Inversions are local movements of nascent sibling hair cells. (A) Scheme of a neuromast, depicting an outer ring of mantle cells (red), internal supporting cells (gray) and central hair cells (light blue) with their axis of planar polarity (dark blue dots). Dashed line indicates the midline of the organ. (B) Scheme of hair-cell development. Unipotent progenitors (UHCP) divide into two hair cells. Sibling hair cells undergo positional inversion to place Notch-on/Emx2(−) and Notch-on/Emx2(+) cells on opposite sides of the epithelium. (C) The inversion is an angular movement of at least 90°. (D) Selected frames from a time-lapse movie of cell-pair inversion in a wild-type neuromast expressing cldnb:EGFP and myo6b:GFP. The timings are relative to the mitotic division that generates the hair-cell pair. Scale bar: 5 µm. (E) One exemplary hair-cell dyad during an inversion. The position of each cell during the inversion is depicted relative to the centroid of the pair. Time is color-coded from dark violet to yellow, where 0 is the time immediately after cell division and 400 is the upper limit of the inversion. (F) Position of the hair-cell progenitor at the time of its mitotic division. The color of the dots indicates whether the resulting hair-cell pair inverts (red) or not (blue). The center was defined as the position of all pre-existing hair cells in the neuromast. Side panels show the density of points along the dorsoventral (D-V) and anteroposterior (A-P) axes of the epithelium. It shows 22 inverting and 18 non-inverting hair-cell pairs from different neuromasts in 22 specimens. (G) Boxplots showing the Pearson correlation coefficient for the movement of cells in the neuromast along the A-P axis. Each point represents the cells during a rotation. Box plots show median values (middle bars) and first (Q1) to third (Q3) interquartile ranges (boxes); upper whisker is either 1.5× the interquartile range or the maximum value (whichever is the smallest) and lower whisker is either 1.5× the interquartile range or the minimum value (whichever is the biggest). For each neuromast, the movement was compared between the rotating hair cells (HC); the rotating hair cells and all other cells; and between all other cells. n=9 independent neuromasts from N=9 different larvae.

Rotations are characterized by strong homotypic cell-cell interactions. (A) Scheme of an inversion (top) and fitting a four-parameter logistic function to the empiric data of the absolute cumulative angles (bottom), revealing the three phases of the inversion process. Green dot represents the transition between Phases 1 and 2, and the blue dot between Phases 2 and 3. These transitions are called onset and termination, respectively. (B) Distance between sibling hair cells (HC) during the three phases. Sibling cells are closest during Phase 2. (C) Time-resolved cumulative angular change (top) for a representative cell pair from Time 0. The two dashed vertical lines mark the beginning and end of the rotation. A negative angle change indicates a clockwise direction of rotation. (D) Circularity of the same cell pair, which, taken as a unit, reaches maximal circularity during Phase 2. The onset and termination of inversion are marked by dashed vertical lines. (E) Length of the junction between hair cell pairs, which is highest during Phase 2. (F) Comparison of mean circularity for inverting and non-inverting cell pairs during the three phases. Phase 2 is characterized by a significantly higher circularity than Phase 1, and the circularity drops dramatically in Phase 3. The circularity for non-inverting pairs is comparable to the Phase 3 of inverting pairs. Trivially, for non-inverting cells there is a single phase. **P<0.01, Wilcoxon rank sum test. Box plots show median values (middle bars) and first (Q1) to third (Q3) interquartile ranges (boxes); upper whisker is either 1.5× the interquartile range or the maximum value (whichever is the smallest) and lower whisker is either 1.5× the interquartile range or the minimum value (whichever is the biggest). Each point represents the cells during a rotation.

