Introduction

The size of some organs is remarkably precise [1]. Although this precision is a functional need, it is not easily explained [2,3]. Most organs are specified as small primordia whose growth is exponential. However, exponential growth is prone to amplify the noise that is inescapable to biological processes. This fact has led to the proposal that organ development must be subject to mechanisms of feedback control [3], which, in the engineering sense, reduce their internal “developmental instability” [4] and increase the precision with which organs reach their species-specific size. Some organs that undergo constant tissue renewal, like the mammalian olfactory epithelium, maintain their size homeostasis through integral feedback [5]. Some other organs, though, grow to a size that, once reached, cannot be further modulated. This is the case of insects. After their last molt, the adult organs cease growth and then become covered in a rigid chitin exoskeleton that precludes further size regulation. The eye of Drosophila fruit flies serves as a good example of this type of organ growth: In Drosophila, the end point of eye development is reached when all retinal progenitor cells differentiate, as differentiation is accompanied by the exit of the cell cycle. Three features should have resulted in a strong evolutionary pressure to maximize the precision in eye size: First, size impacts vision directly, as image resolution and contrast sensitivity is proportional to the number of light sensing units in the eye [6]; second, making and maintaining the eyes is energetically very expensive [7], so there is a pressure to match eye size to vision needs; and third, left and right eyes must survey a symmetrical part of the space, so eye asymmetry, which could be driven by developmental noise, should be minimized. In this paper, we investigate the mechanism by which the Drosophila eye ensures its size precision as an example of organ size control.

The development of the Drosophila eye takes place as a wave of differentiation crosses the eye primordium during the last larval stage (Fig 1A and 1B). As the wave moves, proliferative progenitors anterior to the wave are recruited as differentiating retinal cells that exit the cell cycle. Final eye size is attained when the differentiation wave reaches the anterior-most region of the primordium: With no remaining progenitors, which are the source of growth, the process ends. The movement of the wave is driven primarily by 2 secreted signaling molecules. The first of them is Hh (hedgehog). Hh’s major role is the induction of differentiation of progenitor (“G”) cell into retinal (“R”) cells [8], a role that is shared by its homologue Shh in the differentiation of the ganglion cells of the vertebrate retina [9]. Hh, initially expressed adjacent to the eye primordium, contributes to initiate R differentiation. Once initiated, R cells produce Hh themselves [10,11], resulting in the self-sustained progression of a differentiation wave [12]. The second signal is a BMP2/4 homologue, Dpp (decapentaplegic). dpp expression is induced by Hh in the newly recruited retinal cells (“Rn”) [13,14]. Dpp, by repressing the progenitor transcription factor Hth (homothorax), increases the propensity of progenitors to enter differentiation [15,16]. However, and in contrast with Hh, whose expression is maintained in differentiated R cells, Dpp is expressed only transiently: As newly recruited Rn cells progress along their differentiation to R, dpp expression is turned off [13,17,18]. Thus, a stripe of Dpp marks the front of the differentiation wave (Fig 1A). This process is schematically represented in Fig 1C.

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Fig 1. Eye development and the effects of different genetic manipulations on the distribution of eye size (“rE”) and signed Fluctuating Asymmetry index (“sFAi”).

The eye primordium ((a) “E”, outlined) develops into the adult eye (b) through the action of a differentiation wave that sweeps across it (arrow). (a) Eye primordium (“E”) of a Hh:GFP; dpp-Z larva. The differentiation wave-front expresses dpp-Z. Posterior to it further differentiated photoreceptors lose dpp expression and express hh. (b) Lateral view of an adult Drosophila eye. (c) The recruitment of proliferative progenitor cells (“G”) into early differentiating (dpp-expressing) retinal cells (“Rn”) and then into terminally differentiating (non-dpp-expressing) retinal cells (“R”) is controlled by 2 signaling molecules, Hh and Dpp. (e-h) Frontal views of female heads of the indicated genotypes, with the eyes colored for better visualization. (e) Control, optix>+, (f) optix>tkvRNAi, (g) optix>tkvRNAi + dadRNAi, (h) Bar (B) mutant. See main text for details. (i, j) rE (i) and sFAi (j) distributions of the indicated genotypes. Each violin plot includes the male (left) and female (right) distributions, which were not significantly different from each other in any genotype. The median of each distribution is indicated (solid and dashed line: male and female, respectively). The predicted rE median for each genotype and the statistical model from which they are derived can be found in S1 Table. The variances of each genotype were compared against the variance in the control group (optix>+) in rE and sFAi (S1 Table). (*): p < 0.05; (**): p > 0.01; (***): p < 0.001. Eye area is measured relative to the total head area and expressed as a percentage in this and subsequent figures. The data underlying the graphs shown in the figure can be found in “Fig 1_S6Fig 1_data” in the Supporting information file S1 Raw Data.

