Size control of the inner ear via hydraulic feedback

Kishore R Mosaliganti; Ian A Swinburne; Chon U Chan; Nikolaus D Obholzer; Amelia A Green; Shreyas Tanksale; L Mahadevan; Sean G Megason

doi:10.7554/eLife.39596

. 2019 Oct 1;8:e39596. doi: 10.7554/eLife.39596

Size control of the inner ear via hydraulic feedback

Kishore R Mosaliganti ^1,^†, Ian A Swinburne ^1,^†, Chon U Chan ^2,^†,^‡, Nikolaus D Obholzer ¹, Amelia A Green ¹, Shreyas Tanksale ¹, L Mahadevan ^2,^3,^4,^5,^✉, Sean G Megason ^1,^✉

Editors: Raymond E Goldstein⁶, Didier Y Stainier⁷

PMCID: PMC6773445 PMID: 31571582

Abstract

Animals make organs of precise size, shape, and symmetry but how developing embryos do this is largely unknown. Here, we combine quantitative imaging, physical theory, and physiological measurement of hydrostatic pressure and fluid transport in zebrafish to study size control of the developing inner ear. We find that fluid accumulation creates hydrostatic pressure in the lumen leading to stress in the epithelium and expansion of the otic vesicle. Pressure, in turn, inhibits fluid transport into the lumen. This negative feedback loop between pressure and transport allows the otic vesicle to change growth rate to control natural or experimentally-induced size variation. Spatiotemporal patterning of contractility modulates pressure-driven strain for regional tissue thinning. Our work connects molecular-driven mechanisms, such as osmotic pressure driven strain and actomyosin tension, to the regulation of tissue morphogenesis via hydraulic feedback to ensure robust control of organ size.

Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Research organism: Zebrafish

Introduction

A fundamental question in developmental biology is how different organs acquire their proper sizes, which are necessary for their healthy function. The existence of control mechanisms is evident in the consistency of organ size in the face of intrinsic noise in biological reactions such as gene expression, and in the observed recovery from size perturbations during development (Waddington, 1959; Debat and Peronnet, 2013; Rao et al., 2002; Lestas et al., 2010). However, unlike in engineered systems, where there is often a clear distinction and hierarchy between the controller and the system, in organ growth one may not have a clear hierarchy—instead there may be control mechanisms distributed across tissues and across scales. Furthermore, in developmental biology, we observe an evolved system that is not necessarily robust to all experimental perturbations that we apply when trying to understand their control networks. Consequently, it can be difficult to distinguish what is necessary for growth from what controls size.

Identifying specific mechanisms that coordinate growth—to ultimately control organ size—has been difficult because the phenomenon of growth encompasses regulatory networks that can span the molecular to organismic. Classical organ transplantation and regeneration studies in the fly (Bryant and Levinson, 1985; Hariharan, 2015), mouse (Metcalf, 1963; Metcalf, 1964), and salamander (Twitty and Schwind, 1931) have indicated that both organ-autonomous and non-autonomous mechanisms control size. In his ‘chalone’ model, Bullough proposed growth duration to be regulated by an inhibitor of proliferation that is secreted by the growing organ and upon crossing a concentration threshold stops organ growth at the target size (Bullough and Laurence, 1964). Modern evidence for organ intrinsic chalones exists in myostatin for skeletal muscle, GDF11 for the nervous system, BMP3 for bone, and BMP2/4 for hair (McPherron et al., 1997; Wu et al., 2003; Plikus et al., 2008; Gamer et al., 2009). Several existing models for size control are based on global positional information regulating cell proliferation based on a morphogen gradient until final organ size is achieved (Day and Lawrence, 2000; Rogulja and Irvine, 2005; Wartlick et al., 2011). Other models emphasize the role of local cell-cell interactions in regulating cell proliferation or cell lineages to make tissues of the correct proportions (García-Bellido, 2009; Kunche et al., 2016). Given that cells are coupled to each other through cell-cell and cell-substrate contacts, physical constraints and tissue geometry provide tissue-level feedback. More recent models emphasize the role of tissue mechanics in regulating cell proliferation via anisotropic stresses and strain rates (Shraiman, 2005; Ingber, 2005; Savin et al., 2011; Hufnagel et al., 2007; Behrndt et al., 2012; Irvine and Shraiman, 2017; Nelson et al., 2017; Pan et al., 2016). From a molecular perspective, the insulin, Hippo (Dupont et al., 2011; Legoff et al., 2013; Pan et al., 2016) and TOR signaling pathways (Colombani et al., 2003; Zhang et al., 2000) have been well-established as regulators of organ size. Several studies have demonstrated that genetic mutation in these pathways is sufficient to alter organ or body size through increases in cell number, cell size, or both (Tumaneng et al., 2012), but the mechanisms that control size in the engineering sense (e.g. feedback of size on growth rate) are generally not known.

Most size control theories have focused on regulation of cell proliferation. Control may also arise from regulation of other parameters such as cell shape, material properties, transepithelial transport, adhesion, and the extracellular environment. In particular, fluid accumulation is a feature of developmental growth for several luminized organs including the embryonic brain (Desmond and Jacobson, 1977; Lowery and Sive, 2005), eye (Coulombre, 1956), gut (Bagnat et al., 2007), Kupffer’s vesicle (Navis et al., 2013; Dasgupta et al., 2018), the inner ear (Abbas and Whitfield, 2009; Hoijman et al., 2015), and the whole mammalian embryo (Chan et al., 2019). Water transport across an epithelium underlies these phenomenon (Frömter and Diamond, 1972; Günzel and Yu, 2013; Rubashkin et al., 2006; Fischbarg, 2010), and for the developing brain and eye it was shown that fluid accumulation coincides with increased hydrostatic pressure (Desmond and Jacobson, 1977; Coulombre, 1956). Just as water is fundamental to the size and function of a cell’s cytoplasm, the fluids filling the lumens of these organs, which are central to their development and physiological function, are fundamental components of these organs. Although specific ion transporters necessary for fluid accumulation have been identified (Lowery and Sive, 2005; Bagnat et al., 2007; Navis et al., 2013; Abbas and Whitfield, 2009), it is only very recently that we are beginning to get a glimpse of how how ion transport and transepithelial fluid flow are regulated, and their role in growth control, and much still remains to be explored .

Catch-up growth during development is the phenomenon where, after growth delay or perturbation, an organ transiently elevates its growth rate relative to other organs to get back on course. During fly development, if the growth of one imaginal disc is perturbed then a hormone, ecdysone, signals to the other imaginal discs to slow their growth such that the perturbed organ can catch-up and the animal’s coordinated growth can resume (Parker and Shingleton, 2011). The phenomenon of catch-up growth clarified ecdysone’s activity as being important for size control. Catch-up growth also occurs in vertebrates: if an infant heart or kidney is transplanted into an adult, it grows faster than the surrounding tissue to catch-up to a target size (Dittmer et al., 1974; Silber, 1976). Recently, the related phenomenon of organ symmetry has been addressed in the context of tails and the inner ear; but, the control mechanism underlying catch-growth was not clearly identified (Das et al., 2017; Green et al., 2017). Catch-up growth also occurs during bone growth and its study has clarified insulin signaling activity as being important for bone size control (Roselló-Díez and Joyner, 2015; Roselló-Díez et al., 2017; Roselló-Díez et al., 2018). Nonetheless, catch-up growth has been underused in the study of vertebrate-specific mechanisms of organ size control (Roselló-Díez et al., 2018).

Here we use a newly revealed instance of catch-up growth combined with physical theory to uncover how size control is achieved in the zebrafish otic vesicle, a fluid-filled closed epithelium that develops into the inner ear. We postulate that fluid pressure is a fundamental regulator of developmental growth in lumenized organs and hydraulic feedback can give rise to robust control of size.

Results

In toto imaging of otic vesicle development shows lumenal inflation dominates growth, not cell proliferation

We sought to determine how size control is achieved in the zebrafish otic vesicle, a 3D lumenized epithelial cyst that becomes the inner ear. Prior studies used qualitative observations and 4D imaging to examine the formation of the otic vesicle (Haddon and Lewis, 1996; Hoijman et al., 2015; Dyballa et al., 2017). To systematically investigate inner ear morphogenesis at longer timescales between 12–45 hours post-fertilization (hpf), we used high-resolution 3D+t confocal imaging combined with automated algorithms for quantifying cell and tissue morphology (Figure 1—figure supplement 1A–F) (Megason, 2009). Beginning at 12 hpf, bilateral regions of ectoderm adjacent to the hindbrain proliferate and subcutaneously accumulate to form the otic placodes (Figure 1—video 1, Figure 1A). The complex morphology of the inner ear arises from progressive changes in cell number, size, shape, and arrangement along with tissue-level patterns of polarization (12–14 hpf, Figure 1A), mesenchymal-to-epithelial transition (14–16 hpf, Figure 1B) and cavitation (16–24 hpf, Figure 1C). These steps build a closed ovoid epithelial structure, the otic vesicle, filled with a fluid called endolymph (Figure 1—figure supplement 1G–H). After assembly, the otic vesicle undergoes a period of rapid growth (16–45 hpf, Figure 1D) prior to the development of more complex substructures such as the semicircular canals and endolymphatic sac.

To evaluate growth kinetics, we used 3D image analysis (Figure 1—figure supplement 1I–M) to quantify a number of morphodynamic parameters between 16 and 45 hpf. During this period, cell number increased nearly three-fold from 415 ± 26 to 1106 ± 52 cells (blue curve, Figure 1E, for all data-points in Figure 1 n = 10 otic vesicles, data spread is the standard deviation). However, cell proliferation was offset by a decrease in average cell size from 0.55 ± 0.02 pl at 16 hpf to 0.34 ± 0.03 pl at 28 hpf and stayed constant thereafter (red curve). Tissue volume, the product of cell number and average cell size, remained effectively constant (230.6 ± 7.4 pl) until 28 hpf and subsequently increased linearly by 132 pl to 45 hpf (green curve, Figure 1F). The volume of the otic vesicle increased dramatically, by 572 pl from 235 ± 16 pl to 807 ± 23 pl (orange curve). The majority of the increase in size of the otic vesicle is due to an increase in lumen volume (blue curve) from 0 to 440 ± 18 pl (77% of the total increase) while tissue growth contributed only 23% to the increase in size.

Pressure inflates the otic vesicle and stretches tissue viscoelastically

A mismatch between the volumetric growth of the lumen and the tissue enclosing the lumen indicates a potential role for otic tissue remodeling. Since the size of the luminal vesicle, which scales as the cube root of lumen volume, increases more rapidly than the surface area of the vesicle, which scales as the square root of the cell number enclosing that volume, we investigated how epithelial cell shape changes to accommodate growth. We observed a monotonic increase in average cell apical surface area ( $ψ = S_{l} / N$ is lumenal surface area, $N$ is the cell number, Figure 1G). Since the otic epithelium is not uniform in thickness, we examined regions of the epithelium that contribute to the stretch. Except for the future sensory patches at the anterior and posterior ends (poles), epithelial thickness of the remaining otic vesicle significantly decreased from 20 µm to 4 µm during otic vesicle growth (lateral and medial regions, Figure 1H). The increase in lumenal volume and large cell stretching rates suggested that the vesicle is pressurized and the epithelium is under tension.

In the absence of extrinsic forces, cells round-up to a spherical morphology during mitosis by balancing internal osmotic pressure with tension provided by cortical actomyosin (Stewart et al., 2011). To investigate the development of pressure derived stress in the epithelium, we used mitotic cells as 'strain gauges’ by measuring their deviation in aspect ratios from spheres. We observed that mitotic cells fail to round up fully in regions where the otic epithelium pushes against the hindbrain and ectoderm, in contrast to non-contact regions at the anterioposterior poles (Figure 2A,C–G). Furthermore, cell division planes are closely aligned with the surface-normal to the epithelium (red markers, Figure 2H) in comparison to the broader distribution exhibited by the non-contact cell populations (blue). The overall alignment progressively increases in developmental time as cells become more stretched (Figure 2I), consistent with mechanical stress driven spindle alignment previously observed in various systems including the zebrafish gastrula (Campinho et al., 2013), fly imaginal disc (Legoff et al., 2013), and zebrafish pre-enveloping layer (Xiong et al., 2014). Given that the otic vesicle is wedged between the hindbrain and skin (Figure 1—figure supplement 1G–H), we examined the impact of its volumetric growth on these tissues. We reasoned that if pressure is present, the vesicle would exhibit higher rigidity and consequently deform neighboring structures as it increased in size. To test this idea, we quantified the indentation of the hindbrain and otic vesicle interface. We observed that as the vesicle grows, the initially planar hindbrain surface indents in, and the skin bulges out (Figure 2B–F,J).

Figure 2. — (A) Diagram illustrating inhibition of mitotic rounding just prior to cytokinesis from lumenal pressure and reactionary support from hindbrain tissue (hb, grey). (B) Diagram illustrating the deformation of the adjacent hindbrain tissue (hb, grey) as the otic vesicle grows from internal pressure. (**C–F**) 2D confocal micrographs of the otic vesicle at (C) 16 hpf, (D) 24 hpf, (E) 28 hpf, and (F) 32 hpf highlighting the progressive deformation of adjacent hindbrain and ectoderm tissues relative to the dashed-green line. The red and blue arrow heads highlight the progressive deformation in the shape of mitotic cells at contact and non-contact regions, respectively. (G) Quantification of mitotic cell aspect ratios at contact regions (hindbrain-vesicle or ectoderm-vesicle interface, blue markers) and other non-contact regions (anterioposterior poles, red markers, n = 54 mitotic cells total, 5–10 embryos per timepoint, each embryo provided 0–2 mitotic events such that each datapoint represent 4–5 mitotic events, *p<1.0e-4 at 22 hpf and *p<1.0e-5 at 27 hpf, as determined by student t-test (unpaired)). Aspect ratio is measured as the ratio of apico-basal to lateral cell radii. (H) Distribution of division plane orientation relative to the lumenal surface-normal at contact and non-contact cell populations. (I) Distribution of division plane orientation for all cells across three stages 16–25, 25–35, and 35–45 hpf respectively. (J) Quantification of hindbrain deformation measured as the peak indentation depth (relative to the dashed green line segment in **C-F**). n = 10 embryos per data point. Error bars are SD.

To directly determine the presence of pressure within the otic vesicle, we developed a novel pressure probe able to accurately measure small pressures in small volumes of liquid. This probe consists of a solid-state piezo-resistive sensor coupled to a glass capillary needle filled with water (Figure 3A–B, see Materials and methods). This device is capable of measuring pressure differences of 5 Pascals (≈0.5 mm of water depth) across the range of 50–400 Pascals (Figure 3—figure supplement 1A). Prior to 30 hpf, lumenal pressure is too low for the needle to penetrate the epithelium. From 30 hpf onwards, we observed that the needle can penetrate into the otic vesicle with no observable volume change due to leakage around the needle (Figure 3B). Pressure is transmitted from the otic vesicle lumen through the needle tip to the sensor. Readings after puncture increased gradually before reaching a stable pressure level (Figure 3D). The positive pressure remained until the glass capillary was withdrawn from the otic vesicle, after which the pressure reading dropped to the baseline value (hydrostatic pressure of the buffer due to its depth in the petri dish), further indicating that a pressure difference exists across the epithelium (Figure 3—figure supplement 1F). We measured the pressure level at 30, 36 and 48 hpf and found that the pressure level gradually increases from 100 Pa to upwards of 300 Pa (Figure 3C and D). We are uncertain whether there is a drop in pressure upon insertion of the pressure probe into the otic vesicle because there is no alternate measuring device. These values are similar to prior measurements of the much larger inner ear of adult guinea pigs (Feldman et al., 1979).

