Introduction

A fundamental aspect of animal development is growth. At the organismal level, growth is coupled with morphogenesis and development, and can also be separated into stages with physical constraints (e.g., molting events). At the organ level, growth is coupled with body growth to ensure relative scaling for proper form and function. At the cellular level, growth is interpreted as the decision to divide or not and to increase in size or not. These three levels of growth are integrated with one another to ensure that cells make appropriate growth choices based on feedback from the other two levels.

Growth of the body and its organs are controlled in two ways. The rate of growth over time is internally regulated with an upper limit set independent of such environmental factors as nutrition (Conlon and Raff, 1999). The size setpoint when growth ceases is also internally controlled (Leevers and McNeill, 2005). Typically, the setpoint is reached when the animal transitions to adulthood. The two control processes are linked with one another. For example, Drosophila that are deficient in insulin signaling grow slowly and their final size setpoint is smaller than normal (Rulifson et al., 2002). However, sometimes the growth-arrest process compensates for an abnormal growth rate to generate a normal size setpoint (Leevers and McNeill, 2005; Penzo-Mendez and Stanger, 2015).

The wing of Drosophila is a well-established model system to study organ growth control. In Drosophila larvae, the anlage fated to form the adult wing blade is composed of an epithelial domain embedded within a larger epithelial sheet named the wing imaginal disc or wing disc (Fig. 1A). The anlage, called a wing pouch, is surrounded by wing disc cells that will form the wing hinge and notum, which is the dorsal thorax. Two wing discs reside within the body cavity of a larva (Fig. 1A), and they grow in size as the larva undergoes three successive molts. Wing discs uniformly grow by asynchronous cell division until the animal undergoes the final molt at the end of its third larval instar stage and pupates (Bryant and Levinson, 1985; Neto-Silva et al., 2009). During pupation, each wing pouch develops into a single adult wing blade.

Figure 1.

Growth control of the wing disc operates through several mechanisms (Nijhout and Callier, 2015). Hormones such as insulin-like peptides and ecdysone coordinate wing growth with environmental inputs such as nutrition and molting events (Colombani et al., 2005). Paracrine growth factors are secreted from a subset of wing disc cells and are transported through the disc tissue to stimulate cell proliferation (Baena-Lopez et al., 2012). The BMP morphogen Decapentaplegic (Dpp) and Wnt morphogen Wingless (Wg) are two such growth factors.

Another signal transduction pathway - the Hippo pathway - also operates to regulate growth of the wing disc (Pan, 2010; Boggiano and Fehon, 2012). The Hippo pathway is controlled by two different signals, both of which are locally transmitted. Mechanical stress from local tissue compression caused by differential growth alters the cytoskeletal tension in wing disc cells, which in turn regulates the Hippo pathway (Legoff et al., 2013; Rauskolb et al., 2014; Pan et al., 2016). Increased tension inactivates the Warts kinase, leading to upregulation of the Yorkie (Yki) transcription factor and growth promotion. A second signal that modulates the Hippo pathway in wing disc cells is mediated by two atypical cadherin molecules, Fat and Dachsous (Ds) (Pan, 2010). Ds and Fat are growth inhibitory factors. The two proteins bind to one another on opposing cell membranes at adherens junctions, and Ds is thought to be a ligand for Fat in many circumstances (Clark et al., 1995; Ma et al., 2003; Matakatsu and Blair, 2004). However, Ds has receptor-like properties as well (Matakatsu and Blair, 2006). Binding of Fat and Ds is also modulated by the kinase Four-jointed (Fj) (Ishikawa et al., 2008). When Fat is activated, it induces the destruction of an unconventional myosin called Dachs (Cho et al., 2006; Mao et al., 2006; Rogulja et al., 2008; Zhang et al., 2016).This derepresses Warts, which then inhibits Yki from transcribing growth-promoting genes (Cho et al., 2006; Vrabioiu and Struhl, 2015). A prevailing model for Ds signaling to Fat is not via its absolute concentration but by the steepness of its local concentration gradient (Pan, 2010). Ds is expressed across the wing pouch in a graded fashion, and if the gradient is steep, growth is stimulated whereas if the gradient is shallow, growth is inhibited (Rogulja et al., 2008; Willecke et al., 2008).

Various molecular models for wing growth control have been developed in detail. However, what is unresolved are explanations for how these molecular mechanisms regulate the macroscopic features of growth. Namely, how do the molecular mechanisms regulate growth of the different domains of the wing disc: wing pouch, hinge, notum. How do they regulate the relative scaling of the wing to the body as both are growing in size. How do the different molecular mechanisms precisely regulate the two key growth control processes: growth rate and growth arrest.

Here, we focus on Ds-Fat signaling and address these questions with the aim of connecting the molecular perspective of growth control to a more macroscopic perspective. We find that Ds-Fat signaling tunes a unique feature of cell proliferation found to control the rate of wing pouch growth. The duration of the cell cycle increases in direct proportion to the size of the wing pouch, leading to linear rather than exponential growth. Ds-Fat signaling enhances the rate at which the cell cycle lengthens with wing size, thus diminishing the linear rate of wing growth. Duration of the cell cycle is coupled to relative change in Dpp signaling over time (Wartlick et al., 2011), suggesting that Ds-Fat signaling increases cell sensitivity to fold-changes in Dpp over time. We show that this results in a complex but stereotyped relative scaling of wing growth with body growth in Drosophila. Finally, we examine the dynamics of Fat and Ds protein distribution in the wing pouch, observing graded distributions that change during growth. However, the significance of these dynamics is unclear since perturbations in expression have negligible impact on wing growth.

Results

Quantitative properties of Drosophila larval wing growth

Organ growth in animals is coupled to body growth in complex ways that are specific for both the organ and species (Huxley and Teissier, 1936). We first sought to determine the relationship between growth of the wing and body in Drosophila melanogaster. Although previous work has studied this relationship, none have provided a quantitative description of it. Therefore, we measured body size by both wet weight and volume, while we measured wing pouch size by its volume. As expected, measurements of body weight and body volume showed a strong correlation (Fig. 1 - figure supplement 1). To measure wing pouch volume, we generated a 3D stack of confocal microscopic sections of the wing disc and used morphological landmarks (tissue folds) to demarcate the boundary between wing pouch and surrounding notum-hinge. We validated the efficacy of this method by comparing the landmark-defined boundary to the expression boundary of vestigial, a selector gene specifically expressed in wing pouch cells (Kim et al., 1996). The landmark method gave wing pouch measurements that were within 95.5% of measurements made by vestigial expression (Fig. 1 - figure supplement 2).

We focused our growth study on the third instar larval stage, which occurs over a two-day period. Beginning at 3.0 days after egg laying (AEL), we measured third instar larval bodies and wing discs every 12 hours until the larva-pupa molt. Larval body weight increased linearly from 3.0 to 4.0 days AEL, followed by a 12 hr period of slower growth, and thereafter weight remained constant (Fig. 1B). The time point at which larvae stopped growing (4.5 days AEL) coincided with the time at which they stopped feeding and underwent a 12 hr non-feeding stage (Slaidina et al., 2009). We also monitored weight as larvae underwent their molt into pupae. Weight remained constant during the one-hr white prepupal (WPP) stage and also one hr later at the brown prepupal (BPP) stage (Fig. 1C).

