ~8 times more sensitive to force (fβ R113G = 1.8 ± 0.3 pN) compared with the wild-type bond (fβWT = 13.5 ± 2.0 pN), without altering the elasticity-mediated force dependence of Ceff (Fig. 5f and Supplementary Table 1). As a consequence, the R113G+/+ PCDH15 dimer remains bound to the CDH23 dimer 39% as long as the wild-type at zero-force but lasts just 0.3% as long at a resting tension of 10 pN. These results are also consistent with our biolayer interferometry measurements, which indicate a moderate reduction in a zero-force lifetime (Fig. 5e). Since cochlear hair cells experience considerably more force than vestibular hair cells or the calyceal processes of retinal photoreceptors64, PCDH15–R113G+/+ likely unbinds more rapidly in the cochlea than in the vestibular system or retina, consistent with the more profound deafness phenotype in PCDH15–R113G+/+ human patients compared with the balance or visual phenotype.

Individual tip links are subjected to a resting tension, which maintains transduction channels in their optimally responsive state12,17,30,65. Estimates for the operating range of a single mechanotransduction complex, characterized as the range of forces that change channel open probability Popen from ~10% to ~90%, vary by three-fold or more depending on the organism, type of hair cell, and stimulus method53,66,67,68,69,70,71. However, sensitive experiments in bullfrog saccular hair cells suggest that channels open with a force of ~5 pN added to the resting tension (~10 pN), for an operating range of 10–15 pN53,71. These values are consistent with measurements of hair bundle movements in excised guinea pig cochlea preparations, where a sound pressure level of 60 dB moves a hair bundle <10 nm72.

## Discussion

Our perception of sound and head movement is mediated by a mechanotransduction complex that converts nanometer-scale deflections into electrical signals. Many proteins of the complex have been identified, and how they assemble is beginning to be known. Yet, how this apparatus functions biophysically at the level of individual molecules is poorly understood. Our results characterize the strength and dynamics of the tip-link complex with single-molecule resolution and show how avidity governs the lifetime of the connection in response to force and concentrations of endolymphatic Ca2+.

Our calculation of tip link single-bond kinetics at zero-force matches well with previously published results11,26,46, and appears to be independent of whether tip-link protein was expressed in bacteria and re-folded—which results in no post-translational modifications—or expressed in mammalian HEK293 cells where proteins are glycosylated and modified in the secretory pathway. However, post-translational modifications specific to the hair cell could act to change the affinity of the bond interface or to stabilize the PCDH15–CDH23 interaction, analogous to how phosphorylation of the C-terminal tail of most GPCRs increases their affinity for β-arrestins81. Unidentified accessory proteins may also act to stabilize the tip-link interaction, though high-resolution ultrastructures of the tip-link filament in hair cells depict a smooth strand without bulges of accessory proteins5. Finally, a subset of electron microscopy images from an early study of tip-link ultrastructure suggested the possibility of three tip link strands, based upon indents at the lower end of tip links after BAPTA chelation5, which may modestly extend the lifetime of the tip link. However, further biochemical studies have shown that full-length CDH23 and PCDH15 preferentially form dimers in vitro10, both by themselves and when bound together. Interestingly, although these studies show that tip-link filaments form a helical structure, recent molecular dynamics simulations show that helix unwinding of full-length dimeric PCDH15 bound to CDH23 EC1-2 during stretching does not significantly twist the PCDH15 EC1-2 binding domains, likely due to strong cis-dimerization at EC352.

For the reforming rate to match the ~8 s lifetime (Figs. 3b and 6e), where tip links have a 50% equilibrium bound probability, we can use the calculated on-rate of 3.5 ± 0.7 × 105 M−1 s−1 to estimate that the effective concentration of free CDH23 and PCDH15 dimer ends must be at least ~0.3 µM. This concentration roughly corresponds to the two binding domains occupying a sphere with a diameter of less than ~210 nm. This diameter is ~30% longer than the length of an intact tip link and far longer than the 10–20 nm distance between stereocilia where they touch near their tips5,84,85. However, the concentration of free tip-link dimer ends is likely much higher than ~0.3 µM. From a structural point of view, CDH23 and PCDH15 are relatively stiff at endolymphatic Ca2+ concentration5,52,58, are complexed with membrane and intracellular proteins6,43,86, and their insertion points appear to be spatially constrained even when broken14,77,79. These observations make it likely that free dimer ends occupy a much smaller space than a 210 nm sphere and are consequently at higher than 0.3 µM concentration. From the single-channel conductance of transduction channels and the number of stereocilia, it has been estimated that ~95% of channels in cochlear hair cells transduce during a stimulus87. If the lifetime of the tip link is ~8 s at resting tension, a corresponding ~95% tip link bound probability would necessitate a reforming rate of just hundreds of milliseconds and a local concentration of ~10–15 µM.