Figure 3. — Pressure measurements in the otic vesicle using a piezo-resistive solid-state sensor. (A) Schematic drawing of the pressure probe assembly, not to scale. (B) The capillary-based probe is mounted on a micromanipulator and zebrafish embryos are immobilized and mounted in Danieau buffer. (B’) Under a stereo microscope, the glass capillary is inserted into the otic vesicle. (C) Otic vesicle pressures at different developmental stages of wild-type zebrafish embryos (red diamond: mean value. *p<5.0e-2). (D) Pressure was measured in otic vesicle at 30 hpf, 36 hpf, and 48 hpf. Presented trajectories were live readings from embryos immobilized with $α$ -bungarotoxin protein. Each color represents an individual test. (E) 2D confocal micrographs showing both ears at 30 hpf before (top) and after (bottom) unilateral puncture of the right vesicle. Changes in cell shape from squamous (blue arrows) to columnar (red arrows) are shown. Scale bar is 25 µm. (**F–H**) Quantification of changes from puncturing: (F) lumen volumes ( $V_{l}$ , n = 10, *p<1.0e-4,**p<1.0e-5), (G) average vesicle wall thickness ( $h$ , n = 10, *p<5.0e-3), and (H) average cell aspect-ratio (n = 10, error bars are SD). (I) Model relating vesicle geometry, growth rate, and fluid flux to pressure, tissue stress, and cell material properties. (J) Multi-scale regulatory control of otic vesicle growth linking pressure to fluid transport. Related to Figure 3—figure supplements 1–2.

Figure 3—figure supplement 1. — Pressure measurements in the otic vesicle using a piezo-resistive solid-state sensor. (A) Schematic drawing of the pressure probe assembly, not to scale. (B) The capillary-based probe is mounted on a micromanipulator and zebrafish embryos are immobilized and mounted in Danieau buffer. (B’) Under a stereo microscope, the glass capillary is inserted into the otic vesicle. (C) Otic vesicle pressures at different developmental stages of wild-type zebrafish embryos (red diamond: mean value. *p<5.0e-2). (D) Pressure was measured in otic vesicle at 30 hpf, 36 hpf, and 48 hpf. Presented trajectories were live readings from embryos immobilized with $α$ -bungarotoxin protein. Each color represents an individual test. (E) 2D confocal micrographs showing both ears at 30 hpf before (top) and after (bottom) unilateral puncture of the right vesicle. Changes in cell shape from squamous (blue arrows) to columnar (red arrows) are shown. Scale bar is 25 µm. (**F–H**) Quantification of changes from puncturing: (F) lumen volumes ( $V_{l}$ , n = 10, *p<1.0e-4,**p<1.0e-5), (G) average vesicle wall thickness ( $h$ , n = 10, *p<5.0e-3), and (H) average cell aspect-ratio (n = 10, error bars are SD). (I) Model relating vesicle geometry, growth rate, and fluid flux to pressure, tissue stress, and cell material properties. (J) Multi-scale regulatory control of otic vesicle growth linking pressure to fluid transport. Related to Figure 3—figure supplements 1–2.

To directly test if lumenal pressure ‘inflates’ the otic vesicle to drive inner ear growth, we punctured otic vesicles at different stages between 25–45 hpf (right vesicle in Figure 3E). Immediately following puncture, we observed a significant decrease in vesicle diameter (white arrows, Figure 3E) and loss of lumenal volume (≈30–40%) (Figure 3F). Examination of punctured vesicles showed that as the vesicle shrunk, the epithelium became thicker (Figure 3E and G). Indeed, the excess surface area of the lumenal cavity was absorbed by a significant change in epithelial cell shape to become more columnar while preserving cell volume (in-plane:normal diameter change from 6.7 ± 0.2 µm:13.2 ± 2.9 µm to 5.9 ± 0.2 µm:18.4 ± 4.1 µm at 30hpf) (Figure 3H). A similar transition in cell shape is seen when puncturing was conducted at later stages in development (Figure 3—figure supplement 2E), but importantly to a less columnar resting state suggesting a viscous component. Together, the puncturing experiments provided three insights into the mechanics of the otic vesicle: (i) the lumenal fluid is under hydrostatic pressure that is released when the vesicle is punctured, (ii) lumenal pressure generates stress in the epithelium that alters the shape of epithelial cells, causing them to stretch and become flatter, and (iii) the epithelial tissue response is viscoelastic, being elastic on short time scales, consistent with the epithelium becoming thicker immediately after puncturing, and viscous at longer time scales, consistent with long-term irreversible deformations.

Theoretical framework linking tissue geometry, fluid flux, and osmotic pressure

Given the complex interplay of lumenal pressure, geometry, and viscoelastic mechanics associated with growth, we sought to develop a mathematical model that accounts for these features (Figure 3I, See Materials and methods for mathematical model) (Ruiz-Herrero et al., 2017). In a spherically symmetric setting, the relationship between average vesicle radius ( $R$ ), wall thickness ( $h$ ), and tissue growth rate ( $j$ ) can be specified as $4 π \frac{d (R^{2} h)}{d t} = j$ . Similarly, the relationship between growth in lumenal volume ( $V_{l}$ ) and transport across the lumenal surface (of area $S_{l}$ ) is related to fluid influx per unit surface area $Ω = \frac{d V_{l}}{d t} / S_{l} (t)$ . Defining $P_{0}$ as the homeostatic pressure required to balance the chemi-osmotic potential driving fluid flux and $Ω_{0}$ as the flux in the absence of a pressure differential, we may write the wild-type fluid flux as $Ω$ = $Ω_{0}$ - $K P_{0}$ where $K$ is the permeability coefficient. Intuitively, $Ω$ is the fluid flux that maintains the homeostatic pressure $P_{0}$ , which in turn, remodels tissue to accommodate the incoming fluid.

Changes in luminal volume can be used to directly determine fluid flux because water is incompressible at low pressures. By using population-averaged measurements of lumenal volume and surface area, we calculate that after an initial rapid expansion (16–20 hpf), flux was approximately constant ( $Ω \approx 1 μ m^{3} / (μ m^{2} . h r) \sim 1 μ m / h r$ ) throughout the period 21–45 hpf (Figure 4A). The flux is initially high when there is no pressure but then quickly goes down as pressure builds. Thereafter, fluid accumulation can only occur through viscous expansion of the vesicle. Interestingly, analysis of the system of equations in our model shows that the vesicle will adjust endolymph flux to account for perturbations to vesicle size, via a mechanical feedback loop that links pressure to flux (Figure 3J). Such a control system could be useful to correct natural as well as experimentally induced asymmetry across the left-right axis as we have found in early zebrafish inner ear development (Green et al., 2017), and in the whole mammalian embryo (Chan et al., 2019).

Figure 4. — (A) Numerical calculation of fluid flux ( $Ω$ ) as a function of time using Equation 6 by fitting quadratic polynomials to volume and surface area data. (**B–D**) Confocal 2D micrographs with XZ (top) and XY (bottom) planes depicting the regeneration of a punctured right vesicle (blue) relative to the unpunctured vesicle (left) from (A) 30 hpf right after puncture, to (B) 32.5 hpf, and to (C) 35 hpf. (**E–F**) Quantification of the recovery of volume and wall thickness symmetry. The y-axis plots the difference in lumenal volumes normalized to the unpunctured lumenal volume ( $\frac{Δ V_{l}}{V_{l}}$ , E) and similarly for wall thickness ( $\frac{Δ h}{h}$ , F). Error bars are SD. (G) Fluid flux $Ω$ in the punctured ears (blue) and unpunctured ears (red). Error bars are SD. (H) Scatterplot showing $Ω$ as a function of volume asymmetry ( $\frac{Δ V_{l}}{V_{l}}$ ) in punctured (blue) and unpunctured (red) ears. n = 10 for each data point in (**E–H**) Related to Figure 4—figure supplement 1 and Figure 4—video 1.

Figure 4—figure supplement 1. — (A) Numerical calculation of fluid flux ( $Ω$ ) as a function of time using Equation 6 by fitting quadratic polynomials to volume and surface area data. (**B–D**) Confocal 2D micrographs with XZ (top) and XY (bottom) planes depicting the regeneration of a punctured right vesicle (blue) relative to the unpunctured vesicle (left) from (A) 30 hpf right after puncture, to (B) 32.5 hpf, and to (C) 35 hpf. (**E–F**) Quantification of the recovery of volume and wall thickness symmetry. The y-axis plots the difference in lumenal volumes normalized to the unpunctured lumenal volume ( $\frac{Δ V_{l}}{V_{l}}$ , E) and similarly for wall thickness ( $\frac{Δ h}{h}$ , F). Error bars are SD. (G) Fluid flux $Ω$ in the punctured ears (blue) and unpunctured ears (red). Error bars are SD. (H) Scatterplot showing $Ω$ as a function of volume asymmetry ( $\frac{Δ V_{l}}{V_{l}}$ ) in punctured (blue) and unpunctured (red) ears. n = 10 for each data point in (**E–H**) Related to Figure 4—figure supplement 1 and Figure 4—video 1.

Model prediction and validation: pressure negatively regulates fluid flux

The model predicts that loss of fluid from the lumen (such as by puncture) should lead to a pressure drop and an increased rate of fluid flux back into the lumen and thus a higher than normal growth rate until size is restored, a phenomenon called catch-up growth. To test these model predictions, we experimentally examined whether pressure and fluid flux couple to each other to result in force-based feedback control of development. We first examined the response of the otic epithelium to puncturing perturbations between 25–45 hpf. We injected fluorescent dye (Alexa Fluor 594, 759 MW) into the fluid outside the inner ear (the perilymph) and tracked its movement into the lumen (Figure 3—figure supplement 2A). Puncturing the otic vesicle and withdrawing the needle created a loss in lumenal volume and allowed the dye from the perilymph to move into the lumen immediately (Figure 3—figure supplement 2B,C). However, when the dye was injected into the perilymph 5 min after the puncture, there was no rapid movement of dye into the lumen (Figure 3—figure supplement 2D). This showed that the otic epithelium rapidly seals after puncture and restores the epithelial barrier.

Next, we punctured the vesicle at 30 hpf, withdrew the needle, and evaluated its growth relative to the unpunctured contralateral vesicle (control) from 30 to 45 hpf by simultaneously imaging both otic vesicles. Interestingly, we observed the complete regeneration of lumenal volume in punctured vesicles by an increased growth rate relative to wild type to restore bilateral symmetry (Figure 4B–E, Figure 4—video 1). The cell shape changes were also reversed (Figure 4F) suggesting that the vesicle was re-pressurized. The rate of regeneration from fluid flux ( $Ω$ ) was high immediately after puncture with a slow, gradual decay as bilateral symmetry is restored (Figure 4G). During the rapid recovery phase, $Ω$ in the punctured vesicle (blue curve) was 2-5X higher than that in the unpunctured vesicle (red curve). Our model predicts that upon loss of pressure $P \leq P_{0}$ from puncturing, the vesicle dynamically adjusts the fluid flux $\tilde{Ω} \geq Ω$ in linear proportion to volume lost (Equation 13 Materials and methods). To test this prediction, we pooled data from multiple punctured embryos regenerating from varying levels of pressure loss, to measure how fluid flux related to the volume loss. Consistently, fluid flux in the punctured vesicle correlates with the difference in lumenal volumes between the left and right vesicles (blue markers in Figure 4H and Figure 4—figure supplement 1 for other developmental stages). These data together show that vesicle pressure negatively regulates fluid flux and suggest that this feedback could buffer variations in size and drive catch-up growth in the otic vesicle.

Ion pumps are required for lumenal expansion

The transport of salts and fluid across an epithelium can occur through a variety of mechanisms involving transcytosis, electrogenic pumps/transporters and aquaporins for transcellular or paracellular flow (Preston et al., 1992; Hill and Shachar-Hill, 2006; Fischbarg, 2010). Paracellular transport refers to the transfer of fluid across an epithelium by passing through the intercellular space between the cells. This is in contrast to transcellular transport, where fluid travels through the cell, passing through both the apical membrane and basolateral membrane. Previous work in the chick otic vesicle identified the activity of Na⁺-K⁺-ATPase in setting up a transmural potential (Represa et al., 1986) to drive the selective movement of water and ions. In the zebrafish, a role for ion pumps in ear growth is supported by the previous identification of the Na⁺-K⁺-Cl⁻transporter Slc12a2 as defective in little ear mutants (Abbas and Whitfield, 2009). We administered ouabain, an inhibitor of Na⁺-K⁺-ATPase pump activity, to embryos at the 20 hpf stage and quantified vesicle morphology at 30 hpf. We observed a dose-dependent decrease in otic vesicle volume (blue) and wall thickness deformation (red) compared to the wild-type values (Figure 5A) consistent with previous work (Hoijman et al., 2015). In punctured embryos at 25 hpf, adding 500 µM ouabain to the buffer completely inhibited further growth (left vesicle) and post-puncture regeneration (right vesicle in Figure 5B–C, Figure 5—video 1). Knockdown of Na⁺-K⁺-ATPase expression in morpholino-injected embryos inhibited lumenal fluid transport in a dose-dependent manner (Figure 5D). We additionally find that otic vesicle growth is sensitive to variations in extracellular pH and blockers of chloride channel activity (Figure 5E–F). Together, these data argue that a network of ion transporters for $N a^{+}, K^{+}, H^{+},$ and $C l^{-}$ is required for fluid flux into the lumen.

Figure 5. — (A) Quantification of lumenal volume ( $V_{l}$ ) and wall thickness ( $h$ ) at 30 hpf after ouabain treatment at 20 hpf. Error bars are SD. (**B–C**) Confocal micrographs showing the inhibition of growth in unpunctured (left) and punctured (right) vesicles after incubation in 100 µM ouabain to the buffer at 25 hpf. Scale bar 25 µm. (D) Brightfield images comparing the growth (25-45hpf) of the wild-type otic vesicle against the antisense morpholino (0.25 ng) targeting the translation of Na,K-ATPase α1a.1 mRNA. (E) Quantification of lumenal volumes $V_{l}$ at 30 hpf after acidification of buffer (pH of 6.5–8.0) at 12 hpf. (F) Dose-dependent decrease in lumenal volumes $V_{l}$ observed after the addition of Niflumic acid, a chloride channel inhibitor at 12 hpf (blue) or 20 hpf (red).n = 5 for each data point Related to Figure 5—video 1.

Patterning of tissue material properties causes local differences in epithelial thinning

Our minimal mathematical model assumes that the vesicle is spherical allowing us to understand and predict the qualitative trends of our experiments. For pressure $P$ acting inside a thin spherical shell, the tensional tissue-stress—the force pulling cells apart that arises from the radially-outward pushing force of hydrostatic pressure—is $σ = \frac{P R}{2 h}$ . Since the tissue is elastic on short timescales and viscous on long timescales, the radial strain-rate—the change in radius of the otic vesicle, ( $\dot{ϵ} = \frac{1}{R} \frac{d R}{d t}$ )—may be related to $σ$ via the constitutive relation for a Maxwell fluid given by $\dot{σ} + \frac{σ}{τ} = G \dot{ϵ}$ , where $G$ is the tissue shear modulus—the material property that relates force experienced to deformation—and $τ$ is the ratio of the tissue viscosity μ and elasticity $k$ .

For long timescales, we can use Stokes’ law and force balance (Equations 14, 16, Materials and methods) to derive an effective tissue viscosity where

μ = \frac{P R^{2}}{8 h} {(\frac{d R}{d t})}^{- 1} .

(1)

Using this relationship, our morphodynamic measurements, and pressure measurements we estimate the effective viscosity of the otic vesicle tissue to be about 6.3 ± 0.30 × 10⁶Pa*s from 24 to 36 hpf and then 2.2 ± 0.13 × 10⁷ Pa*s from 36 to 48 hpf (see Materials and methods for error propagation calculations). These values are within the range of tissue viscosities that had been experimentally measured, (Gordon et al., 1972), and indicate that the otic vesicle’s tissue becomes more viscous through development.

