^{1}

^{*}

^{2}

^{3}

^{4}

^{5}

^{2}

^{3}

^{¶}

^{*}

^{1}

^{¶}

^{*}

The author(s) have made the following declarations about their contributions: Conceived and designed the experiments: FH AMdL SB MA. Performed the experiments: FH AMdL. Analyzed the data: FH AMdL. Contributed reagents/materials/analysis tools: GP. Wrote the paper: FH AMdL SB MA.

¶ SB and MA also contributed equally to this work.

The authors have declared that no competing interests exist.

The activity of the Dpp morphogen adapts to tissue size in the growing

The wing of the fruit fly,

Scaling, the fitting of pattern to size, manifests itself in numerous examples around us. During development, individual body parts scale up to fit the overall body size. Starved animals form smaller adults with proportionally smaller parts, and amphibian embryos can form normally proportioned adults after extreme surgical operations. How scaling is achieved is not well understood. Here, we establish the

Matching of pattern to size, a phenomenon referred to as scaling, manifests itself in numerous examples around us. During development, individual body parts scale up with the overall body size, starved animals form smaller adults with proportionally smaller body parts

The fruit fly

The Dpp signal transduction pathway is highly conserved and relatively simple (

While the role of Dad is less well studied, Sal and Omb expression boundaries are crucial for the determination of the positioning of veins L2 and L5 of the adult wing, respectively (

Recently,

Here, we made use of this wealth of information available with regard to the molecular readout of the Dpp signaling activity in the wing imaginal disc and investigated whether the Dpp activity gradients, namely P-Mad and Brk, as well as the downstream domain boundaries (Dad, Sal, and Omb) scale and thus adapt to the size of the growing tissue. After establishing a protocol to reliably quantify the spatial and temporal changes in the Dpp activity gradients, we found that both P-Mad and Brk scale rather well with the tissue size.

We then tried to uncover the molecular mechanisms that ensure proper scaling of these activity gradients. A recent mathematical model termed

The Dpp activity gradient is read out by several target genes, such as

(A) Dashed lines outline the pouch, A/P, and D/V boundaries, defined by Wg and Ptc stainings (red). P-Mad (blue) profiles were extracted with 15% ventral offset from D/V (purple). (B)

Before we could ask questions regarding the scaling behavior of Dpp signaling readout during growth of the wing imaginal disc, it was necessary to establish methods to acquire images that can be quantified. We concentrated our analysis on the pouch of the wing imaginal disc, which gives rise to the future wing. To extract the pouch and determine the A/P and D/V compartment boundaries, we co-stained all discs with Wingless (Wg) and Patched (Ptc) antibodies (

(A) Representative wing imaginal discs from each time class (TC) stained for P-Mad antibodies. (B) Average P-Mad profiles at 15% ventral offset. Profiles are shown separately for each TC and in absolute positions. Error bars show the standard error here and in the similar panels of the following figures. (C) Profiles in (B) shown in relative positions. (D) P-Mad scaling corresponding to an average relative position

To account for the amplitudes of the protein gradients in our analysis and to test for the hypothesis that downstream target gene domains are defined at constant thresholds of P-Mad and Brk, we treated fluorescence intensities as a measure of protein concentrations. To ascertain that the changes in fluorescent intensities reflected changes in protein concentrations in a linear manner, we imaged fluorescent dyes of known concentrations at the same settings we used for our images and determined the linear range for our imaging conditions. We found that the intensities obtained in our experimental recordings indeed fell into the linear range of our imaging conditions (

We define scaling as the preservation of proportions across growth—i.e. if an expression domain spans 30% of the tissue in a young disc, it should also span 30% in an older and larger disc to achieve perfect scaling. In order to assess scaling

The first event downstream of Dpp receptor complex activation is the phosphorylation of the signal transducer Mad, which we visualized and quantified with P-Mad antibodies. We analyzed P-Mad gradients in wing imaginal discs from different TCs (

