Tension transmission across a supracellular network drives increased tissue rigidity in the Drosophila retina

SUMMARY

Organ morphologies generated in development must be maintained in dynamic growth environments over long physical distances and timescales. How complex tissues like the Drosophila retina execute specialized cellular morphogenetic programs while maintaining their larger, tissue-scale morphology is not well understood. Here, we show that the developing retina acquires an organ scale curvature early in pupal development. Concurrently, uniform, sustained Rok-mediated actomyosin contractility organized through apical cellular adhesions in interommatidial pigment cells (IOPCs) increases junctional tension across the ommatidial network to drive a ~5-fold increase in tissue rigidity. Induction of mosaic defects in IOPC junctional tension coupled with in silico modeling of the IOPC network revealed that tension transmission within the IOPC network bridges the cell and tissue scales, providing structural integrity to the retina without changing ommatidial geometry. We propose that tension transmission across tissue-spanning supracellular networks, by uniformly modulating epithelial rigidity, can stabilize three-dimensional organ morphology.

Graphical Abstract

In brief

Decker et al. identify a 5-fold increase in tissue rigidity within the Drosophila retinal epithelium that is required for acquisition and maintenance of stereotyped organ curvature. Long-range transmission of apical junctional tension generated by local Rok-mediated actomyosin contractility in interommatidial pigment cells promotes tissue rigidity and stabilizes curvature.

INTRODUCTION

Generation of functional morphologies requires both controlled shape changes and subsequent maintenance of the acquired tissue form.¹ As its morphogenetic program unfolds, a tissue will be deformed by or resist physical forces, thereby either acquiring a new shape or maintaining a previous shape. How developing tissues respond to force ultimately depends on how their physical properties change over time. While many cell biological processes driving tissue-scale deformations have been well described,^2,3 the cellular processes that determine and modulate tissue mechanical/material properties, and how transitions in these properties contribute to generating and stabilizing organ form, are just beginning to be explored.

The repetitive organization and regular shape of the Drosophila retina offers an opportunity to probe how functional tissue morphologies are maintained in the context of extensive cellular remodeling and physical forces imposed by the growth environment. The adult fly eye is organized into ~750 repeated multicellular units, called ommatidia, that tile across a hemispherical dome-like structure.⁴ This relatively simple 3D shape is critical for optical function, as the stereotyped organ-scale curvature sets the angle between adjacent light-sensitive facet lenses, which in turn determines the spatial resolution of the visual system.⁵ The mature eye structure results from both cell and tissue-scale morphogenesis processes that unfold over 4 days (96 h) of pupal development. During this time, the developing retina is in close contact with other tissues in the head capsule, including the brain and head apex, that undergo dynamic structural changes. Establishing and maintaining regular curvature over a large tissue expanse pose a significant challenge to prevent forces from the cellular morphogenesis programs or imposed by surrounding tissues from physically perturbing retinal structure.

The retinal developmental program is divided into two phases: a “patterning phase” from 0 to 48 h after puparium formation (APF), during which each ommatidium obtains and organizes the correct complement of specialized cells into hexagonal units, followed by an “elongation phase” from 48 to 96 h APF, during which the tissue expands in depth, elaborates and contracts a basal actomyosin stress fiber network, and generates specialized optical structures including the rhabdomere and lens.^6–10 In both phases, the cellular morphogenesis programs require dynamic rearrangements of cellular adhesions and spatially regulated actomyosin contractility.^11–13 While the cellular morphogenesis programs that pattern the ommatidia and give rise to optical structures have been well described,^4,6,10,11 the processes that impact the acquisition and maintenance of retinal curvature have not.

Regulation of retina material properties could facilitate the maintenance of organ-scale curvature by preventing shape deformations from physical forces arising from complex cell morphogenetic programs and variations in the growth environment. However, no studies have investigated tissue rheology in the developing retina. Furthermore, establishing causal connections between local cell-scale activities and transitions in tissue material properties in vivo presents a significant challenge because of the necessity for quantitative description across different physical distances and time scales.

Despite this challenge, recent studies focused primarily on embryonic development have shown that coordinated changes in cellular features, including cell connectivity and adhesion, can drive transitions in tissue material properties that are critical to tissue morphogenesis.^14,15 Additionally, in silico studies of simulated epithelia have predicted that modulation of cell adhesion and contractility will direct sharp transitions in tissue material properties.^16,17 Together, these studies provide a useful conceptual framework for considering the specific cellular parameters that might regulate tissue material properties in other developmental contexts.

To explore how retina material properties are tuned coincident with 3D shape acquisition, we investigated the relationships between local cellular dynamics, tissue-scale rigidity, and curvature in the developing pupal retina. We report a tissue-scale morphogenetic transition that unfolds over ~16 h and is marked by the gradual establishment of retinal curvature and a concomitant increase in tissue rigidity. We find that curvature is established early in pupal development and that the retina gains the ability to maintain its intrinsic shape by 40-h APF. This transition correlates with increases in the tissue elastic modulus, in a process that requires cellular adhesions in the interommatidial pigment cell (IOPC) network. Analysis of the underlying cell biology revealed that Rok-mediated actomyosin contractility increases IOPC tension across the entire retinal field, which promotes increased tissue rigidity and curvature maintenance without significant changes to hexagonal patterning. We propose that the transmission of actomyosin-mediated tension in the supracellular IOPC network provides a mechanism for rigidifying the underconstrained hexagonal lattice to stabilize a robust organ curvature.

RESULTS

Stereotyped curvature is established during the patterning phase of retinal development

Retinal curvature is critical for visual resolution. Reasoning that curvature would be established before lens secretion, we used X-ray micro-computed tomography (μCT) to examine tissue scale changes in the pupal eye-brain complex at 8-h intervals from 24 to 48-h APF.^18,19 24-h APF retinal epithelia appeared as flat discs, with subtle curvature at the periphery (Figure 1A). Radius of curvature measurements indicated that curvature was established by 32-h APF and then maintained (Figures 1B–1D). Other structures within the head capsule also changed during this 24-h window (Figure 1A), indicating that retina curvature is acquired in a dynamic physical environment.

Figure 1. Stereotyped retinal curvature is established early in pupal development, coincident with a transition in tissue-scale response to explantation.

(A–D) Dorsal-ventral sections of μCT scans from 24-h to 48-h APF pupae. Red dashed line outlines the brain, white arrowhead marks the head apex, and yellow arrowhead marks presumptive proboscis in (A). Colored outlines in (A)–(D) identify retinas. r = average radius of curvature for each time point. Measurements from n = 8 replicates.

(E) Projection of a 40-h APF retina expressing Sqh-GFP imaged in situ. Blue dashed line indicates plane of section for orthogonal views.

(F–H) Dorsal-ventral sections of in situ imaged retinas from (F) 24-h, (G) 32-h, and (H) 40-h APF pupae.

(I–K) Orthogonal traces of in situ imaged retinas from 24-h to 40-h APF pupae. r = average radius of curvature for each time point. n = number of replicates.

All scale bars, 50 μm.

To confirm this developmental progression of curvature establishment, we used confocal microscopy to image retinas in intact live pupae expressing a fluorescent Myo-II (Sqh-GFP) reporter (Figures 1E and S1A).²⁰ Consistent with the μCT results, orthogonal sections showed that retinas were mainly flat at 24-h APF (Figure 1F); tissue curvature was apparent at 32-h APF (Figure 1G) and maintained at 40-h APF (Figures 1E, 1H, and S1H). Aligning orthogonal traces of multiple retinas revealed a highly reproducible, stereotyped tissue-scale developmental transition (Figures 1I–1K). Thus, retinal curvature is established early in pupal development, during the patterning phase when the hexagonal ommatidial lattice is organized.

