Nanomechanics of wild-type and mutant dimers of the inner-ear tip-link protein protocadherin 15

Abstract

Mechanical force controls the opening and closing of mechanosensitive ion channels atop the hair bundles of the inner ear. The filamentous tip link connecting transduction channels to the tallest neighboring stereocilium modulates the force transmitted to the channels and thus changes their probability of opening. Each tip link comprises four molecules: a dimer of protocadherin 15 (PCDH15) and a dimer of cadherin 23, all of which are stabilized by Ca²⁺ binding. Using a high-speed optical trap to examine dimeric PCDH15, we find that the protein's mechanical properties are sensitive to Ca²⁺ and that the molecule exhibits limited unfolding at a physiological Ca²⁺ concentration. PCDH15 can therefore modulate its stiffness without undergoing large unfolding events under physiological conditions. The experimentally determined stiffness of PCDH15 accords with published values for the stiffness of the gating spring, the mechanical element that controls the opening of mechanotransduction channels. When PCDH15 exhibits a point mutation, V507D, associated with nonsyndromic hearing loss, unfolding events occur more frequently under tension and refolding events occur less often than for the wild-type protein. Our results suggest that the maintenance of appropriate tension in the gating spring is critical to the appropriate transmission of force to transduction channels, and hence to hearing.

Keywords: cochlea; entropic stiffness; gating spring; genetics of deafness; hair cell.

Fig. 1.

The structure of PCDH15 and measurements with an optical trap. (A) When a hair bundle is deflected toward its tall edge, the tip links (Inset) that interconnect the stereocilia stretch, opening the mechanotransduction channels (purple) atop each stereocilium and allowing cations in the endolymph to flow into the cell and depolarize it. (B) Each strand of a PCDH15 dimer comprises 11 EC domains and a PICA domain at its carboxy terminus. PCDH15 binds with CDH23 at their amino termini in a handshake interaction. (C) EC domains are composed primarily of β-sheets. Ca²⁺ binding in the linker regions and at the edges of the domains stabilizes the structure against unfolding. (D) In our apparatus, a dimeric protein molecule is tethered between two beads and two laser beams act on the probe bead to measure its position and exert force on it. (E) In our experimental construct, we maintain the dimerization sites in PCDH15 while adding two disulfide bonds and a distinct molecular tag at each end. The V507D construct is identical to the wild-type construct save for the insertion of the mutation in place of V507 (purple in Inset). (F) A force-ramp experiment comprises the extension phase of the cycle, during which force is increased at a constant rate, and the relaxation phase of the cycle, during which force is decreased back to a minimum at the same rate. In these experiments, the minimum force is 1 pN and 2 s elapses between successive cycles. Unfolding events can be seen as sudden steps during an individual extension. (G) Repetition of a force-ramp cycle hundreds of times on the same protein molecule yields a heat map in which the brighter colors represent more highly occupied states. The heatmap superimposes both extension and relaxation phases of every cycle. The illustrative record from panel F is overlaid in white.

Fig. 2.

Force-ramp responses of wild-type PCDH15 at three Ca²⁺ concentrations. (A) At a saturating Ca²⁺ concentration of 3 mM, PCDH15 unfolded infrequently. The dashed line represents a fit of Eq. 1 to the extension and relaxation phases of the illustrative cycle. In a fit of Eq. 1 to the extension phase of the cycle, x_E = 39.9 nm and F_HALF = 1.4 pN. In a fit to the relaxation phase, x_E = 40.9 nm and F_HALF = 1.5 pN. For both phases, K = 3.7 mN m⁻¹. (B) In a heatmap for a saturating level of Ca²⁺, 3 mM, the single bright branch indicates one highly occupied state that reflects the infrequent and small unfolding events. (C) The total unfolding length during the extension phases of all cycles in all datasets at 3 mM Ca²⁺ peaked at 1.8 ± 0.1 nm and 6.3 ± 0.2 nm (arrows; means ± SEMs; N = 5 datasets; n = 131 events). (D) Many unfolding events occurred at forces below 10 pN at 3 mM Ca²⁺. (E) At a physiological Ca²⁺ concentration of 20 μM, PCDH15 often did not unfold and was more extensible than with 3 mM Ca²⁺ in the same force range. In a fit of Eq. 1 to the extension phase of the cycle, x_E = 63.8 nm and F_HALF = 2.4 pN. In a fit to the relaxation phase, x_E = 63.1 nm and F_HALF = 2.4 pN. For both phases, K = 2.5 mN m⁻¹. (F) The illustrative heatmap has one bright branch indicative of the infrequent and small unfolding events at 20 μM Ca²⁺. (G) At 20 μM Ca²⁺, the total unfolding per cycle was slightly greater than at a saturating level of Ca²⁺, with peaks at 4.5 ± 0.1 nm and 11.5 ± 0.1 nm (arrows; means ± SEMs; N = 4 datasets; n = 172 events). (H) At 20 μM Ca²⁺, individual unfolding events with a mean of 4.6 ± 0.1 nm occurred predominantly at forces below 40 pN. (I) An illustrative force-ramp cycle in the absence of Ca²⁺ and in the presence of 1 mM EDTA shows a small unfolding event followed by a larger one. In this case, Eq. 1 is fitted separately to each segment demarcated by the unfolding events. In a fit to the segments in the extension phase of the cycle, F_HALF = 4.1 pN, whereas x_E = 55.2 nm, 59.6 nm, and 78.8 nm for the successive segments. In a fit to the relaxation phase, x_E = 84.5 nm and F_HALF = 5.1 pN. For both phases, K = 2.4 mN m⁻¹. (J) The numerous bright branches in the heatmap reflect the multiple preferred conformational states of PCDH15 in the absence of Ca²⁺ and in the presence of 1 mM EDTA. (K) The total unfolding per cycle peaked at 23.3 ± 0.6 nm (arrows; mean ± SEM; N = 6 datasets, n = 490 events), but many larger events occurred in the absence of Ca²⁺ and in the presence of 1 mM EDTA. (L) There is no clear relationship between the size of individual unfolding events and the corresponding forces in the absence of Ca²⁺ and presence of 1 mM EDTA.

