Scaling between cell cycle duration and wing growth is regulated by Fat-Dachsous signaling in Drosophila

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This important research article provides a novel approach to measure imaginal disc growth and uses this approach to explore the roles of Fat and Dachsous, two conserved protocadherins, in late larval development. The authors have addressed all referee concerns and the evidence supporting the authors' findings overall are compelling.

https://doi.org/10.7554/eLife.91572.3.sa0

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Abstract

The atypical cadherins Fat and Dachsous (Ds) signal through the Hippo pathway to regulate growth of numerous organs, including the Drosophila wing. Here, we find that Ds-Fat signaling tunes a unique feature of cell proliferation found to control the rate of wing growth during the third instar larval phase. The duration of the cell cycle increases in direct proportion to the size of the wing, leading to linear-like growth during the third instar. Ds-Fat signaling enhances the rate at which the cell cycle lengthens with wing size, thus diminishing the rate of wing growth. 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, 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.

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-Méndez 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 (Figure 1A). The anlage, called the 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 (Figure 1A). They continuously grow as the larva grows and undergoes three successive molts, from first to second to third instar. Wing discs grow exponentially by asynchronous cell division until the mid-third larval stage, when growth becomes linear-like, and finally stops when the late third instar larva undergoes its transition to the pupal stage (Fain and Stevens, 1982; Graves and Schubiger, 1982; Bryant and Levinson, 1985; Neto-Silva et al., 2009). During pupation, each wing pouch develops into a single adult wing blade.

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Allometric growth of the third instar wing pouch in *Drosophila*.

(A) Schematic depicting relative size of the wing imaginal discs inside a larva starting from 3 days after egg laying (AEL). The wing pouch (blue) begins everting during the larva-pupa transition and eventually becomes the adult wing blade. The notum and hinge (red) surrounding the wing pouch becomes the wing hinge and notum of the adult. (B) Wet-weight of third instar larvae as a function of age measured every 12 hr. Lines connect average weight measurements, and the shaded region denotes the standard error of the mean. (C) At 5 days AEL, the larva-pupa transition begins. Wet-weight of wildtype animals at early pupariation stages. Lines connect average weight measurements, and the shaded region denotes the standard error of the mean. WPP + 1 denotes 1 hr after white prepupae (WPP) stage onset. (D) Volume of the wing pouch as a function of age. Lines connect average volume measurements and the shaded region denotes the standard error of the mean. (E) Volume of wing pouch at early pupariation stages. Lines connect average volume measurements and the shaded region denotes the standard error of the mean. (F) Schematic depicting isometric growth (green arrow) where growth rates of the organ (wing) and the body are the same, positive allometric growth (orange arrow) where the organ is growing faster than the body, and negative allometric growth (magenta arrow) where the organ is growing slower than the body. (G) Allometric growth relationship during third instar between the wing pouch and body weight. Dashed line depicts the trajectory for an isometric growth curve. Error bars denote standard error of the mean.

Growth control of the wing disc operates through several mechanisms (Nijhout and Callier, 2015; Tripathi and Irvine, 2022). Hormones such as insulin-like peptides and ecdysone coordinate wing disc 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 leads to upregulation of the Yorkie (Yki) transcription factor and growth promotion. A second signal that regulates the Hippo pathway is mediated by two atypical cadherin molecules, Fat and Dachsous (Ds), which are growth inhibitory factors (Pan, 2010). The two proteins bind to one another on opposing cell membranes at the adherens junction, and binding is modulated by the Golgi kinase Four-jointed (Fj) (Ishikawa et al., 2008). 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). 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 inhibits Yki from transcribing growth-promoting genes (Cho et al., 2006; Vrabioiu and Struhl, 2015). A prevailing model for how Ds modulates Fat signaling is not via the absolute concentration of Ds 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).

Fat and Ds are thought to regulate growth of the wing pouch by an additional mechanism, termed the feed-forward mechanism (Zecca and Struhl, 2007; Zecca and Struhl, 2010; Zecca and Struhl, 2021). The transcription factor Vestigial (Vg) is expressed in wing pouch cells, where it promotes their growth and survival. Vg also regulates expression of Fj and Ds, creating a boundary of expression of these proteins at the border between the wing pouch and hinge/notum. At the border, wing pouch cells signal to neighboring hinge/notum cells via Fat / Ds interactions. Yki is activated in receiving cells and it stimulates these cells to express Vg. Since Vg regulates Ds and Fj, a feed-forward loop is created to reiteratively expand the wing pouch domain by recruitment rather than proliferation. However, it remains unclear what fraction of wing pouch growth is due to this mechanism.

The various molecular models for wing growth control described above have been developed in detail. However, what is unresolved are explanations for how these molecular mechanisms regulate the macroscopic features of growth. 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 during the mid-to-late third instar stage, Ds-Fat signaling tunes a feature of cell proliferation that controls the rate of wing pouch growth during this stage. The duration of the cell cycle increases in direct proportion to the size of the wing pouch, which leads to the observed linear-like growth of the wing pouch. Ds-Fat signaling enhances the rate at which the cell cycle lengthens with wing size, thus diminishing the rate of wing growth. We show that this results in a complex but stereotyped relative scaling of wing growth with body growth during the mid-to-late third instar stage. 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 third instar 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. In this study, we focused on growth during the 36 hr-long early-to-late third instar stage since this stage experiences linear-like growth, and its termination coincides with growth cessation.

We measured body size by both wet weight and volume. As expected, measurements of body weight and body volume showed a strong correlation (Figure 1—figure supplement 1). To measure wing pouch volume, we generated a 3D stack of confocal microscopic sections of the wing disc, and we used morphological landmarks (tissue folds) to demarcate the border separating the wing pouch from the surrounding notum-hinge (Figure 1—figure supplement 2). We validated the efficacy of this method by comparing the landmark-defined boundary to the expression boundary of the vg gene (Kim et al., 1996). The landmark method gave wing pouch measurements that were within 95.5% of measurements made by vg expression (Figure 1—figure supplement 3).