These mechanisms allow the tip link to act as a mechanical circuit breaker in two ways: the force-dependent unbinding rate becomes faster than the rebinding rate at high force, and the slight elasticity of the bound strand allows the free ends of the unbound cadherins to pull away from each other, decreasing the rebinding rate. This might be a protective mechanism, preventing large stimuli from tearing the transduction complex from the membrane.

Overall, our work reveals how nature uses force distributed across multiple bonds to create a tunable mechanical circuit breaker—a motif that is likely used in other natural systems and could be used as a design principle in synthetic systems.

## Methods

### Protein production and purification

Using antibody Fc heterodimers91,92, we engineered dimeric mouse PCDH15 and CDH23 proteins containing their first five EC domains, and we restricted binding to a single PCDH15–CDH23 bond by removing EC1-2 from one protein of each parallel dimer (Fig. 1b). This design was essential: monomeric EC1-2 and EC1-5 fusion proteins without the paired EC3-5 were unstable and bound non-specifically11. For single-bond tip link proteins with one EC1-2 binding domain, the coding regions of EC1-5 for mouse Pcdh15 and Cdh23 were amplified by PCR from full-length cDNA clones. This corresponds to base pairs 422-2269 from Pcdh15 RefSeq cDNA NM_023115 and base pairs 408-2066 from Cdh23 RefSeq cDNA NM_023370. Fusion proteins containing only the EC1-2 binding domains for each protein were unstable and bound non-specifically, and the addition of EC3-5 was necessary to stabilize these proteins, as determined from both biolayer interferometry and force spectroscopy. The EC3-5 domains were created by deleting amino acids 28–262 for PCDH15 and 25–228 for CDH23 using site-directed mutagenesis (New England Biolabs). This strategy preserved the native signal peptide sequence. The EC1-5/EC3-5 dimer architecture was necessary to eliminate the background binding of monomers when EC3-5 was exposed. Cleavage of the signal peptide was confirmed by transfecting and expressing individual plasmids and ensuring they were secreted from transfected Expi293 cells (ThermoFisher) and by glycosylation-corrected molecular weight determination using SEC-MALS (Wyatt Technology).

The coding sequences of antibody Fc heterodimerization domains were amplified from the pFUSE-hIgG1-Fc1 plasmid (Invivogen) containing two charged mutations on each opposing domain91,92. The SNAPtag sequence was amplified from the pSNAPf vector (NEB). Each of these fragments was cloned into a pFUSE vector (Invivogen) using NEBuilder® HiFi DNA Assembly Master Mix (NEB) along with a tandem 6× polyhistidine tag separated by a GSG linker.

For tip link fusion proteins containing two EC1-5 dimeric binding domains, shown in Fig. 2a, the same assembly principle was applied as described above. For full-length dimeric tip link fusion proteins, the coding sequences for the entire extracellular domain up to the last hydrophilic amino acid before the transmembrane domain for PCDH15 and CDH23 were used. The PCDH15 R113G mutation was introduced using site-directed mutagenesis (NEB). All plasmids encoding these proteins were screened for sequence fidelity by Sanger sequencing (GENEWIZ), and primers used to amplify these sequences are provided in Supplementary Table 2. DNA sequences were analyzed using SnapGene (Version 5.0).

Plasmids encoding each half of the final dimerized proteins were co-transfected into HEK Expi293 suspension culture cells in Expi293 medium at a ratio of 4:1 PEI:DNA (w/w), diluted in OptiMem (Invitrogen). A typical transfection used 15 µg of each plasmid with 120 µg PEI in 30 mL of cells at a confluency of 4 × 105 cells mL−1. Cells were grown in 8% CO2, shaking at 125 RPM. Transfected cells were grown at 37 °C for 16–20 h, then 7 mL Expi293 medium containing 2 mM sodium butyrate and 0.5× penicillin/streptomycin was added, and the cells moved to a 30 °C incubator. Cell supernatant was harvested 72–96 h post-transfection. Cells were removed by centrifugation at 7000 × g for 15 min, and the remaining supernatant was 0.22 µm filtered and stored at 4 °C until purification.