We also measured wing pouch growth. Wing pouch volume increased linearly over time during the early third instar stage and continued to grow during the non-feeding larval stage (Fig. 1D). This was in contrast to body growth, which ceased at the non-feeding stage. However, growth of the wing pouch ceased at the larva-pupa molt and its size remained constant (Fig. 1E). A similar growth trajectory was observed for the notum-hinge although it stopped growing sometime during the non-feeding stage (Fig. 1 - figure supplement 3A,B). End-of-growth of the wing pouch was confirmed by phospho-histone H3 (PHH3) staining, which marks mitotic cells. At larval stages, dividing cells were observed throughout the wing pouch (Fig. 1 - figure supplement 4A,B), whereas at the WPP stage, dividing cells were only found in a narrow zone where sensory organ precursor cells undergo two divisions to generate future sensory organs (Fig. 1 - figure supplement 4C-E).

The scaling of organ growth relative to body growth during development is known as ontogenetic allometry. For most animal species, allometric growth of organs follows a power law (Huxley and Teissier, 1936), such that logarithmic transformation of the organ and body size measurements fits a linear relationship (Fig. 1F). When the organ grows at the same rate as the body, it exhibits isometric growth (Huxley and Teissier, 1936). When the organ grows at a faster or slower rate than the body, it has positive or negative allometric growth, respectively (Fig. 1F). Allometric organ growth in holometabolous insects such as Drosophila presents a special problem arising from the fact that many adult organs derive from the imaginal discs, which are non-functional in larvae. For this reason, there are fewer constraints on relative scaling, and allometric growth is freer to deviate from simple scaling laws. For example, in the silkworm, its wing disc grows linearly with its body while the larva feeds, but then continues its linear growth after larvae have ceased feeding (Williams, 1980). Thus, its allometric growth has two linear phases; the first is isometric and the second is positively allometric.

Since ontogenetic allometric growth of the Drosophila wing pouch has not been studied, we plotted wet-weight body measurements versus wing pouch volume measurements taken from different developmental stages (Fig. 1G). As with silkworms, allometric growth of the wing pouch had two linear phases, both of which showed positive allometry. The inflection point was the time when larvae ceased feeding. In contrast, the notum-hinge exhibited simpler linear-like positive allometric growth (Fig. 1 - figure supplement 3C). Therefore, allometric growth control of the wing imaginal disc appears to be composed of multiple mechanisms.

Global gradients of Fat and Ds in the growing wing pouch

One mechanism for growth control of the wing imaginal disc is through the atypical cadherin proteins Fat and Ds. Both are type I transmembrane proteins with extensive numbers of extracellular cadherin domains: 34 in Fat and 27 in Ds (Fig. 2A). Qualitative descriptions of ds gene expression in the wing pouch indicate that cells transcribe the gene at different levels depending upon their position in the pouch (Strutt and Strutt, 2002; Ma et al., 2003). We confirmed that there is graded transcription across the pouch by using single molecule fluorescence in situ hybridization (smFISH) (Fig. 2 - figure supplement 1A). A previous model hypothesized that this generates a Ds protein gradient across the wing pouch, and the gradient regulates growth by inducing Fat polarization in cells (Pan, 2010). When the Ds gradient becomes flattened, it leads to growth cessation. If correct, the model suggests that the Ds protein gradient should become shallow as the wing pouch reaches its final size. To test this, we used quantitative confocal microscopy to measure endogenous Ds protein tagged with GFP at its carboxy-terminus (Fig. 2A). Wing discs were co-stained with antibodies directed against Wingless (Wg) and Engrailed (En) proteins, which mark the wing pouch midlines (Fig. 2 - figure supplement 2A,B). We measured Ds-GFP across the wing pouch, excluding peripodial signal, along the two midlines to gain a Cartesian perspective of the 2D expression pattern (Fig. 2 - figure supplement 2C). We focused our analysis on wing pouches taken from the third instar larval stage. Beginning at 4.0 days AEL, we measured Ds-GFP in the wing pouch every 12 hours until the larva-pupa molt. We also measured Ds-GFP at the WPP stage of the larva-pupa molt.

Figure 2.

At all timepoints, there was a graded distribution of Ds-GFP along both anterior-posterior (AP) and dorsal-ventral (DV) axes, high at the margins and low in the center of the pouch (Fig. 2C,D). The gradient was asymmetric along the AP axis, being lower at the A margin than the P margin. As the pouch grew larger, the Ds gradient appeared to become progressively shallower. When we normalized all of the Ds-GFP profiles to their corresponding pouch sizes, the profiles along the AP axis collapsed together (Fig 2E). This occurred because the maximum and minimum limits of Ds-GFP abundance were conserved as the wing pouch grew. It implies that dividing cells take up intermediate scalar values from their neighbors during growth, and over time the steepness of the Ds gradient diminishes. In contrast, along the DV axis the normalized profiles remained distinct because both maximum and minimum limits of Ds-GFP progressively diminished as the wing grew (Fig. 2F).

We next turned to quantitative analysis of Fat protein expression. Fat is thought to be uniformly expressed in the wing pouch, though it has also been described as enriched along the DV midline (Garoia et al., 2000; Mao et al., 2009). We measured endogenous Fat protein tagged at its carboxy-terminus with GFP (Fig. 2A and Fig. 2 - figure supplement 2D). Surprisingly, Fat-GFP had a graded distribution along both the AP and DV axes; low at the margins and high in the center of the wing pouch (Fig. 2G,H). The gradient profile was opposite to the one we observed for Ds-GFP. As the pouch grew in size, the Fat gradient appeared to grow shallower, becoming flat along the AP axis by the WPP stage. When we normalized all of the Fat-GFP profiles to their corresponding pouch sizes, the profiles did not collapse (Fig 2I,J). The minimum limit of Fat-GFP was conserved but the maximum limit of Fat-GFP progressively diminished as the wing grew.

The observation of a graded distribution of Fat protein was surprising since it was reported that fat gene transcription is uniform (Garoia et al., 2000). We confirmed this observation using smFISH (Fig. 2 - figure supplement 1B). We considered the possibility that the gradient is generated by a post-transcriptional mechanism. To test the idea, we expressed a fat transgene under the control of a UAS promoter. The transgene’s transcription was activated by Gal4 driven under control of the daughterless (da) promoter (Fig. 2K). da-Gal4 is uniformly expressed in Drosophila tissues (Gilbert et al., 2006). The transgenic Fat protein was epitope tagged for visualization. As a control, cells also expressed Bazooka-mCherry from a second UAS transgene. We then measured the abundance of tagged Fat and Bazooka across the wing pouch. Bazooka protein distribution was fairly uniform along the AP axis while Fat protein was graded in a similar pattern to endogenous Fat (Fig. 2L). Thus, the Fat gradient is generated by a post-transcriptional mechanism.