Beginning at 3.0 days after egg laying (AEL), we measured third instar larval body weight every 12 hr until the larva-pupa transition. 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 (Figure 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 transition into pupae. Weight remained constant during the one-hr-long white pre-pupal (WPP) stage and also one hr later (WPP + 1 stage; Figure 1C).

We measured wing disc growth for 36 hr during the early-to-late third instar stage. Wing pouch volume appeared to increase linearly over time and continued to grow during the non-feeding larval stage (Figure 1D). Growth of the wing pouch ceased at the WPP stage (Figure 1E). End-of-growth of the wing pouch was confirmed by phospho-histone H3 (PHH3) staining, which marks mitotic cells. At the third instar larval stage, dividing cells were observed throughout the wing pouch (Figure 1—figure supplement 4A and 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 (Nolo et al., 2000 Figure 1—figure supplement 4C and D).

We also measured growth of the hinge/notum domain of the wing disc during the early-to-late third instar. A similar linear-like growth trajectory was observed for the notum-hinge as for the wing pouch, although the hinge/notum stopped growing during the non-feeding stage (Figure 1—figure supplement 5A and B). Overall, our volumetric measurements are consistent with earlier studies that found wing disc growth is linear-like, as measured by cell number, during the mid-to-late third instar (Fain and Stevens, 1982; Graves and Schubiger, 1982).

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 (Figure 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 (Figure 1F). Allometric organ growth in holometabolous insects such as Drosophila presents a special situation arising from the fact that many adult organs derive from imaginal discs, which are non-functional in larvae. For this reason, there are fewer constraints on relative scaling, and allometric growth of imaginal discs are potentially 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 phases: the first is isometric and the second is positively allometric.

Since ontogenetic allometric growth of the Drosophila wing disc has not been studied, we plotted wet-weight body measurements versus wing pouch volume (Figure 1G). As with silkworms, allometric growth of the wing pouch had two phases, both of which showed positive allometry. The inflection point was the time when larvae ceased feeding. Allometric growth of the notum-hinge also exhibited two phases, although growth in the second phase was more limited than that observed for the wing pouch (Figure 1—figure supplement 5C). 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 of wing growth control 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 (Figure 2A). Qualitative measurements of ds gene expression found that cells transcribe the gene at different levels depending upon their position in the wing disc (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) (Figure 2—figure supplement 1A). A model hypothesized that this transcriptional gradient generates a Ds protein gradient across the wing pouch, and the gradient regulates growth by inducing Fat signaling in cells (Pan, 2010). If the Ds gradient becomes flattened, it leads to growth cessation.

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Dynamics of Ds and Fat protein distributions across the wing pouch during third instar.

(A) Schematic representation of E-cadherin, Fat and Ds protein structures, which are endogenously tagged with GFP at the C-terminus. Adapted from Tanoue and Takeichi, 2005. (B) Schematic of the wing disc depicting the anterior-posterior (AP, blue) and dorsal-ventral (DV, red) axes of symmetry. (C) Moving line average of Ds-GFP fluorescence as a function of position along the AP axis. Shown are profiles from wing pouches of different ages, as indicated. Shaded regions for each profile represent the standard error of the mean. (D) Moving line average of Ds-GFP fluorescence as a function of position along the DV axis. Shown are profiles from wing pouches of different ages, as indicated. Shaded regions for each profile represent the standard error of the mean. In the WPP, the pouch begins everting and only a portion of the ventral compartment is visible. (E) Moving line average of Ds-GFP fluorescence as a function of position along the AP axis normalized to the total distance of the axis. Shown are profiles from wing pouches of different ages, each normalized independently. (F) Moving line average of Ds-GFP fluorescence as a function of position along the DV axis normalized to the total distance of the axis. Shown are profiles from wing pouches of different ages, each normalized independently. (G) Moving line average of Fat-GFP fluorescence as a function of position along the AP axis. Shown are profiles from wing pouches of different ages, as indicated at right. Shaded regions for each profile represent the standard error of the mean. (H) Moving line average of Fat-GFP fluorescence as a function of position along the DV axis. Shown are profiles from wing pouches of different ages, as indicated at right. Shaded regions for each profile represent the standard error of the mean. (I) Moving line average of Fat-GFP fluorescence as a function of position along the AP axis normalized to the total distance of the axis. Shown are profiles from wing pouches of different ages, each normalized independently. (J) Moving line average of Fat-GFP fluorescence as a function of position along the DV axis normalized to the total distance of the axis. Shown are profiles from wing pouches of different ages, each normalized independently. (K) Schematic of the *da-Gal4* driver, active everywhere in the wing disc, co-expressing *UAS-fat-HA* and the control reporter *UAS-bazooka-mCherry*. (L) Moving line averages of Fat-HA (red) and Bazooka-mCherry (brown) fluorescence along the normalized AP axis in third instar larval wing pouches. Shaded regions for each profile represent the standard error of the mean. (M) Moving line average of Fat-GFP fluorescence along the normalized AP axis of wildtype and *ds^33k/UAO71* mutant wing pouches from 4-day-old larvae. Shaded regions for each profile represent the standard error of the mean.

If correct, the model predicts 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 (Figure 2A). Wing discs were co-stained with antibodies directed against Wg and Engrailed (En) proteins, which mark the wing pouch midlines (Figure 2—figure supplement 2A and B). Focusing on the mid-to-late third instar stage, we measured Ds-GFP levels along these two midlines to gain a Cartesian perspective of the wing pouch expression pattern. Image processing via surface detection enabled us to specifically measure Ds-GFP present in the wing pouch (disc proper) without bleed-through from Ds-GFP in the overlying peripodial membrane or signal distortion due to tissue curvature (Figure 1—figure supplement 2, Figure 2—figure supplement 2C).

There was a graded distribution of Ds-GFP along both anterior-posterior (AP) and dorsal-ventral (DV) axes of the wing pouch. Ds was high near the pouch border and low at the center of the pouch (Figure 2C and D). The gradient was asymmetric along the AP axis, being lower along the anterior pouch border than posterior border. 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 (Figure 2E). 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 pouch grew (Figure 2F).

