Fig. 4: Cis-dimerization and extracellular Ca²⁺ alter the lifetime of the tip-link connection through elastic modulation.

a Avidity under force is enhanced by cis-dimerization. Dimeric tip-link proteins were truncated to just the first five EC domains, to remove cis-dimerization interfaces further from the N termini. Unbinding forces (blue circles, n = 159 unbinding events) were fit with the force-dependent avidity model, with fixed parameters k_off = 0.5 s⁻¹ and f_β = 13.5 pN (EC1-5/1-5). Error is shown as the optimal bandwidth from a kernel density estimation. At the rupture forces tested, the model fit was indistinguishable from a model in which there is no rebinding. a’ Truncated proteins show an enhancement in lifetime above 6 pN primarily attributable to force-sharing. a” C_eff calculated from the fit decreased rapidly with the applied force for EC1-5 dimers. b Low [Ca²⁺] destabilizes the tip link. Unbinding forces in 30 µM Ca²⁺ (blue, n = 339 unbinding events) were nearly identical to those in 2 mM Ca²⁺ (black), but were much lower in 10 µM Ca²⁺ (magenta, n = 344 unbinding events). Error is shown as the optimal bandwidth from a kernel density estimation. Model fits suggested that 10 µM Ca²⁺ weakened the connection both by accelerating the single-bond off-rate (k_off = 2.6 ± 0.8 s⁻¹) and by altering the mechanical properties of the protein complex (f_c = 2.9 ± 1.1 pN). b’ Calculated lifetimes of the tip link in 30 µM Ca²⁺ at forces between 0 and 30 pN were indistinguishable from lifetimes at 2 mM Ca²⁺ but were severely decreased at 10 µM Ca²⁺. b” Calculated C_eff decreased rapidly with applied force at 10 µM Ca²⁺ through increased protein elasticity. c Scatter plot of full-length dimer lifetimes measured from biolayer interferometry experiments at various concentrations of Ca²⁺, and of the truncated EC1-5/EC1-5 dimer in 2 mM Ca²⁺ (mean ± SD). 2 mM: 63 ± 16 s (n = 18 independent experiments), 50 µM: 52 ± 4 s (n = 9 independent experiments), 30 µM: 64 ± 9 s (n = 6 independent experiments), 10 µM: 43 ± 13 s (n = 9 independent experiments), Truncated: 27 ± 12 s. The Student’s two-tailed unpaired t-test was used to determine statistical significance (**p = 0.0028, ***p < 0.001). d Schematic of singly-bound dimeric tip links, illustrating how an increase in elasticity produced by low extracellular Ca²⁺ can separate unbound ends and lower C_eff.