Ds is known to physically interact with Fat protein and so it was possible that the Fat protein gradient was controlled by Ds. To test this, we examined Fat-GFP distribution in a ds mutant background. The magnitude of peak Fat-GFP levels at the wing pouch center was the same as wildtype but the level of Fat-GFP near the margins was abnormally high (Fig. 2M). Since Ds levels are highest and most steep near the margins, perhaps Ds inhibits Fat expression in a dose- or gradient-dependent manner. We also followed Fat-GFP dynamics in the ds mutant. We did not observe the progressive flattening of the Fat-GFP profile to the WPP wing (Fig. 2 - figure supplement 3A). Instead, the Fat-GFP profile was graded at the WPP stage and flattened somewhat more by the BPP stage (Fig. 2 - figure supplement 3B). We also tested whether Fj regulates the Fat expression pattern by examining Fat-GFP in a fj mutant. However, the distribution of Fat-GFP was unchanged in the fj mutant (Fig. 2 - figure supplement 3C). Therefore, Ds regulates the dynamics of Fat protein expression.

The Ds gradient directly scales with pouch volume

The Ds gradient scales with the size of the wing pouch as measured along the length of the AP axis of symmetry (Fig. 2E). Since the wing pouch can be approximated as an ellipse, the scaling we measured was possibly one related to pouch area. However, the wing pouch is a 3D structure and so Ds gradient scaling might be coupled to wing volume rather than area. To test this idea, we altered the dimensions of the wing pouch without changing its volume. Perlecan is a basement membrane proteoglycan required for extracellular matrix functionality across many tissues (Gubbiotti et al., 2017). Knockdown of perlecan expression by RNAi causes wing disc cells to become thinner and more elongated due to the altered extracellular matrix in the wing disc (Kirkland et al., 2020). We used a Gal4 driver under the control of the actin5C promoter (actin5C-Gal4) to knock down trol gene expression via UAS-RNAi. The trol gene encodes perlecan. We measured the dimensions of the wing pouch at the WPP stage and observed that actin5C>trol(RNAi) caused a reduction in the area of the wing pouch and an increase in the thickness of the wing pouch (Fig. 3A,B). The overall change in pouch dimensions had no effect on wing pouch volume (Fig. 3C). We then measured the Ds-GFP profile at WPP stage and found actin5C>trol(RNAi) had no effect on the gradient (Fig. 3D). Thus, Ds appears to scale with the volume and not the area of the wing pouch. We also examined Fat-GFP to see if its dynamics were altered, and found the gradient flattened normally at the WPP stage (Fig. 3E).

Figure 3.

Ds gradient might directly scale to wing pouch volume or it might be a consequence of scaling to another feature such as cell number, which correlates with wing volume. To test this possibility, we decreased cell number while keeping total volume constant by over-expressing the cell cycle inhibitor RBF. Using a Gal4 driver under the control of the engrailed (en) promoter, a UAS-RBF transgene was overexpressed in the posterior (P) compartment of the wing disc. Previous work had found such overexpression resulted in half the number of cells in the P compartment but they were two-fold larger in size, such that the P compartment size was unchanged relative to the anterior (A) compartment (Neufeld et al., 1998). We confirmed that en>RBF generated fewer and larger P cells, and the ratio of P/A compartment ratio was unchanged (Fig. 3F,G). Nevertheless, the Ds gradient in the P compartment at WPP stage was indistinguishable from wildtype (Fig 3H). The Fat gradient also flattened normally at the WPP stage (Fig. 3I). In summary, the Ds gradient appears to directly scale to wing pouch volume as the pouch grows in size. Fat gradient flattening also appears to be coupled to pouch volume rather than cell number or pouch area. Therefore, the dynamics of these atypical cadherins are coupled to a global physical feature of the wing.

Fat and Ds regulate allometric wing growth

We next wanted to understand how Fat and Ds regulate growth of the wing pouch. Prior work had shown that loss-of-function fat mutants delay the larva-pupa molt and overgrow the wing disc (Bryant et al., 1988). We applied our quantitative growth analysis pipeline on loss-of-function fat mutants. Mutant larvae did not stop growing at 4.5 days AEL as wildtype larvae did, but continued to increase in weight for another day until they entered the non-feeding stage and pupated (Fig. 4A,B). The mutant larval notum and wing pouch grew at a faster rate than normal, and at the larva-pupa molt, the wing pouch continued to grow (Fig. 4C,D and Fig. 4 - figure supplement 1A,B).

Figure 4.

Loss-of-function ds mutants also delayed the larva-pupa molt but only by 12 hours. Mutant larvae continued to gain weight past the wildtype plateau, and they only ceased weight gain at the larva-pupa molt (Fig. 4A,B). The mutant larval notum and wing pouch grew at a rate comparable to those of wildtype, but their growth period was extended (Fig. 4C and Fig. 4 - figure supplement 1A). While the mutant notum ceased to grow prior to the larva-pupa molt, the wing pouch only stopped growing at the BPP stage (Fig. 4D and Fig. 4 - figure supplement 1B).

Allometric growth of the fat and ds mutant wing pouch was significantly different from wildtype (Fig. 4E). In wildtype, there are two linear phases to wing allometric growth (Fig. 1G). Allometric growth of the ds and fat mutant wing pouches had a first phase that was more extended than normal and a second phase that was less extended than normal (Fig. 4E). Similar trends were observed for allometric growth of the notum in these mutants (Fig. 4-figure supplement 1C).

Autonomous effects of Fat and Ds on wing growth

Fat and Ds proteins are extensively expressed throughout the developing Drosophila body, and their loss has clear effects on overall body growth (Mahoney et al., 1991; Clark et al., 1995). Therefore, we wished to know what the wing-autonomous effects of Fat and Ds are on allometric growth. We used the nubbin-Gal4 (nub-Gal4) driver, which is expressed in the wing pouch and distal hinge (Zirin and Mann, 2007), to knock down fat and ds gene expression via UAS-RNAi (Fig. 5A). The RNAi resulted in near-complete depletion of Fat and Ds proteins in the wing pouch (Fig. 5 - figure supplement 1A-D).

As expected, knockdown of either fat or ds in the wing pouch had no effect on body growth of larvae, and animals reached a normal final weight setpoint (Fig. 5B,C). The third instar stage ended at the same time as for wildtype. Knockdown of both fat and ds together (nub>fat ds(RNAi)) in the wing pouch had a slight effect on larval growth but animals reached their normal weight setpoint at the normal time (Fig. 5B,C). Thus, fat and ds are not required in the wing to limit body growth.

Figure 5.