Proteins were purified using Ni-NTA or TALON metal affinity purification. First, the supernatant was dialyzed against tris-buffered saline (TBS) containing 2 mM Ca2+ (20 mM Tris, 125 mM NaCl, 2 mM CaCl2, pH 7.4) overnight at 4 °C in 3.5 kDa MWCO dialysis tubing (Repligen). 1–1.5 mL of Ni2+ Sepharose Excel (GE Life Sciences) or TALON resin (Takara) per 30 mL of supernatant was sedimented in a 10 mL purification column and then washed with 3 resin bed volumes of PBS followed by 0.5 bed volumes of TBS + Ca2+ buffer. The filtered supernatant was next passed through the column by gravity at a rate of ~1–2 mL min−1. For Ni-NTA purification, the column was then washed with 3 column volumes TBS-Tween+Ca2+ buffer with 15–30 mM imidazole. For TALON purification, the resin was resuspended and washed with 15 column volumes TBS + Ca2+ in batch mode three times. In each case, the protein was eluted by resuspending the Ni2+ Sepharose with 3 mL TBS + Ca2+ buffer with 200 mM imidazole and incubating in a tube on a rotator for 1 h at 4 °C. This mixture was then filtered through a 0.2 µM filter and concentrated on a 10 kDa (for EC1-5/EC3-5 proteins) or a 100 kDa (for full-length proteins) MWCO column (Vivaspin, GE Healthcare). The protein was buffer exchanged 2-3x using either 7 kDa MWCO Zeba Columns for EC1-5/EC3-5 proteins or 40 kDa MWCO Zeba Columns for full-length proteins (ThermoFisher).

Proteins were purified by size-exclusion chromatography on a Superose 6 Increase 10/300 column (GE Healthcare). Purity and molecular weight were confirmed by staining with a SNAPtag-reactive benzylguanine-Alexa 647 dye (NEB) and running the proteins on a 4–20% NuPAGE Tris-Glycine gel. The gels were stained with Krypton protein stain (ThermoFisher) and imaged using a laser gel scanner (GE Typhoon) at 532 and 635 nm excitation.

### DNA tethers

Circular ssDNA from the M13 bacteriophage (New England Biolabs) was linearized at a single site using the restriction enzyme BtscI (New England Biolabs) and a site-specific oligonucleotide93. A forward primer containing dual 5′ biotins (Integrated DNA Technologies) was purchased and a reverse 5′ benzylguanine primer was synthesized from a primer with a 5′ primary amine on a 12-carbon linker (IDT) (Supplementary Table 2). The synthesis was accomplished with excess BG-GLA-NHS (NEB) in PBS pH 7.4 for 1 h at room temperature and buffer exchanged on a Zeba 7k MWCO desalting column. The forward and reverse primers were used to amplify a 2385 base pair DNA fragment from the linearized M13 template using Q5 DNA Polymerase 2× HotStart Master Mix (NEB). The amplified DNA tether was purified using Ampure XP beads at a ratio of 0.7:1 suspended beads to PCR mix and eluted in TBS + Ca2+ buffer. To minimize damage to the DNA tethers, appropriate techniques were used to minimize unnecessary hydrodynamic stresses, and DNAse-free lab supplies were used to minimize potential degradation. The quality of the DNA tethers was checked with gel electrophoresis, and the tethers were stored at −20 °C in aliquots until use.

### DNA–protein tethering complex

Purified SNAP-tagged tip-link fusion proteins (>1 µM) were reacted with >500 nM purified DNA tethers at room temperature for 1.5 h. Coupling efficiency was assessed by running the DNA–protein complexes on an agarose gel and staining for DNA (Supplementary Fig. 1d). The DNA–protein complex was desalted on Zeba Spin Desalting Columns (ThermoFisher) to remove excess imidazole (if present) and was then purified by Ni-NTA purification using Ni-Sepharose High-Performance resin (GE Healthcare) to remove free DNA tethers. The DNA–protein complex was purified as for protein purification, but the washing steps were carried out in the absence of imidazole and was performed entirely in batch mode. The resulting complex was concentrated to 20 µL on a 10–30 kDa MWCO column (VivaSpin, GE Healthcare) and buffer exchanged using Zeba Spin Desalting Columns (ThermoFisher).

Glass beads (silica microspheres of 3 µm diameter, 200 µL of 1% w/v; Bangs Laboratories) were cleaned and hydroxylated by first washing them in a glass tube in MilliQ water, then cleaning with 1% Hellmanex III detergent (Hellma Analytics) by boiling. Beads were then sonicated in the detergent for 5 min, then washed and sonicated consecutively with acetone, 1 M KOH, and MilliQ water, and were then rinsed in anhydrous methanol.

