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Curr Opin Genet Dev
2011 Dec 01;216:704-10. doi: 10.1016/j.gde.2011.07.011.
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Scaling of morphogen gradients.
Ben-Zvi D
,
Shilo BZ
,
Barkai N
.
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Individuals of the same or closely related species can vary substantially in size. Still, the proportions within and between tissues are precisely kept. This adaptation of pattern with size termed scaling, is receiving a growing attention. We review experimental evidence for scaling, and describe theoretical models for mechanisms that scale morphogen gradients. We particularly note the Expansion-Repression mechanism, in which a diffusible molecule that positively regulates the morphogen gradient width is repressed by morphogen signaling. The Expansion-Repression circuit provides scaling in a robust manner and is readily implemented by a host of molecular mechanisms. We suggest means for identifying such a circuit in a system of interest.
Figure 1. Scaling of morphogen gradients. (a) Left panel: the morphogen gradient paradigm: the morphogen is secreted from a small number of cells (secreting cells, blue) and creates a gradient along a field. Cells close to the morphogen source sense high levels of the morphogen, above threshold T1, and differentiate into fate X (dark gray). Cells that sense intermediate levels, between thresholds T1 and T2 adpot fate Y (medium gray). Cells far from the source sense low levels, below threshold T2 and differentiate into fate Z (light gray). Right panel: general equation describing a morphogen gradient. M is the morphogen concentration, D(M,t) and f(M,t) its diffusion and degradation terms, which may depend on the morphogen concentration through feedbacks and on time. η(t) is the morphogen production term, typically restricted to a small group of cells at the edge of the field {x|0 < x < xorg}. The solution for this equation, M(x,t,L,D,f,η), will scale with size if it is a function of x/L, the relative position rather than of x, with L the size of the field. Robustness to the morphogen production terms implies that the solution is independent of the value of η. (b) Modulation of morphogen flux does not account for scaling. Increasing morphogen flux in larger fields changes the proportions between different cell fates in the field relative to the wild type size. (c) Scaling of morphogen gradients requires modulation of the sharpness of the gradient to maintain the same proportions of cell fates. (d) The ratio (blue) between two gradients emanating from opposing edges of the field (green and red) can provide scaling of a signaling gradient. Left panel: wild type field; right panel: larger field.
Figure 2. Scaling of the BMP gradient in Xenopus laevis embryos. (a) Schematic representation of the BMP gradient (magenta) along the dorso-ventral axis of Xenopus laevis embryos. admp, a BMP ligand, is repressed by BMP signaling and therefore its expression is confined to the dorsal most region of the embryo, the Spemann organizer (white) where it is co-expressed with BMP inhibitors such as Chordin. bmp4, another BMP ligand is expressed at the ventral pole, where BMP signaling is highest. Admp, as well as the other BMP ligands are shuttled ventrally by their inhibitor Chordin. (b) Shuttling of Admp and its accumulation along the DV axis leads to the expansion of the BMP gradient (magenta) and the repression of admp expression (green bars) in virtually the entire field. Light shades of magenta denote earlier stages of the dynamics, dark shades denote later stages. Close to steady state, admp repression fixes signaling at the dorsal region of the field to Tadmp, the admp repression threshold.
Figure 3. The Expansion–Repression mechanism. (a) The Expansion–Repression feedback topology. The morphogen (blue) represses the secretion of an expander (orange). The expander, which is diffusible and stable, expands the morphogen gradient. (b) Expansion of the morphogen gradient (pale to bright blue) leads to the gradual restriction of the expander secretion domain towards the distal region of the morphogenic field (pale to bright orange bars). Texpander is the threshold for expander secretion repression. The gradient continues to expand until the expander is repressed in almost the entire field. The expander accumulates during the expansion of the gradient (pale to bright orange), such that larger fields will require higher levels of the expander. (c) An integral feedback lies at the heart of the Expansion–Repression mechanism. Expander secretion (red) is compared to the reference, no secretion of the expander (white). The error, which is the expander-secretion domain, translates into expander secretion and accumulation over time (yellow). Increase in expander levels leads to gradient expansion (blue), which results in restriction of the expander-secretion domain. The control circuit stabilizes when the error is zero, that is, when the expander is not secreted.
Figure 4. Possible implementations of the Expansion–Repression mechanism.
(a) A morphogen inhibitor can function as an expander: when degradation of the morphogen is mediated by interaction with its receptor, inhibition of the morphogen binding to the receptor decreases the morphogen degradation rate. Therefore, the inhibitor is effectively an expander.
(b) Shedding of HSPGs can be a part of an Expansion–Repression mechanism. In the case where shed HSPG expands the gradient, repression of HSPG expression in the presence of a sheddase (HSPG shedding protein), will lead to scaling through Expansion–Repression.
(c) Pentagone is an expander for the Dpp gradient in the AP axis of the Drosophila wing imaginal disc. pentagone is transcriptionally repressed by Dpp signaling, and expands the Dpp gradient through interaction with Dally, a Drosophila proteoglycan.