Fig. 3.

Force-ramp responses of V507D at three Ca²⁺ concentrations. (A) At a saturating level of Ca²⁺, 3 mM, a subset of V507D molecules underwent only small unfolding events, whereas another subset had more frequent unfolding (SI Appendix, Fig. S5A). The dashed line represents the fit of Eq. 1 to the segmented extension and relaxation phases. In a fit to the segments in the extension phase of the cycle, F_HALF = 2.4 pN, whereas x_E = 34.9 nm, 44.0 nm, and 91.6 nm for the successive segments. In a fit to the relaxation phase, x_E = 99.5 nm and F_HALF = 4.0 pN. For both phases, K = 3.2 mN m⁻¹. (B) The bright branches on the heatmap reflect the frequent unfolding events observed in individual cycles. (C) The frequency distribution of total unfolding length per cycle peaked around 8.8 ± 0.1 nm, 50.0 ± 0.2 nm, and 66.3 ± 0.1 nm (means ± SEMs; N = 24 datasets; n = 1,889 events). (D) As the size of the individual unfolding events grew larger, the force of unfolding declined, with many events occurring around 30 pN. (E) At a physiological concentration of Ca²⁺, 20 μM, frequent unfolding was seen at the single-cycle level. In a fit of Eq. 1 to the segments in the extension phase of the cycle, F_HALF = 2.1 pN, whereas x_E = 48.1 nm, 68.6 nm, and 98.6 nm for the successive segments. In a fit to the relaxation phase, x_E = 110.9 nm and F_HALF = 6.4 pN. For both phases, K = 2.1 mN m⁻¹. (F) The unfolding seen in the individual cycles is reflected by the bright branches on the exemplary heatmap. (G) The frequency distribution of total unfolding length per cycle during the extension phase peaked around 14.2 ± 0.2 nm, 27.3 ± 0.1 nm, and 39.4 ± 0.3 nm (means ± SEMs; N = 16 datasets; n = 1,081 events). (H) As at a saturating level of Ca²⁺, the larger unfolding events were associated with smaller forces of unfolding. (I) When Ca²⁺ was absent, V507D extended easily, even without large unfolding events. In the fit of Eq. 1 to the segments in the extension phase of the cycle, F_HALF = 3.7 pN, whereas x_E = 130.9 nm, 157.6 nm, and 174.0 nm for the successive segments. In a fit to the relaxation phase, x_E = 188.2 nm and F_HALF = 6.2 pN. For both phases, K = 1.6 mN m⁻¹. (J) The bright branches on the illustrative heatmap reflect the unfolding behavior seen on the individual cycle level. The upper limits of the end-to-end distance at this level of Ca²⁺ exceeded those seen at higher concentrations of Ca²⁺. (K) The frequency distribution of total unfolding length per cycle was unimodal, with one peak at 49.3 ± 1.4 nm (mean ± SEM; N = 4 datasets; n = 362 events). (L) In the absence of Ca²⁺, there was no clear relationship between the size of individual unfolding events and the forces at which they occurred.

Fig. 4.

Clustering of force-ramp trajectories and interstate transitions. (A) In a heatmap representing the relaxation-phase trajectories from all Ca²⁺ conditions and both PCDH15 constructs, the lines with different colors demarcate six conformational states. (B) A scatter plot shows the fitted x_E values for individual trajectories through different conformational states. The data represent means ± SEMs. (C–H) Conformational transition maps summarize the trajectories of the two PCDH15 constructs at different Ca²⁺ concentrations. Segmented by conformational changes, the values along the abscissa denote individual segments within a trajectory in ascending order of force. The thickness of each arrow’s shaft is proportional to the frequency of a specific interstate transition. The horizontal arrows indicate conformational changes within a state, whereas the arrows pointing up and to the right denote conformational changes made between distinct states.

Fig. 5.

Entropic stiffness of PCDH15’s states as a function of force. The stiffnesses of the states were calculated by determining the inverse of the slope of each displacement-force relationship. In state 1, when PCDH15 was fully folded, the stiffness approached the enthalpic values above 15 pN of applied force. In states 2 to 6, in which PCDH15 had some unfolded portions, the stiffness of PCDH15 remained below the enthalpic limit. State 1 largely comprises trajectories of the wild-type protein at a saturating level of Ca²⁺, whereas the remaining states predominantly contain trajectories at lower Ca²⁺ concentrations and from the V507D mutant. The results suggest that, under physiological conditions, the effective stiffness of PCDH15 is lower than its enthalpic limit of 40 mN m⁻¹ at a saturating concentration of Ca²⁺ (SI Appendix, Note S7). Error bars represent SEMs.

Fig. 6.

Proposed mechanism of deafness for mutated V507D. (A) Our data suggest that V507D is misfolded or partially unfolded over the physiological range of forces experienced in the cochlea. (B) If the tip links lack sufficient tension to open the mechanosensitive ion channels when stimulated, the ensuing deficit of Ca²⁺ in the stereocilia causes their degeneration.