Volume 113, Issue 8, Pages 1868-1881 (October 2017) A Model for Link Pruning to Establish Correctly Polarized and Oriented Tip Links in Hair Bundles  Nathan Tompkins, Kateri J. Spinelli, Dongseok Choi, Peter G. Barr-Gillespie  Biophysical Journal  Volume 113, Issue 8, Pages 1868-1881 (October 2017) DOI: 10.1016/j.bpj.2017.08.029 Copyright © 2017 Biophysical Society Terms and Conditions

Figure 1 Hair bundles and tip links. (A–C) Given here are adult bullfrog sacculus hair bundles. (A) Given here is an SEM image of a single bundle. (B) Given here is an SEM image of straight links (arrows) and an angled link (asterisk). (C) Given here is a cross section of a bullfrog bundle, labeled with phalloidin to highlight actin. The kinocilium is at the top of the image, so the stereocilia run from short-to-tall from the bottom of the image to the top. Scheme for numbering stereocilia is shown. “KC” marks the position of the kinocilium. (D and E) Shown here are P1 chick cochlea hair bundles. (D) Shown here is an SEM image of single bundle. (E) Given here is an SEM closeup of a bundle, 6 h after treatment with BAPTA. In addition to straight links (arrows) and angled links (asterisks), a double tip link can be seen (double arrows). Scale bars, 0.5 μm. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 2 Tip-link stability. Tip link stability depends on the polarity of the constituent cadherins and the concentration of Ca2+ in the two stereocilia at either end of the link. (A–F) Given here are straight links, which are located along a single column. (A) Normal (PC) orientation is shown; link is stable. (B) Normal polarity is shown; link is still stable because Ca2+ (shaded), diffusing from stereocilia tips due to the presence of a superior link (Sup), does not reach a high concentration at the upper (CDH23) end of the link. (C) Incorrect (CP) polarity is shown; link is unstable because Ca2+ is too low at PCDH15 end. (D) A secondary PC link (Sec) in parallel with a primary PC link is shown; links are unstable because Ca2+ is too high at PCDH15 end. (E) Mixed-orientation double link is shown; the CP link is unstable because it experiences low Ca2+ at the PCDH15 end. By contrast, the PC link is stable. (F) Double reverse links are shown; links are unstable because each CP link experiences low Ca2+ at its PCDH15 end. (G–J), Angled links are shown, which cross from one column to an adjacent one. (G) CP angled link is shown; unstable because PCDH15 motor cannot generate sufficient tension. (H) PC angled link is shown; link is stable because Ca2+ is not high at CDH23 end. (I) PC angled link with normal link at tip of taller stereocilium (a superior link) is shown; the PC angled link is unstable because at the CDH23 end, Ca2+ is too high due to the close presence of a superior link (Sup). (J) PC link connecting to top row is shown; link is stable because there is no Ca2+ entry into tallest stereocilia. To see this figure in color, go online. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 3 Angled links are less likely to be associated with superior links than are straight links. (A) Given here is a hair bundle from control cochlea, cultured for 6 h. Inset shows two tip links, both of which are straight and have superior links in the taller stereocilium (both links are SS). (B) Given here is a bundle from BAPTA-treated cochlea, cultured for 6 h. Inset shows four links, including two straight links and two angled links. One of the straight links is associated with a superior link (SS), whereas the other straight link is not (SN); one of the angled links is associated with a superior link (AS), whereas the other angled link is not (AN). (C) Given here is an overlay of SS, SN, AS, and AN links on the image from (B). Scale bar, 0.5 μm; applies to (A–C). (D) Shown here is quantitation of association of superior links with straight and angled links from 31 hair bundles, imaged from three separate cochlear epithelia. The y axis is the ratio of straight or angled links with a superior link to those without. Each data point corresponds to results from a single bundle that was scored by three observers, and the values plotted are the mean values from those observers. Straight and angled links were quantified in each bundle, and the results from a paired t-test (or generalized linear mixed-effects model) are indicated. (E) Given here is the relationship SS/SN (straight with/without superior link) and AS/AN (angled with/without) for each of the 31 bundles counted. The dashed line indicates the unity line; the solid line represents an exponential fit through zero, where AS/AN = 0.87•(1–exp(−1.36•SS/SN)). To see this figure in color, go online. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 4 Simulation of tip link regeneration and pruning. Panels are all from one simulation; the iteration number is indicated in the upper left. Here, the typical parameters were used: PriGenRate, 15; SecGenRate, 5; IncDegRate, 94; NorSecDegRate, 30; CorAngDegRate, 17; and gen, 50. Black circles are stereocilia; the gray circle is the kinocilium, which indicates that the taller side of the hair bundle is at the top of the panel. Indicated are normal polarity links (PC), reverse polarity links (CP), and secondary PC links. Links are in random orientations in the initial iterations, but progressively become refined along the physiological axis. To see this figure in color, go online. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 5 Fitting the tip-link regeneration model to experimental data. (A) Shown here are experimental data used for fitting simulation and results from best fitting parameter values for simulation. Given is mean ± SD for straight links with a superior link to those without (SS/SN) and angled links with a superior link to those without (AS/AN) ratios, both at 6 h post-BAPTA treatment. The values for the simulation using the typical parameters (Table 1) are shown for comparison. Significance (by t-test): ∗∗∗, p < 0.001; ns, not significant. (B) The fit is insensitive to the rate of degeneration of PC secondary links (NorSecDegRate). RSS is the sum of the squared residuals. Rates for degeneration of CP links (IncDegRate) and angled PC links with a superior link (CorAngDegRate) were set at 94 and 17, respectively. (C) Given here is influence of IncDegRate and CorAngDegRate on the simulation fit to the data. Each vertex corresponds to the point (IncDegRate, CorAngDegRate, RSS). Color-coding for RSS values is indicated by the scale on the right. In (B) and (C), the primary generation rate (PriGenRate) was 15 and the secondary generation rate (SecGenRate) was 5; all simulations used 50 iterations, and 50 runs were averaged to generate each data point. To see this figure in color, go online. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 6 Influence of parameter values on regeneration of primary and secondary links. (A–O) Each row shows variations of a specified parameter (indicated on left). Boxes indicate simulations with the standard parameter values (Table 1). Primary links only are shown for variations of PriGenRate, SecGenRate, and the three degeneration rates. Secondary links are shown for variations of SecGenRate. Parameters used in each simulation are indicated at the top of each panel, and the key is located at the top of the figure. Each run used 50 iterations, and 50 runs were averaged to generate each curve. To see this figure in color, go online. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 7 Transduction channel block induces the formation of angled links. (A and B) Given here is the simulation output, starting with the CanonicalLinks link set and the typical parameter values (Table 1); CorAngDegRate was set to zero to simulate the lack of feedback between a superior link and an angled link. (A) Given here are the straight and angled primary links. Note the increase in angled PC links. All runs used 50 iterations, and 50 runs were averaged to generate each curve. (B) Given here are the link patterns for one run of the simulation. Values in the upper-right corner indicate the iteration number. (C–E) Shown here is scanning electron microscopy of hair bundles to examine the effects of tubocurarine block of transduction channels. (C) Hair cells in control cultures have many straight tip links at stereocilia tips (arrows). Scale bar, 0.5 μm; applies to (C) and (D). (D) Shown here are hair cells that were cultured in the presence of 100 μM tubocurarine to block the transduction channel had both straight links (arrows) and angled links (asterisks). (E) Given here is quantitation of control (C) and tubocurarine (T) link counts; each point corresponds to one bundle, measured at apical, mid, and basal locations. Bundles were imaged from apical and basal regions in one epithelium each for C and T in (E). The experiment was carried out with similar results three times. The y axis indicates the number of straight or angled links counted divided by the number of straight link positions in each bundle that were visible for counting. To see this figure in color, go online. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 8 Ca2+ entry into hair bundle with regenerated tip links. (A) Shown here is the final link distribution for an idealized hair bundle. Note the stable angled links on the last row (arrows) that are not present on the next rank of last-row stereocilia (asterisks). (B) Given here is the Ca2+ entry (shaded stereocilia) during positive deflection of an idealized bundle. Note that some last-row stereocilia show Ca2+ increase because of the presence of angled links. (C) Given here is a scanning electron micrograph showing chick cochlea final-row links. Note that there is a plethora of links running in multiple directions on the last two rows (arrows). In chick cochlea, unlike in frog sacculus, mouse utricle, or mouse cochlea, the last two rows of stereocilia are of the same height; they are also narrower in diameter than the rest of the stereocilia. Scale bar, 0.5 μm. To see this figure in color, go online. Biophysical Journal 2017 113, 1868-1881DOI: (10.1016/j.bpj.2017.08.029) Copyright © 2017 Biophysical Society Terms and Conditions