We next turned to quantitative analysis of Fat protein expression. Fat was thought to be uniformly expressed in the wing pouch, although it had 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 (Figure 2A and Figure 2—figure supplement 2D and E). Surprisingly, Fat-GFP had a graded distribution along both the AP and DV axes of the wing pouch; low near the pouch border and high at the center of the wing pouch (Figure 2G and 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, and it became flat along the AP axis at the WPP stage. When we normalized all the Fat-GFP profiles to their corresponding pouch sizes, the profiles did not collapse (Figure 2I and J). The minimum limit of Fat-GFP was conserved but the maximum limit of Fat-GFP progressively diminished as the wing pouch grew.

The graded distribution of Fat protein was surprising since it was reported that fat gene transcription is uniform (Garoia et al., 2000), which we confirmed by smFISH (Figure 2—figure supplement 1B). Therefore, we considered the possibility that the gradient is generated by a post-transcriptional mechanism. To test the idea, we expressed Fat under the control of an UAS promoter. Transcription was activated by da-Gal4 (Figure 2K), which is uniformly expressed in Drosophila tissues (Gilbert et al., 2006). da-Gal4 also activated transcription of UAS-Bazooka-mCherry as a control. Bazooka-mCherry protein distribution was uniform along the AP axis, reflecting its faithful expression downstream of da-Gal4 (Figure 2L). However, Fat protein was graded in a similar pattern to endogenous Fat (Figure 2L). Thus, the Fat gradient is generated by a post-transcriptional mechanism.

The kinase Fj is known to target Fat protein within cells and so it was possible that the Fat protein gradient was generated by Fj. However, the distribution of Fat was unchanged in a fj mutant (Figure 2—figure supplement 3C). Additionally, Ds levels were unchanged in the fj mutant (Figure 2—figure supplement 3D), and there was no difference in wing pouch volume in fj mutants compared to wildtype (Figure 2—figure supplement 3E).

Ds is known to physically interact with Fat protein through their extracellular and intracellular domains (Ma et al., 2003; Hale et al., 2015; Fulford et al., 2023). These heterophilic interactions affect Fat protein levels within cells (Ma et al., 2003). To test the effect of Ds on formation of the Fat gradient, we examined Fat-GFP distribution in the wing pouch of a ds mutant. The level of Fat-GFP at the wing pouch center was identical to wildtype but the level of Fat-GFP near the pouch border was abnormally high (Figure 2M). Furthermore, we did not observe the flattened Fat-GFP profile at the WPP stage (Figure 2—figure supplement 3A). Instead, the Fat-GFP profile remained weakly graded at the WPP stage and was flattened somewhat more by the WPP + 1 stage (Figure 2—figure supplement 3B).

These observations conflict with a previous study showing that junctional stability of Fat within wing disc cells is reduced in a ds mutant (Hale et al., 2015). However, Ma et al., 2003 observed upregulation of Fat along cell junctions between ds mutant cells of the pupal wing, which is consistent with our observations of Fat-GFP upregulation near the pouch border of a ds mutant disc (Figure 2M).

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 (Figure 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 (Figure 3A and B). The overall change in pouch dimensions had no effect on wing pouch volume (Figure 3C). We then measured the Ds-GFP profile at WPP stage and found actin5C>trol(RNAi) had no effect on the gradient (Figure 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 (Figure 3E).

Figure 3

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Ds and Fat expression dynamics correlate with wing pouch volume during third instar.

(A) Wing pouch area of *nub-Gal4* control and *nub >trol*(RNAi) discs from the WPP stage. Shown are replicates and the mean. (B) Wing pouch thickness of *nub-Gal4* control and *nub >trol*(RNAi) discs from the WPP stage. Shown are replicates and the mean. (C) Wing pouch volume of *nub-Gal4* control and *nub >trol*(RNAi) discs from the WPP stage. Shown are replicates and the mean. (D) Moving line average of Ds-GFP fluorescence as a function of position along the AP axis normalized to the total distance of the axis in *nub-Gal4* control and *nub >trol*(RNAi) WPP wing pouches. Shaded regions for each profile represent the standard error of the mean. (E) Moving line average of Fat-GFP fluorescence as a function of position along the AP axis normalized to the total distance of the axis in *nub-Gal4* control and *nub >trol*(RNAi) WPP wing pouches. Shaded regions for each profile represent the standard error of the mean. (F) Confocal image of DAPI-stained nuclei in an *en >RBF* wing pouch. Note the lower density of nuclei in the P compartment (to the right of the dashed red line). This is due to the enlarged size of cells in this compartment. Scale bar is 30 µm. (G) The area ratio of P compartment to A compartment in *en-Gal4* control and *en >RBF* wing pouches from WPP animals. Shown are replicates and the mean. (H) Moving line average of Ds-GFP fluorescence as a function of position along the AP axis normalized to the total distance of the axis in *en-Gal4* control and *en >RBF* WPP wing pouches. Shaded regions for each profile represent the standard error of the mean. (I) Moving line average of Fat-GFP fluorescence as a function of position along the AP axis normalized to the total distance of the axis in *en-Gal4* control and *en >RBF* WPP wing pouches. Shaded regions for each profile represent the standard error of the mean.

The 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 twofold 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 (Figure 3F and G). Nevertheless, the Ds gradient in the P compartment at WPP stage was indistinguishable from wildtype (Figure 3H). The Fat gradient also flattened normally at the WPP stage (Figure 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 transition 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 (Figure 4A and B). The mutant larval notum and wing pouch grew at a faster rate than normal, and at the larva-pupa transition, the wing pouch continued to grow (Figure 4C and D and Figure 4—figure supplement 1A and B).

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Allometric growth of the wing pouch during third instar is altered in ds and *fat* mutants.