https://doi.org/10.1371/journal.pbio.3002450.g001

Results

To ensure that the target, species-specific final eye size is reached with precision, the rates of growth and of differentiation need to be coordinated within the eye primordium [6,19,20]. For example, a transient halt of the differentiation wave would produce some excess of progenitor cells and a concomitant deviation from the target size—unless this halt were communicated to the progenitors as a negative feedback on their rate of growth. This feedback could be implemented either by slowing down progenitor proliferation or by curving the excess of progenitor cells through cell death (we do not consider a change in cell size as this change would alter the size of the ommatidia and, thus, their optical properties). We noticed that, in wild-type control eye primordia, the apoptosis signal detected using an antibody against the activated form of Caspase-3 is usually very low. However, if an antibody against the cleaved, active form of the terminal caspase Dcp-1 [21] is used instead, we detected a stripe of apoptotic cells just anterior to the differentiation wave-front (S1 Fig). Likely, the activation of Cas-3 is more brief than the activation of Dcp-1 during the apoptotic process, making detection of apoptosis easier with Dcp-1 as a marker.

In any case, we were intrigued by this localized apoptosis happening in normal eye primordia and asked what its role could be. To answer this, we blocked apoptosis by driving, specifically anterior to the differentiation wave-front, a polycistronic RNAi against reaper, hid, and grim, the 3 major proapoptotic genes in Drosophila (optix>Reaper,Hid,Grim-RNAi, abbreviated optix>RHGRI [22]). These flies showed 2 major phenotypic changes: First, the median eye size (“rE” = average intraindividual eye area relative to head area, expressed as percentage) was larger than those of controls (optix>+), and, second, the distribution of eye sizes was also significantly broader (Fig 1I and S1 Table). We do not detect significant changes in ommatidial size in these (and other; see below) genotypes, indicating that the alterations in eye size are attributable to variation in ommatidial number (S2 Fig). When we measured the apoptotic index of optix>RHGRI, it was smaller than that of optix>+ and very close to zero (Fig 2; the apoptotic index is measured as the ratio of Dcp-1 positive pixels relative to the total pixels of the region anterior to the morphogenetic furrow of the eye primordium; see Materials and methods). The increased dispersion in the distribution of eye size is indicative of a loss in size precision. The fluctuating asymmetry index (FAi), which measures the disparity between left and right organs within the same individual, has also been frequently used as a measure of precision as it captures the sensitivity of the process to developmental noise [23]. The FAi is normally calculated as the absolute value of the normalized difference between the size of the left (L) and right (R) organs from the same individual. Here, we use the signed FAi (“sFAi”) to have into account the sign of the asymmetry, (L−R)/(L+R), which allows to compare the asymmetry across different genotypes based on the amplitude of the distribution of this metric for each of them (Fig 1J and S1 Table). In apoptosis-blocked individuals, the variance of sFAi increased significantly as well (Fig 1J and S1 Table). To control for potential nonspecific effects of RNAi overexpression on eye size and its variability, we drove a “neutral” RNAi against the fluorescent protein Cherry (optix>CherryRI) and observed that it did not affect neither of the 2 parameters when compared to control (optix>+) or wild-type (Oregon-R) flies (see S3 Fig).

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Fig 2. Eye size reduction and apoptosis induced by attenuation of the Dpp signaling pathway can be reverted by blocking Dad.