Maintenance of intrinsic retinal curvature temporally correlates with increased tissue rigidity

The observation that retinal curvature is acquired and maintained in a dynamic growth environment suggested that retina morphology might depend on physical constraints from surrounding tissues. To assess this, we dissected eye-brain complexes and assayed retinal curvature after removal from the pupal case. We immediately noticed that upon dissection, retina morphology appeared irregular at 24 and 32-h APF (Figure 2A–B′; Video S1) when compared to retinas imaged in intact pupae at the same time points (Figures 1I and 1J). However, by 40-h APF, the dissected retinas (explants) consistently maintained the expected curvature (Figures 2C and 2C′; Video S1). Comparison of multiple 24-h APF retina explants showed an ensemble of irregular morphologies (Figures 2D and S1B), and average curvature measurements of in situ vs. explanted retinas differed strongly (Figure S1E). From 32-h APF to 40-h APF, retina explant morphology increasingly matched morphologies measured using in situ live imaging (Figures 2E, 2F, S1C, S1D, and S1F–S1H). Vector analysis of fine-scale curvature confirmed that explants became more regular over this period (Figures S1I–S1K). We conclude that by 40-h APF, after curvature acquisition, the retinal epithelium has gained the ability to maintain its native morphology upon explantation. Our data also suggest that the uniform curvature of in situ imaged retinas from earlier time points reflects physical constraints from the growth environment.

Figure 2. Maintenance of intrinsic retinal curvature temporally correlates with increased tissue rigidity.

(A–C′) Whole retina projection and dorsal-ventral orthogonal section of explanted retinas. (A and A′) 24-h APF; magenta dashed line denotes the plane of sectioning for orthogonal view, which is consistent in (B and B′) 32-h APF and (C and C′) 40-h APF.

(D–F) Orthogonal traces of explanted retinas from (D) 24-h, (E) 32-h, and (F) 40-h APF pupae. r = average radius of curvature (when measurable). n = number of replicates.

(G) Indentation scheme shown with stills from a 32-h APF movie. Red arrow, retinal epithelium; red arrowhead, brain; yellow asterisk, indentation probe. Time signature in seconds (s).

(H–J) Still images from indentation movies (Video S2) at the time point of maximal deformation from 24-h to 40-h APF pupae.

(K) Plot of normalized deformation vs. time. Lines represent average indentation dynamics from >5 biological replicates; error bars show SEM. Gray shaded box indicates when force is applied. Average relaxation time: (24 h) 1.60 ± 0.16 s, (32 h) 0.78 ± 0.22 s, and (40 h) 0.31 ± 0.16 s. Wild-type dataset is reused in Figure 3L.

All scale bars, 50 μm.

We hypothesized that the retina’s transition in shape maintenance behavior reflects a change in the tissue’s material properties. Specifically, 40-h APF retinas may be more rigid, allowing them to maintain tissue-intrinsic curvature upon removal from the pupal case. To test this, we examined retina material properties using indentation rheology to measure relative changes in tissue elasticity. The approach involved indenting the retinal epithelium with a fine probe, removing the load, and tracking the tissue response over time (Figures 2G–2J; Video S2). At all time points tested, naive shape was restored after load removal, indicating viscoelastic solid behavior. Plotting normalized deformation vs. time, we compared changes in viscoelastic relaxation time after load removal (Figures 2K and S2A). Using the Kelvin-Voigt model of viscoelastic materials,^21–23 and assuming constant tissue viscosity, we found that the elastic modulus of the retina increased ~5-fold from 24-h to 40-h APF. This increased elasticity likely underlies the ability of older retinas to maintain shape upon explantation.

Retinal curvature maintenance requires increased tissue rigidity mediated via E-cadherin adhesions within the IOPC lattice

Motivated by prior work suggesting that adhesive coupling, junctional tension, and cell packing geometry can influence tissue-scale properties,^14,24,25 we hypothesized that changes in retinal cell adherens junction contacts might influence epithelial rigidity. During this 24–40-h APF window, photoreceptor cells involute and expand their apical junctional domains at the center of each ommatidium,^8,10,11 cone cells elaborate junctional contacts around the photoreceptor clusters,^26,27 and refinement of IOPC contacts and shapes produces precise hexagonal ommatidial patterning (Figure 3A).^10,28–30 To assess the contribution of each of these cellular morphogenesis programs to intrinsic curvature maintenance, we performed cell-type-specific E-cad knockdown and then asked whether retina shape was maintained upon explantation, a behavior potentially indicative of increased tissue rigidity. Using well-validated photoreceptor, primary pigment and cone cell, and IOPC-specific drivers (Elav, Spa, and LL54, respectively)^31–33 (Figures 3B–3D insets), we reduced E-cad protein below detectable levels in the different cell types at 40-h APF (Figures 3A–3D). E-cad adhesions in photoreceptors and cone/primary pigment cells appeared dispensable for tissue rigidity (Figures 3E–3F′, 3H, and 3I). In contrast, E-cad knockdown in IOPCs resulted in highly variable retina shapes (Figures 3G, 3G′, 3J, and 3K). Relative to wildtype, LL54>E-cad retinas imaged in situ had decreased curvature (Figures S2B and S2C) and displayed shape irregularities (Figures S2D and S2E). Hallmarks of compromised epithelial integrity, including merged ommatidia (reflective of IOPC loss), gaps between cells, fallen photoreceptors, or reduced cone cell clusters,⁷ were never observed, ruling out loss of tissue integrity as the cause for the shape irregularities. The combined inability of IOPC-specific E-cad knockdown retinas to display regular curvature within the head capsule and maintain intrinsic curvature upon explantation identified the IOPC network as an essential contributor to retinal curvature maintenance.

Figure 3. Retinal curvature maintenance requires increased tissue rigidity mediated via E-cadherin adhesions within the IOPC lattice.

(A–D) Apical views of 40-h APF retinas stained with α-E-cad. Insets show the cell type specificity of Gal4 driver expression in a wild-type ommatidium. (A) Wild-type, (B) Elav>E-cad RNAi, (C) Spa>E-cad RNAi, and (D) LL54>E-cad RNAi. Scale bars, 10 μm.

(E–G′) Whole retina projection and dorsal-ventral section of 40-h APF explants stained with α-E-cad. (E and E′) Elav>E-cad RNAi, (F and F′) Spa>E-cad RNAi, and (G and G′) LL54>E-cad RNAi. Scale bars, 50 μm.

(H–J) Orthogonal traces of 40-h APF explanted retinas from (H) Elav>E-cad RNAi, (I) Spa>E-cad RNAi, and (J) LL54>E-cad RNAi pupae. n = number of replicates.

(K) Plot of variance in vector alignment along orthogonal traces of wild-type and cell-type specific E-cad RNAi retinas at 40-h APF. Wild-type dataset is reused in Figure S1K.

(L) Plot of normalized deformation vs. time. Lines represent average indentation dynamics from >5 biological replicates; error bars show SEM. Gray shaded box indicates when force is applied. Wild-type 40-h APF dataset is reused from Figure 2K. Average relaxation time: (LL54>E-cad RNAi) 2.08 ± 0.66 s (Video S3).

To confirm the inability of retinas to maintain curvature when E-cad was knocked down in IOPCs resulted from defective tissue rigidity, we measured the elasticity of these retinas using indentation rheology. Loss of E-cad adhesions in IOPCs completely abolished the increased tissue rigidity typical of 40-h APF retinas. Instead, LL54>E-cad RNAi retinas displayed a dramatically expanded viscoelastic relaxation period, similar to 24-h APF wild-type retinas (Figures 3L, 2K, and S2A; Video S3). We conclude that E-cad-mediated cell-biological processes within IOPCs increase tissue rigidity as curvature is acquired.

Increased junctional tension stiffens IOPCs as tissue rigidity increases

To connect retinal curvature maintenance to specific cell-biological processes in the IOPC network, we hypothesized that changes in actomyosin structures might alter the physical properties of IOPCs. Actomyosin networks have well-documented roles in regulating cellular rigidity,³⁴ and refinement of IOPC hexagonal geometry, which occurs between 24- and 40-h APF, requires actomyosin contractility.^12,35–39 Thus, changes in cell mechanics, when aggregated over the entire tissue field, might increase retina rigidity to maintain curvature.