(A) Wet-weight of wildtype, *ds^33k/UAO71*, and *fat^G-rv/8* mutant third instar larvae as a function of age. Shaded regions represent standard error of the mean in this and the other panels. (B) Wet-weight of wildtype and mutant animals during early pupariation. Late L3 corresponds to the last day of the larval stage, that is, 5.0 days for wildtype, 5.5 days for *ds^33k/UAO71* mutants, and 6.0 days for *fat^G-rv/8* mutants. (C) Volume of wildtype and mutant wing pouches as a function of larval age. (D) Volume of wildtype and mutant wing pouches during early pupariation. Late L3 corresponds to the last day of the larval stage, i.e., 5.0 days for wildtype, 5.5 days for *ds^33k/UAO71* mutants, and 6.0 days for *fat^G-rv/8* mutants. (E) Allometric growth relationship of the third instar wing pouch versus body weight in wildtype and mutants.

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

Allometric growth of the fat and ds mutant wing pouch was significantly different from wildtype (Figure 4E). In wildtype, there are two linear phases to wing allometric growth (Figure 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 (Figure 4E). Similar trends were observed for allometric growth of the notum in these mutants (Figure 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 gene expression using UAS-RNAi (Figure 5A). RNAi against the ds gene resulted in near-complete depletion of Ds protein in the wing pouch (Figure 5—figure supplement 1A and B). As expected, knockdown of Ds in the wing pouch had no effect on body growth of larvae, and animals reached a normal final weight setpoint (Figure 5—figure supplement 2A and B). Thus, ds is not required in the wing to limit body growth. Notum growth in nub >ds(RNAi) animals was similar to controls, which would be expected if the gene was not required in the wing pouch for notum growth control (Figure 5—figure supplement 2D–F). However, the nub >ds(RNAi) wing pouch grew at a faster rate than normal. The wing pouch was 28% larger at the WPP stage and continued to grow until it was 42% larger at the WPP + 1 stage (Figure 5B and C).

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Fat and Ds regulate growth autonomously in the third instar wing pouch.

(A) Schematic of the *nub-Gal4* driver inducing RNAi of *fat* or ds in the wing pouch. (B) Volume of *nub-Gal4* control and *nub >ds*(RNAi) third instar wing pouches as a function of age. Shaded regions represent standard error of the mean. (C) Volume of *nub-Gal4* control and *nub >ds*(RNAi) wing pouches during early pupariation. Shaded regions represent standard error of the mean. (D) Volume of *nub-Gal4* control and *nub >fat-GFP*(RNAi) third instar wing pouches as a function of age. Shaded regions represent standard error of the mean. (E) Volume of *nub-Gal4* control and *nub >fat-GFP*(RNAi) wing pouches during early pupariation. Shaded regions represent standard error of the mean. (F) Schematic of the *ap-Gal4* driver inducing RNAi of ds in the D compartment by shRNA expression. (G) Ratio of D compartment area to V compartment area in *ap-Gal4* control and *ap >ds*(RNAi) wing pouches from WPP animals. Shown are replicate measurements and their mean. (H) Wing pouch area of *ap-Gal4* control and *ap >ds*(RNAi) WPP animals. Shown are replicate measurements and their mean. The area is normalized to the average of *ap-Gal4* controls. (I) Cell number in the D compartment of the wing pouch of *ap-Gal4* control and *ap >ds*(RNAi) WPP animals. Shown are replicate measurements and their mean. The cell number is normalized to the average of *ap-Gal4* controls. (J) Average cell size (apical area) in the D compartment of the wing pouch of *ap-Gal4* control and *ap >ds*(RNAi) WPP animals. Shown are replicate measurements and their mean. The cell size is normalized to the average of *ap-Gal4* controls. (K) Schematic of the *en-Gal4* driver inducing RNAi of ds and fat in the P compartment by shRNA expression. (L) Ratio of P compartment area to A compartment area in *en-Gal4* control, *en >fat*(RNAi), *en >ds*(RNAi), and *en >fat ds*(RNAi) wing pouches from WPP animals. Shown are replicate measurements and their mean. (M) Wing pouch area of *en-Gal4* control and RNAi knockdown WPP animals. Shown are replicate measurements and their mean. The area is normalized to the average of *en-Gal4* controls. Samples that were significantly different are marked with asterisks (*, p<0.05; **, p<0.01; ***, p<0.001; ****, p<0.0001).

Allometric growth of the wing pouch was also examined (Figure 5—figure supplement 2C). Knockdown of Ds in the wing pouch caused the entire allometric relationship to shift such that nub >ds(RNAi) wings were consistently bigger for their given body size. Thus, it appears that Ds is required in the wing pouch to tune down the allometric relationship of the wing to the body.

We next used nub-Gal4 driving UAS-GFP(RNAi) to knockdown GFP-tagged endogenous Fat in the wing pouch. There was virtually complete elimination of Fat-GFP expression (Figure 5—figure supplement 1C and D). Correcting for background fluorescence, we estimated that less than 5% of Fat-GFP remained after RNAi treatment (Figure 5—figure supplement 3A). Knockdown of Fat-GFP had a weak effect during mid third instar (Figure 5D), but the wing pouch was 15% larger than normal by the WPP stage, and 42% larger than normal by the WPP + 1 stage (Figure 5E and Figure 5—figure supplement 2G). The nub >fat-GFP(RNAi) wing pouch was of comparable size to the nub >ds(RNAi) wing pouch at WPP + 1 stage (Figure 5—figure supplement 2H). Adult wings from nub >fat-GFP(RNAi) individuals were also 40% larger than controls (Figure 5—figure supplement 2I). Thus, Fat and Ds are autonomously required to inhibit wing pouch growth during the mid-to-late third instar and its transition to the pupal stage.

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 (Figure 5F). 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 (Figure 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% (Figure 5G). Overall wing pouch size was unaffected by ap >ds(RNAi) knockdown (Figure 5H) 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 (Figure 5K). RNAi resulted in strong knockdown of Fat and Ds proteins in the P compartment but not the anterior (A) compartment (Figure 5—figure supplement 1F and G and Figure 5—figure supplement 3B). 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 (Figure 5L). en >fat ds(RNAi) showed an increase in the P/A ratio by 193%, an effect greater than the sum of effects from knockdown of each individual gene alone (Figure 5L). 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 (Figure 5M).