Lateral views of adult eyes (a-c) and L3 eye discs, stained with Dcp-1 (and counterstained with rhodamine phalloidin, “actin”) (a’-c’) of the indicated genotypes. (d) Distribution of apoptosis intensity in L3 discs of the indicated genotypes. Blocking apoptosis driving the UAS-RHG-RNAi reduces the apoptosis caused by tkv attenuation (optix>tkvRI + RHGRI). The statistical analysis corresponding to these data can be found in S2 Table. (*): p < 0.05; (**): p < 0.01; (***): p < 0.001. The data underlying the graphs shown in the figure can be found in “Fig 2_data” in the Supporting information file S1 Raw Data.

https://doi.org/10.1371/journal.pbio.3002450.g002

These results pointed to a role of developmental apoptosis in controlling eye size and its precision. But, in order to be involved in such control, the apoptotic rate in progenitors should be coupled to the rate of eye differentiation. This communication between progenitors and differentiating cells might be exerted by either of the 2 major signals in eye development: Hh and Dpp.

Intuitively, if one of these 2 signals were to be used to convey feedback information to progenitors about the status of retinal differentiation, Dpp would seem a better candidate. Although both Hh and Dpp regulate progenitor gene expression [24], Dpp, by being expressed transiently, can be better used as readout of the rate of retinal differentiation. In contrast, Hh is constantly produced in R cells, regardless of whether the wave is moving or not. If Dpp were used in a feedback control mechanism, it would be expected that the attenuation of its signaling pathway in progenitors should lead to a decrease in final eye size precision. In addition, prior work on dpp mutant alleles had shown an increase in apoptosis in the mutant eye primordia [17,25], reinforcing the idea that Dpp could be this coupling signal.

To test this point, we attenuated the Dpp pathway specifically in eye progenitors during development, by targeting the expression of an RNAi against the Dpp receptor tkv (thickveins) [26] in these cells (optix>tkvRI). This treatment caused 2 effects: First, the median eye size was reduced (Fig 1E, 1F and 1I and S1 Table). This effect—eye reduction—had been described previously for mutant alleles of dpp [27] and explained as a consequence of Dpp’s requirement in progenitor cell recruitment [24,28]. The eye size reduction was concomitant to a dramatic increase of both the dispersion of the eye size distribution and of its sFAi (Fig 1J and S1 Table), something expected if Dpp were involved in feedback control. To confirm that this phenotype resulted from the attenuation of the Dpp pathway, we simultaneously drove expression of RNAis against tkv and against dad (daughters against-dpp), a Smad molecule that acts as a feedback inhibitor of the pathway [29,30]. In individuals of this genotype (optix>tkvRI+DadRI), the eyes almost recovered their control size (Fig 1E, 1F and 1I and S1 Table). Similarly, the dispersion of eye size distribution as well as the sFAi decreased towards values closer to control, although not fully (Fig 1J and S1 Table). The attenuation of the tkv-RNAi effect cannot be attributed to its weaker expression caused by the introduction of a second UAS sequence (UAS-Dad-RNAi) in the genotype (see S4 Fig).

Next, we confirmed that attenuation of the Dpp pathway (optix>tkvRI) caused a dramatic quantitative increase in Dcp-1 apoptotic signal (Figs 2A, 2B, and S8 and S2 Table), while the mitotic rate of progenitors remained unaffected (S7 Fig), and that this increase in apoptosis was rescued by coexpression of the Dad-RNAi (optix>tkvRI+DadRI) (Fig 2C). The expression of UAS-RHGRI alone or in combination resulted in the reduction of apoptosis almost completely (Fig 2D).

Therefore, we expected that any perturbation affecting the coupling between retina and progenitor apoptosis would not be able to fully rescue the size precision observed in control flies (both the dispersion of the eye size distribution or the sFAi). This was the case in all the experiments in which the feedback between retina-produced Dpp and apoptosis was disrupted, either by artificially up-regulating the Dpp pathway (expressing dad-RNAi) or by blocking apoptosis (expressing RHG-RNAi) (Fig 1I and 1J and S1 Table).