Since the vesicle is not actually spherical (Figure 1—figure supplement 1N,O) and the epithelium is not uniform in thickness (Figure 1H; Hoijman et al., 2015), we examined whether (i) the non-spherical vesicle shape creates non-uniform stress distribution as in Laplace’s law and/or (ii) non-uniform patterning of the material properties produce differential strain among cells. To test the first of these possibilities, we tracked anteroposterior pole cells (future sensory) and examined their shapes as they moved from high-curvature to low-curvature regions of the lumenal surface due to epithelial tread milling caused by regional differences in proliferation and emigration (Figure 1—video 1). We found that cells retained their columnar shapes independent of the underlying tissue curvature, suggesting that material property patterning may instead contribute to differential cell strain-rates (Figure 6—figure supplement 1A,B). To test the second possibility, we quantified spatial differences in elasticity ( $k$ ) and viscosity ( $μ$ ) of the otic vesicle using puncturing experiments (Figure 6A). We observed that by eliminating pressure by puncture, medial and lateral cells deformed significantly more compared to the pole cells, indicating that they are softer (smaller $k$ ) (Figure 6B). Likewise, the resting shapes (post-puncture) of medial and lateral cells were more stretched out as the otic vesicle progressed in time, indicative of their lower viscosity ( $μ$ , Figure 6C). The observation that the medial and lateral cells become more viscous during development (Figure 6C) agrees with the increased effective viscosity we independently derived from our model using measurements of unperturbed otic vesicle growth. Thus, puncturing perturbations to eliminate pressure forces allowed us to measure spatial differences in cell viscoelasticity.

Figure 6. — (A) Schematic for experimentally measuring tissue material properties ( $k$ , $μ$ ). The strain of a cell (highlighted in orange) before and after puncturing $(c - a)$ is inversely proportional to the elasticity modulus k. Changes in resting cell-shapes observed over time ( $d - b$ ) is inversely proportional to the viscosity parameter µ. (**B–C**) Quantification of normalized change in wall thickness ( $(c - a) / a$ , (B) and *resting* wall thickness ( $(c - d) / c$ , (C) post-puncture near the hindbrain (medial, blue), ectoderm (lateral, red), and anteroposterior regions (poles, green). Puncturing was done at 25, 30, 35, and 40 hpf. n = 5 for each data point in (**B–C**). (D) Overall lumenal surface area growth rate (blue markers) showing compensatory contributions from proliferation (red) and cell stretching (green). (**E–F**) Timelapse confocal imaging using *Tg(actb2:GFP-Hsa.UTRN)* and *Tg(actb2:myl12.1-eGFP)* embryos report the dramatic apical localization of F-actin (D) and Myosin II (E) respectively prior to lumenization through 12-16hpf. Through early growth between 16–22 hpf, cells at the poles and lateral regions (red arrows) retain their fluorescence while medial cells lose their fluorescence (blue arrows). (**G–H**) 3D rendering of F-actin (G) and myosin II (H, right) data at 30 hpf show co-localization to apicolateral cell junctions as cells stretch out. (I) Quantification of long-term cell shape deformation ( $\frac{Δ h}{h}$ ) between 16–22 hpf as a function of the rate of change in apical concentration ( $\frac{Δ u}{u}$ ) of F-actin (blue markers) and Myosin II (red). n = 22. (J) Quantification of the short-term puncture-induced deformation in cell shapes ( $\frac{Δ h}{h}$ ) as a function of the normalized apical concentration ( $\frac{u}{< u >}$ ) of F-actin (blue markers) and Myosin II (red). < u > represents the mean apical fluorescent intensity across the vesicle. Error bars are SD, n = 22. (K) Quantification of fluid flux in embryos treated with 2 mM cytochalasin D at different developmental stages (hpf). Before 25 hpf, embryos failed to grow ( $Ω \approx 0$ ) or lose lumenal volume. After 25 hpf, embryos increased their secretion rate by 2-5X over wild-type values (dashed black line, 1 µm/hr, n = 15). (L) Quantification showing the change in apical Myosin II fluorescence ( $\frac{Δ u}{u}$ ) as positively correlated with fluid flux ( $Ω$ , n = 16). (M) Quantification of vesicle shape change show maximal change in dorsoventral radius (green markers) compared to the mediolateral (blue) and anteroposterior radius (red, n = 12). Related to Figure 6—figure supplement 1 and Figure 6—videos 1–4.

Figure 6—figure supplement 1. — (A) Schematic for experimentally measuring tissue material properties ( $k$ , $μ$ ). The strain of a cell (highlighted in orange) before and after puncturing $(c - a)$ is inversely proportional to the elasticity modulus k. Changes in resting cell-shapes observed over time ( $d - b$ ) is inversely proportional to the viscosity parameter µ. (**B–C**) Quantification of normalized change in wall thickness ( $(c - a) / a$ , (B) and *resting* wall thickness ( $(c - d) / c$ , (C) post-puncture near the hindbrain (medial, blue), ectoderm (lateral, red), and anteroposterior regions (poles, green). Puncturing was done at 25, 30, 35, and 40 hpf. n = 5 for each data point in (**B–C**). (D) Overall lumenal surface area growth rate (blue markers) showing compensatory contributions from proliferation (red) and cell stretching (green). (**E–F**) Timelapse confocal imaging using *Tg(actb2:GFP-Hsa.UTRN)* and *Tg(actb2:myl12.1-eGFP)* embryos report the dramatic apical localization of F-actin (D) and Myosin II (E) respectively prior to lumenization through 12-16hpf. Through early growth between 16–22 hpf, cells at the poles and lateral regions (red arrows) retain their fluorescence while medial cells lose their fluorescence (blue arrows). (**G–H**) 3D rendering of F-actin (G) and myosin II (H, right) data at 30 hpf show co-localization to apicolateral cell junctions as cells stretch out. (I) Quantification of long-term cell shape deformation ( $\frac{Δ h}{h}$ ) between 16–22 hpf as a function of the rate of change in apical concentration ( $\frac{Δ u}{u}$ ) of F-actin (blue markers) and Myosin II (red). n = 22. (J) Quantification of the short-term puncture-induced deformation in cell shapes ( $\frac{Δ h}{h}$ ) as a function of the normalized apical concentration ( $\frac{u}{< u >}$ ) of F-actin (blue markers) and Myosin II (red). < u > represents the mean apical fluorescent intensity across the vesicle. Error bars are SD, n = 22. (K) Quantification of fluid flux in embryos treated with 2 mM cytochalasin D at different developmental stages (hpf). Before 25 hpf, embryos failed to grow ( $Ω \approx 0$ ) or lose lumenal volume. After 25 hpf, embryos increased their secretion rate by 2-5X over wild-type values (dashed black line, 1 µm/hr, n = 15). (L) Quantification showing the change in apical Myosin II fluorescence ( $\frac{Δ u}{u}$ ) as positively correlated with fluid flux ( $Ω$ , n = 16). (M) Quantification of vesicle shape change show maximal change in dorsoventral radius (green markers) compared to the mediolateral (blue) and anteroposterior radius (red, n = 12). Related to Figure 6—figure supplement 1 and Figure 6—videos 1–4.

Cell stretching and steady proliferation contribute to tissue viscosity

Our model, calculations, and experimental measurements of cell material properties show that cells progressively become more rigid and more viscous. With diminished ability to remodel cell shape, we examined how otic vesicle growth can be sustained with lumenal pressure. To sustain the same growth rates, our model predicts that overall tissue viscoelasticity should be invariant to changes in cell material properties. While otic tissue elasticity arises from reversible cell stretching ( $k$ ), tissue viscosity is the net result of irreversible cellular stretching ( $μ$ ) as well as proliferation-driven increase in tissue surface area. Thus, we speculated that cell stretching has a more significant role in early growth while proliferation plays a more important role in later stages of growth.

To test these predictions, we evaluated the growth in lumenal surface area ( $d S_{l} / d t$ ) in terms of individual contributions from division ( $ψ \frac{d N}{d t}$ ) and cell stretching ( $N \frac{d ψ}{d t}$ ) (Figure 6D). Our analysis shows that lumenal surface area growth is linear through time (blue markers). To support this growth, the contribution from cell-stretching is high initially but monotonically decreasing (green markers) and buffered by division (red markers). A break-even point occurs at around 33 hpf when the contribution to tissue viscosity from cell proliferation exceeds that from cell stretching (dashed black line). Interestingly, our data also show that cell shape stabilizes by this time (Figure 1H). Thus, cell stretching and proliferation play complementary roles through time to sustain a uniform increase in lumenal surface area.

Tissue material properties are patterned through actomyosin regulation

To identify how cell material properties are patterned, we examined localization patterns of F-actin and Myosin II using transgenic zebrafish (Tg(actb2:myl12.1-eGFP)^e2212 for visualizing myosin II distribution, and Tg(actb2:GFP-Hsa.UTRN)^e116 for visualizing F-actin distribution (Behrndt et al., 2012). Both, F-actin (Figure 6E and Figure 6—video 1) and Myosin II (Figure 6F and Figure 6—video 2) were apically localized prior to lumenization through 12–16 hpf to form a band around the cavity. Through early growth between 16–22 hpf, gradual and non-uniform changes in the apical density of these molecules are observed. By 30 hpf, we find that these proteins are localized to apicolateral junctions inside cells (Figure 6G–H). Expression levels are retained at pole cells but reduced in medial and lateral cells. Using the movies, we tracked individual cells to understand the relationship between cell shape change and apical marker intensity. We find that wild-type cell deformation during normal growth is positively correlated to localized accumulation of F-actin and Myosin II (Figure 6I). In the transgenic embryos, we used a mosaic labeling strategy for tracking cells to measure the relationship between apical localization and deformation of individual cells immediately following puncture (Figure 6—figure supplement 1C). We find that upon puncture, the instantaneous deformation observed in individual cells is linearly correlated with the levels of apical localization of F-actin and Myosin II suggesting that actomyosin tension sets effective tissue elasticity (Figure 6J). As it is unclear what contribution the neighboring tissue has to the effective material properties of the growing otic vesicle, we are unable to distinguish whether the correlation between actomyosin patterns and tissue thinning is organ autonomous or whether elastic forces from neighboring tissue are influencing these behaviors.

To further link spatial patterning of actomyosin localization with epithelial thickness, we conducted loss-of-function experiments and used our model to interpret experimental results. Upon reducing cell elasticity ( $k$ ), our model predicts: (i) an increase in strain-rate ( $\dot{ϵ}$ ) to equilibrate with pressure forces, and (ii) an increase in lumenal dimensions to accomodate increased strain and secretion rates. To decrease cell elasticity, we inhibited actin dynamics by treating embryos at different stages between 16–35 hpf with 100 μM cytochalasin D and used high frame-rate imaging (one frame/s) to measure vesicle deformations. As predicted by theory, we observed an increase in $Ω$ by a factor of 2-5X over the wild-type values (Figure 6K and Figure 6—video 3). The decrease in apical myosin fluorescence positively correlated with the increase in secretion rates (Figure 6L and Figure 6—video 3). In these embryos, the DV diameter was found to increase most, compared to LR and AP diameters that experience reactionary forces from the hindbrain and skin (Figure 6M and Figure 6—video 3). We also observed that embryos between 16–25 hpf lost volume, presumably, due to a loss in epithelial connectivity and lack of pressure needed for deformation (Figure 6—video 4). Together, these data show how spatial patterning of the actomyosin cytokskeleton can lead to spatially varied strain in responses to spatially uniform pressure, and thus contribute to regional differences in the otic vesicle epithelium during growth.

Discussion

Here, we show that hydrostatic lumenal pressure develops in the zebrafish otic vesicle in response to fluid transport across the otic epithelium to drive growth. We used in toto imaging and newly developed quantitative image analysis tools to track changes in cell number, tissue volume, and vesicle lumen volume—which is fluid flux because water is nearly incompressible. We developed a pressure probe device that is amenable to low pressures and small volumes, which enabled us to quantify a developmental increase in hydrostatic pressure. Furthermore, we identified and characterized a new instance of catch-up growth that we leveraged to develop a theoretical framework for otic vesicle size control. With the aid of a multiscale mathematical model, we hypothesized and experimentally confirmed the presence of a hydraulic negative feedback loop between pressure and fluid transport for achieving size control. Modeling helped us systematically integrate the individual contributions of cell physioligical mechanisms underlying pressure and fluid flux, cell proliferation and shape, vesicle geometry, tissue strain-rate and viscoelasticity, to show how growth of the early otic vesicle is controlled. The negative feedback architecture that we found is similar to the chalone model of size control in that the act of growth feeds back to inhibit the rate of growth. However, compared to chalones or morphogen based growth control strategies which are limited in speed by diffusion, the pressure based strategy allows nearly instant communication between different parts of a tissue via hydraulic coupling to allow for 'course corrections’ to developmental trajectories. Indeed, our study is in line with the fact that hydraulic interactions are relevant to the developmental growth of many internal organs with vesicular and tubular origins (Ruiz-Herrero et al., 2017), and most recently the entire mammalian embryo (Chan et al., 2019).

Cause of cell thinning and origin of endolymph

Prior work found that when cells enter into mitosis and round up, their neighbors are stretched and become thinner (Hoijman et al., 2015). This was interpreted as being the mechanism by which cells thin to increase the surface area of the otic vesicle. Here we show that the otic epithelium is fairly elastic and cells can re-thicken following loss of lumenal pressure when the vesicle is punctured (Figure 3G,H), so stretching by neighboring mitotic cells may be short lived. Rather, in our model we postulate that sustained cell thinning during otic vesicle development is caused by in-plane epithelial tension in response to lumenal pressure. It was also noted that cells decrease in volume during early stages of otic vesicle growth and suggested that volume lost from cells is used to inflate the lumen (Hoijman et al., 2015). We attribute the reduction in cell size during early otic development to be due to cell division, and note that the net tissue volume (number of cells multiplied by average cell size) is constant at this stage (Figure 1F). Further, our measurements show that the lumen volume continues to grow until it exceeds the tissue volume (Figure 1F). We thus infer that transepithelial fluid flow is the primary if not sole source of fluid accumulation in the lumen.

Potential application of the lumen growth model to other systems

Our model for vesicle growth integrates a range of cellular behaviors including division, transport, force generation, material property patterning, and tissue thinning. By tailoring our model equations to different geometries and growth parameters, a unified mathematical framework can be realized to understand size control in hollow organs including the eyes, brain, kidneys, vasculature, and heart. The advantages of such a mesoscale model are several. First, a mesoscale model can be more easily applied to other contexts since the level of abstraction is higher making it less dependent on the specifics of the original context (fewer parameters). Second, growth kinetics and geometry parameters can be experimentally measured using in toto imaging approaches. New optical technologies for measuring tissue stresses in vivo using oil droplets (Campàs et al., 2014) and laser-ablation (Campinho et al., 2013; Hoijman et al., 2015), ionic gradients using fluorecent ionophores (Adams and Levin, 2012), and pressure (Link et al., 2004) via probes—like the one developed here—hold promise in providing reliable biophysical measurements necessary for understanding morphogenesis. Indeed, some of these very approaches have recently been taken in helping understand how the size of a mammalian embryo is controlled (Chan et al., 2019). And finally, the contribution of different molecular pathways in regulating model parameters can be prioritized for experimental investigation.

Boundary conditions of the otic vesicle and our model

The otic vesicle is not growing in isolation. In the embryo, it is immediately surrounded by extracellular matrix, mesenchymal cells, skin, and the brain. Within our model, these influences are abstracted as the effective material properties of the otic vesicle tissue. In fact, they may set limits to growth where the tension within the tissue begins to increase rapidly. We are likely observing an influence of these boundary conditions when we observe the spatial patterning of actinomyosin localization and regional tissue thinning (Figure 6). This boundary condition may accelerate cellular and molecular feedback mechanisms that were beyond the scope of this work. For instance, the cells within the tissue may respond to elevated tension by modulating proliferation rates, which may effectively alter the material properties of the tissue and alter strain (Halder and Johnson, 2011; Gudipaty et al., 2017; Gnedeva et al., 2017).