We therefore examined non-muscle myosin-II (Myo-II) expression dynamics and subcellular localization to gain insight into the mechanisms that interconnect IOPC mechanics and increased tissue rigidity. Myo-II was prominently enriched at the junctional and medial apical cortices of IOPCs throughout this ~16-h developmental window (Figures 4A–C). Relative to the apical network and consistent with previous reports,^7,26 basal Myo-II intensity was weaker and less organized before 40-h APF, when it became enriched at basal IOPC footprints (Figures 4A’–4C′). We found no obvious regional differences at the tissue scale in levels of either Myo-II or its upstream regulator Rho-kinase (Rok)^40,41 (Figures 1E–1H and S2F–S2K) that might indicate spatially heterogeneous contractile activity. IOPC apical profiles became increasingly constricted during this period (Figures 4A–4C and 4J), consistent with previous reports,^10–12 raising the possibility that this change in the IOPC shape reflects changes in cell mechanics. Bolstering the idea that changes in IOPC mechanics might collectively drive epithelial rigidity and curvature maintenance, in-plane IOPC movements and ommatidia area fluctuations were maximal at 24-h APF and then progressively decreased, such that by 40-h APF, IOPCs appeared fixed in place and ommatidial shapes fluctuated very little (Figures 4D–4F; Video S4).

Figure 4. Increased junctional tension stiffens IOPCs as tissue rigidity increases.

(A–C′) Apical and basal views of wild-type ommatidia expressing Sqh-GFP (green) and stained with α-E-cad (magenta). Yellow arrowheads mark basal fenestrations in (B)–(C′). Scale bars, 10 μm.

(D–F) Color timelapse overlays of live cell dynamics in 24–40-h APF retinas (Video S4). Scale bars, 5 μm.

(G–I′) Apical views of control and hypo-osmotic shocked ommatidia (40% OS) from wild-type retinas stained with α-E-cad. Yellow lines mark where 2° IOPC widths were measured. Scale bars, 5 μm.

(J) Plots showing 2° IOPC widths in control and hypo-osmotic shock conditions across 24–40-h APF time points. >50 cell measurements from >7 biological replicates were taken for each condition. Error bars show SD. Significance was measured using a Student’s t test with Welch’s correction. **** denotes p value < 0.0001. Wild-type 40-h APF dataset is reused in Figure 5B.

To confirm IOPC mechanics change during this period, we assayed the cellular response to hypo-osmotic shock. Response to hypo-osmotic shock provides a readout of cortical tension, which may be modulated during this period by the apical actomyosin network in IOPCs.⁴² Width of secondary IOPCs in control vs. hypo-osmotic shock conditions provided a quantitative metric of the response. From 24-h to 40-h APF, IOPCs displayed a progressive increase in resistance to hypo-osmotic swelling (Figures 4G–4J), indicating increased cellular rigidity.

We next asked whether IOPCs increase their cellular rigidity via increased junctional tension, by performing laser cutting experiments and measuring cellular recoil velocities.^43,44 Recoil velocities increased significantly from 24-h to 40-h APF (Figure S4A; Video S6), indicating increased IOPC junctional tension. Thus, increased IOPC junctional tension underlies the increased cellular rigidity that enables 40-h APF IOPCs to resist hypo-osmotic swelling. We also noticed that the planar geometries of ommatidia distal to the cut site changed, demonstrating that junctional tension transmitted through the IOPC network influences ommatidial shape (Figures S4B and S4B′). The temporal coincidence of increased IOPC junctional tension with increased tissue rigidity suggests that IOPCs alter their cellular mechanics to promote curvature maintenance while maintaining hexagonal ommatidial geometry.

Rok-mediated contractile pre-strain is required for IOPC network rigidity and intrinsic curvature maintenance

Actomyosin contractility has well-studied roles in regulating the mechanical rigidity of cells, typically through promoting junctional tension.^45,46 Thus, sustained actomyosin contractile activity in the IOPCs might promote tissue rigidity and curvature maintenance by altering cellular mechanics. To test this, we knocked down an upstream activator of actomyosin contractility, Rok, specifically in IOPCs (LL54>Rok RNAi). Rok RNAi IOPCs failed to apically constrict by 40-h APF (Figures 5A and 5B), displayed disrupted actomyosin organization compared to wildtype (Figures S3A–S3C′), and failed to resist hypo-osmotic swelling (Figures 5A′ and 5B). Genetic interaction experiments between Rok and its downstream target myosin heavy chain (Zip) showed that Rok functions upstream of Zip to alter IOPC apical cell shapes (Figures S3D–S3H). Together, these results suggest that Rok activity is required in IOPCs to promote actomyosin contractility and drive increased IOPC rigidity, likely via junctional tension.

Figure 5. Rok-mediated contractile pre-strain is required for IOPC network rigidity and intrinsic curvature maintenance.

(A and A′) Apical view of ommatidia from control (A) and 40% OS (A′) LL54>Rok RNAi pupae at 40-h APF. Scale bars, 10 μm.

(B) Plots of 2° IOPC widths in control and hypo-osmotic shock conditions in wild-type and LL54>Rok RNAi retinas. >50 cell measurements from >7 biological replicates were taken for each condition. Wild-type dataset is reused from Figure 4J.

(C) Plots of bristle cell track distance in μm from 20-min timelapse movies. >15 tracks were measured from ≥4 biological replicates for each condition. 40-h APF wild-type dataset is reused in Figure 7D.

(D) Plots of ommatidia area CoV from 20-min timelapse movies. Area fluctuation measurements were from >10 ommatidia across ≥4 biological replicates for each condition. 40-h APF wild-type dataset is reused in Figure 7E.

(E and E′) Whole retina projection and dorsal-ventral section of LL54>Rok RNAi retina explant at 40-h APF. Scale bars, 50 μm.

(F) Orthogonal traces of LL54>Rok RNAi retinal explants at 40-h APF. n = 14 replicates.

(G and G′) Schematic of the IOPC network and computational spring network.

(H and H”) Simulated network under pre-strain application. Heatmap denotes strain on individual springs, with gray, blue, and red indicating no strain, compression, and tension, respectively.

(I) Plot of minimum frequency (MIN(ω_i)) vs. applied pre-strain (ε_app) for network with geometry matched to wildtype.

(J) Plot of geometric disorder (d) vs. applied pre-strain (ε_app) for network with initial d = 0.0875. Yellow arrowhead, rigidity onset.

In all plots, error bars show SD and significance was measured using a Student’s t test with Welch’s correction. **p value < 0.01, ***p value < 0.001, and ****p value < 0.0001.

To further confirm defective IOPC rigidity, we compared live-cell dynamics of Rok RNAi vs. wild-type IOPCs. By tracking bristle cell position (their stable morphology provided reliable fiducial marks) and ommatidial area, we measured in-plane cellular movement and fluctuation in multicellular organization, respectively (Videos S4 and S5). While in-plane cellular motion and ommatidial area fluctuation progressively decreased in wild-type retinas from 24-h to 40-h APF, IOPC dynamics from 40-h APF Rok RNAi retinas were quantitatively similar to those from 32-h APF wildtype retinas, strongly suggesting IOPC rigidity defects (Figures 5C and 5D). LL54>Rok RNAi retinal explants also displayed variable curvatures and irregular gross morphologies (Figures 5E and 5F), confirming that retina rigidity and curvature maintenance require Rok-mediated actomyosin contractility in IOPCs.

Our in vivo data showed that the hexagonal network constructed by the IOPC apical junctional contacts is necessary and sufficient for increased tissue rigidity. Although the retina is a 3D tissue, local interactions within the apical IOPC network are quasi-2D. We therefore used a planar spring model to explore how changes in IOPC mechanics could promote curvature maintenance via increased tissue rigidity.⁴⁷ Because the spring network model simulates each side of a given ommatidial hexagon as an independent mechanical element and does not permit rearrangements among unit cells, it captures a fundamental feature of the retina, namely the lack of neighbor exchange between ommatidia.