Knockdown of ds caused the wing pouch to grow at a faster rate than normal. The wing pouch was 28% larger at the WPP stage and continued to grow an additional 14% to the BPP stage (Fig. 5D,E). Knockdown of fat had a weak effect; nub>fat(RNAi) wings at WPP stage were approximately 11% larger than controls but were no larger at the BPP stage (Fig. 5D,E). The weak effect was not due to incomplete knockdown, since increasing the number of UAS-fat(RNAi) transgenes did not lead to more overgrowth (data not shown). Knockdown of both fat and ds together resulted in wing growth that resembled growth of nub>ds(RNAi), although the final wing size was slightly larger when both fat and ds were knocked down (Fig. 5D,E). In contrast, notum growth in nub>fat(RNAi), nub>ds(RNAi), and nub>fat ds(RNAi) animals was similar to controls, which would be expected if the genes were not required in the wing pouch for notum growth control (Fig. 5 - figure supplement 2). In conclusion, the autonomous effects of fat and ds on wing growth were less severe than those of whole-body loss of fat and ds, suggesting there are additional, non-autonomous requirements for Fat/Ds in wing growth.

Allometric growth of the wing pouch was also examined (Fig. 5F). Knockdown of ds caused the entire allometric relationship to shift such that nub>ds(RNAi) wings were consistently bigger for their given body size. A similar trend was observed for nub>fat ds(RNAi) wings, although like the fat loss-of-function mutant, the first linear phase of allometric growth was extended (Fig. 5F). In summary, it appears that Ds is required to tune down the allometric relationship of the wing to the body. Allometric wing growth appears to have little autonomous need for Fat alone. However, Fat may have some overlapping function with Ds since allometric growth of nub>fat ds(RNAi) wings is slightly different from nub>ds(RNAi) wings.

To further explore the autonomous requirements for Fat and Ds, we used ap-Gal4 to specifically drive ds RNAi in the dorsal (D) compartment of the wing disc (Fig. 5G). This allowed us to measure growth effects by comparing the affected D compartment to the unaffected ventral (V) compartment, serving as an internal control. As expected, RNAi resulted in undetectable Ds protein in the D compartment, though it was detected in the V compartment (Fig. 5 - figure supplement 1E). We measured the final set-point size of each compartment in the wing pouch. Knockdown of ds caused the D/V ratio of compartment size to increase by 60% (Fig. 5H). Overall wing pouch size was unaffected by ap>ds(RNAi) knockdown (Fig 5I) since there are mechanisms in which the compartments sense overall pouch size, resulting in undergrowth of one compartment when there is overgrowth in the other compartment (Diaz-Benjumea and Cohen, 1993). We also used an en-Gal4 driver to specifically generate RNAi of fat or ds in the posterior (P) compartment of the wing disc (Fig. 5L). As expected, RNAi resulted in undetectable Fat and Ds proteins in the P compartment but not the anterior (A) compartment (Fig. 5 - figure supplement 1F,G). After knockdown, the P/A ratio of compartment size was increased by 63% and 23% in en>ds(RNAi) and en>fat(RNAi) wing pouches, respectively (Fig. 5M). This was consistent with wing pouch knockdown of the genes, where nub>ds(RNAi) was more severe than nub>fat(RNAi) (Fig. 5D,E). en>fat ds(RNAi) showed an increase in the P/A ratio by 193%, a synergistic effect greater than the sum of effects from knockdown of each individual gene alone (Fig. 5M). This synergism had not been observed in the nub-Gal4 knockdown experiments (Fig. 5D,E). Possibly non-autonomous effects of knockdown in the P compartment of the notum are influencing wing pouch growth properties. en>fat(RNAi), en>ds(RNAi), and en>fat ds(RNAi) affected overall wing pouch size to a lesser extent, with respective 10%, 19%, and 32% increases (Fig 5N).

Ds and Fat regulate wing pouch size by affecting cell proliferation

To determine whether Ds regulates cell number, cell size or both, we segmented cells in the imaged wing pouch of ap>ds(RNAi) WPP animals using E-cadherin tagged with mCherry to outline the apical domains of cells. We used a computational pipeline that segments imaginal disc cells with >99% accuracy (Gallagher et al., 2022). The number of ds(RNAi) cells in the D compartment was 42% higher than the wildtype control (Fig. 5J). The average size of ds(RNAi) cells in the D compartment, as measured by apical domain area, was unchanged (Fig. 5K). Thus, the enhanced size of ds(RNAi) wing pouches is primarily driven by an increase in cell number.

Ds might autonomously regulate wing cell number by stimulating apoptosis or by inhibiting cell proliferation. There is little to no apoptosis reported to occur in the third instar larval wing pouch (Milan et al., 1997), which we confirmed by anti-caspase 3 staining (data not shown). To monitor cell proliferation, we developed a method to infer the average cell cycle time from fixed and stained wing discs. Discs were stained with anti-PHH3, which exclusively marks cells in M phase of the cell cycle. During the third instar larval stage, sporadic PHH3-positive cells are uniformly distributed throughout the wing pouch, as expected for uniform asynchronous proliferation (Fig. 1 - figure supplement 4A,B). Using manual and computational segmentation of the images, we identified and counted the number of wing cells in M phase and also counted the total number of wing cells. The ratio of number of M-phase cells to total cells is known as the mitotic index (MI). We found the average time for third instar larval wing pouch cells to transit M phase to be 20.5 min or 0.34 hr (Fig. 6 - figure supplement 1), which is highly similar to previous measurements (Wartlick et al., 2011). Therefore, the average cell cycle time T_cc can be inferred as

We then estimated the average cell cycle time for the wing pouch at various times during the third instar larval stage. It had been previously reported that there was a progressive lengthening of the cell cycle over developmental time (Fain and Stevens, 1982; Wartlick et al., 2011). Our results corroborated these reports but also expanded upon them, finding that the average cell cycle time linearly scales with wing pouch volume (Fig. 6A). The estimated scaling coefficient (slope of the linear fit) predicts that the cell cycle length increases 16 hr as wing pouch volume increases by 1 nL.

Figure 6.

We then estimated T_cc for the wing pouch in which ds was knocked down by nub-Gal4 driven RNAi. The nub>ds(RNAi) cell cycle time linearly scaled with wing pouch volume (Fig. 6B). However, the scaling coefficient for ds(RNAi) cells was much smaller than wildtype (p = 6.2 x10^-4). This meant that cell cycle duration was not lengthening as rapidly as normal and so cell cycle times were consistently shorter. The shorter cell cycle in nub>ds(RNAi) cells would account for the higher growth rate of the wing pouch size observed for nub>ds(RNAi) (Fig. 5D).

We also examined the scaling relationship between cell cycle time and wing pouch volume when fat was knocked down by nub-Gal4 driven RNAi (Fig. 6C). The scaling coefficient for nub>fat(RNAi) cells was highly similar to the wildtype control. This is consistent with our observation that wing pouch size in nub>fat(RNAi) animals was close to normal (Fig. 5D). Finally, we examined the scaling between cell cycle time and wing pouch volume when both ds and fat were simultaneously knocked down by nub-Gal4 driven RNAi (Fig. 6D). This resulted in a much smaller scaling coefficient than normal (p = 9.6 x10^-6), which was similar to the ds(RNAi) effect on the scaling coefficient (p = 0.089 comparing ds(RNAi) to fat ds(RNAi) (Fig. 6E).