Comparison of pressure-regulation mechanisms

Our integrated approach combining quantitative imaging and theory-guided experimentation allowed us to identify a novel hydraulic-based mechanism for regulatory control of 3D vesicle growth. This mechanism enables long-range, fast, and uniform transmission of force and connects effects at multiple scales from global pressure forces to supracellular tension and cell stretching mechanics to molecular-scale actions of ion pumps and actomyosin regulation. Later, in the adult ear, tight control of inner ear fluid pressure and ionic composition is necessary to properly detect sound, balance, and body position. Pressure is also important to maintain the structural integrity of organs. Dysregulation of pressure homeostasis can give rise to diseases including hypertension in the vasculature, Ménière’s disease in the inner ear, glaucoma in the eye, and hydrocephalus in the brain. Pressure homeostasis mechanisms may vary. In the inner ear, pressure is initially regulated by feedback between pressure and lumenal fluid flux. However later in development, we have found that a physical pressure relief valve is necessary for pressure homeostasis in the inner ear (Swinburne et al., 2018). Together, we expect that these new insights on ear development and physiology will be critical to the development of effective clinical therapies for hearing and balance disorders, and for understanding size control in closed epithelial tissues.

Materials and methods

Key resources table.

Reagent type (species) or resource	Designation	Source or reference	Identifiers	Additional information
Strain, strain background (Danio rerio)	Tg(actb2:myl12.1-EGFP)e2212	gift from CP Heisenberg's lab, PMID: 25535919	e2212; ZFIN ID: ZDB-ALT-130108-2	Behrndt et al., 2012
Strain, strain background (Danio rerio)	Tg(actb2:GFP-Hsa.UTRN)e116	gift from CP Heisenberg's lab, PMID: 25535919	e116; ZFIN ID: ZDB-ALT-130206-3	Behrndt et al., 2012
Strain, strain background (Danio rerio)	Tg(actb2:mem-citrine-citrine)hm30	Megason lab, PMID: 25303534	hm30; ZFIN ID: ZDB-ALT-150209-1	Xiong et al., 2014
Strain, strain background (Danio rerio)	Tg(actb2:mem-citrine)/(actb2:Hsa.H2b-tdTomato)hm32	Megason lab, PMID: 27535432	hm32; ZFIN ID: ZDB-ALT-161213-1	Aguet et al., 2016
Strain, strain background (Danio rerio)	Tg(actb2:mem-citrine)/(actb2:Hsa.H2b-tdTomato)hm33	Megason lab, PMID: 27535432	hm33; ZFIN ID: ZDB-ALT-161213-2	Aguet et al., 2016
Strain, strain background (Danio rerio)	Tg(actb2:mem-mcherry2)hm29	Megason lab, PMID: 23622240	hm29; ZFIN ID: ZDB-ALT-120625-1	Xiong et al., 2013
Strain, strain background (Danio rerio)	AB	ZIRC, Eugene, OR	ZFIN ID: ZDB-GENO-960809-7
Chemical compound, drug	Dextran, Texas Red, 3000 MW	Thermo Fisher Scientific, Waltham, MA	D-3329
Chemical compound, drug	AlexaFluor 594	Thermo Fisher Scientific, Waltham, MA	A10442
Chemical compound, drug	Oubain	Sigma Aldrich	11018-89-6
Chemical compound, drug	Cytochlasin D	Sigma Aldrich	C8273
Chemical compound, drug	Niflumic acid	Sigma Alrich	4394-00-7
Sequence-based reagent	Morpholino	Gene tools	5'-gccttctcctcgtcccattttgctg-3'	Blasiole et al., 2003
Commercial assay or kit	mMessage mMachine T7 ULTRA kit	Thermo Fisher Scientific, Waltham, MA	AM1345
Other	Board mount pressure sensor	Honeywell	HSCDANT001PG3A5	pressure probe
Other	glass capillary	World Precision Instrument	1B100-6	pressure probe
Other	NanoPort Assembly Headless, 10-32 coned for 1/16"	idex-hs.com	n-333	pressure probe
Other	Sleeve- 1517 Tefzel (ETFE) Tubing, ID 0.04", OD 1/16"	idex-hs.com	1517	pressure probe
Other	Arduino uno	sparkfun.com	R3	pressure probe
Sequence-based reagent	pmtb-t7-alpha-bungarotoxin	addgene, Swinburne et al., 2015	Addgene #69542
Software, algorithm	In toto image analysis toolkit (ITIAT)	Megason lab	https://wiki.med.harvard.edu/SysBio/Megason/GoFigureImageAnalysis
Software, algorithm	Cmake
Software, algorithm	ITK libraries		www.itk.org
Software, algorithm	VTK libraries		www.vtk.org
Software, algorithm	GoFigure2	Megason lab, in preparation	www.gofigure2.org
Software, algorithm	Powercrust	Amenta et al., 2001	https://github.com/krm15/Powercrust
Software, algorithm	ACME software	Mosaliganti et al., 2012
Software, algorithm	MATLAB (R2014A)	www.mathworks.com

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Contact for reagent and resource sharing

Further information and requests for resources and reagents should be directed to and will be fulfilled by Lead Contact, Sean Megason (megason@hms.harvard.edu).

Experimental model and subject details

Embryos were collected using natural spawning methods and the time of fertilization was recorded according to the single cell stage of each clutch. Embryos are incubated at 28°C during imaging and all other times except room temperature during injection and dechorionation steps. Staging was recorded using hours post-fertilization (hpf) as a measure and aligned to the normal table (Kimmel et al., 1995).

Zebrafish strains and maintenance

The following fluorescent transgenic strains were used in this study: (i) nuclear-localized tomato and membrane-localized citrine (Tg(actb2:Hsa.H2B-tdTomato); Tg(actb2:mem-citrine)^hm32,33), Tg(actb2:mem-citrine-citrine)^hm30 (ii) membrane-localized mCherry2 (Tg(actb2:mem-mcherry2)^hm29) (iii) Tg(actb2:myl12.1-eGFP)^e2212 for visualizing myosin II distribution, and (iv) Tg(actb2:GFP-Hsa.UTRN)^e116 for visualizing F-actin distribution (Aguet et al., 2016; Behrndt et al., 2012; Xiong et al., 2014; Xiong et al., 2013). All fish are housed in fully equipped and regularly maintained and inspected aquarium facilities. All fish related procedures were carried out with the approval of Institutional Animal Care and Use Committee (IACUC) at Harvard University under protocol 04877. Full details of procedures are given in Extended Experimental Procedures.

Method details

Timelapse confocal imaging

A canyon mount was cast in 1% agarose from a Lucite-plexiglass template and filled with 1X Danieau buffer (Figure 1—figure supplement 1A). The composition of the Danieau buffer is 14.4 mM sodium chloride, 0.21 mM potassium chloride, 0.12 mM magnesium sulfate, 0.18 mM calcium nitrate, and 1.5 mM HEPES buffered to pH 7.6. The template created three linear-ridges of width 400 µm, depth of 1.5 mm, and length 5 mm (Figure 1—figure supplement 1B). Canyon-mounted embryos developed normally for at least 3 days with a consistent orientation (lateral or dorsal or dorso-lateral) and can be continuously imaged during this time. Embryos at 15 hpf stage were dechorionated using sharp tweezers (Dumont 55) and mounted dorsally or dorso-laterally (Figure 1—figure supplement 1C,D) into the immersed canyon mount with a stereoscope (Leica MZ12.5). Multiple embryos for concurrent imaging were mounted in arrays (Figure 1—figure supplement 1B). Live imaging was performed using a Zeiss 710 confocal microscope (objectives: Plan-Apochromat 20 × 1.0 NA, C-Apochromat 40 × 1.2 NA) with a home-made heating chamber maintaining 28°C. For experiments requiring the imaging of both left and right ears in an embryo simultaneously, embryos were mounted dorsally and a Plan-Apochromat 20 × 1.0 NA objective was used. The inner ear is situated closest to the embryo surface when viewed along the dorso-lateral axis. Dorso-lateral mounting permitted the imaging of the entire ear structure with the best resolution and minimizes the depth of imaging. High-resolution imaging with a C-Apochromat 40 × 1.2 NA objective facilitated the use of automated image analysis scripts for cell and lumen segmentation, and tracking the movement of fluorescent dyes. Laser wavelengths 488 nm, 514 nm, 561 nm and 594 nm lasers were used for confocal time-courses and other single Z-stacks. Embryos were immobilized by injecting 2.3 nl of 20ng/µl $α$ -bungarotoxin mRNA (paralytic) at the 1 cell stage for experiments requiring long-term time-lapse imaging (Swinburne et al., 2015).

Wild-type growth curves

The process of anaesthetizing an embryo to prevent twitching and preparing an embryo for continuous imaging can alter wild-type growth dynamics in the long-term. Therefore, we collected single Z-stacks for separate sets of embryos (n = 10–15) to establish the wild-type growth curves at hourly intervals between 16–45 hpf. These sets of embryos were immobilized rapidly by soaking in 1% tricaine.

Confocal microscope settings

Image settings vary by brightness of signal from maternal deposit. For example, (please see Figure 1—video 1): labels:membrane-citrine; lasers: 514 nm (20 mW, 3%); objective: C-Apochromat 40 × 1.2 NA at 1.0 zoom; pixel dwell time: 1.58 µs; pinhole size: 89 µm; line averaging: 1; image spacing: 0.2 × 0.2 µm, and 1024 × 1024 pixels per image, with an interval of 1.0 µm through Z for 80 µm and a temporal resolution of 2 min. The starting Z location for the embryo is ≈20 µm above the top of animal pole to allow sufficient space for it to stay in the field of view or sink in the agarose (Figure 1—figure supplement 1E,F). A total of 25 control time-lapse (covering the developmental time-period of 15–45 hpf), 450 control Z-stacks (covering the developmental time-period of 15–45 hpf), 45 perturbation-related time-lapse datasets, and 65 perturbation-related Z-stacks were collected for the current report. Embryos were screened for their health before imaging.

Vesicular fluid pressure probe

Our pressure probe design was inspired by capillary-based pressure sensing techniques (Hüsken et al., 1978; Tomos and Leigh, 1999). A piezo-resistive solid-state pressure sensor (Honeywell, HSC series) with high resolution (≈2 Pa, 2 kHz) and minimal mechanical deformation (detailed below) was chosen as the sensing element. The sensor was coupled via a high pressure fitting to a ≈2 cm long glass capillary (World Precision Instruments) with a conical tip of 6–13 µm inner diameter (Figure 3A). Before they were coupled, both the capillary and sensor were filled with deionized water and the sensor was carefully degassed to ensure the entire interior volume is filled with water. Thus, the fabricated pressure probe had a water-filled dead-end cavity with the only opening at the capillary tip. A detailed fabrication procedure will be available in a separate publication. The digital output from the sensor was sampled by a developer board at 10 Hz (Arduino Uno-R3, and in-house Matlab program). We calibrated our fabricated pressure probe by measuring the hydrostatic pressure at different water depths (Figure 3—figure supplement 1A) that matched with the sensor calibration provided by the manufacturer. Similar tests were conducted with various capillary diameters and ionic concentration within the bath (deionized water and a solution that resembles mature endolymph) to ensure there was no additional effect (Figure 3—figure supplement 1B). The composition of our synthetic endolymph was 5 mM sodium chloride, 150 mM potassium chloride, 0.2 mM calcium chloride, 0.5 mM glucose, 10 mM tris, buffered to pH 7.5.

To measure the lumenal pressure in otic vesicle, zebrafish embryos were immobilized by injecting $α$ -bungarotoxin mRNA and dorsolaterally positioned in a canyon mount as before. The pressure probe was mounted on a micro-manipulator typically used for injection. Puncturing was done under a stereo-microscope (Figure 3B, Figure 3—figure supplement 1F): the capillary tip was first placed next to the otic vesicle to measure the reference hydrostatic pressure, and then the tip was punctured into the otic vesicle from the lateral direction. A tight sealing was indicated by the vesicle being intact while the capillary tip was inside the vesicle. The pressure profiles are shown in Figure 3D. We took the mean pressure value at the plateau, that is after the initial pressure rise and before any drop due to leakage (Stage III in Figure 3—figure supplement 1F), as the fluid pressure inside the vesicle. The data is presented in Figure 3C in the main text. As a negative control, we also punctured in bulk tissue regions such as in the neural tube and measured no pressure rise.

Since the sensor, glass capillary and otic vesicle form a closed volume after puncture, any deformation on the sensing element is compensated by out-flux of the luminal fluid from the vesicle. To verify that the volume change of the piezoresistive element is negligible, and therefore does not significantly reduce the luminal pressure, we calculated the elastic deformation of the sensing membrane and compare against the otic vesicle volume. We disassembled the sensor housing and measured the membrane area to be a square with edge length $L$ =850 µm. The membrane thickness, $h$ , is estimated to be 5-50 µm (Ruiz et al., 2012). The material is simplified as an isotropic silicon plate with Young’s modulus $E$ =163 GPa (Chicot et al., 1996; Hess, 1996; Dolbow and Gosz, 1996) and Poisson’s ratio $ν$ =0.27 (Hess, 1996; Gan et al., 1996). The small transverse displacement, $w$ , of a thin plate under an uniform transverse hydrostatic pressure, $P$ , can be calculated using the Kirchhoff-Love plate theory (Timoshenko and Woinowsky-Krieger, 1959) $\nabla^{2} \nabla^{2} w = P / D$ , where the bending stiffness $D = 2 h^{2} E / 3 (1 - ν^{2})$ . The boundary condition for the built-in edges satisfies $\partial w / \partial \hat{n} = 0$ , where $\hat{n}$ is the in-plane normal of the edges. The transverse deformation field, $w (x, y)$ , was obtained by solving the above partial differential equation with a finite element solver (Matlab, Mathwork). An analytical solution exists for the deformation at the center as (Timoshenko and Woinowsky-Krieger, 1959 Article 44) $w_{c} = 1.26 \times 10^{- 3} P L^{4} / D$ , which agrees well with the numerical solution (Figure 3—figure supplement 1C). The corresponding volume change, $V = \iint_{L} w (x, y) 𝑑 x 𝑑 y$ , was depicted in Figure 3—figure supplement 1D. Comparing to the volume of a 200 µm diameter sphere (dotted line in Figure 3—figure supplement 1D), the volume change is at least 2 orders of magnitude smaller and hence the resultant pressure drop is negligible.

We also estimated the time scale at which the endolymph is diluted by diffusive exchange. The vesicle is a spherical domain of $100$ µm diameter with the initial ionic concentration, $C_{0} = 200$ mM, the estimated value in the wild type endolymph. It is connected with a conical tube ( ${10.5}^{o}$ full cone angle, $1.8$ mm long) with variable inner diameter of 5 - 15 µm. The tube is initially filled with liquid of 0 mM, despite the actual concentration being slightly higher due to exchange with the bath (Danieau buffer, mainly composed with 14.4 mM sodium chloride). The boundary condition of all surfaces is zero flux, except for the back end of the tip being fixed at 0 mM. The temporal evolution of concentration field was obtained by numerically solving the diffusion equation , $\partial C / \partial t = D \nabla^{2} C$ , where $C (\vec{r}, t)$ is the concentration field and $D = {1.61}^{- 9}$ m²/s is the diffusion coefficient of sodium chloride in water (Guggenheim, 1954). Example solutions and the normalized average concentration in the vesicle, $C / C_{0}$ , is shown in Figure 3—figure supplement 1E. At the typical rise time (around 0.5 min) of the probing stage, (Stage II in Figure 3—figure supplement 1F), the concentration remains at about 70%-90% for inner diameter of 15 µm - 5 µm. We expect the impact on the pressure reading was small at this time scale. After about 5 to 12 min, the concentration drops to 10%, which may significant modify the chemical potential. Together with the imperfection in sealing, they could contribute to the fluctuation measured at the longer time scale. However, we have ignored some factors that can maintain the ionic concentration such as active transport of ions or higher viscosity in the lumen of the otic vesicle.