We modeled the IOPC network as an underconstrained network of springs, each with a defined stiffness (k_w), attached to moveable nodes with a periodic hexagonal geometry (Figures 5G and 5G′). To account for other forces the apical IOPC network might experience, including those along the orthogonal plane, we included a term that accounts for the energy contributions of out-of-plane network deformations that might influence tissue rigidity (e.g., tissue buckling or bending). Because 2D hexagonal networks are underconstrained—that is, for any spring stiffness, the overall network does not have a well-defined elasticity and is materially “floppy,”⁴⁸ in order to become rigid, they require the application of “pre-strain,” which simulates increases in junctional tension (Figures 5H and 5H”).⁴⁸ Since ommatidia are not perfectly hexagonal, we matched spring network geometry to ommatidial geometry by introducing a disorder parameter (d) (Figures S4C and S4F). We tested whether this network rigidified under strain by plotting the lowest-frequency non-trivial normal mode (ω_min) vs. increasing applied pre-strain (ε_app; Figure 5I). ω_min is a proxy for network rigidity, as a nonzero frequency represents energetic penalties associated with node movement or network deformation. As expected, this network rigidified under strain, and the rigidity increased as pre-strain increased.

A key feature of the retina is its ability to increase its rigidity while only minimally refining ommatidial geometry (Figures 4H, 4I, and S4F). Further validating our spring network as a model of the IOPC network, plotting geometric disorder vs. applied pre-strain showed network geometry became slightly more ordered as rigidity increased (Figure 5J). These results suggest that contractile pre-strain of the IOPCs, which effectively increases junctional tension, likely drives the increased tissue rigidity required to maintain curvature.

IOPC network tension is sufficient to increase tissue rigidity even when network geometry is perturbed

Multiple studies report that epithelial packing geometry influences tissue rheology.^16,49 Therefore, the requirement for hexagonal ommatidial packing may constrain tissue rigidification strategies in the retina. Assuming that IOPC tension is critical for retinal curvature maintenance, programmed changes to IOPC mechanics might regulate tissue rigidity while preserving the regular hexagonal geometry of ommatidia. Alternatively, naturally occurring hexagonal structures confer structural stability in other contexts, so hexagonal ommatidial packing itself might promote retinal rigidity.^50–53

To explore the influence of ommatidial geometry on tissue rigidity and curvature maintenance, we returned to the IOPC-specific E-cad knockdown retinas. Reasoning that defects in cellular adhesions might perturb patterning, we assayed ommatidial geometry. To visualize IOPC contacts, we used α-Cor, a septate junction component localized directly basal to the adherens junction belt (Figures S5D and S5D′).^54,55 Despite the loss of E-cad-mediated cell adhesion, IOPCs remained mechanically coupled through their septate junction cell-cell contacts (Figures 6A and 6B). However, ommatidial patterning was strongly perturbed, as ommatidia displayed a range of irregular polygonal geometries (Figures 6A–6C, S4D, and S4F).

Figure 6. IOPC network tension is sufficient to increase tissue rigidity even when network geometry is perturbed.

(A–D and G–K) Images and analysis of retinas from 40-h APF pupae.

(A and B) Apical view of (A) wild-type and (B) LL54>E-cad RNAi ommatidia co-stained with α-E-cad (green) and α-Cor (magenta). Scale bars, 10 μm.

(C) Plots of ommatidia shape parameter from wild-type, LL54>E-cad RNAi, and Ey>Abl pupae. >25 ommatidia were measured from >6 biological replicates for each condition. LL54>E-cad RNAi and Ey>Abl datasets are reused in Figure S4D.

(D) Plots showing secondary IOPC widths in control and hypo-osmotic shock conditions in wild-type and LL54>E-cad RNAi retinas. >50 cell measurements from >7 biological replicates were taken for each condition. Wild-type and LL54>E-cad RNAi are reused in Figure S7D.

(E) Computational spring networks with increasing geometric disorder (d).

(F) Plot of minimum frequency (MIN(ω_i)) vs. applied pre-strain (ε_app) for networks of increasing geometric disorder.

(G–H) Apical view of Ey>Abl ommatidia in control (G) and 40% OS (H) conditions. Scale bars, 10 μm.

(I) Plots showing 2° IOPC widths in control and 40% OS conditions from Ey>Abl pupae.

(J and J′) Whole retina projection and accompanying dorsal-ventral section of explant from Ey>Abl pupa. Scale bars, 50 μm.

(K) Orthogonal traces of Ey>Abl retina explants. n = 14 replicates.

In all plots, error bars show SD and significance was measured using a Student’s t test with Welch’s correction. **p value < 0.01, ***p value < 0.001, and ****p value < 0.0001.

In addition to tissue-scale patterning defects, E-cad knockdown IOPCs also had less constricted morphologies (Fig 6A–B) and a reduced ability to resist hypo-osmotic shock (Figures 6D and S5E–S5F′), both indicators of reduced cellular rigidity. As junctional tension—which we demonstrated likely underlies IOPC cellular rigidity—primarily occurs through mechanical coupling of the contractile actomyosin cytoskeleton and the cell membrane,^56,57 E-cad knockdown in IOPCs could prevent cell-autonomous tension generation by disrupting this physical linkage.⁵⁸ Validating this assumption, β-catenin (Arm), an essential mediator of cell membrane and actomyosin cytoskeleton coupling,^59,60 was no longer detected in the 40-h APF apical IOPC lattice (Figures S5A and S5B) upon E-cad knockdown; actomyosin structures in IOPCs were also perturbed (Figures S5G and S5H′). Together, these analyses of IOPC-specific E-cad knockdown phenotypes further suggested that junctional tension alters IOPC mechanics to increase tissue rigidity but did not independently assess the effect of ommatidial hexagonal geometry on tissue rigidity.

To decouple the effects that defects in tension generation and ommatidial packing geometry may have on increasing tissue rigidity, we tested how adding geometric disorder affected the rigidification of our spring network model.⁴⁷ To do this, we increased the disorder parameter (d) used in wild-type networks by 1.5-, 2-, or 4-fold (Figures 6E and S4F) and then rigidified the disordered networks via pre-strain. Plotting network ω_min vs. applied pre-strain revealed that all networks reached similarly rigid states regardless of geometric disorder, but the onset of rigidity shifted to higher applied pre-strains as d increased (Figure 6F). After rigidity onset, the curves quickly converged, suggesting that the process of increasing network rigidity is largely independent of network geometry. The relationship between rigidification via pre-strain and network geometry was the same for models with either periodic (Figure 6F) or fixed boundary conditions (Figure S4G), indicating that the type of boundary condition was not important in this context.

To test these conclusions in vivo, we introduced a genetic perturbation (mild over-expression of the Abelson kinase [Ey>Abl]) that significantly disrupted ommatidial geometry (Figures 6C, 6G, S4E, and S4F) but did not compromise IOPC rigidity or cytoskeletal organization; thus, 40-h APF Ey>Abl IOPCs effectively resisted hypo-osmotic shock (Figures 6H and 6I) and maintained actomyosin structures that were visually indistinguishable from wildtype (Figures S4H, S4H′, S3B, S3B′, and S5G). The uniform curved morphology of 40-h APF retina explants from these pupae suggested successful establishment and maintenance of retinal curvature, despite irregular IOPC patterning (Figures 6J and 6K). We conclude that the regular hexagonal patterning of ommatidia is dispensable for curvature maintenance and increased tissue rigidity and that tension in the IOPC network is sufficient to drive tissue rigidity when ommatidial geometry is perturbed.

Tension transmission through a supracellular network enforces uniform cellular mechanics across the retinal field

The observation that IOPC tension influences both cell and tissue-scale properties prompted us to consider the IOPC lattice as a supracellular network that transmits cellular tension across the retinal field to promote uniform tissue rigidity. Given our demonstration that IOPC tension drives cellular rigidity downstream of actomyosin contractility and that IOPC tension is transmitted to neighboring cells via junctional connections across the tissue, we predicted that tension transmission might buffer the programmed increase in tissue rigidity against cell-autonomous tension variability that might otherwise result in nonuniform tissue properties and shapes.