To further substantiate our results, we decided to analyze the phenomenon of eye size control in another mutant situation in which the dpp pathway was affected. We chose the Bar (“bar-eyed”) mutant. Bar-mutant eyes are reduced [31] (Fig 1E and 1H), and this size reduction is associated with the control of dpp expression and an increased apoptosis during larval development [32]. In Bar eye primordia, we detected a fragmented dpp expression, monitored by the dpp-Z transcriptional reporter, and an increased Dcp-1-positive apoptosis (S5 Fig). Bar eyes are smaller and more variable (Fig 1I) as well as more asymmetric (Fig 1J) than control flies (see also S1 Table). Similarly to what happened in our previous experiments, in which the Dpp pathway was attenuated directly by targeting the Dpp receptor with an RNAi, either blocking apoptosis (Bar; optix>RHGRI) or derepressing the Dpp pathway (Bar; optix>DadRI) partly rescued eye size (Fig 1I) and reduced both eye dispersion (Fig 1I) and their fluctuating asymmetry (Fig 1J and S1 Table).

The results obtained so far indicated that a major role of Dpp during eye development was the regulation of developmental apoptosis. Losing this regulation, by either blocking apoptosis directly or by “disconnecting” retina and progenitors by the attenuation of Dpp signal (by tkvRI expression or in Bar mutants), led to a decreased size precision. Therefore, not only the size of the eye but also its precision is under the control of the Dpp pathway.

The fact that the effects on eye size and precision caused by dpp signaling attenuation were almost fully rescued by preventing apoptosis pointed to the regulation of this process as a key phenomenon. In order to explore further how the regulation of apoptosis impinges on eye size, we built and analyzed a mathematical model of the process. With this model, we first explored whether our description of the biological phenomenon is complete by testing if the model recapitulates the biological results when parameterized using experimental measurements.

Our model comprises G (progenitors), Rn (newly differentiated retinal cells, expressing dpp), and R (differentiating retinal cells, no longer expressing dpp but producing Hh) cells as variables, as well as their transformations: proliferation of progenitors (“self-renewal”: G ➔ G + G), apoptosis of progenitors (G ➔ ∅), initial differentiation of progenitors into dpp-expressing early retinal cells (G ➔ Rn) and final differentiation of these cells into hh-expressing photoreceptors (Rn ➔ R) (Fig 3A and 3B), and includes noise in all 4 differentiation steps. Its full description is available as S1 Materials. Conceptually, our model expresses the rates at which the G, Rn, and R cells change over time as in Fig 3c, where the variables influencing each of the steps (e.g., “proliferation”) are within the parentheses (e.g., “G, Rn”).

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Fig 3. Overview of the model of the G➔Rn➔R including apoptosis (∅).

(a) Schematics of the process. R cells stimulate the differentiation process (by expressing Hh). Rn cells negatively regulate apoptosis (by producing Dpp). G cells can divide, die, or progress further into differentiation by transiting to Rn. (b) This process, schematized in space. MF: morphogenetic furrow is the differentiation wave-front that moves (arrow) from posterior (right) to anterior (left). L_A, L_P are the maximum distances anterior and posterior to the MF, respectively. The L_p can be used as a proxy for developmental time: As the MF moves with constant speed, L_p increases as time passes. L_A corresponds to G cells. L_p comprises Rn (orange bar) + R cells. (c) “Qualitative” model. (d) Typical temporal profiles of all populations as predicted by the model. (e) Fit of the model to experimental data (L_AP as minor axis of elliptical fits of eye primordia (blue points) and L_A = L_AP − L_p (orange points)). Each curve is an independent realization produced with the optix>+ parameter set (see main text and S1 Materials for details), differences between curves are an effect of the stochastic nature of the model.

https://doi.org/10.1371/journal.pbio.3002450.g003

The key processes are modeled as follows: Apoptosis is a decreasing function of the Dpp-producing Rn cells, because the more Dpp, the less apoptosis, and is proportional to the number of progenitors (G). All G cells not entering apoptosis will be proliferating. As for the rate of G to Rn differentiation (“early differentiation”), we have considered 2 factors. First, the activation of differentiation would depend on an increasing function of the Hh-producing R cells. Second, the induction of G cells to differentiate is limited to the range of action of Dpp produced by Rn. Therefore, since beyond a certain point having more G cells will not result in increased differentiation (that is, those G cells out of the range of action of the signals will not be recruited), we modeled the function describing G growth as a saturating sigmoidal function, with the condition that once the G population has been exhausted, no further differentiation can occur. In addition to Dpp (represented by the action of Rn) also Hh has a contribution to the differentiation of G cells [16,24,33], which is represented by the action of the Hh-producing R cells. Finally, the final differentiation, or transition from Rn into R, can be expressed as being proportional to Rn, indicating that Rn differentiates into R cells with a constant pace, simplifying a complex process of successive cell induction leading to the formation of the ommatidial cell types [34]. However, eye size does not depend on this latter process, as the number of ommatidia and, therefore, the size of the eye, is directly related to the number of G cells that are recruited as Rn cells. The expressions of the relevant functions (a(Rn), f(G) and h(R)) can be found in the full description of the model in S1 Mathematical Model. These functions allow us to model the RNAi treatments as well.