Ouabain and cytochalasin D treatment

In order to inhibit the activity of Na⁺,K⁺-ATPase, embryos at the 20 hpf stage were soaked in 1% DMSO + ouabain (Sigma Aldrich, CAS 11018-89-6) across a range of concentrations from 0 to 1 mM. Ouabain was stored at 10 mM in 1% DMSO and diluted to required concentrations in 1X Danieau buffer before use. Ear size was assessed at 30 hpf as an endpoint. For long-term imaging, ouabain was added to 1% agarose mold used for mounting the embryos. To ensure consistent penetration, 2.3 nl of 0.75 mM ouabain was injected (Nanoject) into the cardiac chamber for circulation throughout the embryo. Assuming an average embryo volume of ∼180 nl, this injected dose guarantees an effective concentration of 10 µM. In order to perturb the actin network in the otic vesicle, 2.3 nl of 2 mM cytochalasin D was injected into the cardiac chamber for an effective concentration of 25 µM in the ear.

Buffer pH and niflumic acid perturbation

To study the effect of pH on otic vesicle size, embryos at the 12 hpf stage were soaked in 1X Danieau buffer titrated to different pH levels ranging from 6.5 to 8.5 at 12 hpf. We chose to use the 12 hpf to ensure that the embryo pH homeostasis was adequately perturbed before ear growth commenced. We assessed sizes at 25 and 30 hpf. In order to inhibit the activity of chloride channels and pH regulation in the embryos, embryos at the 20 hpf stage were soaked in 1% DMSO + niflumic acid (Sigma Aldrich, CAS 4394-00-7) across a range of concentrations from 0 to 1 mM. Ear size and cell shape was assessed at 30 hpf.

Antisense morpholino injection

A total of four α1-like and two β subunit Na,K-ATPase genes have been identified in the inner ear with distinct spatiotemporal patterns of expression (Blasiole et al., 2003). Antisense morpholino (Gene Tools LLC; Philomath, OR) with sequence (5’-gccttctcctcgtcccattttgctg-3’) targeted against the Na,K-ATPase α-subunit gene atp1a1a.1 (α1a.1) was developed to knockdown expression in the early otic vesicle (Blasiole et al., 2006). The ability of the morpholino to act specifically to knockdown translation of only the relevant isoform of the Na,K-ATPase mRNA was previously demonstrated using an in vitro translation assay (Blasiole et al., 2006). To examine the role of the Na,K-ATPase in controlling ear growth, the morpholino was injected into 1 cell wild-type zebrafish embryos. Here, we report our results from using two different doses consisting of 0.25 ng in Figure 5D. In comparison to wild-type phenotypes, 0.5 ng morphants developed smaller otic vesicles, displayed smaller or absent otoliths, curved tails, and lagged in overall development (data not shown). Higher doses of morpholino injection (>1 ng) made embryos unhealthy prior to otic vesicle lumenization.

Puncturing of otic vesicle

To study the development of pressure in the otic vesicle, embryos were mounted dorso-laterally in a canyon mount (1% agarose by weight) with 1X Danieau buffer and an unclipped glass needle was slowly inserted into the otic vesicle. The needle pierced the vesicle in a lateral direction. Puncturing locally affected epithelial connectivity, causing on average 1–2 otic cell and 1–2 ectodermal cell deaths. Lumenal fluid (endolymph) leaked out along the circumference of the needle and the epithelium (Figure 3—figure supplement 2B,C). Needles were positioned using a micromanipulator. The needle was later slowly withdrawn to study regeneration dynamics. Thereafter, the embryo was re-mounted in a dorsal orientation for imaging both the ears simultaneously.

Quantifying the viscoelastic material properties

To identify the viscoelastic material properties of otic cells, we punctured vesicles and noted the deformation in cell shape. The puncturing experiment was carried out at 5 hr intervals (25, 30, 35, 40 hpf) to determine trends in material property patterning (Figure 6A). We used a sample size of $n = 5 - 10$ at each timepoint. The observed deformation in the shape of a cell (before vs. after puncture) located at position $x$ and time $t$ is inversely proportional to the spring constant (Figure 6B). The rate of change in the resting shapes (after puncture) is inversely proportional to the viscosity coefficient (Figure 6C).

Mathematical model: linking geometry, growth, mechanics and regulation

To understand otic vesicle growth, we developed a compact mathematical model that links vesicle geometry, tissue mechanics, and cellular behavior. Quantitative imaging identified aspects of cell behavior including cell division, cell size, cell shape, and material properties as being relevant to the size control problem. The process of realizing a multiscale model enabled the identification of two fundamental mechanisms regulating growth: (i) We identified a negative feedback signal linking the development of hydrostatic pressure to the inhibition of lumenal fluid flux for robust control of size; and, (ii) Spatial patterning of actomyosin contractility affected tissue response to pressure forces to shape the ear. In this section, we elaborate on the development of model equations and explain how theory-guided experimentation allowed us to arrive at the correct representation of the process.

Conservation of mass links tissue flux and fluid flux to geometry

Quantitative analysis of vesicle geometry pointed to two critically changing parameters, namely, vesicle radii and tissue wall thickness (Figure 1—figure supplement 1N,O and Figure 1H). A simple model treats the geometry of the otic vesicle as a spherical shell (Figure 3I) of average radius $R = (R_{o} + R_{l}) / 2$ (µm) and wall thickness $h = R_{o} - R_{l}$ (µm). As notation, variable subscripts $o$ , $l$ , and $t$ refer to entire otic vesicle, otic lumen, and otic tissue components respectively. To account for changes in geometry parameters from growth, we represent otic tissue growth rate as $j$ ( $p l / h r$ ) and fluid flux (per unit surface-area) as $Ω$ (µm/hr).

Conservation of tissue mass implies the rate of change of the otic tissue volume $j = d V_{t} / d t$ is related to the change in tissue geometry. Since the average thickness $h \approx 12.27 \pm 0.32$ µm and the smallest otic vesicle radius $R \approx 36.2 \pm 0.92$ µm at 30 hpf, we can make the assumption that wall-thickness is relatively small compared to the average radius ( $h ≪ R$ ), so that

j = \frac{d V_{t}}{d t} = 4 π \frac{d (R^{2} h)}{d t}

(2)

We quantified the parameters $R$ , $h$ , and $j$ and found that average radius increased linearly (Figure 1—figure supplement 1N,O), wall-thickness (Figure 1H) reduced asymptotically, and tissue volume (Figure 1F) was constant initially (16–28 hpf, $j = 0$ ) but linearly increased thereafter (28–45 hpf, $j ≃ 230 p l / h r$ ). Since tissue volume is a product of cell number ( $N$ ) and average cell-size ( $s$ ), we further investigated the role of these cellular parameters during growth.

\frac{d V_{t}}{d t} = \frac{d N}{d t} s + N \frac{d s}{d t}

(3)

From Figure 1E, cell number $N$ monotonically increased non-linearly between 16–45 hpf. In contrast, average cell-size monotonically decreased till 28 hpf and stabilized to a constant value ( $≃ 0.35 p l$ ) thereafter. Therefore, between 16–28 hpf, the increase in cell number was offset by a decrease in cell-size (Figure 1E), effectively keeping tissue mass constant. In addition, between 28–45 hpf, increase in tissue mass occurred due to increase in cell number alone with a constant average cell-size.

Similar to volume, we note that lumenal surface area is the product of cell number ( $N$ ) and average cell apical surface area ( $ψ$ , µm²). Therefore, we investigated their individual contribution in driving the increase in surface area.

S_{l} = ψ N

(4)

\frac{d S_{l}}{d t} = N \frac{d ψ}{d t} + ψ \frac{d N}{d t}

(5)

From Figure 1G and E, we find that lumenal surface area and cell number increase monotonically from 16 to 45 hpf. Average apical cell surface showed a saturating response instead. By analyzing both the terms in Figure 6D, we find that both terms contribute significantly to lumenal surface area growth in a temporally complementary manner. Cell stretching ( $N \frac{d ψ}{d t}$ ) harbors a more significant role during early growth (≤32 hpf) with a slow diminishing influence. In contrast, division ( $ψ \frac{d N}{d t}$ ) is more significant role during later growth (> 32 hpf). Note that this is a second role of division during growth, in addition to the earlier role in regulating tissue volume increase (Equation 3).

Conservation of fluid volume implies the rate of change in lumenal volume ( $\frac{d V_{l}}{d t}$ ) is equal to product of surface area ( $S_{l}$ ) and fluid flux $Ω$ .

\frac{d V_{l}}{d t} = S_{l} Ω

(6)

For a spherical geometry, lumenal volume is $\frac{4 π}{3} R^{3}$ and surface-area is $4 π R^{2}$ , so that

\frac{4 π}{3} \frac{d (R^{3})}{d t} = 4 π R^{2} Ω

(7)

\frac{d R}{d t} = Ω

(8)

In other words, fluid flux is the same as the rate of change of lumenal radius. From Figure 4A and Figure 1—figure supplement 1N, we find that average radius increased linearly and lumenal fluid flux was approximately constant ( $≃ 1 μ m / h r$ ) between 16–45 hpf.

Thus, our analysis of growth kinetics using simple conservation laws points to the role of mechanisms involved in regulating cell division, cell volume, fluid transport, and cell shape in controlling size.

Modeling pressure generation and feedback to fluid transport mechanisms

Since lumenal volume growth contributes the most to vesicle growth, we examined the phenomenon of fluid transport into a closed cavity (Figure 1F). Prevailing theories of fluid transport suggest the movement of charged ions and fluid through intercellular junctions and channels on cell surfaces (Hill and Shachar-Hill, 2006; Fischbarg, 2010). To model the phenomenon of fluid transport into a closed cavity, we denote the rate of transport of solute as $M (m o l . μ m^{- 2} . h^{- 1})$ and its concentration in the lumen as $c (m o l . μ m^{- 3})$ . Then, fluid flux required to retain this concentration is given by the relationship:

Ω = \frac{M}{c}

(9)

Earlier, our analysis showed that lumenal fluid flux $Ω$ is a constant throughout growth. Under the assumption of isotonic transport ( $c$ is a constant), we inferred that lumenal solute flux $M$ is also constant throughout growth. Since solute and fluid flux are coupled, we investigated which of these parameters are regulated. Two possible scenarios exist: (i) Otic epithelium ensures a solute flux of exactly $M$ leading to a fluid flux of $Ω = \frac{M}{c}$ , or (ii) Otic epithelium restricts fluid flux to $Ω$ on account of wall distensibility and pressure gradient, which effectively retains a net solute flux of $M = Ω c$ . Indeed, the existence and presence of lumenal pressure is evident in terms of causing shape deformation in hindbrain tissue and mitotic cells (Figure 2). To concretely show the existence of pressure and how it restricts fluid transport, we performed simple perturbation experiments:

Puncturing experiments to verify the presence of pressure by assaying the loss of lumenal volume (Figure 3).
Regeneration experiments to demonstrate that the otic vesicle is capable of increased rates of solute and fluid transport in the absence of pressure. We measured regeneration dynamics (Figure 4) and found that vesicles were able to increasing flux by a factor $k = 3 \times - 4 \times$ the wild-type values (Figure 4—figure supplement 1).

Experimental outcomes suggest that pressure creates an opposing force to the osmotic potential forces to inhibit the movement of fluid, thus setting growth rates appropriate to the developmental stage. Thus, in unperturbed wild-type embryos, the observed fluid flux ( $Ω$ ) is a function of the difference between the osmotically-derived flux ( $Ω_{0}$ , arising purely due the osmotic potential alone) and the deviation from a set-point pressure, that we term the homeostatic pressure in the vesicle $P_{0}$ . Making the assumption that the functional form is linear then suggests the equation

Ω = Ω_{0} - K P_{0}

(10)

In punctured embryos, the loss in pressure ( $P \leq P_{0}$ ) leads to a larger flux following regeneration ( $\tilde{Ω} \geq Ω$ ).

\tilde{Ω} = Ω_{0} - K P

(11)

that is the increase in flux relative to the unperturbed value is proportional to the loss in pressure relative to its homeostatic value, with

\tilde{Ω} - Ω = K (P_{0} - P)

(12)

For small changes in the radius in the neighborhood of the fixed point, the loss-in-pressure is proportional to the loss-in-volume $(V_{0} - V)$ , where $V_{0}$ and $V$ are unperturbed and perturbed volumes respectively), so that we arrive at the following relationship:

\tilde{Ω} - Ω \approx κ (V_{0} - V)

(13)

We validate model predictions of a correlation between regeneration flux ( $\tilde{Ω}$ ) and volume-loss between punctured and unpunctured ears ( $V_{0} - V$ ). Our experimental data (regeneration in blue curve in Figure 4H and Figure 4—figure supplement 1E,F) depicts a proportional relationship, thus validating the accuracy of our model. Our data shows that the unperturbed flux $Ω ≃ 1 μ m / h r$ and slope $κ$ is approximately 3–5.

Modeling pressure-driven growth and deformation of the vesicle shape

The otic vesicle is expected to deform under the action of pressure, thus leading to growth and reshaping of the tissue. We therefore sought to assess how these forces affect individual cells. Given the vesicle geometry, cells in the otic vesicle experience three types of pressure-derived forces: (i) pressure force ( $P$ , $N . μ m^{- 2}$ ) normal to the apical membranes in a direction that flatten cells, (ii) tissue stress ( $σ$ , $N . μ m^{- 2}$ ) distributed normal to lateral membranes, and (iii) reactionary or support forces from hindbrain and skin tissue.

To formalize this, we modify a recent framework introduced to study the growth of cellular cysts (Ruiz-Herrero et al., 2017). In a closed geometry, tissue stress $σ$ is related to lumenal pressure $P$ by a simple force balance equation. For a spherical pressure vessel, the pressure force pushing one hemisphere is counterbalanced by tissue tension.

P π R^{2} = 2 π R h σ \Leftrightarrow σ = \frac{P R}{2 h} .

(14)

To link tissue stress to deformation, we investigated the material properties of the tissue ( $G$ ). We initially modeled otic tissue as being similar to a purely viscous fluid flowing under a tangential shear stress $σ$ with a strain-rate of $\dot{ϵ} = \frac{1}{R} \frac{d R}{d T}$ .

σ = G \dot{ϵ} .

(15)

For a purely viscous fluid with viscosity coefficient $μ$ ( $P a . h$ ) deforming in a spherically-restricted geometry, the shear stress ( $σ$ ) in the fluid layers relates to rate of radius change using Stokes’ law as:

σ = 4 μ \frac{1}{R} \frac{d R}{d t} .

(16)

Since a viscous material deforms continuously under the action of a force and retains the deformation when force is removed, we validated our assumption by studying the temporal trends in resting shapes of cells after pressure forces are eliminated. Indeed, we observed that the resting shape of cells (after puncture) had undergone irreversible deformation in developmental time (Figure 3G and D (red bars progressively decrease)). In other words, a cell at 35 hpf has a relatively squamous morphology at rest compared to the same cell at 25 hpf. When compared to the contralateral unpunctured ear, however, we observed an elastic response in punctured vesicles wherein cells had dynamically reshaped to more columnar morphologies (Figure 3E and F,H (difference between red and blue bars)). This suggested that the tissue behaved elastically in short time-scales and viscous in long time-scales. To incorporate elastic behavior on short timescales, we modeled the overall deformation as:

\dot{σ} + \frac{σ}{τ} = G \dot{ϵ}

(17)

We next quantified cell material properties by quantifying the short (elastic) and long timescale (viscous) responses in response to puncturing perturbations (Figure 6A). The reversible component of a cell’s deformation, when all acting forces are eliminated, is inversely proportional to its elasticity ( $K$ ). The irreversible component of a cell’s deformation that accumulates over time is inversely proportional to the viscosity coefficient ( $μ$ ). We also investigated and identified the molecular origins of material property patterning in terms of actomyosin networks that were found to be apically expressed in the otic cells (Figure 6). Thus, our model identifies the role of pressure forces in deforming cells and driving growth. Material property patterning was found to locally modulate the deformation to anisotropically shape the vesicle through growth.

