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WIREs Dev Biol
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The wing and the eye: a parsimonious theory for scaling and growth control?

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How a developing organ grows and patterns to its final shape is an important question in developmental biology. Studies of growth and patterning in the Drosophila wing imaginal disc have identified a key player, the morphogen Decapentaplegic (Dpp). These studies provided insights into our understanding of growth control and scaling: expansion of the Dpp gradient correlated with the growth of the tissue. A recent report on growth of a Drosophila organ other than the wing, the eye imaginal disc, prompts a reconsideration of our models of growth control. Despite striking differences between the two, the Dpp gradient scales with the target tissues of both organs and the growth of both the wing and the eye is controlled by Dpp. The goal of this review is to discuss whether a parsimonious model of scaling and growth control can explain the relationship between the Dpp gradient and growth in these two different developmental systems. WIREs Dev Biol 2015, 4:591–608. doi: 10.1002/wdev.195 This article is categorized under: Establishment of Spatial and Temporal Patterns > Gradients Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing
Wing versus Eye. SEM images of the entire fly (a), the wing (b), and the eye (c). Confocal microscopy images of the wing (d, green signal is the fluorescently labeled Decapentaplegic (Dpp), the wing disc is outlined by the white punctuate line) and eye (e, the red signal is an antibody staining of Hairy, the target gene of Dpp, the eye disc is outline by the white punctuate line) discs with corresponding Dpp spatial profiles (f and g). Letters A and P indicate the anterior and the posterior compartments, respectively. The red arrow in (g) represents the direction of the movement of the furrow.
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The temporal growth rule. (a and b) Relative temporal differences () can explain the uniform spatial proliferation profile in the wing disc and the spatial profile of proliferation in the eye. (c and d) General temporal growth rule expressions for and the growth rate (g). From these general expressions, the specific cases of the wing (e) and the eye (f) can be derived. (c) This general equation accounts for all the inputs into (relative changes of Dpp in time) both in the wing and the eye: (i) The change of the amplitude Cmax with time (); (ii) Changes due to the movement of cells relative to the Dpp source (and therefore relative to the Dpp gradient) with the velocity vcell. There are two components of this movement: the movement of the source with the velocity vs and the movement due to the proliferation of cells with the velocity vg; (iii) Because of the gradient scaling with La, the term captures the change (increase or decrease) in the signaling levels of a cell, when La expands or shrinks, which is accompanied by an expansion or shrinkage of the gradient. (e) The temporal growth rule expression for the case of a system with a nonmoving Dpp source (vs = 0) and homogeneous growth. Therefore, (Drosophila wing disc). (f) The temporal growth rule expression for the case in which the source moves (vs ≠ 0) and the target tissue length (La) and the gradient amplitude (Cmax) are constant in time. The sole cause of increase of cellular Dpp concentration is therefore the movement of cells upward the gradient due to the movement of the furrow (Drosophila eye disc during the developmental time between 65 and 85 h after hatching).
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Growth rules. (a) Absolute concentration model: the absolute concentration is not homogeneous in space thus cannot yield homogeneous growth. (b) In combination with the effect of the mechanical stress on growth, the absolute concentration model can explain homogeneous growth. (c) Spatial differences model. Spatial differences are not homogeneous in space and cannot explain homogeneous growth. (d) Relative spatial differences are spatially uniform and can explain homogeneous growth.
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Scaling mechanisms. (a) Expansion–repression mechanism. (b) Expansion–dilution mechanism. (c) Two opposing gradients. (d) In the case of the advection–dilution scaling mechanism, the spread of the morphogen in the target tissue is described by the kinetic parameters of morphogen transport: the diffusion and the degradation of the morphogen and by two phenomena related to the growth of the tissue: advection and dilution.
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Decapentaplegic (Dpp) gradient and proliferation profiles. (a) Dpp is secreted from a distinct source in the center of a wing disc (in red) and spreads in the target tissue to form a gradient of concentration. (b) The Dpp concentration profile in the target tissue of the growing wing disc increases in width and in amplitude from t1 to t2. (c) The proliferation rate in the wing disc is roughly homogeneous in the entire target tissue. (d) In the eye disc Dpp is transcribed at the morphogenetic furrow (in red) that separate the differentiating ommatidia from the anterior undifferentiated cells (on the right of the Dpp source). (e) The furrow sweeps across the tissue from anterior to posterior. This results in a moving Dpp gradient from t1 to t2. (f) As the Dpp gradient starts moving, growth in the anterior target cells becomes strongly position‐dependent: there is a peak of proliferation in front of the furrow. Anterior to this peak the growth rate decays.
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