Notch1a/Emx2 asymmetry is dispensable for cell-pair rotations. (A) Illustration of the cell-cell interfaces, shapes of which are classified as curved (C), linear (I), S or Ƨ shaped. Because an Ƨ cannot be rotated into an S, a distinction is made of the rotation direction. (B) The frequency of distinct interface shapes during inversion. The most common shape is a straight interface (63.41%), followed by curved (21.31%) and then S-shaped curves (S: 6.57% and Ƨ: 8.7%). No shape consistently correlated with the chirality of rotation. (C) Scheme of the topological interactions between all epithelial cells during the inversion of a cell pair (representing one empirical example). Each circle is an individual cell. The area of each circle is proportional to the area of real cells from microscopy images. Straight lines (edges) represent a physical contact between any two cells. Cells are considered neighbors if there is an edge connecting them. A pair of hair cells is colored blue and orange. Neighboring cells are colored light blue if they connect only to the blue sibling in a given frame; yellow if they only connect to the other sibling; or green if they are connected to both. (D) Absolute cumulative difference in the number of neighbors for each cell of inverting (blue) and non-inverting (red) pairs. The difference of neighbors at a given time is the number of neighbors of Cell A minus the number of neighbors of Cell B. The cumulative difference at any given time T is the sum of the neighbor differences from time 1 to time N. Therefore, if there is no cell with a constantly higher number of neighbors over time, the cumulative difference remains close to zero. However, if either one of the cells constantly has more neighbors, over time the absolute cumulative difference will go up. Vertical dashed line and gray shaded areas mark the median and standard deviation of the Phase 2I for the inverting cells in this sample. Shown is the LOESS smoothing of inverting and non-inverting trajectories. (E) Fraction of hair-cell pairs that invert in wild type, emx2 mutant and notch1a mutant larvae. n (number of cell pairs)=71 from wild type, 42 from emx2 mutant, 22 from notch1a mutant larvae.

Loss of Notch1a but not Emx2 impacts cell-pair rotations. (A) Handedness of cell-pair inversions in wild-type, emx2 and notch1a mutant larvae. (B) Comparison of the onset (duration of Phase 1) of inverting cell pairs from wild type, emx2 and notch1a mutants. (C) Comparison of the rotation duration (Phase 2) of inverting cell-pairs from wild-type, emx2 mutant and notch1a mutant larvae. (D) Comparison of the termination time (Start of Phase 3) of inverting cell pairs from wild-type, emx2 mutant and notch1a mutant larvae. (A-D) n (number of cell pairs)=40 from wild-type, 23 from emx2 mutant, 9 from notch1a mutant larvae. Statistics were calculated using an unpaired two-sided Student's t-test. Box plots show median values (middle bars) and first (Q1) to third (Q3) interquartile ranges (boxes); upper whisker is either 1.5× the interquartile range or the maximum value (whichever is the smallest) and lower whisker is either 1.5× the interquartile range or the minimum value (whichever is the biggest). Each point represents the cells during a rotation.

Mutations in notch1a impact the precision of the inversion. (A) Overshooting versus final turn in the rotations of cell pairs from wild type, emx2 and notch1a mutants. We defined overshooting as the difference between the maximal turn and the final turn (absolute cumulative angle). (B) The maximal and final turns of >90° and >180° for cell pairs from wild-type, emx2 mutant and notch1a mutant larvae. The sketches below illustrate the definition of categories with an example. (C) Comparison of cell pair wobbling and final turn. Wobbling was defined as the cumulative angle changes minus final turn. (D) Noise of rotating cell pairs was calculated as the arc length of each trajectory normalized by the shortest path from starting position to final position. Statistics were calculated using the Anderson-Darling test. (A-D) n (number of cell pairs)=71 from wild-type, 42 from emx2 mutant, 22 from notch1a mutant larvae. Box plots show median values (middle bars) and first (Q1) to third (Q3) interquartile ranges (boxes); upper whisker is either 1.5× the interquartile range or the maximum value (whichever is the smallest) and lower whisker is either 1.5× the interquartile range or the minimum value (whichever is the biggest). Each point represents the cells during a rotation.