With this model, we can calculate the evolution of all these cell populations over time (Fig 3D). First, we fitted the model to an experimentally determined growth curve of the eye primordium (Fig 3E; data from [35]). Since the differentiation velocity is about constant during most of development [35,36], the width of the R + Rn domain (the distance between the posterior margin of the primordium to the differentiation wave-front, called “posterior length”, or “Lp”) is a proxy for elapsed developmental time, and we used it as a time axis (as in [35]). The fitting demanded that the growth rate of G cells declined over developmental time, something that had been shown experimentally [36,37]. With these parameters, the fitting of the model to the data was very good, indicating that the model captured the biology underneath the control of eye size and its variability (Figs 3E, 4A, and 4B).

Despite the excellent qualitative agreement of theory and experiment, it is important to remark that this is a very minimalistic model. The concentrations of signaling molecules Dpp and Hh are not explicitly modeled; instead, we model their effect as being proportional to the width of the regions producing them, Rn and R, respectively. In doing so, we are formulating a mean field model: We do not model the spatial dynamics of morphogen gradients. Our rational for this simplification is not simplicity, but data availability: We have not measured those gradients, so their inclusion in the model would be unconstrained. In principle, this simplification would undermine the power of our model to reproduce experiments, but we found that this worked fine except for one aspect: Progenitor cells can only differentiate when they are close to the differentiation wave-front. In a mean field setting without an explicit modeling of space and gradients, there is no way to model this constraint from first principles. To restrict progenitor differentiation G ➔ Rn to the vicinity of the morphogenetic furrow, we introduce an ad hoc length scale of differentiation modeled through a sigmoidal function with a single parameter, K_G. This allowed to capture a spatial effect in a phenomenological way, and as our sensitivity analysis of the model shows (see the “S1 Mathematical Model” supporting information), the model results are very insensitive to the exact value chosen for this parameter. Finally, since we do not model individual cells, our model does not capture the effects of cellular variability. However, our formulation of fluctuations using Langevin dynamics can be rigorously derived for the network of interactions shown in Fig 3A, and this framework is flexible enough to allow distinct modeling of the different sources of noise in our model. Table 1 points out some of the biological aspects in our model and the assumptions and simplifications we have made to formalize them mathematically.

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Table 1. Simplifications in the formalization of some biological processes and how these have been modeled.

https://doi.org/10.1371/journal.pbio.3002450.t001

Since the model was able to recapitulate well the dynamics of eye differentiation and the final eye size and its precision, we asked which conditions allow the system to reach robustly a final size. This can be done by carrying out a linear stability analysis of the system. The finalization of the process is attained when G = 0 and Rn = 0: Without any G and Rn cells left, the eye has reached its final size. The stability of this size means that for low G and Rn values, close to the end of the process, it is irreversible and effectively G and Rn will go to zero. Our analysis (see Linear stability analysis of the deterministic model in S1 Mathematical Model) shows that Dpp regulates stability through apoptosis, and Hh through differentiation: high apoptotic probability or differentiation rate favor stability. Actually, we derive a formula predicting that the maximum potential probability of apoptosis (that would be observed only in the absence of Dpp) of 50% would be enough to ensure stability by itself. This is not far from 40% of apoptosis determined experimentally in optix>tkvRI. Therefore, high propensity of apoptosis in progenitor G cells seems to be a requirement for robust size. Next, we used our model to predict the effects that noise would have on eye size in different genotypes with different rates of apoptosis.