In conclusion, we found that Fat and Ds have autonomous effects on wing pouch growth consistent with fat and ds mutant phenotypes. However, the autonomous RNAi knockdown phenotypes were less severe than those of whole-body loss of fat and ds, suggesting there might be additional, non-autonomous requirements for Fat/Ds in wing growth.

Ds and Fat regulate wing pouch size during third instar 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 (Figure 5I). The average size of ds(RNAi) cells in the D compartment, as measured by apical domain area, was unchanged (Figure 5J). 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 (Milán 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 (Figure 1—figure supplement 5A and 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 (Figure 6—figure supplement 1), which is highly similar to previous measurements (Wartlick et al., 2011). Therefore, the average cell cycle timeT_CC can be inferred as

T_{c c} = \frac{0.34 h r}{M I}

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 during the mid-to-late third instar (Figure 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 with 2 supplements see all

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Cell cycle duration scaling with wing size is regulated by Ds and Fat during the third instar.

The average cell cycle time for third instar wing pouch cells is plotted against wing pouch volume for wing discs sampled over 1.5 days of third instar larval growth. Solid lines show the linear regression models, and dotted lines show the 95% confidence intervals of the fits. p Values denote the significance tests comparing the slopes (scaling coefficients) between RNAi-treated and control regression models. (A) *nub-Gal4* control. (B) *nub >ds*(RNAi) and *nub-Gal4* control. (C) *nub >fat-GFP*(RNAi) and *nub-Gal4* control.

Figure 6—source data 1 Summary statistics of linear regression analysis of average cell cycle time versus wing pouch volume.: https://cdn.elifesciences.org/articles/91572/elife-91572-fig6-data1-v1.docx
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Figure 6—source data 2 Summary statistics of linear regression analysis of average cell cycle time versus larval age (hours).: https://cdn.elifesciences.org/articles/91572/elife-91572-fig6-data2-v1.docx
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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 (Figure 6B). However, the scaling coefficient for ds(RNAi) cells was much smaller than wildtype (Figure 6—source data 1; p=6.2 × 10^–4). This meant that cell cycle duration was not lengthening as rapidly as normal and so cell cycle times were consistently shorter. We also examined the scaling relationship between cell cycle time and wing pouch volume when Fat was knocked down by nub >fat-GFP(RNAi) (Figure 6C). The scaling coefficient for nub >fat-GFP(RNAi) cells was also much smaller than wildtype (Figure 6—source data 1; p=3.1 × 10^–4).

The diminished cell cycle scaling coefficient caused by Fat and Ds knockdown could possibly account for their larger wing pouch size (Figure 5C and E). To more fully explore this possibility, we adapted a modeling framework (Wartlick et al., 2011) that relates instantaneous growth rates of cells to tissue growth. Assuming exponential cell growth, the average cell cycle time can be converted to instantaneous cell growth rate r, using the formula

r = \frac{\ln (2)}{T_{c c}}

We plotted our T_cc measurements as a function of larval age and found that the average cell cycle time linearly scales with age (Figure 6—source data 2). Using this fit, we converted T_cc to r as a function of time. We then used this relationship to simulate growth in cell number over time. Assuming that cell size remains invariant, cell number proportionally converts to tissue volume, allowing us to simulate growth in wing pouch volume over time. We compared model simulations to our measured volumes of the wing pouch over time (Figure 6—figure supplement 2). Strikingly, the model predictions were very close to the observed pouch growth for wildtype wings and for wings in which either Fat or Ds were knocked down by RNAi. This agreement between quantitative model predictions and experiment indicates that during the mid-to-late third instar, cell cycle control primarily accounts for wing pouch growth, and the effects of Fat/Ds on wing pouch growth are primarily exerted by their regulation of cell cycle dynamics.

In summary, during the third instar, 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 Fat/Ds expression gradients shallow.

To test the hypothesis, we first altered the Ds gradient. Using nub-Gal4, which drives expression high near the center of the wing pouch and low near the pouch border (Figure 7—figure supplement 1A and B), we misexpressed Ds with UAS-ds (Figure 7A). This drastically altered the Ds protein gradient (compare Figure 2C vs. Figure 7B and Figure 7—figure supplement 1C). The altered Ds gradient caused a change in the Fat gradient (Figure 7C). The gradient peak became skewed to the anterior, and the gradient did not flatten at the WPP stage. We then measured larval and wing pouch growth (Figure 7—figure supplement 1D–G). The growth curve of the third instar wing pouch was indistinguishable from wildtype, and wing growth ceased normally at the WPP stage of the larva-pupa transition (Figure 7—figure supplement 1F and G). This result suggests that drastically altering the Ds gradient does not impact wing growth.

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The endogenous graded distributions of Fat and Ds are not essential for controlling growth rate of the third instar wing pouch.