The cleaned beads were aminosilanized by resuspending them in methanol and 20% v/v glacial acetic acid, then adding 1% v/v APTES (Sigma) in a glass tube and mixed by swirling. The solution was then covered with argon gas and rotated end-over-end for 10 min at room temperature. The beads were then rinsed repeatedly with methanol and MilliQ water to remove free aminosilane.

The beads were passivated with polyethylene glycol (PEG) using a variant type of “cloud point” PEGylation94 (Supplementary Fig. 1a, b). 10 mg of mPEG-5k-NHS and 10 mg of Biotin-PEG-5k-NHS were dissolved in 86.2 µL of 0.5 M Na2SO4 in separate tubes. These reagents were mixed in varying ratios between 1:1 and 1:640 to a final volume of 86.2 µL, giving a cloudy solution. The varying ratios resulted in different surface biotin densities, used later to tune the density of DNA–protein tether on the surface of the beads. 13 µL of 1-M NaHCO3 was added to the mixed PEG solution until the solution just became clear. The cleaned beads were pelleted using centrifugation, the supernatant removed, the PEGylation solution added to the beads, and the beads mixed into the solution by carefully pipetting without forming bubbles. The beads were then mixed on an end-over-end rotator with the top end of the tube at a 90° angle from the axis of rotation for 2 h. The beads were then washed with TBS + Ca2+ buffer with 0.02% Tween-20 via successive centrifugation, bubbled with argon, and stored at 4 °C.

The surfaces of the beads were functionalized with streptavidin to enable the binding of biotinylated DNA tethers. 1 µL of PEGylated beads containing surface biotin were diluted 1:50 with TBS + Ca2+ buffer + 0.02% Tween-20 + 0.1 mg mL−1 Roche Blocking Reagent (TBS-TB + Ca2+ buffer), and then 50 µM streptavidin was added and allowed to coat the surface for 10 min at room temperature while rotating. One batch of beads was coated with NHS-Alexa 594 labeled streptavidin to enable identification under the microscope via fluorescence and to distinguish PCDH15-linked beads from CDH23-linked beads. To remove free streptavidin, the beads were then washed five times by consecutive pelleting at 300 × g for 1 min and washing with 200 µL TBS-TB + Ca2+ buffer.

The beads were coated with the DNA–protein tethers by resuspending pelleted beads with 3–5 µL of the concentrated, His-purified, DNA–protein complex. The beads were rotated for 1 hr at room temperature and then washed three times with 200 µL TBS-TB + Ca2+ buffer and resuspended in 10 µL of TBS-TB + Ca2+ buffer. The coated beads were rotated at 4 °C until use.

For full-length tip link fusion proteins under some conditions (10 µM Ca2+, R113G mutations, fast loading rates), it was necessary to perform experiments without the DNA tether in order to increase the rate of data collection. For these experiments, fusion proteins were directly biotinylated with BG-Biotin (NEB), buffer exchanged with a Zeba Desalting Column (ThermoFisher) three times, and directly coated onto streptavidin-coated beads. Individual tethers were verified using a WLC fit to the force-extension traces95, and tether frequency was kept below 1:10 tethers:attempts. For the 95.62 pN s−1 loading rate for full-length dimer fusion proteins in Fig. 3a, data were acquired with and without DNA tethers to confirm that the DNA tethers were not a source of mechanical instability in our measurements.

### Recording chamber preparation

Plain 75 × 25 mm glass microscope slides (VWR) and 22 × 22 mm glass coverslips (Gold Seal, ThermoFisher) were cleaned by boiling in 1% Hellmanex III (Hellma Analytics) in MilliQ water. The glass was then sonicated for 30 min at 37 °C. After washing thoroughly in MilliQ water, the slides were dried and stored at room temperature in a sealed and desiccated container.

A recording chamber was prepared by laying thin strips of Kapton Tape (DuPont) onto a pre-cleaned microscope slide, then placing and sealing the glass coverslip on top by applying pressure along the tape lines. This created several channels with a height of ~1 mm. Each channel was flushed with 5 mg mL−1 Roche Blocking reagent dissolved in PBS and allowed to sit in a humidified chamber for 10–30 min at room temperature in order to block the glass surfaces and prevent bead sticking. The channel was then flushed with 10–20 chamber volumes of TBS-TB + Ca2+ buffer. Each chamber was used immediately after blocking and washing.