We reasoned at the onset that regulating organ size would rely on the differentiating retina feeding information about its status on progenitor growth rates (something we have shown to occur through the modulation of apoptosis). Therefore, we simulated the effects of increasing the noise in the recruitment of Rn cells (“initial differentiation”), which are the source of Dpp, on eye size and its variation in 3 genotypes: two in which apoptosis is possible (control (optix>+) and dpp signaling attenuated (optix> tkv-RNAi)) and one in which apoptosis is blocked (optix>RHG-RNAi) (Fig 4C). While increasing noise in Rn affects very little the median eye size in the 2 genotypes where apoptosis is allowed, it results in a steady increase of eye size if apoptosis is blocked (until the noise levels are very high, when allowing apoptosis or not becomes irrelevant). This computational result reinforces the idea that the dpp-sensitive apoptosis of progenitors is instrumental in maintaining the developmental stability of eye size.

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Fig 4. Assessment of the degree of fit between experimental and computational results and effects of increasing noise strength on median eye size (rE).

Using our computational model, sets of 1,000 eye sizes were simulated for each condition and from these, samples of equal size to the experimental samples were taken to calculate the medians of rE (a) and interindividual FA (FAn) (b). The sampling was repeated 1,000 times to generate the distribution of medians shown in the graphs, where each point in gray corresponds to the median of one of those 1,000 samples (“Computational data”). The triangles represent the medians of the experimental results (“Real data”) of all genotypes. The computational data were scaled such that the median rE of experimental control coincides with the center of the distribution for the computational control group. The experimental medians for both metrics fall within the respective computational distributions for all genotypes. This is especially striking for the rE medians, for which the experimental medians coincide almost perfectly with the most probable value of the computational median distributions. This fact indicates that the model captures the process of eye development in those different genotypes very accurately (See S1 Statistical Methods for further details). (c) If apoptosis is blocked in the computational model (by strongly reducing the apoptotic rate of progenitors, equivalent to optix>RHGRI), eye size increases more rapidly than in the other 2 genotypes, in which apoptosis is allowed, until noise is too high (beyond 102), point at which allowing apoptosis or not becomes irrelevant. Computational results. Data for each point is from 200 simulations per genotype. The horizontal axis represents 1/V_p (see S1 Mathematical Model supporting information file). The data used in the graphs shown in the figure can be found in “Fig 4A,4B_data” in the Supporting information file S1 Raw Data.

https://doi.org/10.1371/journal.pbio.3002450.g004

In his paper of 1942, Waddington noted that while the morphological phenotype of wild-type strains was usually developmentally stable, or “canalized,” “there is scarcely a mutant which is comparable in constancy with the wild type” [4]. That is, the phenotype of mutants is often “decanalized.” We would expect decanalization of the phenotype if the mutants were affecting control feedback mechanisms. The observation that this decanalization is frequently exhibited by mutants with overt morphological alterations might indicate that most genes with major roles in the development of an organ are also part of the feedback control mechanism themselves or affect this mechanism. In the case of eye development, these would be mutants uncoupling retinal differentiation and progenitor growth, blocking Dpp reception or its control over apoptosis in progenitors. However, perturbations that maintain the feedback mechanism intact might result in phenotypic changes, but without major effects on precision. In the eye, one such perturbation could be the variation of progenitor proliferation rate. This is an input to the system and subject to the feedback control, but not itself part of the feedback mechanism. Indeed, the sensitivity analysis of our computational model indicates that, while eye size is highly sensitive to variations in progenitor growth rate, the FAi is much less so (see Fig 12 in S1 Mathematical Model)—that is, despite a major phenotypic change (eye size), the result of this perturbation should remain canalized. This perturbation of eye development can be induced in vivo by the genetic overexpression of the mitogenic cytokine and ligand of the JAK/STAT pathway unpaired 1 (Upd) [38]. Expression of Upd using the eye-specific enhancer GMR results in overgrown eyes [38], about 1.4 times those of wild-type flies (S9A and S9B Fig). Although there is interindividual variability in rE (S9C Fig), the developmental noise of eye size, measured by its FAi, remains similar to that of control animals (S9D Fig). This latter result—the maintenance of organ size precision—is expected as long as apoptosis is operating under feedback control. Indeed, GMR>Upd discs exhibit apoptotic signal of progenitor cells (S9E and S9F Fig). Therefore, the mechanism controlling eye development can accommodate changes in final organ size while maintaining its precision as variations in progenitor cell proliferation do not interfere with the feedback control.