For further analyses, we concentrated on the posterior half of the pouch to exclude Dpp secreting anterior cells from the analysis and to avoid complications arising from the modifications of Dpp receptor levels via Hh, which is active only in the anterior compartment _{p}, where L_{p} stands for the length of the posterior compartment). The individual discs are represented with color-coded circles according to their age (

In order to obtain a position-dependent picture of scaling, we considered several other protein concentration thresholds and calculated a scaling coefficient at each threshold (

_{p} throughout development, suggesting that behind this relative position, P-Mad levels are too low to suppress

(A) Representative images of wing discs for each TC stained with Brk antibodies. (B) Average Brk profiles per TC, measured at 15% ventral offset. (C) Profiles in (B) normalized for L_{p}. Note that the Brk concentration at a relative position increases with time. (D) Brk versus P-Mad concentrations for every position in the posterior compartment at 15% ventral offset (P-Mad and Brk from dataset 1 were co-stained). P-Mad and Brk concentrations were normalized to their maximum over all TCs: max ([P-Mad]) = 0.12, max ([Brk]) = 0.22. Arrow points to 40% of max ([P-Mad]). (E) Brk profiles were fitted with a decaying exponential function, yielding a decay length λ_{Brk}. For each disc, the average P-Mad concentration at the position x = λ_{Brk} was calculated. The weighted linear regression with 95% confidence interval (gray area) and its _{p}. (G) Brk scaling (o) and correlation(x) for several threshold concentrations. Error bars represent the 95% confidence intervals.

As a result of P-Mad gradients scaling while keeping their amplitudes roughly constant, cells at the same relative position in the disc have very similar P-Mad levels across development. Interestingly, the same cells are subject to increasing levels of Brk: while the magnitude of the increase tends to be smaller away from the D/V boundary, we detected a 10- to 20-fold increase in the average amplitudes in the 40-h interval we studied (

How are the constant P-Mad levels at a given relative position translated into increasing Brk levels? Since discs were co-stained for Brk and P-Mad, we investigated the relation between Brk concentrations and P-Mad concentrations within each disc.

Finally, we studied the scaling properties of the Brk profiles. Apart from being non-quantitative, looking at the collapse of the profiles adjusted to compartment size is a good indicator of the level of scaling (

Since there are no antibodies available which recognize Dad, we visualized changes in _{dad}

(A) Representative images of wing discs from larvae carrying the _{p} and for their amplitudes. (D) dad-GFP profiles were fitted with a Hill function describing the transition point K_{dad}_{-GFP} of the domain (see _{dad}_{-GFP} against L_{p} for each disc were plotted and the weighted linear regression with 95% confidence interval (gray area) and its _{dad}_{-GFP} plotted against L_{p} for each disc. (F) For each disc, the log-deviations in _{p}. The scaling coefficient S is obtained by weighted linear regression (95% confidence interval in gray). The correlation ρ of the data with 95% confidence interval is shown.

Similar to Brk levels, _{dad}

Proper positioning of the veins in the developing wing requires Dpp signaling and is important to ensure adult wing functionality

(A) Representative images of Sal antibody stainings at each TC. (B) Average Sal profiles obtained from the individual profiles normalized to their maximum in the anterior compartment at 15% ventral offset, in relative positions. (C) For each disc, the log-deviations in Sal anterior domain boundary position were plotted as a function of the log-deviations in the anterior compartment length L_{a}. The scaling coefficient S and the correlation ρ of the data with 95% confidence intervals are shown. (D–E) Average P-Mad (D) and Brk (E) concentrations at the position x = K_{Sal} plotted against L_{a} for each disc. The weighted linear regression with 95% confidence interval (gray area) and its

(A) Representative images of Omb antibody stainings at each TC. (B) Average Omb profiles at 15% ventral offset, obtained from the individual profiles normalized to their maximum. (C) For each disc, the log-deviations in Omb posterior domain boundary position were plotted as a function of the log-deviations in the posterior compartment length L_{p}. The scaling coefficient S and the correlation ρ of the data with 95% confidence intervals are shown. (D–E) Average P-Mad (D) and Brk (E) concentration at the position x = K_{Omb} plotted against L_{p} for each disc. The weighted linear regression with 95% confidence interval (gray area) and its