1 µL each of the coated beads containing either PCDH15 or CDH23 protein-DNA tethers was diluted 1:100 in TBS-TB + Ca2+ buffer and injected into the recording chamber. The chamber was then hermetically sealed with vacuum grease and locked onto the microscope stage of the instrument. For each condition, measurements were taken from experimental and sample replicates.

### Instrument description

The optical tweezers system used in these experiments is functionally similar to the one previously described96, with several important differences. First, the micropipette was replaced with a second optical trap. This was achieved by using a polarizing beam splitter to split the 1064 nm laser beam into two polarized components. One beam remained stationary as in the previous setup, and the second beam was driven by a piezo-mirror with fine control (Mad City Labs, Madison WI), steered in the back focal plane of the objective.

The coverslip containing the recording chambers was mounted on an M-686 XY Stage with Piezoceramic Linear Motors (Physik Instrumente) which was directly attached to the microscope.

### Single-molecule experiments

Experiments in 2 mM Ca2+ were performed at room temperature in TBS-TB + Ca2+ buffer. For experiments in Ca2+ concentrations below 2 mM, TBS-TB + Ca2+ buffer was made without Ca2+ or Tween-20 (20 mM Tris, 125 mM NaCl, pH 7.40) using an established method58. Residual Ca2+ from this solution was removed by passing 100 mL of TBS buffer over 5 g of pH-neutralized Chelex 100 resin (BioRad) in a column three times at a flow rate of ~3 mL min−1, which yields a solution containing <0.2 μM Ca2+ 58. Ca2+ was added back to the Ca2+-free TBS buffer to the desired concentration from a stock standard of 1 M CaCl2 solution (Sigma).

Beads were identified on the optical tweezer microscope by Alexa 594 fluorescence and picked up in each of the trapping beams. Custom software (LabVIEW) was used to control data acquisition and piezo motion. Bead positions were determined in real time at 1400 frames per second with sub-pixel fitting of a polynomial to the dark edges of the beads. The stiffness of each trap was calibrated at 50 mW of laser power using a blur-corrected power spectrum fit97. Experiments were performed at 950 mW of laser power, which corresponded to a trap stiffness of ~0.1 pN nm−1.

Experiments were performed by bringing the piezo-mirror-driven bead close to the stationary trapped bead for 0.05–5 s and then retracting at a constant velocity. The formation of an individual tether was cursorily checked by tether length and by displacement of the stationary bead from the center of the trapping beam (Supplementary Fig. 1f). When the software detected a single tether, the bead was brought back to the original bead, just close enough that the tether was slack but that there was no chance of forming a second tether. The tether was then quickly pulled out at a constant velocity until the tether ruptured completely. Bead retraction was performed at force-loading rates between 0.39 and 377.8 pN s−1.

### Data analysis

Unbinding forces from at least three experimental replicates were averaged together for each loading rate tested, to account for preparation variability (see Supplementary Table 1 for rupture data statistics). The most-probable unbinding force is the force where the unbinding probability density is at a maximum. For each set of unbinding forces at a given loading rate we used a kernel smoothing function (ksdensity in MATLAB with default options) to estimate the unbinding probability density as a function of force98,99,100. The error estimate for each most-probable unbinding force was taken to be the kernel bandwidth, which was systematically chosen based on the spread of the unbinding force data and the number of rupture forces measured.

Single-bond unbinding data were analyzed using an Evans–Ritchie model for the dynamic strength of molecular adhesion bonds39:

$$f^ \ast = f_\beta \cdot {\mathrm{ln}}\frac{{r_{\mathrm{l}}}}{{f_\beta \,k_{\mathrm{off}}^0}}$$
(1)

where f* is the most-probable rupture force, fβ is the force scale, rl is the force-loading rate, and koff0 is the off rate at zero-force. The force scale fβ is defined as:

$$f_\beta = \frac{{k_{\mathrm{B}}T}}{{x_{\mathrm{ts}}}}$$
(2)

where kB is the Boltzmann constant, T is absolute temperature, and xts is the distance to the transition state for unbinding. Double-bond unbinding data were fit with a multi-state avidity force-dependent avidity model in MATLAB.