(A) Schematic of the *nub-Gal4* driver expressing ds under the UAS promoter. (B) Moving line average of Ds protein stained with anti-Ds as a function of position along the AP axis and normalized to the total distance of the axis. Shown are staged larval wing pouches from *nub >ds* animals. This measurement also detects expression from the endogenous ds gene. Shaded regions for each profile represent the standard error of the mean. (C) Moving line average of Fat-GFP fluorescence as a function of position along the AP axis and normalized to the total distance of the axis. Shown are staged larval and pupal wing pouches from *nub >ds* animals. Shaded regions for each profile represent the standard error of the mean. (D) Moving line average of Ds protein stained with anti-Ds as a function of position along the AP axis and normalized to the total distance of the axis. Shown are 4.5-day-old larval wing pouches from *ds-Gal4* and *ds >Ds* animals. *ds >Ds* overexpression of Ds protein is generated using a Trojan-Gal4 insertion that disrupts the endogenous ds gene and drives ds under a UAS promoter. Since all fluorescence intensities are normalized to the maximum level detected in *ds >Ds*, the endogenous ds gradient (brown) appears artificially flattened. This shows the scale of overexpression. Shaded regions for each profile represent the standard error of the mean. (E) Moving line average of Fat-GFP fluorescence as a function of position along the AP axis and normalized to the total distance of the axis. Shown are staged larval and pupal wing pouches from *fat-GFP; ds-Gal4* animals. Shaded regions for each profile represent the standard error of the mean. (F) Moving line average of Fat-GFP fluorescence as a function of position along the AP axis and normalized to the total distance of the axis. Shown are staged larval and WPP wing pouches from *ds >Ds* animals. Shaded regions for each profile represent the standard error of the mean. (G) Schematic of the *nub-Gal4* driver expressing *fat-HA* under the UAS promoter. (H) Moving line average of transgenic Fat-HA protein stained with anti-HA as a function of position along the AP axis and normalized to the total distance of the axis. Shown are staged larval and pupal wing pouches from *nub >fat HA; fat-GFP* animals. This measurement does not detect expression from the endogenous *fat-GFP* gene. Shaded regions for each profile represent the standard error of the mean. (I) Moving line average of endogenous Fat-GFP fluorescence as a function of position along the AP axis and normalized to the total distance of the axis. Shown are staged larval and pupal wing pouches from *nub >fat HA; fat-GFP* animals. Shaded regions for each profile represent the standard error of the mean. (J) The average cell cycle time for wing pouch cells plotted against wing pouch volume for wing discs from *nub-Gal4* control animals and *nub >fat HA; fat-GFP* animals. Solid lines show the linear regression model, and dotted lines show the 95% confidence intervals for the fit. There is no significant difference between the slopes (p=0.65).

Figure 7—source data 1 Summary statistics of linear regression analysis of average cell cycle time as a function of wing pouch volume when Fat is misexpressed under nub-Gal4 control and when the Ds gradient is amplified under Trojan-Gal4 control.: https://cdn.elifesciences.org/articles/91572/elife-91572-fig7-data1-v1.docx
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We further manipulated the Ds gradient so that it was amplified relative to wildtype. This was done by overexpressing Ds using a Trojan-Gal4 driver. Trojan-Gal4 transgenes are constructed with a splice acceptor sequence followed by the T2A peptide, the Gal4 open-reading frame, and a stop codon (Diao et al., 2015). When the transgene is inserted into the intron of an endogenous gene, it simultaneously inactivates the endogenous open reading frame and hijacks the gene to produce Gal4. When such a Trojan-Gal4 construct drives a UAS version of the disrupted gene, it amplifies expression levels while retaining endogenous transcriptional control (Lee et al., 2018). We crossed a line with Trojan-Gal4 inserted into the ds gene (Lee et al., 2018) to a UAS-ds line. Ds expression in the wing pouch was strongly amplified while its gradient pattern was preserved (Figure 7D and Figure 7—figure supplement 2A). In such ds >Ds wing pouches, the Fat protein gradient resembled wildtype (Figure 7E and F). Interestingly, the wing pouch was approximately 12% larger than wildtype at the WPP stage, as well as in the adult (Figure 7—figure supplement 2B and C). We also measured the scaling coefficient between cell cycle time and wing pouch volume for ds >Ds (Figure 7—figure supplement 2D). Although the scaling coefficient was slightly smaller than wildtype, it was not significant (Figure 7—source data 1; p=0.108). Thus, graded overexpression of Ds only weakly affects growth. Overall, cells appear to be relatively insensitive to the levels and pattern of Ds expression in terms of their growth.

Alternatively, it was possible that growth is controlled by the flattening of the Fat gradient in the wing pouch, since flattening normally occurs at the WPP stage when growth stops. To test this idea, we expressed HA-tagged Fat using the nub-Gal4 driver without eliminating endogenous Fat-GFP (Figure 7G and Figure 7—figure supplement 3A). 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 at the pouch center (Figure 7H, I). Strikingly, both transgenic and endogenous Fat gradients did not diminish in magnitude as larvae approached pupariation. Moreover, the gradients did not flatten at the WPP stage but only did so at the later WPP +1 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 (Figure 7J and Figure 7—source data 1). This was consistent with the observation that final wing pouch size in nub >fat HA animals was normal (Figure 7—figure supplement 3B). 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 during the mid-to-late third instar stage. Fat and Ds attenuate the rate of third instar 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 third instar 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; Martín et al., 2009; Wartlick et al., 2011). A link has been found between doubling time of wing disc cells 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 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 each 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 divides when Dpp increases by 40% relative to its level at the beginning of the division cycle (Wartlick et al., 2011). The correlation was observed throughout larval development, indicating that the progressive lengthening of the cell cycle may be caused by a slowing rate of increase in local Dpp concentration over time.

Do Fat and Ds tune this relationship? Fat inhibits apico-cortical localization of the atypical myosin Dachs, consistent with genetically antagonistic roles played by fat and dachs (Cho and Irvine, 2004; Mao et al., 2006; 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-Fat signaling between third instar wing 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 third instar wing cells do not lengthen their cell cycle as rapidly as normal when Fat or Ds are knocked down.

Other mechanisms are also possible. Dpp signaling represses Brinker, and it has been proposed that Brinker is the primary mediator of growth control by Dpp (Schwank et al., 2011). Moreover, Fat and Dpp may act in parallel rather than sequentially to regulate growth (Schwank et al., 2011). Therefore, Ds-Fat signaling via the Hippo pathway may regulate the cell cycle duration of wing pouch cells independent of Dpp. Another known mechanism by which Fat/Ds regulates growth of the wing pouch is by a feedforward recruitment of neighboring hinge/notum cells to become wing pouch cells (Zecca and Struhl, 2007). This mechanism does not involve cell proliferation control. Our analysis of Fat/Ds function during the mid-to-late third instar suggests that they are not working through the feedforward mechanism to any large extent. Model simulations of wing pouch growth assuming Fat/Ds only control cell cycle duration strongly fit with our measurements of pouch growth during the third instar (Figure 6—figure supplement 2). This would argue that any contribution of Fat/Ds towards recruitment of pouch cells must be minor at this stage of larval growth.