The

We also investigated whether the boundaries of Sal and Omb expression domains are defined at constant P-Mad and Brk levels. We found that the anterior Sal domain boundary corresponds to decreasing P-Mad levels and increasing Brk levels over time (

Overall, we have shown that the P-Mad gradient and the expression domains of its target genes scale rather well with the growing wing disc. Additionally, Teleman et al. found that when the posterior compartment is enlarged or reduced in size via modifications of Insulin signaling activity, the size of the Sal domain adjusts accordingly

We recently identified a Pent-dependent feedback loop as a major modifier of the Dpp activity gradient ^{2–5}

(A–B) Representative images of P-Mad (A) and Brk (B) antibody stainings at each TC in ^{2–5}^{2–5}^{2–5}^{2–5}^{2–5}

Are these changes in P-Mad dynamics in _{p} in wild-type discs (

Next, we asked whether this failure of Dpp activity gradients to adjust to tissue size in _{p} = 0.26). Despite this shrinkage, the Omb domain overlaps significantly with the Brk domain in this background, especially at the end of the third instar stage, a phenomenon not observed to this extent in wild-type discs. A large stripe of cells express both Omb and Brk, raising the possibility that failure to define L5 might be due to this extensive overlap (

We conclude that the adaptation of the Dpp activity gradient to tissue size described in the first part of this study strictly requires Pent function.

In this study, we carefully analyzed the dynamics and the scaling properties of the Dpp activity readouts in the growing wing imaginal discs. We discuss our findings with regard to models that were put forward to explain scaling (the expansion-repression model)

We measured pathway activity using an antibody specific to the phosphorylated form of Mad, and compared the P-Mad levels in space and time with the activity levels of direct target genes, such as

We found that P-Mad levels scale very well posterior to 0.4 L_{p} with the exception of TC5 profiles near the D/V boundary. Previous studies that examined P-Mad scaling reached contradictory conclusions: the P-Mad gradients in late stage discs were reported to correlate with tissue size in a previous study

Since P-Mad is an early signature of the activation of the Dpp signaling pathway, we wanted to find out how its scaling properties translate to its immediate key target, the _{p}. By contrast, levels of Brk increase steadily as the discs grow and cannot be explained by P-Mad dynamics alone. This increase in Brk levels could be due to the build-up of the unknown activator of

Traditionally, Dpp and P-Mad gradients have been described by a decaying exponential with characteristic decay length λ ^{rd} instar stage (note that they used the length of the pouch along the A/P boundary as a measure of tissue size,

Consistent with our results, Wartlick et al. recently showed that the decay lengths of Dpp-GFP, P-Mad,

In our work, we used the raw intensity measurements without fitting any function to the corresponding profiles, since the exponential is not the best fit at all time classes. Similarly, we wanted to assess scaling in the whole field and not just at one characteristic position. To this end, in addition to looking at the collapse of the profiles, we used our measure of scaling

For comparison, we also show in _{P-Mad} = 0.21 L_{p} and λ_{Brk} = 0.18 L_{p}. We note that our estimate of λ_{P-Mad} is smaller than the previously reported value (0.34 L_{p}), likely due to the fact that we measure tissue size along the D/V boundary, from the intersection of the A/P to the limits of the pouch, as opposed to the length of the posterior compartment at its widest position. Our measure of λ_{Brk} is very similar to that of Wartlick et al. Hence, considering that we have a larger value for the tissue size, Brk protein must form a gradient with a larger decay length than the

A recent mathematical model termed “expansion-repression integral feedback control” suggests that scaling can emerge as a natural consequence of a feedback loop

More than 40 y ago, Lewis Wolpert proposed the French flag model to explain pattern formation by morphogens (^{2}/Brk is constant at the domain boundary (^{2–5}^{5}*Brk^{4} is constant (^{2–5}