### A model for force-dependent avidity

Conforming to the overall structure of the tip-link connection, we modeled the system as two bonds loaded in parallel. In this condition, the force applied to the tip link is distributed equally between the two-component bonds. If one bond breaks, the remaining bond assumes the entire force load unless and until the other bond rebinds. We, therefore, described the two-bond interaction using the following differential equations:

$$\frac{{{\mathrm{d}}B_2}}{{{\mathrm{d}}t}} = C_{\mathrm{eff}}k_{\mathrm{on}}B_1 - 2k_2B_2$$
(3)
$$\frac{{{\mathrm{d}}B_1}}{{{\mathrm{d}}t}} = - \left( {C_{\mathrm{eff}}k_{\mathrm{on}} + k_1} \right)B_1 + 2k_2B_2$$
(4)

where B2 represents the fraction of tip links in the double-bound state, and B1 represents the fraction of tip links in the single-bound state. kon is the solution on-rate of a single PCDH15–CDH23 bond. Ceff is the effective concentration of the unbound EC1-2 interface domains. k2 is the force-dependent off-rate of the PCDH15–CDH23 bond when there are two bonds splitting the force load (B2 → B1):

$$k_2 = k_{\mathrm{off}}^0 \cdot e^{\frac{F}{{2f_\beta }}}$$
(5)

where koff0 is the solution off-rate of a single PCDH15–CDH23 bond, F is the applied force, and fβ is the force, which accelerates the off-rate by e-fold.

k1 is the force-dependent off-rate of the PCDH15–CDH23 bond when there is one bond bearing the entire force (B1 → U):

$$k_1 = k_{\mathrm{off}}^0 \cdot e^{\frac{F}{{f_\beta }}}$$
(6)

In the case where F = 0, these equations can be solved analytically. From this we calculate the mean lifetime τ to be:

$$\tau = \frac{{C_{\mathrm{eff}}k_{\mathrm{on}} + 3k_{\mathrm{off}}}}{{2k_{\mathrm{off}}^2}}$$
(7)

In these experiments, the force changes linearly in time with a loading rate lr:

$$F = l_{\mathrm{r}}t$$
(8)

We assume the effective concentration can change as force is applied due to the extensibility of the filaments. Each filament can be thought of as a series of springs each with a spring constant κ. If one strand breaks, the free ends separate, and tension on the bound strand is doubled, leading to a lower effective concentration Ceff.

$$C_{\mathrm{eff}}\left( F \right) = C_{\mathrm{eff}}^0 \cdot e^{ - \left( {\frac{F}{{f_{\mathrm{c}}}}} \right)^2}$$
(9)

$$C_{\mathrm{eff}}^0$$ is the local effective concentration at zero-force; the reduction in Ceff with force is characterized by a force50:

$$f_{\mathrm{c}} = \sqrt {2\kappa k_{\mathrm{b}}T}$$
(10)

The most-probable unbinding force of the dimeric interaction is calculated by finding the most-probable unbinding time and multiplying it by the loading rate. The most-probable unbinding time is calculated by finding the maximum of the unbinding probability density function:

$$- \left( {\frac{{{\mathrm{d}}B_2}}{{{\mathrm{d}}t}} + \frac{{{\mathrm{d}}B_1}}{{{\mathrm{d}}t}}} \right) = k_1B_1$$
(11)

The heterogeneous system is described by the following reaction equations:

$$\frac{{{\mathrm{d}}B_2}}{{{\mathrm{d}}t}} = C_2k_{{\mathrm{on}}[1]}B_{12} + C_1k_{{\mathrm{on}}[2]}B_{11} - 2\left( {k_{21} + k_{22}} \right)B_2$$
(12)
$$\frac{{{\mathrm{d}}B_{12}}}{{{\mathrm{d}}t}} = - \left( {C_2k_{{\mathrm{on}}[1]} + k_{12}} \right)B_{12} + k_{21}B_2$$
(13)
$$\frac{{{\mathrm{d}}B_{11}}}{{{\mathrm{d}}t}} = - \left( {C_1k_{{\mathrm{on}}[2]} + k_{11}} \right)B_{11} + k_{22}B_2$$
(14)

where B2 represents the fraction of tip links with two bonds. B1j represents the fraction of tip links with one bond where the index j indicates which bond type. kon[j] is the solution on-rate of a single PCDH15–CDH23 bond. kij is the force-dependent off-rates of the PCDH15–CDH23 bond, where the index i denotes the number of bonds and j denotes the bond type:

$$k_{ij} = k_{{\mathrm{off}}[j]}e^{\frac{F}{{if_\beta }}}$$
(15)

koff[j] is the solution dependent off rate for the jth bond type. Cj is the force-dependent concentration for the jth bond type.

$$C_j = C_{\mathrm{o}}e^{ - \left( {\frac{F}{{f_{{\mathrm{c}}[j]}}}} \right)^2}$$
(16)

Here we assume that the effective concentration for the jth bond type decays as force is applied with a characteristic for fc[j].