To investigate tension transmission in the IOPC network further, we first expressed E-cad RNAi using a “half-eye” Gal4 driver (18D08),⁶¹ which activates expression in IOPCs only in the ventral half of the eye (Figures 7A and S6A–S6C″). As judged by both E-cad and Arm protein levels, the efficiency of E-Cad knockdown appeared comparable to that achieved with the LL54 “whole-eye” IOPC-specific driver (Figures S5B, S5C, S6A′, and S6A″). To rule out any caveats of using two different drivers, we generated an 18D08>Gal80 transgene and combined it with LL54-Gal4 to restrict E-cad knockdown to the dorsal half of the eye (LL54>E-cad RNAi, 18D08>Gal80; Figure 7B). Using a separate genetic method⁶² (FLP^ON Gal80 system, see STAR Methods), we also generated small patches of wild-type IOPCs (<5% of IOPCs) in IOPC-specific E-cad knockdown retinas (Figure 7C).

Figure 7. Tension transmission through a supracellular network enforces uniform cellular mechanics across the retinal field.

(A–F) Images and analysis of retinas from 40-h APF pupae. (A–C) Apical view of ommatidia and whole retina projections (insets in A and B) of retinas co-stained with α-E-cad (green) and α-Cor (magenta) from (A) 18D08>E-cad RNAi, (B) LL54>E-cad RNAi, 18D08>Gal80, and (C) LL54>E-cad RNAi, FLP^ON Gal80. White dashed line marks RNAi expression boundary; yellow arrowheads point to constricted IOPCs in (A) and (B). White arrowheads indicate IOPCs with constriction defects in (C). (D) Plots of 2° IOPC initial recoil velocities after laser ablation. >15 recoil velocity measurements from >10 biological replicates per condition. Significance was measured using a Student’s t test with Welch’s correction. ****p value < 0.0001. Wild-type dataset is reused from Figure S4A. (E and F) Color overlay of IOPCs expressing Cd8-RFP from (E) LL54>E-cad RNAi and (F) 18D08>E-cad RNAi retinas at 40-h APF, before (magenta) and 1 s after laser ablation (green). Blue arrowhead, ablated IOPC; yellow arrowheads, distal IOPCs that change position; white dashed line, 18D08-Gal4 expression boundary.

(G) Plots of bristle cell track distance in μm from 20-min timelapse movies (Video S6). >15 tracks measured from ≥4 biological replicates for each condition. Wild-type dataset is reused from Figure 5C.

(H) Plots of ommatidia area CoV from 20-min timelapse movies. Area fluctuation measurements from >10 ommatidia across ≥4 biological replicates for each condition. Wild-type dataset is reused from Figure 5D.

(I) Progression of half-network pre-strain experiments with softened springs (k = 10⁻³). Changes to bond tension and compression after pre-strain application shown in red and blue, respectively.

(J) Plot of MIN(ω_i) vs. ε_app for networks with decreased spring stiffness (k).

In all plots, error bars show SD and significance was measured using a Student’s t test with Welch’s correction. **p value < 0.01 and ****p value < 0.0001..

All scale bars, 10 μm.

With the clonal (FLP^ON) approach, we found that tension generated in IOPCs within the wild-type patches was unable to rescue tension defects in neighboring E-cad RNAi IOPCs (Figures 7C and S7C). In striking contrast, the presence of a wild-type IOPC network in half the eye restored wild-type-constricted morphologies to E-cad knockdown IOPCs in ommatidia located multiple rows distal to the E-cad RNAi expression boundary (Figures 7A and 7B). Hypo-osmotic shock experiments revealed similar cellular rigidity levels in both E-cad knockdown and wild-type IOPCs (Figures S7A–S7C).

To assay junctional tension in E-cad knockdown IOPCs directly, we returned to laser ablation. Decreased cellular recoil velocities revealed junctional tension defects when E-cad was knocked down across the entire IOPC network (Figures 7D and 7E; Video S6). However, when E-cad was only knocked down in IOPCs in the ventral half of the eye, cellular recoil velocities were similar to those measured in wild-type IOPCs (Figures 7D and 7F; Video S6), and ommatidial geometries were visibly altered upon ablation (Figure 7F). These results indicate that junctional tension is nonautonomously transmitted from wild-type IOPCs in the retina to E-cad knockdown IOPCs, increasing cellular rigidity. Consistent with this interpretation, E-cad depletion in the entire IOPC network caused aberrant increases in in-plane cell motion and ommatidial area fluctuation at 40-h APF (Figures 7G and 7H; Video S5). However, “half-eye” E-cad RNAi retinas displayed wild-type in-plane motion and ommatidial shape fluctuations in both the wild-type and E-cad knockdown halves (Figures 7G and 7H; Video S5). Thus, junctional tension generated in a critical mass of IOPCs is transmitted within the IOPC network at the scale of multiple ommatidia.

Reasoning that E-cad knockdown likely decreases IOPC junctional elasticity, we used the spring model to probe further how long-range tension transmission might compensate for regional defects in autonomous tension generation. We generated spring networks where spring stiffness (k_w) was decreased in a contiguous half of the network to simulate the softened cell junctions of E-cad RNAi IOPCs. We then pre-strained only the half of the network with unperturbed k_w (Figure 7I). Upon half-network pre-strain, springs with decreased k_w initially exhibited larger strains than the pre-strained half of the network, indicating their ability to feel tensile forces despite decreased spring stiffness. In these experiments, all networks became rigid at the same value of half-network pre-strain and increased in rigidity at similar rates with increasing pre-strain, regardless of the boundary condition (Figures 7J and S7D). Final network rigidity decreased as k_w decreased. These simulations provide a proof-of-principle that underconstrained hexagonal networks like the IOPC lattice can increase in rigidity via long-range tension forces and that regional defects in spring stiffness and autonomous tension generation are buffered by transmitted tension. We propose that long-range transmission of junctional tension throughout the IOPC network coordinates cell mechanics across the retina to facilitate the uniform increase in tissue-scale rigidity needed for the acquisition of stable organ morphology.

DISCUSSION

Effectively bridging the cell and tissue scales coordinates and stabilizes morphogenetic change in complex multicellular systems. In this study, we show that a tissue-scale increase in rigidity, driven by a tension-based transition in local cell-scale mechanics of IOPCs, accompanies the acquisition of organ-scale curvature in the Drosophila retina. Programmed changes to IOPC apical shapes and mechanics, carried out by contractile actomyosin networks, facilitate increased tissue rigidity and promote curvature maintenance while preserving the hexagonal ommatidial geometry. Transmission of tension within the IOPC network may enhance structural rigidity by integrating cellular mechanics across the retinal field.² We propose that supracellular structures like the IOPC network provide a versatile regulatory strategy for uniformly tuning tissue material properties over large physical distances and long timescales.

Tissue material properties likely influence morphogenesis processes in significant ways, as they govern the physical response to applied force. Adding complexity, developing organs will experience active stresses from both intrinsic cellular morphogenesis processes and dynamic changes in the tissue’s extrinsic growth environment. How cellular processes are coordinated to produce the collective behaviors required to regulate tissue material properties remains an important unanswered question. Supracellular structures, which can transmit physical forces and readily reach an equilibrium state, are a way to address this challenge.

The supracellular IOPC network may facilitate uniform rigidification of the retinal epithelium by integrating and equilibrating the rigidity of individual IOPCs across the tissue. At the cellular scale, we propose that sustained cortical actomyosin contractility downstream of Rok progressively increases IOPC tension and rigidity via a ratcheting mechanism. Prior work has shown that cortical contractility can induce membrane deformation and remodeling via mechanical coupling of actomyosin machinery to adherens junctions, effectively shortening junction length.^12,36,63 By decreasing the IOPC apical surface area below a preferred value, such a ratcheting mechanism would gradually increase junctional tension and IOPC rigidity. Consistent with this framework, we found that IOPC apical constriction temporally correlates with increased tension. The progressive nature of the tissue rigidity increase, combined with the relatively constant apical actomyosin and E-cadherin levels throughout this ~16 h period, argues against an alternative mechanism where rigidity is driven by a temporally isolated sharp increase in contractility and membrane remodeling.