We used our data to further test a model that was recently proposed to explain the uniform growth in the wing imaginal disc

Wartlick et al. monitored Dpp signaling levels using a

Flies were constantly kept in a 26°C incubator and the eggs were collected on grape juice plates. It is known that the females can keep the fertilized eggs for up to 8 h, so a freshly laid egg can be anywhere between minutes to 8 h old. We circumvented this problem by treating flies with CO_{2} prior to collection, which is thought to relax the muscles and facilitate the deposition of old eggs. This first collection was discarded and the flies were transferred to a clean collection chamber. Additionally, as sexual dimorphism exerts itself early on, only male larvae were included in our analysis where possible. Indeed, male flies are comparatively smaller than female flies and including both sexes could bias our scaling results during wing imaginal disc growth. Male larvae were positively selected for by the presence of a clear, oval genital disc, which is clearly visible starting from 80 h AEL. Therefore, our 70 h collections had both male and female larvae. We observed that 70 h AEL corresponds to the beginning of the third instar stage at 26 °C as hatching larvae were frequently encountered. Dissected larvae were fixed immediately, washed, and stored at 4°C. Once all time classes were obtained (usually within 2 d), all samples were processed for antibody staining in parallel using identical solutions.

Larvae of different time classes (TC1: 65–75 h AEL, TC2: 75–85 h AEL, TC3: 85–95 h AEL, TC4: 95–105 h AEL, TC5: 105–120 h AEL) were transferred into cold fixative (4% pfa in PBS, pH = 7) and fixed for 25 min at room temperature on a rotator. Following extensive washes in PBT (PBS+0.03% TritonX), the discs were blocked in PBTN (PBT+2% Normal Donkey Serum, Jackson Immuno Research Laboratories) for 1 h at 4°C on a rotator, and incubated with primary antibodies overnight at 4°C. The discs were washed several times with cold PBT and incubated in secondary antibodies for 2 h at room temperature on a rotator. After another round of washes with PBT, the excess fluid was removed and replaced with Vectashield mounting media (Vector Labs). All discs from a dataset (i.e. all 5 TCs) were mounted on the same slide to reduce potential variation in thickness between the slide and the coverslip across different samples. Brain discs were used as spacers. All discs from a dataset were imaged under identical microscopy settings using a Leica SP5 confocal microscope (1 µm thick sections).

Rb-α-P-Mad (1∶1,500, Ed Laufer,

After the image acquisition, we manually selected by visual inspection four consecutive slices above and below the brightest slice from each stack and performed a mean projection of these nine slices. Using a reduced number of slices and performing the mean projection allowed us to reduce the noise as well as avoid the signal from the peripodial membrane. Indeed, we made sure that these nine slices contained signal from the columnar cells of the pouch only. We then manually contoured the inner pouch boundary as well as the anterior-posterior (A/P) and dorsal-ventral (D/V) boundaries, as marked by the Wg and Ptc stainings. All discs were rotated to have anterior to the left and dorsal upwards orientation. The remaining analyses were applied solely to the pouch. We extracted the profiles along the D/V boundary, since it is a natural coordinate in the wing pouch, or parallel to it with a small offset of 5% of the height of the pouch into the dorsal compartment to avoid potential interference with Wg, which is expressed at the D/V boundary. We repeated our analysis also with 15% and 25% offsets into the ventral compartment. Note that since the D/V boundary is not a thin line but a stripe, we applied mean filtering with a rectangular sliding window of fixed size (20×3) pixels (height×width) to smoothen the images of (1024×1024) pixels before further analyses. Also, because we used nuclear markers, the 1 d extracted profiles looked very rugged and we therefore applied Gaussian filtering before quantifying scaling. We assumed that the changes in cell density are negligible.