The Ds expression pattern has a graded distribution with a steep slope in the proximal region of the wing pouch (near the pouch border) and a shallow slope in the distal region of the pouch (near the pouch center). We find that Fat protein is distributed in a gradient that is complementary to the Ds protein gradient – Fat is most abundant in cells where Ds levels are minimal and its gradient is most shallow. Global loss of Ds affects Fat distribution across the wing pouch such that Fat is abnormally elevated near the pouch border while remaining unchanged at the pouch center, effectively making a more shallow Fat gradient. This might suggest that cells repress Fat expression if they sense a steep Ds gradient. Alternatively, cells might repress Fat expression in a manner dependent on Ds levels. Indeed, ds mutant clones exhibit upregulated Fat localized to junctions between mutant cells (Ma et al., 2003). However, these interpretations of loss-of-function experiments are complicated by our results manipulating the Ds gradient. Ectopically increasing Ds expression in central regions of the pouch with nub >ds did not repress Fat abundance in those regions. Nor did amplifying the slope of the Ds gradient and boosting the maximal levels of Ds with ds >Ds lead to stronger repression of Fat near the pouch border. Thus, the distribution of Fat is insensitive to the absolute level or differential in Ds abundance above some minimal level that is non-zero. Below this minimum and Fat is somehow upregulated. The mechanism behind these interactions remains to be elucidated. It is tempting to speculate that heterophilic binding of Ds to Fat, either in trans or in cis, is responsible (Hale et al., 2015; Fulford et al., 2023). If so, then it is likely distinct from the stabilizing interactions that Ds has on Fat at cell junctions (Ma et al., 2003; Hale et al., 2015).

The graded distributions of Fat and Ds proteins across the pouch are not stable over time but become progressively more shallow as the larva-pupa transition is reached. For Ds, its gradient scales with the size of the wing pouch. This occurs because the maximum and minimum limits of Ds-GFP abundance are conserved as the wing pouch grows. It would imply that dividing cells take up intermediate scalar values from their neighbors during growth, and over time the steepness of the Ds gradient consequently diminishes. Such a mechanism would also explain why the Ds gradient scales with pouch volume and not cell number. Whether cells are many or few in number, if they adopt intermediate levels of Ds from their neighbors by local sensing, then the gradient scales as the tissue expands.

Our observation of shallowing gradients of Fat and Ds expression fits with a long-standing model for growth regulation by Fat and Ds. 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 (stimulates growth), whereas a shallow gradient activates Fat signaling (inhibits growth). Thus, a progressively shallowing gradient of Ds would progressively slow down growth, which is what occurs during the third instar. Although the model did not consider a Fat gradient, our finding a shallowing gradient of Fat might also fit within this gradient model of growth control. However, when we manipulated the graded distributions of Fat or Ds protein in the wing pouch, there was little or no effect on its growth. Enhancing the gradient of Fat by its overexpression did not stimulate growth. Nor did amplifying the Ds gradient by severalfold overexpression using ds >Ds lead to greatly enhanced growth but only a weak response. These results are not consistent with the gradient model. Moreover, loss of Fat and Ds diminishes the scaling coefficient that couples cell cycle time to pouch size, and this effect is constant over 36 hr of third instar growth (Figure 6). Thus, Ds and Fat are not progressively tuning their impact on growth rate of the wing, as the gradient model predicts. Instead, we suggest that third instar wing cells are tolerant of differences in Fat/Ds abundance, and instead, the gradients may be linked to the planar cell polarity functions of these proteins (Ma et al., 2003).