In summary, Fat and Ds regulate a mechanism that couples the duration of the cell cycle to overall wing pouch size. They are not essential for the coupling mechanism itself but rather they tune the mechanism so as to ensure the growth rate of the wing is attenuated relative to the body. This coordinates the relative scaling of the wing to the final body size.

The gradients of Fat and Ds protein have little effect on wing pouch growth

Fat and Ds regulate the mechanism by which the cell cycle progressively lengthens as wing size increases, ensuring a proper allometric growth relationship between wing and body. As the wing grows in size, the complementary gradients of Fat and Ds protein across the wing pouch progressively diminish in steepness. These observations suggest a hypothesis that connects the two; namely, wing growth progressively slows because the Fat and Ds gradients become shallower, and growth ultimately ceases when the Fat gradient flattens. To test the hypothesis, we used nub-Gal4, which drives graded expression in the larval wing pouch, high in the center of the pouch and low at the margins (Fig. 7A). Using nub-Gal4 to express UAS-ds, we were able to reverse the normal Ds protein gradient (Fig. 7B-D and Fig. 7 - figure supplement 1A). A peak of Ds was centered along the DV axis and skewed towards the anterior along the AP axis. As larvae reached the end of the third instar, the artificial gradient became shallower but was still reversed. Interestingly, the reversed Ds gradient caused a change in the Fat gradient (Fig. 7E). Its peak also became skewed to the anterior and did not normally flatten at the WPP stage. We then measured growth in the nub>ds larvae (Fig. 7 - figure supplement 1B-E). The growth curve of the larval wing pouch was indistinguishable from wildtype, and wing growth ceased normally at the WPP stage of the larva-pupa molt (Fig. 7 - figure supplement 1D,E). This result suggests that the dynamics of graded Ds expression do not control wing growth.

Figure 7.

The Fat protein profile did not flatten at the WPP stage in nub>ds animals, and yet wing growth ended. It suggests that the flattening of the Fat gradient does not trigger growth cessation. To further test this idea, we expressed HA-tagged Fat using the nub-Gal4 driver without eliminating endogenous Fat (Fig. 7F and Fig. 7 - figure supplement 2A). We monitored both transgenic and endogenous sources of Fat protein, and found both were distributed across the wing pouch in a gradient that was highest in the pouch center (Fig 7G,H). Strikingly, both transgenic and endogenous Fat gradients did not diminish in magnitude as larvae approached the pupa molt. Moreover, the gradients did not flatten at the WPP stage but only did so at the later BPP stage. We then examined the growth properties in nub>fat-HA animals. The relationship between the cell cycle time in the nub>fat-HA wing pouch and wing pouch size was indistinguishable from wildtype (Fig. 7I). This was consistent with the observation that final wing pouch size in nub>fat-HA animals was normal (Fig. 7 - figure supplement 2B). In summary, Fat and Ds gradient dynamics do not appear to play a significant role in wing growth control.

Discussion

Growth control of the Drosophila wing utilizes numerous mechanisms, ranging from systemic mechanisms involving insulin-like peptides and ecdysone secreted from other tissues, to autonomous mechanisms involving paracrine growth factors (Dpp and Wg), Hippo signaling, and cadherin molecules such as Fat and Ds. Here, we have focused on the macroscopic features of Fat and Ds that function in wing growth control. Fat and Ds attenuate the rate of wing growth so that it properly scales with body growth via a complex allosteric relationship. They do so by tuning the rate at which the cell cycle progressively lengthens in a linear fashion as the wing grows in size. This rate of lengthening is enhanced by the actions of Fat and Ds.

It has been long known that the cell cycle in the wing disc slows down, with a cell doubling time of 6 hr during the second instar increasing to 30 hr by the end of third instar (Fain and Stevens, 1982; Bryant and Levinson, 1985; Bittig et al., 2009; Martin et al., 2009; Wartlick et al., 2011). Although this phenomenon is expected to have an impact on the overall rate of wing growth, the phenomenon has not been extensively studied. It was found that lengthening of the G2 phase of the cell cycle is primarily responsible for the longer doubling times (Fain and Stevens, 1982). A more recent study found a link between the cell doubling time and the morphogen Dpp (Wartlick et al., 2011). Dpp is continually synthesized in a stripe of cells at the AP midline of the wing disc and is transported to form a stably graded distribution of protein that is bilaterally symmetric around the midline (Teleman and Cohen, 2000). The Dpp gradient is maintained over days of larval development, during which its relative size adapts to the increasing size of the wing disc. The gradient precisely scales to remain proportional to the size of the growing disc by a mechanism involving the extracellular protein Pentagone and tissue-scale transport of recycled Dpp after endocytosis (Ben-Zvi et al., 2011; Hamaratoglu et al., 2011; Wartlick et al., 2011; Wartlick et al., 2014; Zhu et al., 2020; Romanova-Michaelides et al., 2022). As the gradient scales with the wing, the local concentration of Dpp any wing cell experiences continuously increases over time (Wartlick et al., 2011).

The doubling time of wing disc cells was found to strongly correlate with this temporal increase in Dpp concentration, such that an average cell divided when Dpp increased by 40% relative to its level at the beginning of the division cycle (Wartlick et al., 2011). This correlation suggests that cell cycle time is defined by a temporal increase in Dpp signaling, a hypothesis supported by mathematical modeling (Averbukh et al., 2014). The correlation was observed across larval development, indicating that progressive lengthening of the cell cycle may be caused by a slowing rate of increase in local Dpp concentration over time.

How then might Fat and Ds tune this relationship? Fat acts through an atypical myosin named Dachs; loss of the dachs gene completely suppresses the overgrowth phenotype of fat mutants (Cho and Irvine, 2004; Mao et al., 2006). Fat signaling inhibits or destabilizes apico-cortical localization of Dachs protein, consistent with the genetically antagonistic roles played by fat and dachs (Mao et al., 2006; Brittle et al., 2012). Loss of dachs also suppresses overproliferation of wing disc cells when a constitutively-active form of the Dpp receptor protein is expressed (Rogulja et al., 2008). In contrast, loss of fat enhances Dpp signaling within wing disc cells (Tyler and Baker, 2007). Therefore, it is possible that local Ds and Fat signaling between cells attenuates their sensitivity to Dpp as a mitogen. It would then require a larger temporal increase in Dpp concentration to trigger cells to divide. This model is consistent with our observation that fat ds (RNAi) wing cells do not lengthen their cell cycle as rapidly as normal.