We aimed to quantify scaling of Dpp target genes. In a previous work

In our analysis, we concentrated on the posterior compartment and used the length of the posterior compartment (L_{p}) as a measure of the tissue size. L_{p} is indeed a good measure of tissue size as it changes proportionally with the square-root of the area of the posterior compartment (

For assessing the scaling properties of P-mad, we took into account its amplitude, assuming that the absolute concentrations are important for the signal interpretation by the target genes. Moreover, we wanted to characterize scaling over the whole field where the protein is expressed and not just at one particular position, because the gradient can scale differently across positions. We therefore considered several thresholds of protein concentration readout. Note that while an exponential function can provide a reasonable fit to P-Mad and Brk profiles away from their source, we did our calculations without fitting any specific curve to the profiles. For each threshold, we plotted the corresponding positions against the lengths of the posterior compartments for our collection of discs (

All the linear regressions that we perform are weighted if the data points on the plot have an error bar (weight = 1/error^{2}). The gray area represents the 95% confidence interval on the linear regression, that we approximate using the estimated standard error

All the

Dpp signal transduction and vein formation. (A) Representative images of expression patterns referred to in this study. Red arrows point to the effect of posterior Dpp source on various target gene expression patterns. (B) In the medial cells (left), type I (Thickveins-Tkv) and type II (Punt) receptors—both Ser/Thr kinases—form heterodimers upon Dpp binding allowing constitutively active Punt to phosphorylate and activate Tkv, which in turn phosphorylates the Mad proteins (Receptor-Smad). P-Mad molecules form complexes with Medea (co-Smad) and translocate into the nucleus where they can both activate as well as inhibit transcription of target genes with the help of co-factors. P-Mad/Medea/Schnurri complex represses transcription of

(TIF)

Methods. (A) Discs of varying ages stained with Wg and Ptc antibodies. Wg staining gets refined by 71–72 h AEL. (B) The posterior compartment length measured along the D/V axis (L_{p}) correlates well with the square root of the posterior compartment area (area_{p}) both in wt (black) and ^{2–5}

(PDF)

P-Mad is repressed along the D/V boundary at the end of third instar. (A) The dashed yellow lines outline the pouch as well as the A/P and the D/V compartment boundaries, as defined by Wg and Ptc stainings in red. P-Mad profiles were extracted along the D/V and with 5% (yellow), 15% (purple), 25% (orange) offsets from it. (B–F) P-Mad profiles averaged per TC in relative positions along the D/V (B), with 5% offset into the dorsal compartment (D), and with 5% (C), 15% (E), and 25% (F) offsets into the ventral compartment. Positions in the posterior compartment are normalized relative to the posterior compartment length L_{p}, while positions in the anterior compartment are normalized relative to the anterior compartment length L_{a}.

(PDF)

P-Mad profiles and amplitudes at various positions. (A–D) P-Mad profiles averaged per TC along the D/V (A), and with 5% dorsal (B), 15% ventral (C), 25% ventral (D) offsets. (A′–D′) The amplitude of the P-Mad profile (i.e. the concentration at A/P compartment boundary, x = 0) plotted versus the posterior compartment length. Each dot represents a disc and is color-coded according to its age. The linear regression with 95% confidence interval (gray area) and its

(PDF)

A second dataset for Brk. (A–B) The amplitudes of the Brk profiles (i.e. the peak concentration in the lateral region) at 15% ventral offset versus the posterior compartment length for dataset 1 (A) and dataset 2 (B). Taking the extremes, the ratio between the extreme values of the Brk amplitudes (Amp) are max(Amp)/min(Amp) = 48.7 for dataset 1 and max(Amp)/min(Amp) = 48.3 for dataset 2, respectively. (C) Brk profiles averaged per TC with 15% ventral offset (dataset 2). (D) Profiles in (C) in relative positions. (E) Profiles in (D) with normalized amplitudes. (F) Brk scaling for several threshold concentrations. Error bars represent the 95% confidence intervals. To compute scaling at each position, the Brk profiles with normalized amplitudes were used (dataset 2). (G) Brk profiles were fitted with a decaying exponential function (dataset 2) to obtain the decay length λ_{Brk} of the profile. For each disc, the average P-Mad concentration at the position x = λ_{Brk} was plotted against the L_{p} of the disc. The weighted linear regression with 95% confidence interval (gray area) and its

(PDF)

_{p} for each disc, at 15% ventral offset. (D) _{p} show hyper-scaling due to the increasing dad-GFP levels, while positions posterior to it show hypo-scaling.