Materials and methods

Key resources table

Reagent type (species) or resource	Designation	Source or reference	Identifiers	Additional information
Gene (Drosophila melanogaster)	w¹¹¹⁸	Bloomington Drosophila Stock Center	BDSC: 3605 Flybase: FBst0003605
Gene (Drosophila melanogaster)	E-cadherin-GFP	Bloomington Drosophila Stock Center	BDSC: 60584 Flybase: FBal0247908
Gene (Drosophila melanogaster)	E-cadherin-mCherry	Bloomington Drosophila Stock Center	BDSC: 59014 Flybase: Fbti0168567
Gene (Drosophila melanogaster)	fat^G-rv	Bloomington Drosophila Stock Center	BDSC: 1894 Flybase: Fbal0004805
Gene (Drosophila melanogaster)	fat⁸	Bloomington Drosophila Stock Center	BDSC: 44257 Flybase: Fbal0004794
Gene (Drosophila melanogaster)	fj^d1	Bloomington Drosophila Stock Center	BDSC: 6373 Flybase: Fbal0049500
Gene (Drosophila melanogaster)	fj^p1	Bloomington Drosophila Stock Center	BDSC: 44253 Flybase: Fbal0049503
Gene (Drosophila melanogaster)	ds^UAO71	Bloomington Drosophila Stock Center	BDSC: 41784 Flybase: Fbal0089339
Gene (Drosophila melanogaster)	ds^33k	Bloomington Drosophila Stock Center	BDSC: 1580 Flybase: Fbal0028155
Gene (Drosophila melanogaster)	ds-GFP	Brittle et al., 2012	Flybase: Fbal0344517	Gift from Ken Irvine
Gene (Drosophila melanogaster)	fat-GFP	Hale et al., 2015	Flybase: Fbal0385338	Gift from Helen McNeill
Gene (Drosophila melanogaster)	UAS-fat-HA	Sopko et al., 2009	Flybase: Fbal0239166	Gift from H. McNeill
Gene (Drosophila melanogaster)	UAS-ds	Matakatsu and Blair, 2004	Flybase: Fbal0180099	Gift from Ken Irvine
Gene (Drosophila melanogaster)	UAS-bazooka-mCherry	Bloomington Drosophila Stock Center	BDSC: 65844 Flybase: Fbti0183177
Gene (Drosophila melanogaster)	UAS-fat(RNAi)	Bloomington Drosophila Stock Center	BDSC: 34970 Flybase: Fbti0144840
Gene (Drosophila melanogaster)	UAS-ds(RNAi)	Bloomington Drosophila Stock Center	BDSC: 32964 Flybase: Fbti0140473
Gene (Drosophila melanogaster)	UAS-trol(RNAi)	Bloomington Drosophila Stock Center	BDSC: 29440 Flybase: Fbti0129068
Gene (Drosophila melanogaster)	UAS-GFP(RNAi)	Bloomington Drosophila Stock Center	BDSC: 9330 Flybase: Fbti0074363
Gene (Drosophila melanogaster)	UAS-RBF	Bloomington Drosophila Stock Center	BDSC: 50747 Flybase: Fbti0016888
Gene (Drosophila melanogaster)	ap-Gal4	Bloomington Drosophila Stock Center	BDSC: 3041 Flybase: Fbti0002785
Gene (Drosophila melanogaster)	nub-Gal4	Bloomington Drosophila Stock Center	BDSC: 42699 Flybase: Fbal0277528
Gene (Drosophila melanogaster)	en-Gal4	Bloomington Drosophila Stock Center	BDSC: 30564 Flybase: Fbti0003572
Gene (Drosophila melanogaster)	da-Gal4	Bloomington Drosophila Stock Center	BDSC: 55850 Flybase: Fbti0013991
Gene (Drosophila melanogaster)	actin5c-Gal4	Bloomington Drosophila Stock Center	BDSC: 3954 Flybase: Fbti0012292
Gene (Drosophila melanogaster)	ds-Trojan-GAL4	Bloomington Drosophila Stock Center	BDSC: 67432 Flybase: Fbti0186258
Gene (Drosophila melanogaster)	UAS-GFP-NLS	Bloomington Drosophila Stock Center	BDSC: 4776 Flybase: Fbti0012493
Gene (Drosophila melanogaster)	5xQE-dsRed	Zecca and Struhl, 2007	Flybase: Fbal0219107	Gift from Gary Struhl
Antibody	Mouse monoclonal anti-Wg	Developmental Studies Hybridoma Bank	4D4	IF (1:1000)
Antibody	Mouse monoclonal anti-En	Developmental Studies Hybridoma Bank	4D9	IF (1:15)
Antibody	Rat monoclonal anti-E-cadherin	Developmental Studies Hybridoma Bank	Dcad2	IF (1:10)
Antibody	Rat polyclonal anti-Ds			IF (1:1000), Gift from Helen McNeill
Antibody	Rat monoclonal anti-HA	Roche		IF (1:1000)
Antibody	Rabbit polyclonal anti-PHH3	Sigma	H0412	IF (1:400)
Antibody	Goat polyclonal anti-Rabbit Alexa Fluor 546	Invitrogen	A11035	IF (1:200)
Antibody	Goat polyclonal anti-Mouse Alexa Fluor 405	Invitrogen	A48255	IF (1:200)
Antibody	Goat polyclonal anti-Rat Alexa Fluor 647	Invitrogen	A48265	IF (1:200)
Other	18x18 mm number 1.5 coverslip	Zeiss	474030-9000-000	Coverslip used in all microscopy experiments, see Methods Immunohistochemstry section
Other	24x60 mm number 1.5 coverslip	VWR	48393–251	Coverslip used in all microscopy experiments, see Methods Immunohistochemstry section
Chemical compound, drug	Vectashield Plus	Vector Labs	H-1900
Chemical compound, drug	4′,6-diamidino-2-phenylindole (DAPI)	Life Technologies	D1306
Chemical compound, drug	Triton X-100	Sigma Aldrich	T9284-500ML
Chemical compound, drug	Paraformaldehyde (powder)	Polysciences	00380–1
Software, algorithm	ImSAnE 1.0 MATLAB software	Heemskerk and Streichan, 2015; Heemskerk, 2021	https://github.com/idse/imsane
Software, algorithm	Trained CNN model for pixel classification of epithelial fluorescence confocal data	Gallagher et al., 2022	https://drive.google.com/drive/folders/1I-nRpn1esRzs5t4ztgbNvkBQuTN2vT7L?usp=sharing
Software, algorithm	MATLAB pipeline to estimate larval volume	This paper; copy archived at Liu, 2023b	https://github.com/andrewliu321/LarvaSeg
Software, algorithm	MATLAB pipeline to measure protein fluorescent intensity in the wing pouch	This paper; copy archived at Liu, 2023a	https://github.com/andrewliu321/ProteinIntensity

	Total Cell Number = β₀ + β₁Pouch Volume
Genotype	β₀	β₁	R²	p
nub-Gal4	352.0±187.7	7261.3±355.2	0.95	8.43E-16
nub >ds(RNAi)	653.9±191.0	4533.5±221.5	0.95	8.19E-16
nub-Gal4	637.3±200.9	4793.3±269.5	0.96	5.24E-11
fat-GFP; nub >fat(RNAi)	648.3±319.9	4359.0±364.3	0.91	4.50E-9
nub >fat HA	2321.5±324.4	5212.9±516.4	0.80	2.65E-10
ds-Gal4	–1875±3,293	7726±2970	0.63	0.059
ds >ds	725.9±1688.4	4839.7±1382.3	0.58	0.0067

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Allometric growth of the third instar wing pouch in Drosophila.

Dynamics of Ds and Fat protein distributions across the wing pouch during third instar.

Ds and Fat expression dynamics correlate with wing pouch volume during third instar.

Allometric growth of the wing pouch during third instar is altered in ds and fat mutants.

Fat and Ds regulate growth autonomously in the third instar wing pouch.

Cell cycle duration scaling with wing size is regulated by Ds and Fat during the third instar.

Figure 6—source data 1

Figure 6—source data 2

The endogenous graded distributions of Fat and Ds are not essential for controlling growth rate of the third instar wing pouch.

Figure 7—source data 1

Summary statistics of linear regressions.

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Andrew Liu

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Jessica O’Connell

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Farley Wall

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Richard W Carthew

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