Fat acts through Dachs to regulate the Hippo pathway (Pan, 2010). Dachs physically binds to Warts when overexpressed in cells and promotes its destruction. It is thought that Fat signals through Warts to attenuate the nuclear abundance of Yki, thus downregulating transcription of Yki target genes. What target genes might mediate the effects of Fat and Ds on cell cycle dynamics in the wing pouch? Target genes such as myc and cycE regulate the length of G1 phase (Lee and Orr-Weaver, 2003; Gallant, 2013). However, the length of G2 phase was found to determine the progressive lengthening of the cell cycle in the wing (Fain and Stevens, 1982). A more likely transcriptional target of Yki might be bantam, which indirectly activates Cdc25, a key regulator of the G2/M transition (Oh and Irvine, 2011; Gerlach et al., 2019). Hence, Fat signaling could attenuate bantam expression and Cdc25 activity, thus expanding the length of the G2 phase. This mechanism is particularly attractive since the transcriptional effector of Dpp signaling, Mad, also activates bantam transcription (Oh and Irvine, 2011). Yki and Mad proteins directly bind one another and associate with an enhancer in the bantam gene. Enhancer activity is weaker if Yki is knocked down but Dpp signaling is still present (Oh and Irvine, 2011). Perhaps Fat and Ds tune the cell cycle time though this common effector gene.

An alternative model is that Fat and Ds control the rate at which Dpp levels increase in the wing pouch over time. In this model, cells experience a slower rate in the rise of Dpp levels because of Fat/Ds signaling. Evidence to support the model comes from studies finding that the dally and dally-like (dlp) genes are transcriptionally activated by Yki in the wing pouch (Baena-Lopez et al., 2008). Dally and Dlp are glypicans that contribute to boosting the Dpp morphogen gradient range, perhaps by ensuring retention of Dpp at the cell surface (Stapornwongkul and Vincent, 2021). Fat and Ds signaling appears to diminish dally and dlp expression, and mutations in dally and dlp suppress the overgrowth phenotypes of fat and ds (Baena-Lopez et al., 2008).

Ds is required in both signal-sending cells as well as signal-responding cells, suggesting that Ds has both ligand- and receptor-like activities (Casal et al., 2006; Willecke et al., 2008). We find growth dependence on Ds and Fat is consistent with such complex activities. Knockdown of Ds alone stimulates growth while knock down of Fat alone does not. Thus, Ds is not solely acting through Fat to signal cells. Knockdown of both Ds and Fat has a slightly stronger effect on growth stimulation. Thus, Fat and Ds have overlapping functions in signaling cells to limit their growth. Absence of both cadherins results in cells having a cell cycle that lengthens in time at a slower pace than normal.

Ds and Fat have unusual properties for a ligand and receptor. Based on experiments with clones expressing Ds at different levels than their neighbors, it was suggested that Fat signaling is regulated by the steepness of a Ds gradient across a field of cells (Rogulja et al., 2008; Willecke et al., 2008). A steep gradient of Ds inactivates Fat signaling, whereas a shallow gradient activates Fat signaling. Indeed, we find the natural Ds expression pattern has a graded distribution with a steep slope in the lateral region of the wing pouch (near the margin) and a shallow slope in the medial region of the pouch (near the center). This is consistent with experiments finding Fat primarily inhibits growth in the medial region, where a shallow distribution of Ds occurs (Schwank et al., 2011). We find that Ds not only regulates Fat activity but also its abundance. Fat is distributed in a gradient that is complementary to the Ds gradient - Fat is most abundant in cells where the Ds gradient is lowest and most shallow. Loss of Ds affects the Fat gradient such that distribution of Fat is uniformly upregulated to peak levels. Likewise, inversion of the Ds gradient has a similar effect on Fat distribution. These results suggest that Fat protein levels might be upregulated when cells sense a shallow gradient of Ds.

The graded distribution of Fat protein across the pouch is not stable over time but becomes progressively flatter as the larva-pupa molt is reached. The significance of these dynamics is unclear, but the flattening of the Fat gradient is not a trigger for growth cessation. Since Ds regulates the Fat gradient, perhaps Ds activity is variable over time, leading to these dynamics.

Materials and Methods

Key Resource Table

,Experimental model and subject details

Animals were raised at 25°C under standard lab conditions on molasses-cornmeal fly food. Only males were analyzed in experiments. For staged collections, 100 adult females were crossed with 50 adult males and allowed to lay eggs for 4 hours (6 pm to 10 pm) in egg-laying cages with yeast paste. First-instar larvae that hatched between 7 and 9 pm the following day were collected, thus synchronizing age to a 2-hour hatching window. Approximately 200 - 300 larvae were transferred into a bottle. Third-instar larvae were collected from the bottle every 12 hours at 8 am and 8 pm, from 3.5 days after egg laying (AEL) until pupariation (i.e., 5 days for wildtype). We also collected animals at the white-prepupae (WPP) stage and the brown-prepupae (BPP) stage. The BPP stage is 1 hour after the WPP stage, when the pupal case begins to turn brown (Bainbridge and Bownes, 1981).

Collected animals were weighed in batches of 5 individuals to account for instrument sensitivity. They were individually photographed using a Nikon SMZ-U dissection scope equipped with a Nikon DS-Fi3 digital camera at 1920 × 1200 resolution with a 8 µm x-y pixel size. Length and width were measured in a custom-built Matlab pipeline as follows. The outline of the body was recorded with manual inputs. The midline was calculated by the Matlab bwskel function and manually corrected. The midline was recorded as the length. At every pixel along the midline, a perpendicular line was computed, and the width recorded. The mean width was then calculated. We approximated the volume of each larva by treating it as a cylinder and using the measured length and average width of the larva for length and diameter, respectively.

Genetics

fat-GFP (Hale et al., 2015) and ds-GFP (Brittle et al., 2012) are tagged at their ORF carboxy-termini within the respective endogenous genes. This had been done using homologous recombination and pRK2 targeting vectors. The vg 5xQE-dsRed transgenic line expresses fluorescent protein specifically in wing pouch cells (Kim et al., 1996; Zecca and Struhl, 2007). To mark proneural cells in the wing pouch, we used sfGFP-sens (Giri et al., 2020), which is a N-terminal tag of GFP in the senseless (sens) gene. To count cell numbers we used either E-cadherin-GFP, which has GFP fused at the carboxy-terminus of the ORF in the endogenous shotgun gene, or E-cadherin-mCherry, which has mCherry fused at the endogenous carboxy-terminus (Huang et al., 2009).

Loss of function fat alleles used were: fat⁸, with a premature stop codon inserted at S981; and fat^G-rv, with a premature stop codon at S2929 (Matakatsu and Blair, 2006). Loss of function ds alleles used were: ds^33k, derived by X-ray mutagenesis and expected to produce a truncated protein without function; and ds^UAO71, derived by EMS mutagenesis and presumed to be amorphic (Clark et al., 1995; Adler et al., 1998). Loss of function fj alleles used were: fj^p1, in which P{LacW} is inserted into the 5’ UTR; and fj^d1in which sequences accounting for the N-terminal 100 amino acids are deleted. For all experiments using loss of function mutants, we crossed heterozygous mutant parents to generate trans-heterozygous mutant offspring for study. This minimized the impact of secondary mutations on phenotypes.