The most-probable unbinding time of the dimeric heterogeneous interaction is calculated by finding the maximum of the unbinding probability density function:

$$- \left( {\frac{{{\mathrm{d}}B_2}}{{dt}} + \frac{{{\mathrm{d}}B_{12}}}{{{\mathrm{d}}t}} + \frac{{{\mathrm{d}}B_{11}}}{{{\mathrm{d}}t}}} \right) = k_{11}B_{11} + k_{12}B_{12}$$
(17)

The most-probable unbinding time is multiplied by the loading rate to yield the most-probable unbinding force.

Each model was fit to the data using fminsearch in MATLAB to find the minimum of the χ2.

$$\chi ^2 = \mathop {\sum}\limits_{i = 1}^N {\frac{{\left( {F_i^{\mathrm{exp}} - F_i^{\mathrm{model}}} \right)^2}}{{{\mathrm{d}}F_i^2}}}$$
(18)

where Fiexp is the ith experimental most-probable unbinding force and Fimodel is the most-probable unbinding force predicted by the model. dFi2 is the estimated square error for the ith unbinding force. To estimate the error for each fit parameter obtained, we calculated the local curvature of the χ2 as a function of that fit parameter. The variance (σxi)2 of the fit parameter xi is estimated by:

$$\left( {\sigma _{xi}} \right)^2 = 2\left( {\frac{{\partial \chi ^2}}{{\partial x_i^2}}} \right)^{ - 1}.$$
(19)

### Biolayer interferometry

Proteins were produced and purified in the same manner as for force spectroscopy experiments. Protein molarity was verified using two complementary methods: UV absorbance at 280 nm in solution, and fluorescence intensity in an SDS-PAGE gel stained with the quantitative Krypton (ThermoFisher) protein stain relative to a BSA standard (ThermoFisher). To create passivated two-dimensional streptavidin-coated biosensors, we used Aminopropylsilane Dip and Read Biosensors (ForteBio), which contain a two-dimensional surface of primary amine groups. Dry sensors were first hydrated in a variant cloud-point buffer (100 mM HEPES, 0.6 M K2SO4, pH 7.75) in the sensor tray for at least 5 min. All experiments were performed in a 384-well tilted-bottom microplate (Pall ForteBio). Amine-reactive NHS-PEG12-Biotin (ThermoFisher) was dissolved to 4 mM in cloud-point buffer and distilled water was added in ~5 µL drops until the buffer just became clarified. Sensors were immediately coated in NHS-PEG12-Biotin solution for 2300 s on an Octet Red384 instrument (ForteBio) in real time to assess sensor coating efficiency. Sensors whose signals did not group together during the coating were discarded. Sensors were then repeatedly and sequentially washed in cloud-point buffer and ultrapure water, then equilibrated in TBS-Tween+Ca2+ buffer. Biotinylated sensors were then coated for 200 s with 5 µM streptavidin (ProZyme) and washed twice in TBS-Tween+Ca2+ buffer. Drift sensors were quenched with 10 µM biocytin (Sigma Aldrich).

In each experiment, CDH23 was biotinylated using a custom-synthesized benzylguanine-PEG15-biotin linker, excess linker was removed using a desalting column or polyhistidine purification, and the proteins were buffer exchanged into TBS-Tween+Ca2+ buffer. CDH23 was immobilized to a binding signal of 0.175–0.25 nm above baseline in TBS-Tween+Ca2+ buffer and washed in at least four separate wells of TBS-Tween+Ca2+ buffer before association with PCDH15. Biocytin-quenched drift sensors were dipped into the same concentration of CDH23 for the same length of time as the experimental sensors, in parallel. To assess kinetics, the CDH23+ and CDH23− sensors were dipped into a baseline solution of TBS-Tween+Ca2+ buffer, then dipped into a solution of 10–300 nM PCDH15 or PCDH15 lacking EC1-2 in TBS-Tween+Ca2+ buffer to measure association, and finally into the same baseline solution to measure dissociation. PCDH15 and PCDH15 lacking EC1-2 proteins were kept equimolar during each experiment. Experiments were performed using both biological and experimental replicates. Solutions for low Ca2+ experiments were prepared as described for single-molecule experiments.

PCDH15 proteins lacking EC1-2 were produced by deleting the EC1-2 coding region from DNA plasmids encoding the full-length extracellular fusion proteins using the same genetic deletion strategy employed for the EC1-5/EC3-5 dimers used for force spectroscopy. The change in apparent molecular weight was confirmed on an SDS-PAGE gel and via size-exclusion chromatography (Supplementary Fig. 2a).