At the tissue scale, IOPCs transmit cellular tension to mechanically coupled neighboring IOPCs across the epithelial field. In the half-eye E-cad RNAi experiments, IOPCs lacking the ability to increase tension through cell-autonomous mechanisms still reached a high-tension state. We speculate that IOPCs “feel” tensile forces from their neighbors even in the absence of E-cadherin-based adhesions and that a combination of other cell adhesion molecules and/or epithelial packing constraints confers sufficient elasticity to propagate tension. Long-distance tension transmission mechanisms may enable complex tissues to leverage changes in tissue material properties to direct organ-scale morphogenetic programs. In the retina, in addition to stabilizing curvature, a coordinated and uniform transition in tissue material properties may facilitate the ommatidium-to-ommatidium accuracy and reproducibility of subsequent morphogenetic change, including lens deposition, photoreceptor growth, and retinal floor elaboration and contraction.

While the contribution of cell-scale active forces in morphogenesis is well established, there are fewer examples of tissues that acquire functional morphologies through the interplay of tissue-extrinsic/environmental forces and temporally controlled transitions in tissue material properties. Whether tissue-extrinsic forces are challenges to functional morphologies that must be resisted or instructive morphological cues remains an open question. While basal contractility of the retinal floor has been hypothesized to drive curvature formation,^13,64 our results indicate that the retina’s curved morphology is established by 32-h APF (Figures 1B, 1G, and 1J), over 16 h before the appearance of basal actomyosin stress fibers (Figures 4B’ and 4C′).^13,26 Instead, we propose that retina curvature could be established via tissue-extrinsic forces.

Several candidate extrinsic factors could instruct retina shape. Growth of the underlying brain could push the retina into the pupal envelope, inducing curvature. Consistent with this, μCT imaging reveals close apposition of the retina and brain during retinal curvature establishment. Alternatively, it has been proposed that the internal pressure of the pupa varies during development.^65,66 Thus, increasing pupal internal pressure could generate outward forces that induce retinal curvature, in a mechanism similar to anole lung morphogenesis.⁶⁷ While technically challenging, experimental exploration of the relationship between 3D organ morphology and surrounding environment in varied developmental contexts is needed to understand how tissues resist or integrate physical signals from crowded growth environments.

The tension-driven increase in rigidity we describe in this study could be the first of multiple redundant processes that contribute structural rigidity and stable functional curvature to the adult eye. Subsequent deposition of the crystalline lens on the apical surface of ommatidia, biogenesis of the central rod-like rhabdomeres, and the formation of the basal stress fibers could all independently increase structural rigidity.¹³ Overall, the morphogenetic strategy of first establishing a “template” with correct shape and material properties may optimize the developing retina’s ability to support and withstand the subsequent cell and tissue-scale remodeling events and variations in the growth environment that together determine its final form.

Limitations of this study

Using Spa-Gal4 to knock down E-cad tested the contribution of adhesions between cone and primary pigment cells to tissue rigidity. However, cellular adhesions within the cone cell cluster are predominantly N-cad mediated,³⁸ so this study did not fully assess possible contributions of cone-cone adhesions. Our Hookean spring network model of the IOPC lattice coarse-grains the “sides” of ommatidial hexagons as one spring. Because each side is composed of one elongated secondary pigment cell flanked by either a small tertiary pigment cell or a bristle cell cluster, treating this group of cells as one mechanical entity ignores how differences in individual cell mechanics might contribute to tissue rigidity. Our 2D model is useful for identifying cell-scale changes in mechanics that may influence tissue rigidity, but further work is necessary to understand the process in 3D.

Retinal indentation rheology experiments were done using a manually controlled micromanipulator, which, in some cases, also induced minor deformation of the underlying brain. Quantitative assessment showed that the retina was deformed on average by 49.9 ± 6.2%, while the brain only 2.4 ± 1.09% (n = 20 replicates for both the retina and brain). Therefore, any contribution of brain elasticity to the relaxation kinetics of retinal tissue measured with our indentation rheology approach is minimal.

RESOURCE AVAILABILITY

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Ilaria Rebay (irebay@uchicago.edu).

Materials availability

We are happy to share 18D08-Gal80 fly line and plasmid generated during this study upon request.

Data and code availability

• Spring model network data and model output (minimum eigenvalues) have been deposited in a Mendeley Data repository and are publicly available as of the date of publication at: https://doi.org/10.17632/v5m5mc9t9p.1.

• All of the original codes used to perform spring model simulations have been deposited at: github.com/AyannaMatthews/Fly_Eye_Prestress and are publicly available as of the date of publication.

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

STAR★METHODS

Detailed methods are provided in the online version of this paper and include the following:

EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

Flies were raised on standard food at 18°C. Crosses were performed at 25°C unless stated otherwise, for details on the generation of heat-shock clones, see method details section “Drosophila genetics.” For strain details, please consult the key resources table.

KEY RESOURCES TABLE.

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
Rat a-E-cad	Developmental Studies Hybridoma Bank	DCAD2
Mouse a-Arm	Developmental Studies Hybridoma Bank	N2 7A1
Guinea pig a-Cor	Fehon et al.54	–
Cy3 Donkey a-Guinea Pig secondary antibody	Jackson ImmunoResearch	Cat# 706-165-148; RRID: AB_2340460
Alexa Fluor 488 Donkey a-Mouse secondary antibody	Jackson ImmunoResearch	Cat# 715-545-020; RRID: AB_2340844
Alexa Fluor 488 Donkey a-Rat secondary antibody	Jackson ImmunoResearch	Cat# 712-545-150; RRID: AB_2340683
Cy3 Donkey a-Rat secondary antibody	Jackson ImmunoResearch	Cat# 712-165-150; RRID: AB_2340666
Deposited data
Spring model network data and minimumeigenvalues	This study	Mendeley Data: https://doi.org/10.17632/v5m5mc9t9p.1
Experimental models: Organisms/strains
w1118	BDSC	3605
Elav-Gal4	BDSC	8765
Spa-Gal4	BDSC	26656
LL54-Gal4	BDSC	5129
UAS-E-cad RNAi	BDSC	32904
Sqh-GFP	BDSC	57144
Rok-GFP	BDSC	52289
GMR-Gal4	BDSC	1104
UAS-p35	BDSC	5072
Ey-Gal4	BDSC	5534
UAS-Rok RNAi	BDSC	28797
Spider-GFP	BDSC	59025
hs-FLP	BDSC	279
FLPON-Gal80	BDSC	38878
UAS-Zip RNAi	BDSC	65947
UAS-RokCA	BDSC	6668
UAS-mCd8::GFP	BDSC	32187
UAS-mCd8::RFP	BDSC	32218
UAS-Abl GFP	O’Donnell and Bashaw68	–
18D08-Gal4	Sarkar et al.61	–
18D08-Gal80	This study	–
Oligonucleotides
5′AAAAAGAATTCGCATAACTCGAACGCCTCTTGCCAT3′	–	–
5′AAAAAGGCCGGCCCAGTTCTTCACTTGTCGCCGTCTGT3′	–	–
Recombinant DNA
pBPGAL80Uw-6	Addgene	plasmid #26236
Software and algorithms
Spring network computational model	Modified from Hagh et al.47	Github: Github.com/AyannaMatthews/Fly_Eye_Prestress
Other
Alexa Fluor 568 Phalloidin	ThermoFisher	A12380

METHOD DETAILS

Drosophila genetics

All crosses were carried out at 25°C in standard laboratory conditions. w1118 (3605), Elav-Gal4 (8765), Spa-Gal4 (26656), LL54-Gal4 (derived from 5129), UAS-E-cad RNAi (32904), Sqh-GFP (57144), Rok-GFP (52289), GMR-Gal4 (1104), UAS-p35 (5072), Ey-Gal4 (5534), UAS-Rok RNAi (28797), Spider-GFP (59025), hs-FLP (279), FLP^ON-Gal80 (38878), UAS-Zip RNAi (65947), UAS-Rok^CA (6668), UAS-mCd8GFP (32187), and UAS-mCd8RFP (32218) were from the Bloomington Stock Center. UAS-Abl-GFP⁶⁸ (O’Donnell and Bashaw, 2013) was a gift from G. Bashaw (University of Pennsylvania, PA, USA). 18D08-Gal4 (Sarkar et., al., 2018) was a gift from A. Singh (University of Dayton, OH, USA). 18D08-Gal80 was generated in this study.