To measure expression driven by nub-Gal4 (Bloomington Drosophila Stock Center BDSC # 42699), we used UAS-GFP-NLS (BDSC # 4776). To change Ds expression, fat-GFP, nub-Gal4 flies were crossed to fat-GFP; UAS-ds flies. UAS-ds (Matakatsu and Blair, 2004) was a gift from Ken Irvine. To change Fat expression, fat-GFP, nub-Gal4 flies were crossed to fat-GFP, UAS-fat-HA flies. UAS-fat-HA expresses Fat with a C-terminal HA tag (Sopko et al., 2009). To test whether Fat expression is transcriptionally regulated, fat-GFP; da-Gal4 flies were crossed to fat-GFP, UAS-fat-HA; UAS-Bazooka-mCherry. da-Gal4 (BDSC # 55850) and UAS-Bazooka-mCherry (BDSC # 65844) were used.

To knockdown Fat in the wing pouch and distal hinge, fat-GFP, nub-Gal4 flies were crossed to fat-GFP; UAS-fat-RNAi flies. The RNAi vector is a TRiP Valium 20 (BDSC # 34970). To knockdown Ds in the wing pouch and distal hinge, fat-GFP, nub-Gal4 flies were crossed to fat-GFP; UAS-ds-RNAi flies. The RNAi vector is a TRiP Valium 20 (BDSC # 32964). To knockdown both genes, fat-GFP; UAS-fat-RNAi, UAS-ds-RNAi flies were crossed to fat-GFP, nub-Gal4 flies. To knockdown Fat specifically in the posterior compartment, fat-GFP, en-Gal4 flies were crossed to fat-GFP; UAS-fat-RNA flies. en-Gal4 flies were from BDSC # 30564. To knockdown Ds specifically in the posterior compartment, ds-GFP, en-Gal4 flies were crossed to ds-GFP; UAS-ds-RNAi flies. To knockdown both genes, fat-GFP; UAS-fat-RNAi, UAS-ds-RNAi were crossed to fat-GFP, en-Gal4 flies. To knockdown Ds specifically in the dorsal compartment, ds-gfp, ap-Gal4 flies (BDSC # 3041) were crossed to E-cadherin-mCherry; UAS-ds-RNAi flies.

To alter cell number, en-Gal4 flies were crossed to UAS-RBF (BDSC # 50747). The crosses also carried either ds-GFP or fat-GFP so that resulting animals had two copies of each gene. To alter wing disc area and thickness, actin5c-Gal4 (BDSC # 3954) flies were crossed to UAS-trol-RNAi flies. The RNAi line is a TRiP Valium 10 (BDSC # 29440). The crosses also carried either ds-GFP or fat-GFP so that resulting animals had two copies of each gene.

Immunohistochemistry

Wing discs were fixed in 4% (w/v) paraformaldehyde in PBS at room temperature for 20 min and washed three times for 5-10 min each with PBS containing 0.1% (v/v) Triton X-100 (PBSTx). The following primary antibodies were used: rat anti-Ds (1:1,000, a gift from Helen McNeill), mouse anti-Wg (1:1000, Developmental Studies Hybridoma Bank DHSB # 4D4), mouse anti-En (1:15, DHSB # 4D9), rat anti-HA (1:1000, Roche), rat anti-E-cadherin (1:10, DHSB # Dcad2), and rabbit anti-PHH3 (1:400, Sigma # H0412). All antibodies were diluted in PBSTx and 5% (v/v) goat serum and incubated overnight at 4°C. After 5 washes in PBSTx, discs were incubated at room temperature for 90 min with the appropriate Alexa-fluor secondary antibodies (Invitrogen #’s A11035, A48255, or A48265) diluted 1:200 in PBSTx and 5% goat serum. After 3 washes in PBSTx, between 5 - 40 wing discs were mounted in 40 µL of Vectashield Plus between a 18×18 mm number 1.5 coverslip (Zeiss # 474030-9000-000) and a 24×60 mm number 1.5 coverslip (VWR # 48393-251). Mounting between two coverslips allowed the samples to be imaged from both directions. The volume of mounting media used was critical so that discs were not overly compressed by the coverslips. Compression led to fluorescent signals from the peripodial membrane to be too close in z-space to the disc proper, making it difficult to distinguish the two during image processing.

Single molecule fluorescence in situ hybridization (smFISH)

A set of 45 non-overlapping oligonucleotide probes complementary to the GFP sense sequence were labeled with Alexa 633. The set is described in Bakker et al. (2020). We used the protocol of Bakker et al. (2020) to detect fat-GFP and ds-GFP mRNAs in wing discs. Discs were counterstained with DAPI to visualize nuclei and mounted in Vectashield.

Live disc imaging

Wing discs were dissected from third instar larvae bearing two copies of E-cadherin-GFP. These were cultured ex-vivo in live imaging chambers following the protocol exactly as described in Gallagher et al. (2022). The samples were imaged using an inverted microscope (Leica DMI6000 SD) fitted with a CSU-X1 spinning-disk head (Yokogawa) and a back-thinned EMCCD camera (Photometrics Evolve 512 Delta). Images were captured every 5 minutes with a 40x objective (NA = 1.3) at 512 × 512 resolution with a 0.32 µm x-y pixel size.

Image acquisition of fixed samples

All experiments with fixed tissues were imaged using a Leica SP8 confocal microscope. Whole wing discs were imaged using a 10x air objective (NA = 0.4) and 0.75x internal zoom at 1024 × 1024 resolution, with a 1.52 µm x-y pixel size. Wing pouches were imaged using a 63x oil objective (NA = 1.4) and 0.75x internal zoom at 1024 × 1024 resolution, with a 0.24 µm x-y pixel size and 0.35 µm z separation. Scans were collected bidirectionally at 600 MHz and were 3x line averaged in the following channels to detect: anti-PHH3 (blue), Fat-GFP and Ds-GFP (green), anti-Wg and anti-En (red), and anti-HA or anti-Ds or anti-E-cadherin (far red). Wing discs of different genotypes and similar age were mounted on the same microscope slide and imaged in the same session for consistency in data quality.

Image processing

Raw images were processed using a custom-built Matlab pipeline with no prior preprocessing. The pipeline consists of several modules: 1) surface detection, 2) wing disc, pouch, and midline segmentation, 3) volume measurement, 4) fluorescence intensity measurement, 5) cell segmentation, 6) mitotic index measurement.

1) Surface detection

Fat-GFP and Ds-GFP proteins localize to the apical region of cells in the wing disc proper. These proteins are also localized in cells of the peripodial membrane, which is positioned near the apical surface of the disc proper. In order to get a 2D projection of the signal in the wing disc proper excluding the peripodial membrane signal, we used an open-source software package called ImSAnE – Image Surface Analysis Environment (Heemskerk and Streichan, 2015). The detailed parameters we used have been previously described (Gallagher et al., 2022). Briefly, we used the MIPDetector module to find the brightest z-position of every xy pixel followed by tpsFitter to fit a single layer surface through these identified z-positions. Using the onionOpts function in ImSAnE, we output a 9-layer z-stack, 4 layers above and below the computed surface that capture the entire signal from the wing disc proper. However, this operation still sometimes includes fluorescence signals from the peripodial membrane. Therefore, we manually masked the residual peripodial signal using FIJI 1.53t. The resulting z-stack was sum-projected to form a 2D surface projection of the wing disc proper.