Quantification and statistical analysis

Each data point of morphodynamic quantification was obtained using our automated bioimage informatics pipeline (ITIAT) on images from 10 different embryos that were immobilized with $α$ -bungarotoxin mRNA. 30 time-points were analyzed—every hour between 16 and 45 hpf—which included 300 otic vesicle lumen measurements and more than 200,000 segmented cells. For Figure 1E–H, Figure 1—figure supplement 1N–O the translucent spread of the data is the standard deviation.

For analysis of mitotic cell deformation, we identified 54 mitotic cells. The spread of the data presented as translucent overlays in Figure 2G is the calculated standard deviation. For measuring the hindbrain deformation in Figure 2J, n = 10 embryos/timepoint were used.

Pressure measurements were acquired from 5, 8, and nine different embryos at 30, 36, and 48 hpf (Figure 3C).

For puncture experiments, 10 otic vesicles were measured that were punctured and there morphometrics were compared to 10 unpunctured otic vesicles (Figures 3E–H and 4E–H, Figure 4—figure supplement 1). The error bars are standard deviation and the p-values were obtained using a student t-test.

For ion-channel and pH perturbations, each data point is five embryos and error bars are standard deviation (Figure 5).

For calculating the effective tissue viscosity from Equation 1, the time-averaged data of all variables were obtained from the datasets shown in Figure 3C,E–F. The instantaneous growth rate, $R^{'} = d R / d t$ , was calculated from the difference of radius $R$ of each time point before averaging. A formula for error propagation (Ku, 1966) was derived from Equation 1:

\frac{δ_{μ}}{μ} = \frac{1}{8} \sqrt{{(\frac{δ_{P}}{P})}^{2} + 2 {(\frac{δ_{R}}{R})}^{2} + {(\frac{δ_{h}}{h})}^{2} + {(\frac{δ_{R^{'}}}{R^{'}})}^{2}},

where $δ_{X}$ is the standard deviation of variable $X$ . The mean and standard deviations are summarized in the table below:

Mean (Standard deviation)
$t$	$P$	$R$	$h$	$R^{'}$	$μ$
hpf	Pa	µm	µm	10^-4 µm/s	10⁶ Pa⋅s
24-36	116 (23.1)	36 (0.18)	13 (0.12)	2.31 (0.73)	6.26 (0.30)
36-48	166 (23.4)	48 (0.22)	10 (0.21)	2.15 (0.95)	22.2 (1.29)

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For the derivation of relative differences in tissue elasticity and viscosity, each data point was obtained from 10 different punctured embryos (Figure 6A–C) and the translucent spread represents the standard deviation.

Figure 6I-J, 22 utrophin expressing cells and 22 myosin expressing cells were analyzed. Figure 6K–L–M, scatterplots with 15, 16, and 12 embryos were used respectively.

Data and software availability

Image analysis

Our entire bioimage informatics pipeline called ‘In toto image analysis toolkit (ITIAT)’ is available online at: https://wiki.med.harvard.edu/SysBio/Megason/GoFigureImageAnalysis. The pipeline can be used for generating 3D surface reconstructions, automatic whole-cell and nuclei segmentations, and cell tracking. The code is open-source and written using the C++ programming language. The code can be downloaded and compiled in any platform using CMake, a tool for generating native Makefiles. The code is built by linking to pre-compiled open-source libraries, namely, ITK (http://www.itk.org) (Yoo et al., 2002) and VTK toolkit (http://www.vtk.org) (Schroeder et al., 2006) for image analysis and visualization respectively. We also used the open-source and cross-platform GoFigure2 application software for the visualization, interaction, and semi-automated analysis of $3 D + t$ image data (http://www.gofigure2.org) (Gelas, Mosaliganti, and Megason et al., in preparation). Measurement of mitotic cell aspect-ratios was carried out using ZEN (Carl Zeiss) software 3D distance functionality. Measurements were analysed and plotted with Matlab (Mathworks) and Microsoft Excel. To obtain 3D models of the otic vesicles, 2D contours were first placed along regularly-sampled z-planes in GoFigure2 (Figure 1I). 3D reconstructions were obtained using the Powercrust reconstruction algorithm (https://github.com/krm15/Powercrust) (Amenta et al., 2001). Automatic cell and lumen-segmentation were performed using ACME software for whole-cell segmentations (Mosaliganti et al., 2012; Xiong et al., 2013) (Figure 1—figure supplement 1J–M).

Acknowledgements

We thank members of Megason lab for feedback, Mr. Dante D’India for fish care, and Ms. Suzanne Mosaliganti for help in proof-reading the manuscript. This work was supported by the National Institute of Health grant K25 HD071969 (KRM), Novartis Fellowship for Systems Biology (IAS), National Institute of Health grant 5F32HL097599 (IAS), A*STAR International Fellowship (CUC), Hearing Health Foundation (IAS), the MacArthur Foundation (LM), National Science Foundation grant BMMB 15–36616 (LM), National Institute of Health grant R01 DC010791 (SGM), and National Institute of Health Grant R01 DC015478 (SGM).

Funding Statement

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Contributor Information

L Mahadevan, Email: lmahadev@g.harvard.edu.

Sean G Megason, Email: megason@hms.harvard.edu.

Raymond E Goldstein, University of Cambridge, United Kingdom.

Didier Y Stainier, Max Planck Institute for Heart and Lung Research, Germany.

Funding Information

This paper was supported by the following grants:

National Institutes of Health K25 HD071969 to Kishore R Mosaliganti.
Hearing Health Foundation to Ian A Swinburne.
National Institutes of Health 5F32HL097599 to Ian A Swinburne.
National Institutes of Health DC010791 to Sean G Megason.
National Institutes of Health DC015478 to Sean G Megason.
John D. and Catherine T. MacArthur Foundation to L Mahadevan.
National Science Foundation BMMB 15-36616 to L Mahadevan.
Agency for Science, Technology and Research to Chon U Chan.

Additional information

Competing interests

No competing interests declared.

Author contributions

Conceptualization, Software, Formal analysis, Investigation, Writing—original draft, Writing—review and editing.

Investigation, Writing—original draft, Writing—review and editing.

Formal analysis, Investigation, Methodology, Writing—original draft, Writing—review and editing, Designed and characterized the pressure probe.

Investigation, Writing—review and editing.

Conceptualization, Formal analysis, Supervision, Writing—original draft, Writing—review and editing, Designed and characterized the pressure probe.

Conceptualization, Formal analysis, Supervision, Funding acquisition, Writing—original draft, Project administration, Writing—review and editing.

Ethics

Animal experimentation: This study was performed in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. The Harvard Medical Area Standing Committee on Animals approved zebrafish work under protocol number 04487.

Additional files

Transparent reporting form

elife-39596-transrepform.docx^{(246.3KB, docx)}

DOI: 10.7554/eLife.39596.020

Data availability

All data generated or analyzed during this study are included in the manuscript and supporting files.

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eLife. doi: 10.7554/eLife.39596.023

Decision letter

Editor: Raymond E Goldstein¹

Reviewed by: Ksenia Gnedeva²

In the interests of transparency, eLife includes the editorial decision letter, peer reviews, and accompanying author responses.

[Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed.]

Thank you for submitting your article "Size control of the inner ear via hydraulic feedback" for consideration by eLife. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Didier Stainier as the Senior Editor. The following individual involved in review of your submission has agreed to reveal her identity: Ksenia Gnedeva (Reviewer #3).

The Reviewing Editor has highlighted the concerns that require revision and/or responses, and we have included the separate reviews below for your consideration. If you have any questions, please do not hesitate to contact us.

Summary:

This paper examines the potential role of pressure in regulating the volume of the otic vesicle during zebrafish development. The authors present several lines of evidence that there is indeed transepithelial pressure: the shapes of adjacent epithelial cells are perturbed, the vesicle deflates when punctured and, using a clever device, they present some direct measurements of transepithelial pressures (values on the order of 100 Pa). They calculate, based on the geometry, the flux of fluid into the vesicle, which is fairly constant over the developmental times that they are studying. After puncturing the vesicle, the luminal volume "catches up" through an increase in the flux; they conclude that the pressure is inhibiting the flux, establishing a feedback loop.

Major concerns:

The reviewers have noted that the pressure measurements themselves are very noisy, and their reproducibility is unclear. These features make it difficult to judge the extent to which the very plausible theoretical model is or is not quantitatively consistent with the measurements. They have requested clarification on a number of aspects of the pressure measurements themselves, and asked if the connection between the theory and data can be made more precise than the mostly correlative comparison described in the paper.

Additionally, the reviewers have suggested that further analysis is warranted in order to solidify the claim that there is a causative connection between changes in hydrostatic pressure and changes in the rate of cell growth, cell proliferation, and/or cell cycle length. They have also asked about the connection between tissue-level tension and cell proliferation, the role of elasticity of the surrounding tissues, and the possibility of measuring that elasticity directly.

Separate reviews (please respond to each point):

Reviewer #1:

This is a very interesting paper on the problem of organ size regulation. It combines an impressive set of imaging and in vivo measurements with a simple mathematical model to paint a clear picture of a plausible mechanism at work the zebrafish. The logic of the analysis is very clear, as is the presentation.

Having said the above, I find that the manuscript falls short on two major fronts. First, if Figure 3—figure supplement 1B-D are a general indication of the repeatability of the pressure measurements in vivo, then it is not clear to this reviewer the extent to which truly quantitative conclusions about the system can be inferred. The authors have not included any discussion about the potential sources of the large fluctuations seen in these experiments and their variability from one experiment to the next. The case for publication in eLife would be substantially enhanced if the reliability of the measurements were quantified and understood more deeply.

A second major issue concerns the connection between the eminently plausible theory presented in the paper and the quantitative observations. The verbal discussion in the paper regarding a whole range of qualitative observations dovetails nicely with what would be expected from the theory, but yet the paper does not appear to have a single graph in which a quantitative prediction of the theory is compared against experiment. The case for publication in eLife would be much stronger if such a comparison were possible. Can the authors show that there is more than a qualitative relationship between the two?

Minor Comments:

As a minor comment I would urge the authors to move the essential aspects of the presentation of the theory into the Results section. The mathematics is very straightforward and it would increase readability to have it interspersed within the Results section where appropriate.

Reviewer #2:

This paper examines the potential role of pressure in regulating the volume of the otic vesicle during the zebrafish development. The authors present several lines of evidence that there is indeed transepithelial pressure: the shapes of adjacent epithelial cells are perturbed, the vesicle deflates when punctured and, using a clever device, they present some direct measurements of transepithelial pressures (values on the order of 100 Pa). They calculate, based on the geometry, the flux of fluid into the vesicle, which is fairly constant over the developmental times that they are studying. After puncturing the vesicle, the luminal volume "catches up" through an increase in the flux; they conclude that the pressure is inhibiting the flux, establishing a feedback loop.

I think that the most interesting aspect of the manuscript is the pressure measurements. All the rest is indirect and based on correlations: the pressure feedback model is a plausible explanation for the observed morphological changes. Without the pressure measurements, this is not be an eLife paper.

However, the pressure measurements themselves are poorly developed and not convincing. There are many technical aspects that are not addressed, and many controls that need to be done.

1) Are the pressure measurements themselves dependent on the ionic composition and/or electrical potential? This is potentially important as the endolymph has an unusual ionic concentration and voltage, at least in adults. Is the high potassium concentration established at these early times?

2) Does the pressure measurement depend on the diameter of the capillary. I am surprised and concerned by the wide range of diameters (2-20 microns).

i) Is there a problem with damage – does the capillary tend to puncture the vesicle like the puncture needle. If not, why not? No details are given about the puncture needle: an "unclipped glass needle", whatever that is. What is the diameter?

ii) Is there a problem with mixing of the deionized water in the capillary with the endolymph? I would expect the diffusive exchange of fluid to be large, especially with 20 micron diameter capillaries. It looks like the total volume of the capillary is much larger than the vesicle, so the endolymph will be greatly diluted, unless the ion pumps can keep up. How long is mixing expected to take.

3) There simply are not enough measurements of pressure to be convincing, given the variabilities of the individual measurements in Figure 3—figure supplement 1.

4) Figure 3—figure supplement 1 shows only a small part of the time traces. What is happening before time zero. For me to be convinced, I would like to see the whole time course starting with the capillary in the (undefined) Dannieau (sic) buffer, then the penetration of the skin, followed by the epithelium and finally entry into the vesicle lumen. How often does this experiment work? Have the recordings in Figure 3—figure supplement 1 been cherry-picked?

5) A key experiment will be to measure the pressure while puncturing and showing that it goes down (and perhaps recovers).

In summary. The most novel aspect of this paper is the pressure measurement. However, this is much too preliminary to be included in the current work. I suggest taking them out and submitting the manuscript to another journal. I do not believe that such a manuscript meets the level of conceptual advance for an eLife paper: the arguments are correlative and the model is only at the level of plausibility. In other words, the results in this manuscript are suggestive of a pressure-flux feedback model, which therefore remains a hypothesis. I encourage the authors to develop the pressure measurements, but there is a long way to go.

Reviewer #3:

The manuscript by Mosaliganti et al. investigates the mechanism of organ size control in the developing otic vesicle in zebrafish. In particular, the authors demonstrate that fluid transport into the otic vesicle results in stress and stretching of the otic epithelium, and claim that constitutes the major driving force in lumen expansion and organ growth. The authors also suggest that buildup of the pressure in the otocyst inhibits further fluid transport, thus repressing growth. Such a negative feedback mechanism can explain the observed robustness of the otic vesicle growth, and explain a catch-up growth phenomenon that they observe after puncturing the otocyst.

The authors characterize the vesicle's size using unbiased quantitative measurements, including direct measurements of the luminal pressure. Ouabain and morpholino experiments convincingly demonstrate the involvement of Na+-K⁺-Cl transporter, Slc12a2, in the fluid flux into the vesicle. Overall, the article is well written and beautifully illustrated. The experiments are easy to follow. All the numerical comparisons are accompanied by adequate statistical analysis. However, I believe the following concerns should be addressed in order to support the proposed conclusions.

Major concerns:

I do not entirely agree with the author's definition of growth. Organ growth is determined by an increase in tissue mass (via increase in cell number, cell size, or both). To be precise, otic vesicle growth, characterized in Figure 1F, is represented by the green curve (otic tissue volume), and not the blue curve (otic vesicle volume). Increase in the vesicle's lumen, especially after the puncture experiments, should not be called growth, if tissue volume does not change in these experiments. I, however, agree with the overall idea that hydrostatic pressure can be a driving force for tissue growth, as it may cause tissue stretching and cell proliferation, however, this is not characterized in the manuscript. In this regard, the effect of hydrostatic pressure on the rate of cell growth and proliferation, not on the changes in lumen volume, should be characterized. This should be done for all their experiments, especially for normal development and Slc12a2 morpholino experiments. It will be critical to demonstrate that there is a causative connection between changes in hydrostatic pressure, and changes in the rate of cell growth, cell proliferation, and/or cell cycle length. These data are already present in the time-lapse videos provided by the authors, and should be extracted/analyzed, as it is critical to link hydrostatic pressure to organ growth control mechanisms discussed by the authors in the Introduction of the manuscript.