The Gal4/UAS system was used for targeted gene knockdown or overexpression. To generate clones, LL54-Gal4; UAS-E-cad RNAi/TM6B, Gal80 virgin females were crossed to FLP^ON-Gal80/CyoGFP; hs-FLP/TM6B males. Third-instar larvae of the appropriate genotype were selected and heat-shocked in a 37°C water bath for 45 min and then allowed to grow until the appropriate pupal stage. For developmental staging, white pre-pupae (0 h APF) were selected and aged at 25°C for 24, 32, 40, or 48 h. Staging was confirmed by morphological landmarks prior to dissection and by cellular features after dissection.

Construction of 18D08-Gal80 transgenes

The genomic fragment that provides expression in the ventral half of the retina (Sarkar, 2018) was PCR amplified using primers (5′AAAAAGAATTCGCATAACTCGAACGCCTCTTGCCAT3′ and 5′AAAAAGGCCGGCCCAGTTCTTCACTTGTCGCCGTCTGT3′ and then subcloned into the EcoRI and FseI sites of pBPGAL80Uw-6 (Addgene; plasmid #26236). Genomic DNA was prepared from w1118 flies using the Gentra Puregene Cell Kit (Qiagen). After sequencing, the plasmid was integrated into the AttP2 docking site⁶⁹ (Bateman et al. 2006).

μCT sample preparation and imaging

Pupal samples for μCT imaging were prepared according to methods detailed in (Schoborg, 2019 and Schoborg, 2020). Pupae of the appropriate stage were collected in a 1.7 mL microcentrifuge tube with 1mL of PBST (PBS with 0.1% Triton X-100) and incubated for 5 min while vigorously tapping to remove hydrophobic coating, allowing pupae to sink. Pupae were fixed in Bouin’s solution (5% acetic acid, 9% formaldehyde, 0.9% picric acid; Sigma Aldrich) for 2 h, washed 3 times with PBS for 5 min, transferred to a 9-well dissection dish with PBS and holes were poked in the puparium with fine forceps to allow liquid penetration. Pupae were fixed again in Bouin’s solution for 24 h, washed 3 × 30 min in PBS, stained with 0.1N Iodine Solution (Fisher Chemical) at room temperature and then mounted in P10 pipette tips, as detailed in (Schoborg, 2019). Samples were imaged on a Bruker SkyScan 1172 Micro-CT (Micro Photonics) controlled by Skyscan software (Bruker) using the following parameters: 40 kV, 110 μA, 4W of power. ~1800 projection images were captured using a Hamamatsu 11Mp CCD camera at 0.59 μm pixel size. Random movement was set to 10 and frame averaging was set to 4. Reconstructions were performed using NRecon software (Bruker). Images were post processed using ImageJ software.

Immunostaining

Pupal eye-brain complexes were dissected in cold S2 media (Sigma S9895) and fixed for 10 min in 4% paraformaldehyde in PBS. For osmotic shock experiments, dissected eye-brain complexes were incubated for 5 min in S2 diluted 40% with deionized water before fixation. After fixation, eye-brain complexes were washed 5 times with PBST and rocked at room temperature for 2 h to permeabilize the tissue and allow associated fat body tissue to fall off. Eye-brain complexes were then blocked in PNT (PBST with 4% normal goat serum) for at least 2 h while rocking at 4°C, washed twice with PNT, incubated with primary antibodies overnight at 4°C, washed 3 × 40 min in PNT, incubated with secondary antibody overnight at 4°C, washed 10 × 10 min in PBST and transferred to a slide with 30μL of mounting media (90% glycerol in 0.1 M Tris (pH 8.0) with 0.5% n-propyl gallate). Retinas were separated from brains with a tungsten wire dissection tool and mounted on glass microscope slides prepared with two layers of Scotch tape (3M) as spacers to prevent sample compression.

Antibodies used

Developmental Studies Hybridoma Bank (DSHB): mouse anti-Arm (1:100) and rat anti-Ecad DCAD2 (1:1000). Guinea pig anti-Cor (1:25,000) was a gift from R. Fehon (R. Fehon et al., 1994). Alexa 488/Cy3-conjugated secondaries were diluted 1:1000 (Jackson ImmunoResearch, 706-165-148, 715-545-020, 712-545-150, and 712-165-150)

Indentation rheology experiments

Eye-brain complexes of appropriately staged pupae were dissected in room temperature S2 media and mounted in a Vaseline log within a puddle of S2 media on slides that had been soaked overnight in PBST. Eye-brain complexes inserted in Vaseline had one retina freely floating in media while the brain was immobilized. Slides were mounted on an Olympus CK2 inverted microscope and retinas were poked with a fine hair probe controlled by a micro-manipulator. Timelapse images were acquired with an AmScope 5.0MP C-Mount microscope camera (AmScope, MU500-HS) controlled with AmLite software. Quantitative measurements and image processing were performed using ImageJ software. To measure relative deformation of retinal epithelia versus underlying brain, the percent change in retina width along the apical-basal axis and percent change in cross-sectional width of the underlying optic lobe were calculated at non-indented vs. maximally indented timepoints from timelapse movies. Measurements were made from 20 replicates of 24hr APF eye-brain complexes where the brain is most clearly visible.

Fixed microscopy

An inverted Leica SP8 laser scanning confocal with a 40× oil-immersion lens was used to acquire still images in Figures 4A–C’. An inverted Zeiss LSM880 laser scanning confocal microscope with a 40× oil-immersion lens, equipped with a GaAsP spectral detector and an Airyscan module was used for all other imaging. All still images in Figures 1E–1H, 2A–2C′, 3A–3G′, 4G–4I′, 5A, 5A′, 5E, 5E′, 5G, 6G, 6H, 6J, 6J′, S3D–S3G, S4C–S4E, S5A–S5C, S5E, and S5F′ were taken using the Airyscan module in super-resolution mode.

Live imaging

Pupae for live imaging were selected and the outer puparium was peeled away using fine forceps to expose the underlying retina while keeping the underlying soft pupal cuticle totally intact. Pupae were inserted into a log of Vaseline on a cover glass bottomed dish with a thin layer of Halocarbon 700 oil (Halocarbon). Pupae were inserted in Vaseline by their posterior end and oriented such that the retina was in contact with the coverslip. Timelapse images were taken using a Zeiss LSM 880, using an Airyscan module in super-resolution mode, acquiring one z stack every minute.

Laser ablation experiments

Pupae were mounted for live imaging as described above. Timelapse images were captured with a 3i Marianas Yokogawa-type spinning disk confocal microscope with Evolve EM-CCD camera (Photometrics, Tucson, AZ) running SlideBook software (Intelligent Imaging Innovations, Denver, CO) and outfitted with an Ablate! 532 nm laser module. Linear ablation ROIs were drawn using SlideBook software to bisect sloping secondary IOPCs. Ablations were made using the Ablate! laser with a 30ms pulse, a raster block size of 5, and laser power of 185–190. Images were acquired once every second for 1 min, with ablation laser pulse occurring at the sixth time-point. Initial recoil velocity (in μm/s) was calculated by measuring the difference in IOPC length before and one second after laser ablation.