2) Wing disc, pouch, and midline segmentation

Wing discs were counterstained for both Wg and En proteins, which mark the wing pouch dorsal-ventral (DV) midline and anterior-posterior (AP) midline, respectively. Although both Wg and En proteins were stained with the same Alexa 546 fluorescent antibody, the two signals were readily distinguished by their distinct separation in z space. Wg is apically localized in cells of the disc proper and En is nuclear localized more basally in the disc proper. Moreover, the Wg signal was far stronger than En, allowing for detection of its stripe in the posterior compartment even with a max projection.

We built a semi-automated Matlab script that computationally segments the wing disc into discrete objects. i) Wing disc segmentation. Endogenous Fat-GFP or Ds-GFP signal was used to segment the wing disc from surrounding media. ii) Wing pouch segmentation. The 3D morphology of the wing disc creates narrow and deep tissue folds that surround the wing pouch (Fig. 1 - figure supplement 2A). Using these morphological landmarks that were visualized by the Fat-GFP or Ds-GFP signals, the Matlab script recorded user-derived mouse-clicks that defined the wing pouch boundary. This method was validated to be 95.5% accurate when compared to a wing pouch boundary that was defined by the expression boundary of a reporter for the vestigial quadrant enhancer, 5x-QE-DsRed (Fig. 1 - figure supplement 2B,C). iii) DV midline segmentation. The Wg signal was used to segment the DV midline running through the segmented wing pouch. Since the Wg and En signals are distinguishable in z space, the upper third of the z-stack was max projected to segment Wg. An adaptive threshold of 0.6 was used to binarize the image into Wg-positive pixels. The binarized and raw images were used to inform manual input of the DV midline. iv) AP midine segmentation. The En signal was used to segment the AP midline running through the segmented wing pouch. The lower two-thirds of the z-stack was max projected and binarized in En+ pixels. The binarized and raw images were used to inform manual input of the AP midline.

3) Volume measurement

Areas of each of the segmented objects were calculated by summing the number of pixels in each object and multiplying by the pixel dimensions in xy physical space. Notum-hinge area was calculated by subtracting the segmented pouch area from total segmented wing disc area. The thickness of the wing pouch was measured at the intersection of the AP and DV midlines using the orthogonal views tool in FIJI. The first layer is defined by the initial signal of Fat-GFP or Ds-GFP at this xy position. The last layer is defined by the first appearance of background signal in the composite image. Thickness of the object was calculated by multiplying the sum of z-slices by the z-separation. To calculate the volume of segmented objects, we multiplied the thickness of the object (in µm) by the object’s surface area (in µm²). Conversion from µm³ to nL units was performed.

4) Fluorescence intensity measurement of Fat-GFP and Ds-GFP

Fluorescence intensity values were averaged across a vector of 50 pixels length that was orthogonal to the segmented boundary of interest and having 25 pixels residing on each side of the segmented line. These values were then averaged in a sliding window of 100 pixels length that moved along the segmented boundary of interest. Physical distance along the boundaries were measured using ImSAnE function Proper_Dist to account for the curvature of the segmented objects. The intersection of the segmented DV and AP midlines was defined as the center (0,0 µm) of the wing pouch, with the anterior/dorsal annotated in units of negative µm and the posterior/ventral annotated in units of positive µm. A minimum of three wing discs of the same age and genotype were aligned by their (0,0) centers and their fluorescent measurements were averaged along the AP and DV midlines.

Older third instar, WPP, and BPP wing discs begin to evert such that the ventral compartment is partially folded underneath the dorsal compartment. However, the ventral compartment can still be accurately segmented to measure area and thickness even under these conditions. For GFP measurements, the folded specimen resulted in dimmer fluorescent signals from the compartment farthest from the objective due to tissue thickness and light scattering. Thus, measurements were limited to the compartment closest to the objective.

5) Cell boundary segmentation

To count cell numbers and cell sizes in the wing pouch, we analyzed wing discs imaged from E-cadherin-GFP or E-cadherin-mCherry larvae. We used a machine learning pixel-classification model based on a convolutional neural net to segment cell boundaries in the surface projections. This model was trained on a broad range of image data derived from Cadherin-GFP labeled Drosophila imaginal discs (Gallagher et al., 2022). The model is > 99.5% accurate at segmenting cells when compared to ground truth. Cell size (surface area) and number were computed for specific compartments in the wing pouch.

6) Mitotic index measurement

Phospho-histone H3 (PHH3) has been used to estimate mitotic index previously (Wartlick et al., 2011). Wing discs were immunostained for PHH3, which labels nuclei undergoing mitosis. These nuclei were manually recorded by user-defined mouse clicks at or near the center of each nucleus. Their Euclidean distances relative to the segmented AP and DV midlines were calculated as was the number of PHH3+ cells. To estimate the total cell number in a wing pouch, we used E-cadherin to computationally segment cells as described above. Each imaged wing pouch had a subset of cell boundaries segmented in a subdomain of the pouch. This was then used to calculate cell density: number of segmented cells divided by subdomain area. The density value was multiplied by total wing pouch area to estimate the total number of wing pouch cells for that sample. We then derived an averaged conversion factor to apply to each volume measurement in order to estimate total cell number. This was done by plotting the estimated total cell number versus wing pouch volume for all discs of a given genotype. Linear regression of the data produced an equation to convert pouch volume to cell number (Table 1).

Table 1

The number of PHH3+ cells in a wing pouch was divided by the estimated cell number in that wing pouch to obtain the mitotic index, the fraction of cells in M phase at the time of fixation. Average M phase time, measured by live-imaging, was divided by the mitotic index to obtain the average cell cycle time.

Statistical analysis

Statistical tests included two-tailed Student’s t-tests to compare between genotypes. We conducted linear regression modeling to fit pouch volume as an independent variable and cell cycle time as a dependent variable. To statistically test for differences between genotypes, we used a multiple linear regression model:

Genotype was entered into the model as a covariate to test for differences in intercepts of the fits. Interaction of volume × genotype was entered to test for differences in slope of the fits. Linear regression models were plotted with 95% confidence intervals.

Acknowledgements

Fly stocks from Ken Irvine, Helen McNeill, Gary Struhl, and the Bloomington Drosophila Stock Center are gratefully appreciated. Antibodies were gifts from Helen McNeill and purchases from the Developmental Studies Hybridoma Bank. We thank Hamdi Kucukengin for help in processing some of the images. We thank Kevin Gallagher for his advice on building the Matlab pipelines. We thank Jessica Hornick and the Biological Imaging Facility at Northwestern. Financial support was provided from the NIH (GM118144), NSF (1764421), and Simons Foundation (597491).

Figure Legends

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Figure 6 - supplement table 1.

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Figure 7 - figure supplement 2.