Each experimental kinetic trace was first analyzed using the ForteBio Octet Data Analysis Software 10.0 (Pall ForteBio). Each sensor trace from the biocytin-quenched drift sensor was subtracted from the corresponding experimental sensor, and the subtracted traces were processed using Savitzky-Golay filtering. The drift-corrected sensor trace from the control PCDH15 lacking EC1-2 was then subtracted from the drift-corrected PCDH15 experimental sensor trace. The final subtracted traces were exported into Prism 8.1 software (GraphPad) and each dissociation phase was fitted using single-exponential kinetic equations. On-rates were measured at 300 nM PCDH15. Data were collected several times in experimental replicates (WT 2 mM Ca2+n = 18, 50 µM Ca2+n = 9, 30 µM Ca2+n = 6, 10 µM Ca2+n = 9; PCDH15 R113G+/+ 2 mM Ca2+n = 5).

We used an established quantitative model of hair bundle mechanics65 to calculate the force on a single tip link in response to an oscillatory bundle deflection, at frequencies from 1 Hz to 10 kHz. We modeled a hair bundle with a gating spring stiffness of 0.6 mN m−1 and a geometry factor of γ = 0.12 (Fig. 6a, b); thus positive deflection by 133 nm would increase tip-link tension by 9 pN, enough to open essentially all channels if the gating swing is 4 nm68,71. We assumed a resting tension of 10 pN53. In this model, the gating spring does not exert compressive force, so a waveform with high amplitude cannot produce negative tension. For each δt of the simulation (1–10 µs depending on conditions), we calculated the tip-link tension, the force-dependent off-rates, the force-dependent Ceff and the rebinding rate, and then the probability that the tip link remained bound. Each simulation was run until both strands unbound, typically 5–10 s. To obtain a histogram of lifetimes, we ran the Monte Carlo simulation 5000 times for each condition, with phase-randomized sinusoidal stimuli (Fig. 6d, e).

To model “slow adaptation”, we used a motor climbing rate of 1.6 µm s−1 and a motor slip rate of 0.01 s−1, yielding a resting tension of 10 pN. When calculating the effect of adaptation, we calculated the slipping and climbing of the adaptation motor in each δt and how that affected tip-link tension.

### Quantification and statistical analysis

All kinetic measurements using biolayer interferometry were measured at least five times in each experimental condition (n = 5–18). Experimental replicates were performed at least three times. We used ForteBio Octet Data Analysis Software 10.0 (Pall ForteBio) and Prism 8.1 software (GraphPad) for kinetic fitting. The Student’s two-tailed unpaired t-test was used to determine statistical significance (*p < 0.05, **p < 0.01, ***p < 0.001).

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

Data supporting the findings of this manuscript are available from the corresponding authors upon reasonable request. A reporting summary for this Article is available as a Supplementary Information file. Source data are provided with this paper.

## Code availability

Code used to analyze data in this paper were performed in MATLAB, and are available at a dedicated Github repository [https://github.com/Corey-Lab/Mulhall-et-al-Nature-Communications].

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## Acknowledgements

We thank Dr. Marcos Sotomayor for helpful discussion and early conceptualization, and members of the Corey and Wong Laboratories for helpful discussions and for critical reading of the manuscript. This work was supported by the NIH (F31 DC016199 to E.M.M., R01 DC000304 to D.P.C., R01 DC002281 to D.P.C. and W.P.W., and R35 GM119537 to W.P.W.). E.M.M. was a Harvard Medical School Department of Neurobiology Graduate Fellow.

## Author information

Authors

### Contributions

Conceptualization, E.M.M., A.W., M.A.K., D.P.C., and W.P.W.; formal analysis, E.M.M., A.W., W.P.W., and D.P.C.; funding acquisition, D.P.C. and W.P.W.; investigation, E.M.M., A.W., and M.A.K.; methodology, E.M.M., A.W., D.Y., D.P.C. and W.P.W.; software and instrumentation, A.W. and W.P.W; supervision, D.P.C. and W.P.W.; visualization, E.M.M., A.W., D.P.C., and W.P.W.; writing—original draft, E.M.M., A.W., D.P.C., and W.P.W.

### Corresponding authors

Correspondence to David P. Corey or Wesley P. Wong.

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### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks Peter Barr-Gillespie and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Mulhall, E.M., Ward, A., Yang, D. et al. Single-molecule force spectroscopy reveals the dynamic strength of the hair-cell tip-link connection. Nat Commun 12, 849 (2021). https://doi.org/10.1038/s41467-021-21033-6

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