– One of the concerns I have with the manuscript is that the authors seem to conclude that growth rate in the organ is determined by an equilibrium between hydrostatic pressure, regulated by fluid flux into the vesicle, and tension in the otic epithelium. Biologically, such an assumption is unlikely, as an increase in epithelial tension is a well-described trigger for cell proliferation and growth. Gudipaty et al., 2017 and Elosegui-Artola et al., 2017 are just a couple of recent articles on the matter. Authors do not consider the elastic forces exerted by the tissues surrounding the otic vesicle (e.g. mesenchyme, brain, and skin). In addition to the otic tissue viscoelastic properties, these forces are very likely to counteract the hydrolytic pressure in the vesicle, and to affect its growth. In fact, such a mechanism of growth control was recently shown to take place in the vestibular sensory organ in mice. This should be accounted for in the theoretical model proposed by the authors and mentioned in the discussion.

– Related to the previous comment, the authors estimate effective viscosity of the otic vesicle tissue from their theoretical model. To test this prediction, and to confirm the accuracy of the model, Young's modulus of the tissue should be measured directly (e.g via atomic force microscopy). Also in this context, the authors claim that puncturing perturbations (to eliminate pressure forces) allowed them to measure spatial differences in cell viscoelasticity. These experiments only suggested the local differences in tissue viscosity, direct measurements of cell stiffness should be done to confirm this suggestion.

– It is not apparent to me that the authors demonstrate clearly the causality of spatial differences in cell viscoelasticity. Again, although hydrostatic pressure sensed by all the cells in the vesicle should be the same, the local difference in the opposing elastic forces from surrounding tissues can create differential thinning of the vesicle's wall; this in turn may result in actomyosin skeleton remodeling and stiffness changes, rather than vice versa.

– In the section "tissue material properties are patterned through actomyosin regulation" the authors talk about WT and transgenic animals, without explaining what transgenes are used. It made it hard to review this section.

I'd like to disclose that as a biologist with limited biophysics background, I cannot fully review the mathematical aspects of the work, and trust that one of the other reviewers has the expertise necessary to judge the accuracy of the theoretical model proposed here.

Minor Comments:

– To test their model's predictions, the authors conduct puncture experiments to evaluate the role of hydrolytic pressure on the growth rate of the otic vesicle. Although the authors demonstrate that punctures heal fast relative to the growth rate of the organ, such manipulations are invasive and are not fully sufficient to support their conclusions. Direct manipulation of the chemi-osmotic potential, for example, could be done to change the rate of endolymph accumulation, and to test its effect on organ growth. This could be achieved by injecting hydrophilic inert compounds, such as ficoll, into the otic vesicle or into the tissue surrounding it. If water transport across an epithelium is, in fact, the main driving force for otic vesicle growth, increasing osmolality of the endolymph should induce accelerated growth and increase cell proliferation rates.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Size control of the inner ear via hydraulic feedback" for further consideration at eLife. Your revised article has been favorably evaluated by Didier Stainier (Senior Editor), a Reviewing Editor, and two of the original reviewers.

The reviewers are of the opinion that the manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:

i) In the interests of clarity, we would like to see the pressure traces in the manuscript proper rather than in the supplementary figures.

ii) If indeed there is no direct measurement of the pressure drop during puncture this should be stated explicitly.

Other points:

1) Abstract: what is meant by "noise in underlying molecular and cellular processes"? This premise is not established in the paper. It is a straw man. How much expression noise would it take to mess up otic development?

2) Results: SD or SE? what is n?

3) Figure 1E: start the y-axes at zero (zero is important in this case)

4) Figure 1F: match the colors to Figures 1A-D

5) Figure 5: the Na,K-ATPase is generally referred to as a pump rather than an ion channel.

eLife. 2019 Oct 1;8:e39596. doi: 10.7554/eLife.39596.024

Author response

Major concerns:

The reviewers have noted that the pressure measurements themselves are very noisy, and their reproducibility is unclear. These features make it difficult to judge the extent to which the very plausible theoretical model is or is not quantitatively consistent with the measurements. They have requested clarification on a number of aspects of the pressure measurements themselves, and asked if the connection between the theory and data can be made more precise than the mostly correlative comparison described in the paper.

We have performed additional pressure measurements, controls and clarifications to address the concerns, which are detailed below.

Our theoretical model has two aspects: 1. By accounting for geometry and conservation laws, a mechanical feedback mechanism emerges that regulates endolymph flux and organ size. 2. Once the mechanical equilibrium is reached, the epithelial tissue is further remodeled at a longer time scale determined by an effective tissue viscosity.

The first aspect is verified by successfully predicting the catch-up growth dynamics after puncturing experiments (see ‘Model prediction and validation: Pressure negatively regulates fluid flux’). Notably, the experimental data (Figure 4H and Figure 4—figure supplement 1E,F) can be fitted with the prediction (equation 13) with a proportional relationship related to the permeability coefficient K.

The second aspect is a general description of the force balance and the tissue’s viscoelastic material property. If the epithelial tissue viscosity can be independently measured, it would further support our pressure measurement, but not our theoretical framework. Nevertheless, we have considered measurement methods, such as pipette aspiration methods for living cells (Hochmuth, 200). However, the effective viscosity of the epithelial tissue, based on our estimation from pressure measurements, is 4-5 orders of magnitude higher than the cellular viscosity. Deploying the same tool on the epithelial tissue, it would require a much higher suction or a much longer waiting period. It is not possible to measure the viscosity of the in vivo tissue without perturbing its structural properties and shape.

In summary, the framework of our model has been verified with qualitative data. The effective tissue viscosity measurement agrees up to the order of magnitude with other systems. Independent viscosity measurement is not possible due to technical difficulty, yet this is not relevant to the basis of our model.

Hochmuth, R.M., 2000. Micropipette aspiration of living cells. Journal of biomechanics, 33(1), pp.15-22.

Additionally, the reviewers have suggested that further analysis is warranted in order to solidify the claim that there is a causative connection between changes in hydrostatic pressure and changes in the rate of cell growth, cell proliferation, and/or cell cycle length. They have also asked about the connection between tissue-level tension and cell proliferation, the role of elasticity of the surrounding tissues, and the possibility of measuring that elasticity directly.

May we clarify that there are no claims within the manuscript on causality between pressure and the rate of cell growth, proliferation, and cell cycle length. Pursuing these connections, while of great interest to us, is beyond the original scope of this study.

Separate reviews (please respond to each point):

Reviewer #1:

This is a very interesting paper on the problem of organ size regulation. It combines an impressive set of imaging and in vivo measurements with a simple mathematical model to paint a clear picture of a plausible mechanism at work the zebrafish. The logic of the analysis is very clear, as is the presentation.

We thank reviewer #1 on the positive feedback and critical review.

Having said the above, I find that the manuscript falls short on two major fronts. First, if Figure 3—figure supplement 1B-D are a general indication of the repeatability of the pressure measurements in vivo, then it is not clear to this reviewer the extent to which truly quantitative conclusions about the system can be inferred. The authors have not included any discussion about the potential sources of the large fluctuations seen in these experiments and their variability from one experiment to the next. The case for publication in eLife would be substantially enhanced if the reliability of the measurements were quantified and understood more deeply.

We have performed more characterization on the pressure probe (see Figure 3—figure supplement 1 and further discussion in reviewer #2). Also, more measurements were performed and the statistics are depicted in Figure 3C.

“Pressure measurements were acquired from 5, 8, and 9 different embryos at 30, 36, and 48 hpf (Figure 3C).”

“Otic vesicle pressures at different developmental stages of wild-type zebrafish embryos (red diamond: mean value. *p<5.0e-2).”

The additional measurements altered the mean pressure measurements used to approximate the viscosity of the tissue.

Adjusted calculations are detailed in the text:

“Using this relationship, our morphodynamic measurements, and pressure measurements we estimate the effective viscosity of the otic vesicle tissue to be about 6.3+/-0.30 x 10^6 Pa*s from 24-36 hpf and then 2.2+/-0.13 x 10^7 Pa*s from 36-48 hpf (see Materials and methods for error propagation calculations).”

“The mean and standard deviations are summarized in the table below”:

(see table in manuscript)

A discussion on the potential sources of the fluctuations is added:

“At the typical rise time (around 0.5 minute) of the probing stage, (Stage II in Figure 3—figure supplement 1F), the concentration remains at about 70%-90% for inner diameter of $15-5um. We expect the impact on the pressure reading was small at this time scale. After about 5 to 12 minutes, the concentration drops to 10%, which may significant modify the chemical potential. Together with the imperfection in sealing, they could contribute to the fluctuation measured at the longer time scale. However, we have ignored some factors that can maintain the ionic concentration: the active transport of ions and the potentially higher viscosity in the lumen.”

A second major issue concerns the connection between the eminently plausible theory presented in the paper and the quantitative observations. The verbal discussion in the paper regarding a whole range of qualitative observations dovetails nicely with what would be expected from the theory, but yet the paper does not appear to have a single graph in which a quantitative prediction of the theory is compared against experiment. The case for publication in eLife would be much stronger if such a comparison were possible. Can the authors show that there is more than a qualitative relationship between the two?

As discussed above, the most important prediction of a negative feedback mechanism (equation 11-13) is verified by obtaining a proportional relationship between regeneration flux and volume-loss between punctured and unpunctured ears (see ‘Modeling pressure generation and feedback to fluid transport mechanisms’). Eliminating this single fitting parameter requires an independent measurement of the permeability coefficient, which is not feasible.

Minor Comments:

As a minor comment I would urge the authors to move the essential aspects of the presentation of the theory into the Results section. The mathematics is very straightforward and it would increase readability to have it interspersed within the Results section where appropriate.

We agree with the inclination to place the theory in front of the Results section. However, much of our audience (see reviewer #3) may be distracted by the theory. We have decided to keep the theory consolidated within the Materials and methods section.

Reviewer #2:

[…] I think that the most interesting aspect of the manuscript is the pressure measurements. All the rest is indirect and based on correlations: the pressure feedback model is a plausible explanation for the observed morphological changes. Without the pressure measurements, this is not be an eLife paper.

However, the pressure measurements themselves are poorly developed and not convincing. There are many technical aspects that are not addressed, and many controls that need to be done.

We thank reviewer #2 for the suggestions on the pressure measurements, which help us to clarify the measurement technique to general readers.

1) Are the pressure measurements themselves dependent on the ionic composition and/or electrical potential? This is potentially important as the endolymph has an unusual ionic concentration and voltage, at least in adults. Is the high potassium concentration established at these early times?

We have added controls where calibrations were performed with distilled water or a solution that resembles mature endolymph. There is no dependence on the ionic composite regardless of the tip size. We have added Figure 3—figure supplement 1B and the following paragraph:

“Similar tests were conducted with various capillary diameters and ionic concentrations within the bath (deionized water and a solution that resembles mature endolymph) to ensure there is no additional effect (Figure 3—figure supplement 1B).”

In Caption of Figure 3—figure supplement 1E:

“Calculations of diffusive mixing between endolymph and capillary filling after puncturing. Their initial ionic concentration are C0 and 0, respectively. The mean ionic concentration inside the vesicle C decreases over time t at a rate depending on the capillary inner diameter d. (Inset) Selected solutions are shown for d=5,15um in the first 5 minutes.”

and:

“The composition of our synthetic endolymph is 5 mM sodium chloride, 150 mM potassium chloride, 0.2 mM calcium chloride, 0.5 mM glucose, 10 mM tris, buffered to pH 7.5.”

While it is unknown what the ionic composition is for the early zebrafish otic vesicle, it is most likely of high sodium content, like plasma, as it is within embryonic otic cysts of mammals.

2) Does the pressure measurement depend on the diameter of the capillary. I am surprised and concerned by the wide range of diameters (2-20 microns).

We now perform the pressure measurement on a microscope with higher resolution and the tip size are more accurately measured. We found that the inner diameter is between 6-13 microns and have changed the text accordingly.

“The sensor was coupled via a high pressure fitting to a 2 cm long glass capillary (World Precision Instruments) with a conical tip of 6-13 μm inner diameter (Figure 3A).”

To address the potential dependency on capillary diameter, we performed calibrations with tips of 4.5 and 10 microns inner diameter (as presented in comment #1 above) and found no dependence. Additionally, there is no dependence in our test data, as shown in Author response image 1:

i) Is there a problem with damage – does the capillary tend to puncture the vesicle like the puncture needle. If not, why not? No details are given about the puncture needle: an "unclipped glass needle", whatever that is. What is the diameter?

The puncture needles were similar sizes (5-10 microns) but wiggling is required to promote a larger wound upon removal. Insertion of the pressure probe was a much gentler and controlled motion to help a seal around the inserted glass capillary. Since the epithelium is under tension, we observe that it wraps around the tip once being punctured.

ii) Is there a problem with mixing of the deionized water in the capillary with the endolymph? I would expect the diffusive exchange of fluid to be large, especially with 20 micron diameter capillaries. It looks like the total volume of the capillary is much larger than the vesicle, so the endolymph will be greatly diluted, unless the ion pumps can keep up. How long is mixing expected to take.

To estimate the time scale at which the endolymph is diluted by the diffusive exchange, we numerically solve the diffusion equation with the vesicle-tip geometry and calculate the average ionic concentration inside the vesicle. As the inner diameter of the tip increases from 5 microns to 15 microns, the period before the endolymph drops to 10% decreases from 12 minutes to 5 minutes. As it typically takes less than one minute for the pressure to build up after the puncture, the diffusive exchange should not affect the plateau pressure reading. The subsequent exchange dilutes the endolymph and may be partly responsible to the pressure fluctuation. We added Figure 3—figure supplement 1E and the following paragraph:

“We also estimated the time scale at which the endolymph is diluted by the diffusive exchange. […] However, we have ignored some factors that can maintain the ionic concentration: the active transport of ions and the potentially higher viscosity in the lumen of the otic vesicle.”

3) There simply are not enough measurements of pressure to be convincing, given the variabilities of the individual measurements in Figure 3—figure supplement 1.

We have performed additional experiments and the statistics are shown in Figure 3C. The result is statistically significant to show that the pressure builds up with ages and therefore agrees with our prediction. A discussion on the potential source of fluctuation is added (see comment #2 of reviewer #1).

4) Figure 3—figure supplement 1 shows only a small part of the time traces. What is happening before time zero. For me to be convinced, I would like to see the whole time course starting with the capillary in the (undefined) Dannieau (sic) buffer, then the penetration of the skin, followed by the epithelium and finally entry into the vesicle lumen. How often does this experiment work? Have the recordings in Figure 3—figure supplement 1 been cherry-picked?

From the microscope, we observed that the capillary tip first indents the vesicle slightly before it punctures and being wrapped by the epithelium. Therefore, there is no distinguishable moment between skin and epithelium entry.

The criteria for accepting a measurement is the following: 1. The capillary is punctured at the correct location and depth. 2. The vesicle remains visually intact 3. The pressure builds up after the puncture and reaches a plateau. 4. After withdrawing the capillary the pressure drops rapidly to near the hydrostatic pressure at that depth, indicating the pressure is not built up from clogging. The overall successful rate of the puncturing attempts is about 10%. The traces of all data points in Figure 3C are shown in Figure 3—figure supplement 2.

Before time zero, the tip is placed beside the vesicle to measure the hydrostatic pressure at that depth. At that moment, the trace is the same as the calibration curve. We further clarify the measurement dynamic by adding Figure 3—figure supplement 1F:

“F. Stages in an otic vesicle pressure measurement. Upper: zooming into the first 1.5 minute. I: the tip was placed near the vesicle. The hydrostatic pressure was used as the baseline. II: after puncturing, the pressure built up gradually. III: after reaching a plateau, the pressure fluctuated around a mean value. This value was taken as the measurement result. IV: Upon withdrawing the tip from the vesicle, the pressure dropped to the base line, proving that the probe had been sensing the hydrostatic pressure in the enclosed domain.”