Discussion

For organs to attain a final size with low variability, mechanisms of control must exist to reduce the effects of developmental noise. In this paper, we describe one such mechanism, in which the processes of eye growth and differentiation are coupled through a feedback control. In this feedback, the discrepancies between the rates of growth and differentiation of progenitors are adjusted through the modulation of the progenitor cells’ propensity to enter apoptosis, so that any production of progenitors in excess is curved, as a proportion of these progenitors will not receive sufficient Dpp signaling to overcome apoptosis. In this way, it is the Dpp production, which, acting as a surrogate of the process of differentiation, feeds back onto the growth rate of progenitors, a rate that depends on their combined proliferation and apoptosis (this latter Dpp-signaling dependent). When analyzing our data, comparing the actual FAi versus the fluctuating asymmetry of randomized pairs generated from the same experimental data (FAn), we observed that FAn was slightly larger than FAi, and this difference (FAn>FAi) was invariant across genotypes. This indicated a small but consistent effect of the individual. Therefore, although most variation in size can be attributed to organ-autonomous variation, the 2 eyes from an individual are slightly correlated (S6 Fig). This is expected though, as it has been shown that, besides organ-autonomous mechanisms of growth control, the growth discrepancies among organs in an individual affect the systemic growth of the organism through neuroendocrine communication mediated by insulin-like peptides [39,40]. In addition, each larva might be exposed to small microenvironmental variations during its growth [41]. Still, our results indicate that the feedback mechanism we have described operates mostly in an organ-autonomous manner.

Our experiments show that a major role of dpp signaling during eye development is the regulation of apoptosis, since the effects on eye size caused by attenuating this pathway are almost fully recovered just by blocking it. This role is very different from the function in cell differentiation that has normally been attributed to dpp during eye development [28]. We note, however, that in our experiments, by using RNAi, we are attenuating, rather than fully abrogating, dpp signaling. This could mean that the low levels of signaling presumably remaining could still participate in cell fate specification. This would be similar to the situation found in the wing disc, in which different signaling thresholds are important for distinct functions, with high dpp signaling being necessary for wing patterning, while lower levels sufficing for tissue growth [42–44]. Recently, the Kumar laboratory showed that the main role of the Pax6 gene eyeless (ey), a gene essential for normal eye development [45], is the activation of dpp transcription [46]. Interestingly, loss of ey function causes abundant cell death in eye progenitors [47]. The role of the dpp pathway in preventing progenitor cell death we have discovered would, in principle, connect ey function to cell death. At present, we do not have a mechanistic explanation for why eye progenitor cells are prone to die (a tendency akin to the “death by default” state of cells proposed by Raff [48]), or how dpp signaling prevents it, but these are very relevant questions worth pursuing. However, organ size control does not come for free: It requires extra energy expenditure in generating progenitors that are going to undergo apoptosis. Note that these progenitors are perfectly normal cells: If their death is prevented genetically, they become incorporated into eyes (that is why blocking apoptosis results in larger eyes). Our model also suggests that, in order to reproduce the experimental data, the rate of apoptosis should be the noisiest variable. Therefore, precise control of eye size requires an apparently wasteful and noisy mechanism.

Is this control mechanism, based on regulating the rate of cell death of proliferating progenitors, working beyond the eyes? Although not tested formally, the result from Neto-Silva and colleagues, showing that wing asymmetry increased dramatically in mutants for the apoptosis regulator hid [49], suggests that apoptosis regulation may be involved in the control of developmental stability of wings too. Beyond Drosophila, developmental apoptosis is very frequent [50] and, in some cases, associated to the regulation of cell number, with the mammalian immune cells [51] and the nervous system [52] being striking examples. Therefore, it seems very possible to us that mechanisms similar to the one we have described here will use the feedback modulation of apoptosis as a means not only to controlling organ size but also size robustness in other developmental systems as well.

Materials and methods

Supporting information

Acknowledgments

We thank Mustafa Khammash, Maike Kittelman, and Alistair McGregor for discussions; Erika Bach for the GMR-Upd strain, and ALMIA/CABD (especially Jose M. Urbano), for imaging support.