(PDF)

Sal amplitudes increase over time and the posterior Sal domain hyper-scales. (A) Representative Sal contour plots for each TC. Lower concentrations are in light blue, higher concentrations in pink. (B) Sal profiles averaged per TC at 15% ventral offset. (C, E) Sal amplitudes (i.e. the maximum concentration in the vicinity of the A/P compartment boundary at x = 0) for each disc at 15% ventral offset versus the anterior (C) and posterior (E) compartment lengths. (D, F) Sharpness of the Sal domain boundary (n) in the anterior (D) and the posterior (F) compartments plotted against tissue size. (G) Scaling and correlation of the Sal domain boundary in the posterior compartment at 15% ventral offset. (H–I) The average P-Mad (H) and Brk (I) concentrations at the position x = K_{Sal_P} (Sal boundary in the posterior compartment) were plotted against the L_{p} for each disc. The weighted linear regression with 95% confidence interval (gray area) and its

(PDF)

Omb domain scales with tissue size. (A) Representative Omb contour plots for each TC. Lower concentrations are in light blue, higher concentrations in pink. (B) Omb profiles averaged per TC at 15% ventral offset. (C) Omb amplitudes (i.e. the concentration at A/P compartment boundary, x = 0) versus the posterior compartment length for each disc at 15% ventral offset. The linear regression with 95% confidence interval (gray area) and its

(PDF)

Lack of size adaptation of P-Mad profiles in ^{2–5}^{2–5}_{p}, while positions in the anterior compartment are normalized relative to the anterior compartment length L_{a}. (A′–D′) The amplitude of the P-Mad profile in ^{2–5}

(PDF)

Expression patterns of target genes in ^{2–5}^{2–5}^{2–5}^{2–5}

(PDF)

Omb and Brk domains overlap extensively in ^{2–5}^{2–5}^{XA}+/−^{2–5}

(PDF)

Decay length λ correlates with tissue size. (A) P-Mad, Brk, and _{p}. The text in the plot shows the average λ/L_{p} ratio with its standard error. Relationships obtained from the linear regression are displayed in the boxes on the right. Note that L_{p} is measured along the D/V compartment boundary. (B) Same as (A), but the

(PDF)

Changes in P-Mad, Brk, and _{p}, the log-concentration as a function of L_{p} was plotted for each disc (not shown). The linear regression yields an estimate of dlog(c)/dL_{p}, where c is the protein concentration. Here, the relative increase in protein concentration for each of these relative positions in the pouch is shown (Δlog(c) = 1 represents a 100% increase from TC1 to TC5):

(PDF)

We thank Thomas Schaffter, Simon Restrepo, and Konrad Basler for their input during the initial setup of this project. We are grateful to Vincent Dion, Georg Halder, Amanda Ochoa-Espinosa, and Gerald Schwank for critical reading of the manuscript, and to Oguz Kanca and Heinz-Georg Belting for discussions. Laurent Gelman (FAIM, FMI, Basel) provided us with valuable advice regarding linear imaging, and Emmanuel Caussinus wrote a macro for ImageJ. We thank Stefan Harmansa for the Dpp-GFP image. The Ptc and Wg monoclonal antibodies developed by I Guerrero and SM Cohen, respectively, were obtained from the Developmental Studies Hybridoma Bank developed under the auspices of the NICHD and maintained by The University of Iowa, Department of Biology, Iowa City, Iowa.

after egg laying

anterior-posterior

Brinker

Daughters against Dpp

Decapentaplegic

dorso-ventral

Mothers against Dpp

Optomoter blind

phospho-Mad

Patched

Spalt

Schnurri

time class

Wingless