We have corrected the spelling errors and defined Danieau buffer.

“The composition of the Danieau buffer is 14.4 mM sodium chloride, 0.21 mM potassium chloride, 0.12 mM magnesium sulfate, 0.18 mM calcium nitrate, and 1.5 mM HEPES buffered to pH 7.6.”

5) A key experiment will be to measure the pressure while puncturing and showing that it goes down (and perhaps recovers).

Unlike an isolated cyst in which two capillaries can be punctured from both sides, it is challenging to introduce another capillary to otic vesicle without perturbing the sealing. Particularly, a wiggling action is required to open up a wound (as discussed above). An alternative way to confirm the fact that we are sensing the hydrostatic pressure, as we applied to all our tests, is to monitor the rapid pressure drop after withdrawing from the closed domain between the sensor and lumen (Stage IV Figure 3—figure supplement 1F).

In summary. The most novel aspect of this paper is the pressure measurement. However, this is much too preliminary to be included in the current work. I suggest taking them out and submitting the manuscript to another journal. I do not believe that such a manuscript meets the level of conceptual advance for an eLife paper: the arguments are correlative and the model is only at the level of plausibility. In other words, the results in this manuscript are suggestive of a pressure-flux feedback model, which therefore remains a hypothesis. I encourage the authors to develop the pressure measurements, but there is a long way to go.

While we appreciate the recognition of the novelty, we believe that there are additional features of the manuscript that are novel and of interest to the eLife audience. For instance, the systematic analysis of the organ growth, as summarized in Figure 1, is a more complete picture of an organ’s early growth than those previously presented. Additionally, the finding and quantification of a novel instance of catch-up growth are of general interest (Figures 3 and 4). Also, the theoretical model that accounts for geometry and conversation laws is self-consistent with various quantitative observations. Although the result may appear to be just correlative, they are supported by physical principles, quantification data, and experiments, which is beyond a hypothesis.

Reviewer #3:

[…] The authors characterize the vesicle's size using unbiased quantitative measurements, including direct measurements of the luminal pressure. Ouabain and morpholino experiments convincingly demonstrate the involvement of Na+-K⁺-Cl transporter, Slc12a2, in the fluid flux into the vesicle. Overall, the article is well written and beautifully illustrated. The experiments are easy to follow. All the numerical comparisons are accompanied by adequate statistical analysis. However, I believe the following concerns should be addressed in order to support the proposed conclusions.

We thank reviewer #3 for the positive feedback and insightful comments that help us to clarify the concepts.

Major concerns:

I do not entirely agree with the author's definition of growth. Organ growth is determined by an increase in tissue mass (via increase in cell number, cell size, or both). To be precise, otic vesicle growth, characterized in Figure 1F, is represented by the green curve (otic tissue volume), and not the blue curve (otic vesicle volume). Increase in the vesicle's lumen, especially after the puncture experiments, should not be called growth, if tissue volume does not change in these experiments.

Although organ growth is commonly simplified to just an increase in cell number, we argue that this ignores a great amount of developmental biology and physiology which show how water, ECM, mineralization, and other factors besides cell proliferation are essential aspects of organs. While cell size and cell number contribute to organ growth, we think it is incorrect to dismiss the contribution of luminal volume. 70% of an average cell’s volume (and mass) is water, but one would never consider dismissing this tightly regulated volume as not being part of a cell’s size and function.

The composition and volume of the ear’s lumen, which contributes upwards of 50% of the organ’s volume, is as necessary to the organ’s function and physiology as the composition of the cytoplasm within its tissue’s cells. Because of this, there exist mechanisms in which it is regulated by the ear’s tissues. Additionally, lumen size and expansion are necessary during development to create space for sculpting the semicircular canals. The luminal volume and composition are as critical to the ear as extracellular collagen and hydroxyapatite are to a bone’s size and function (they contribute the majority of volume and mass to bones). To understand the growth of a bone, one should consider how the developing organ controls the deposition of these extracellular components. Likewise, to understand the growth of the ear and other fluid filled organs, it is essential to consider the lumen as part of the organ. We have added the following text to our manuscript to clarify this definitional point.

“Just as water is fundamental to the size and function of a cell's cytoplasm, the fluids filling the lumens of these organs, which are central to their development and physiological function, are fundamental components of these organs.”

I, however, agree with the overall idea that hydrostatic pressure can be a driving force for tissue growth, as it may cause tissue stretching and cell proliferation, however, this is not characterized in the manuscript. In this regard, the effect of hydrostatic pressure on the rate of cell growth and proliferation, not on the changes in lumen volume, should be characterized. This should be done for all their experiments, especially for normal development and Slc12a2 morpholino experiments. It will be critical to demonstrate that there is a causative connection between changes in hydrostatic pressure, and changes in the rate of cell growth, cell proliferation, and/or cell cycle length. These data are already present in the time-lapse videos provided by the authors, and should be extracted/analyzed, as it is critical to link hydrostatic pressure to organ growth control mechanisms discussed by the authors in the Introduction of the manuscript.

While we are interested in the molecular and cellular feedback response to pressure controlled growth, these avenues were beyond the original scope of this manuscript.

– One of the concerns I have with the manuscript is that the authors seem to conclude that growth rate in the organ is determined by an equilibrium between hydrostatic pressure, regulated by fluid flux into the vesicle, and tension in the otic epithelium. Biologically, such an assumption is unlikely, as an increase in epithelial tension is a well-described trigger for cell proliferation and growth. Gudipaty et al., 2017 and Elosegui-Artola et al., 2017 are just a couple of recent articles on the matter. Authors do not consider the elastic forces exerted by the tissues surrounding the otic vesicle (e.g. mesenchyme, brain, and skin). In addition to the otic tissue viscoelastic properties, these forces are very likely to counteract the hydrolytic pressure in the vesicle, and to affect its growth. In fact, such a mechanism of growth control was recently shown to take place in the vestibular sensory organ in mice. This should be accounted for in the theoretical model proposed by the authors and mentioned in the discussion.

Although we do not quantify the cellular feedback response to pressure, the cell proliferation and growth have been captured by the effective viscosity of the epithelial tissue (see equations 3, 7 and 16). We now point out that neighboring tissues likely contribute to the material properties of the otic vesicle’s tissue.

“Global constraints on the otic vesicle

The goal of the model was to relate fluid flux, hydrostatic pressure, material properties, and tension, geometry, and size to better understand organ growth. To simplify the model, we did not explicitly account for the molecular changes that can occur within cells in response to pressure to modulate its material properties by changing molecular adhesion states, cell division, or cell contraction. We now recognize the importance of this connection when we speculate on the underlying molecular mechanisms that modulate the mesoscopic features of interest.

– Related to the previous comment, the authors estimate effective viscosity of the otic vesicle tissue from their theoretical model. To test this prediction, and to confirm the accuracy of the model, Young's modulus of the tissue should be measured directly (e.g via atomic force microscopy). Also in this context, the authors claim that puncturing perturbations (to eliminate pressure forces) allowed them to measure spatial differences in cell viscoelasticity. These experiments only suggested the local differences in tissue viscosity, direct measurements of cell stiffness should be done to confirm this suggestion.

Young’s modulus is a measure of the material’s elastic properties, which dominates on short time-scales as seen during organ collapse when the vesicle is punctured. Viscosity, on the other hand, dominates on the longer timescales of organ growth. We measure relative elasticity and viscosity over time and space in Figure 6. An absolute measurement of Young’s modulus with AFM would either require isolating the otic vesicle tissue (which we tried but it is too fragile, and the properties would likely change) or if left in vivo the measurement would be a composite of all the tissues. We also think our theoretical model stands without this measurement.

– It is not apparent to me that the authors demonstrate clearly the causality of spatial differences in cell viscoelasticity. Again, although hydrostatic pressure sensed by all the cells in the vesicle should be the same, the local difference in the opposing elastic forces from surrounding tissues can create differential thinning of the vesicle's wall; this in turn may result in actomyosin skeleton remodeling and stiffness changes, rather than vice versa.

This is a great point and we have clarified our interpretation of the pattern we observed.

“As it is unclear what contribution the neighboring tissue has to the effective material properties of the growing otic vesicle, we are unable to distinguish whether the correlation between actomyosin patterns and tissue thinning is organ autonomous or whether elastic forces from neighboring tissue are influencing these behaviors.”

– In the section "tissue material properties are patterned through actomyosin regulation" the authors talk about WT and transgenic animals, without explaining what transgenes are used. It made it hard to review this section.

The transgenes were previously defined within the figure legend, Materials and methods, and Key Resource Table. We added labels to the figure panels and clarified the text within the Results, as follows:

“To identify how cell material properties are patterned, we examined localization patterns of F-actin and Myosin II using transgenic zebrafish (Tg(actb2:myl12.1-eGFP)^e2212 for visualizing myosin II distribution, and Tg(actb2:GFP-Hsa.UTRN) ^e116 for visualizing F-actin distribution (Behrndt et al., 2012).”

I'd like to disclose that as a biologist with limited biophysics background, I cannot fully review the mathematical aspects of the work, and trust that one of the other reviewers has the expertise necessary to judge the accuracy of the theoretical model proposed here.

Minor Comments:

– To test their model's predictions, the authors conduct puncture experiments to evaluate the role of hydrolytic pressure on the growth rate of the otic vesicle. Although the authors demonstrate that punctures heal fast relative to the growth rate of the organ, such manipulations are invasive and are not fully sufficient to support their conclusions. Direct manipulation of the chemi-osmotic potential, for example, could be done to change the rate of endolymph accumulation, and to test its effect on organ growth. This could be achieved by injecting hydrophilic inert compounds, such as ficoll, into the otic vesicle or into the tissue surrounding it. If water transport across an epithelium is, in fact, the main driving force for otic vesicle growth, increasing osmolality of the endolymph should induce accelerated growth and increase cell proliferation rates.

The otic vesicle’s lumen is both a small volume (~0.2 nL) and pressurized. We are unable to inject a consistent small volume (~0.01 nL) in a manner where the tissue was not perturbed. We are pursuing better ways to understand the molecular and cellular feedback response to pressure controlled growth, but these avenues were beyond the scope of this manuscript.

Our addition:

Since our initial submission, an excellent paper studying bone catch-up growth and size control was published. We have updated the Introduction to recognize this work.

“Recently, the related phenomenon of organ symmetry has been addressed in the context of tails and the inner ear; but, the control mechanism underlying catch-growth was not clearly identified (Rosello-Diez, Stephen and Joyner, 2017; Das et al., 2017, Green et al., 2017). Catch-up growth also occurs during bone growth and its study has clarified insulin signaling activity as being important for bone size control (Rosello-Diez and Joyner et al., 2015, Rosello-Diez et al., 2018). Nonetheless, catch-up growth has been underused in the study of vertebrate specific mechanisms of organ size control (Rosello-Diez et al., 2018).”

[Editors' note: further revisions were requested prior to acceptance, as described below.]

The reviewers are of the opinion that the manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:

i) In the interests of clarity, we would like to see the pressure traces in the manuscript proper rather than in the supplementary figures.

The pressure traces have been moved to Figure 3D. Figure references within text have been changed accordingly.

ii) If indeed there is no direct measurement of the pressure drop during puncture this should be stated explicitly.

We do not know whether there is a pressure drop upon insertion of the probe into the otic vesicle and have stated this explicitly.

“We are uncertain whether there is a drop in pressure upon insertion of the pressure probe into the otic vesicle because there is no alternate measurement device.”

Other points:

1) Abstract: what is meant by "noise in underlying molecular and cellular processes"? This premise is not established in the paper. It is a straw man. How much expression noise would it take to mess up otic development?

We have changed the Abstract to the following:

“Animals make organs of precise size, shape, and symmetry. How developing embryos consistently make organs is largely unknown.”

2) Results: SD or SE? what is n?

“for all data-points in Figure 1 n=10 otic vesicles, data spread is the standard deviation)”

3) Figure 1E: start the y-axes at zero (zero is important in this case)

The y-axes now begins at zero.

4) Figure 1F: match the colors to Figures 1A-D

The colors now match Figures 1A-D.

5) Figure 5: the Na,K-ATPase is generally referred to as a pump rather than an ion channel.

The title in Figure 5 is now:

“Figure 5: Ear size is affected by disruptions in ion transport.”

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Transparent reporting form

elife-39596-transrepform.docx^{(246.3KB, docx)}

DOI: 10.7554/eLife.39596.020

Data Availability Statement

Image analysis

All data generated or analyzed during this study are included in the manuscript and supporting files.

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PERMALINK

Size control of the inner ear via hydraulic feedback

Kishore R Mosaliganti

Ian A Swinburne

Chon U Chan

Nikolaus D Obholzer

Amelia A Green

Shreyas Tanksale

L Mahadevan

Sean G Megason

Roles

Abstract

Introduction

Results

In toto imaging of otic vesicle development shows lumenal inflation dominates growth, not cell proliferation

Figure 1. Morphodynamic analysis of inner ear growth from 16 to 45 hpf using in toto imaging.

Figure 1—figure supplement 1. Zebrafish inner ear growth dynamics can be quantified using in toto imaging protocols.

Figure 1—video 1. Inflation of the otic vesicle.

Pressure inflates the otic vesicle and stretches tissue viscoelastically

Figure 2. Otic vesicle growth is correlated with deformations in mitotic cell shapes and neighboring tissues that are indicative of pressure-driven strain.

Figure 3. Lumenal pressure drives otic vesicle growth.

Figure 3—figure supplement 1. Pressure probe calibration and characterizations.

Figure 3—figure supplement 2. Otic vesicle puncturing experiments.

Theoretical framework linking tissue geometry, fluid flux, and osmotic pressure

Figure 4. Pressure negatively regulates fluid flux.

Figure 4—figure supplement 1. The otic vesicle regenerates to stage-specific volumes when punctured between 25–45 hpf.

Figure 4—video 1. Otic vesicle catch-up growth after puncture.

Model prediction and validation: pressure negatively regulates fluid flux

Ion pumps are required for lumenal expansion

Figure 5. Ear size is affected by disruptions in ion transport.

Figure 5—video 1. Abscence of both regular and catch-up growth when salt transporters inhibited.

Patterning of tissue material properties causes local differences in epithelial thinning

Figure 6. Spatial patterning of material properties results in regional thinning of tissue.

Figure 6—figure supplement 1. Pole cells retain their aspect ratios as they move from high to low-curvature tissue regions between 25–30 hpf.

Figure 6—video 1. Spatiotemporal dynamics of F-actin localization.

Figure 6—video 2. Spatiotemporal dynamics of myosin II localization.

Figure 6—video 3. Deformation of the inflated otic vesicle after treatment with cytochalasin D.

Figure 6—video 4. Vesicle fails to grow upon treatment with cytochalasin D drug at 20 hpf.

Cell stretching and steady proliferation contribute to tissue viscosity

Tissue material properties are patterned through actomyosin regulation

Discussion

Cause of cell thinning and origin of endolymph

Potential application of the lumen growth model to other systems

Boundary conditions of the otic vesicle and our model

Comparison of pressure-regulation mechanisms

Materials and methods

Key resources table.

Contact for reagent and resource sharing

Experimental model and subject details

Zebrafish strains and maintenance

Method details

Timelapse confocal imaging

Wild-type growth curves

Confocal microscope settings

Vesicular fluid pressure probe

Ouabain and cytochalasin D treatment

Buffer pH and niflumic acid perturbation

Antisense morpholino injection

Puncturing of otic vesicle

Quantifying the viscoelastic material properties

Mathematical model: linking geometry, growth, mechanics and regulation

Conservation of mass links tissue flux and fluid flux to geometry

Modeling pressure generation and feedback to fluid transport mechanisms

Modeling pressure-driven growth and deformation of the vesicle shape

Quantification and statistical analysis

Data and software availability

Image analysis

Acknowledgements

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Competing interests

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Data availability

References

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