Cell-pair asymmetry affects the precision and accuracy of Phase 3. (A) Relationship between the final and initial angles. The initial angle is the positional angle of the cell pair immediately after the division. The final angle is where cells come to rest (regardless of whether they have rotated). Note that both angles were normalized to 0-180° (from 0-360°). (B) Relationship between the initial angle and the final turn of cell pairs of wild type, emx2 mutant and notch1a mutants. Note the initial angle was normalized to 0-180° (from 0-360°). (C) Comparison of the final turn of cell pairs from wild type, emx2 mutant and notch1a mutant larvae. Statistics were calculated using an unpaired two-sided Student's t-test. Box plots show median values (middle bars) and first (Q1) to third (Q3) interquartile ranges (boxes); upper whisker is either 1.5× the interquartile range or the maximum value (whichever is the smallest) and lower whisker is either 1.5× the interquartile range or the minimum value (whichever is the biggest). Each point represents the cells during a rotation. (D) Final angle of cell pairs from wild type, emx2 and notch1a mutants. The difference in the distribution of final angles from wild type and the two mutants are statistically significant (P<0.05), Statistics were calculated using a two sample Kolmogorov–Smirnov test (P=0.004 for wild type and emx2 mutant, and P=0.01 for wild type and notch1a mutant). (A-D) n (number of cell pairs)=71 from wild type, 42 from emx2 mutant, 22 from notch1a mutants.

Computational modeling of cell-pair inversion. (A,B) Sketch of the two-cell computational model. Each cell freely rotates around a circle of a fixed radius, with its angle with respect to the x-axis (representing the A-P axis) as the degree of freedom for each cell. The arrows in each cell indicate the direction as +1 or −1 for anti-clockwise and clockwise movement, respectively. Each cell is attracted to one and only one Gaussian well. The depth of each well determines the strength with which its corresponding cell is attracted. The depth of one well can be different from the other. (A) In the asymmetrical model both cells have their attractive wells on opposite sides of the A-P axis. (B) In the symmetrical model both attractive wells lie on one side of the system, leading to a competition. (C,D) Two typical trajectories of the inverting pair in cumulative angle, as defined in Fig. 2C, for the asymmetrical and symmetrical model, respectively. The background colors indicate the phases of the process: blue (Phase 1), orange (Phase 2), green (Phase 3). (E) Distribution of final angles predicted by both models. Well depths are 0 and 50 (relative well depth=0) for the asymmetric model, and 50 and 20 (relative well depth=0.4) for the asymmetric model. (F,G) The final angle (F) and the noise (G) predicted by the asymmetric (symmetric) model are robust (sensitive) against the relative well depth. The depth of the reference well was fixed at 50 in these simulations. Asymmetric and symmetric models are represented in blue and red, respectively. Box plots show median values (middle bars) and first (Q1) to third (Q3) interquartile ranges (boxes); upper whisker is either 1.5× the interquartile range or the maximum value (whichever is the smallest) and lower whisker is either 1.5× the interquartile range or the minimum value (whichever is the biggest).

A model of cell-pair rotation in vivo. Overview of cell-pair inversion process summarizing the key elements of the inversions in wild type on the left, and stating major differences occurring in the notch1a^−/− and emx2^−/− larvae on the right. The precision of the angular movement in vivo approaches that of cells in vitro. Phase 1 starts immediately after division of the UHCP, is characterized by a coordinated shape of the cells and expansion of the homotypic bond. Phase 2 marks the maximum of circularity of the dyad, the length of the homotypic bond and of angular velocity. Mutant rotations are characterized by significant wobbling, denoted by double-headed arrows. A computational model recapitulates this dynamic difference just by assuming that the minima of energy potentials are either symmetric or asymmetric (green and blue curves represent the Gaussian wells to which minima the respective cells are attracted in our computational model). In Phase 3 the angle between the cells and the A-P axis (blue lines) is 0 with high accuracy and precision but it is misaligned in mutants. The symmetric and asymmetric models can also explain these differences.