Image analysis

ImageJ was used for basic image processing, including generation of maximum projections, generation of colored temporal overlays, orthogonal views, background subtraction, and unsharp mask filtering. To measure radius of curvature, orthogonal traces were treated as sections of a circle bounded by a chord of length $\left(\mathrm{L}\right)$ with a height of length $\left(\mathrm{h}\right)$. $\mathrm{L}$ and $\mathrm{h}$ were measured in ImageJ and radius of curvature $\left(\mathrm{r}\right)$ was calculated as: $r=\frac{h}{2}+\frac{L^2}{8h}$. To measure ommatidia shape parameter, IOPC width, and junction length, ROIs were drawn by hand and measured in ImageJ. Shape parameter $\left(\mathrm{S}\right)$ is given as $S=\frac{\mathit{Perimeter}}{\sqrt{\mathit{Area}}}$. To measure retinal cell dynamics from movies, bristle cells were tracked using the Manual Tracking ImageJ plugin and ommatidia shape variance was calculated by measuring ommatidial area with manually applied ROIs over successive frames. To measure initial recoil velocity of IOPCs from laser ablation experiments, IOPC length was measured manually in Fiji immediately before and immediately after ablation. The difference between these two measurements represents the initial recoil velocity in μm/s.

Quantitative analysis of orthogonal traces

Orthogonal traces were made in Keynote and then imported into ImageJ, made binary, and exported as XY coordinates. XY coordinates of traces were converted into vector coordinates in Python, and relative vector orientations were computed as the dot product of a given vector to a chosen vector along the trace. Vector orientations were binned by relative distance along the trace and the average or standard deviation of each bin was calculated using scipy.binned_statistic.

Computational modeling of the IOPC network

Hookean spring network:

We modeled the IOPC lattice as a Hookean spring network using the rigidPy framework (Hagh, V.F., 2022)⁶⁰ that mathematically describes how underconstrained spring networks rigidify under tension. In such networks, a given spring that connects the nodes $i$ and $j$ can be deformed, displacing the nodes by ${\mathbf{u}}_i$ and ${\mathbf{u}}_j$, respectively. Deformation changes their separation vector $\left({\mathbf{r}}_{ij}\right)$ to ${{\mathbf{r}}^{\prime }}_{ij}={\mathbf{r}}_{ij}+{\mathbf{u}}_{ij}$. The energy stored in this spring after a deformation is given as:

$$V\left(r_{ij}^{\prime }\right)\approx V\left(r_{ij}\right)+V^{\prime }\left(r_{ij}\right)\left(r_{ij}^{\prime }-r_{ij}\right)+\frac{1}{2}{V}^{″}\left(r_{ij}\right){\left(r_{ij}^{\prime }-r_{ij}\right)}^2\approx V\left(r_{ij}\right)+V^{\prime }\left(r_{ij}\right)\left(u_{ij,\Vert }+\frac{u_{ij,\perp }^2}{2r_{ij}}\right)+\frac{1}{2}{V}^{″}\left(r_{ij}\right)u_{ij,\Vert }^2.$$

Replacing the second derivative of the energy with $V^{″}\left(r_{ij}\right)=K_{ij}$, which represents bond stiffness, and the first derivative of the energy $V^{\prime }\left(r_{ij}\right)=-f_{ij}$, which represents the force between $i$ and $j$ due to pre-stress, we can express the change in total energy upon pre-strain application as:

$$\delta V=V\left(r^{\prime }\right)-V(r)=-\sum _{ij}{f}_{ij}{u}_{ij},\Vert -\sum _{ij}{f}_{ij}\frac{u_{ij,\perp }^2}{2r_{ij}}+\sum _{ij}\frac{1}{2}{K}_{ij}{u}_{ij,\Vert }^2.$$

Force on bonds that cause out of plane deformations is captured by the middle term of the above equation: $\sum _{ij}{f}_{ij}\frac{u_{ij,\perp }^2}{2r_{ij}}$

The executable code can be accessed at: https://github.com/AyannaMatthews/Fly_Eye_Prestress.

Generating Networks:

Networks were created using the hexagonal_lattice_graph function in the networkx package to create a periodic hexagonal lattice of ${\mathrm{N}}_{\mathit{rows}}$ hexagons by $N_{\mathit{cols}}$ hexagons. $N_{\mathit{rows}}$ is an input parameter and $N_{\mathit{cols}}$ was calculated to make the lattice as close to a square as possible due to the $2:\sqrt{3}$ aspect ratio of hexagons. $N_{\mathit{cols}}$ was calculated from $N_{\mathit{rows}}$ by rounding $\frac{2}{\sqrt{3}}{\mathrm{N}}_{\mathit{rows}}$ to the nearest integer value. Since networkx does not allow for an odd number of columns with periodic boundary conditions, when $N_{\mathit{cols}}$ as calculated above was odd, 1 was added to $N_{\mathit{cols}}$ if in the last step it was rounded down and 1 was subtracted if it was rounded up.

Because networkx adds a drift value to the y-coordinates of points in the hexagonal lattice when there are periodic boundaries, this was corrected by resetting the y-coordinates for all points to be consistent with the first column which does not have a drift.

Applying disorder to the network:

Disorder was added to the network by adding a displacement vector of size d whose angle was selected randomly from a uniform distribution of values from $-\pi$ to $\pi$. The resulting network served as the starting network where all bond-lengths are equivalent to the rest-lengths so that it starts with no energy in the system. Rest-lengths were then altered to add prestress in the system as detailed below. We used networks with disorder values: $\mathrm{d}=0.0875$ (Wildtype ommatidia), $\mathrm{d}=0.123,\mathrm{d}=0.158$, and $\mathrm{d}=0.316$.

Pre-straining Networks:

To pre-strain only one portion of the network, we identified bonds with a location (defined by the center-point of the bond) in the relevant area of interest from the version of the network with no disorder. We made sure to include periodic bonds which may have a position that is negative due to wrap-around. Although depending on the initial network construction from the sizing and aspect ratio considerations mentioned above, the area percentage may not be exact, network sizes run were chosen such that area percentages of 50% were exact. These bonds were contracted by a target pre-strain value ${ϵ}_p=\frac{1}{l_0}-1$ by resetting their rest-lengths to ${\mathrm{I}}_0=\frac{1}{1+{ϵ}_{\rho }}$.

Energy minimization:

After the application of prestress, the network was equilibrated to see the propagation of stress through the network. Equilibration was done using the rigidpy package configuration class and the scipy.optimize.minimize function with a tolerance of 1e-20.

Evaluation of rigidity:

Network rigidity can be determined by finding the lowest non-trivial eigenvalue of the system. This was done using the rigidpy package which calculates the hessian matrix of the system and finds the corresponding eigenvalues. The hessian matrix is given as:

$${\mathit{H}}_{ij}^{\alpha \beta }=\frac{{\partial }^{2}V}{\partial r_i^{\alpha }\partial r_j^{\beta }}.$$

Model parameters:

Network sizes (# of hexagons): 10 × 10, 22 × 22, 25 × 25, and 28 × 28; Node coordination number: 3; Disorder values: 0.0875, 0.123, 0.158, and 0.316; Range of pre-strain values: (10⁻⁴, 10⁰); Pre-strain areas: 50%, 100%; Range of spring stiff-nesses (k values): (10⁻³, 10⁰); and Boundary conditions tested: Periodic, Fixed.

QUANTIFICATION AND STATISTICAL ANALYSIS

All statistical tests and plots were generated in GraphPad Prism software. A student’s t test with Welch’s correction was used for all statistical tests. Significance values are reported within plots and/or figure legends.

Supplementary Material

SUPPLEMENTAL INFORMATION

Supplemental information can be found online at https://doi.org/10.1016/j.celrep.2025.116355.

Highlights.

• Retinal epithelium increases 5-fold in rigidity coincident with curvature acquisition

• Epithelial rigidity is essential for retinal curvature maintenance

• Rok-mediated actomyosin contractility increases pigment cell apical junctional tension

• Tension transmission across a supracellular hexagonal network rigidifies the tissue