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First published online September 5, 2008
doi: 10.1242/10.1242/dev.018697


Development 135, 3175-3183 (2008)
Published by The Company of Biologists 2008


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Regulative feedback in pattern formation: towards a general relativistic theory of positional information

Johannes Jaeger1,*,{dagger}, David Irons2,* and Nick Monk3,*

1 Laboratory for Development and Evolution, University Museum of Zoology, Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, UK.
2 School of Medicine, University of Sheffield, Sheffield S10 2JF, UK.
3 School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.


Figure 1
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Fig. 1. The French flag model. Based on Wolpert (Wolpert, 1968Go). Positional specification by a morphogen gradient is implemented as a two-step process. Step 1: localised production of a morphogen at its source (green cell) and degradation at its sink (pink cell) leads to a linear gradient of decreasing morphogen concentration through the as yet undifferentiated tissue. Cells in the tissue sense whether they are exposed to morphogen concentrations below or above given thresholds (T1, T2). Step 2: cells become specified and later differentiate by turning on specific target genes (indicated by blue, white and red). Boundaries of target gene expression correspond exactly to the thresholds in the gradient. The arrow indicates the strictly feed-forward flow of information in this system. This `classical' two-step view of positional specification naturally extends to more realistic non-linear gradients and systems where degradation is not restricted to a sub-population of cells (Slack, 1987Go).

 

Figure 3
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Fig. 2. Examples of regulatory feedback involved in positional specification by morphogen gradients. (A) The gap gene system of Drosophila melanogaster. Maternal morphogen gradients (such as Bcd) bias target nuclei towards the expression of specific gap genes according to their position along the anteroposterior (AP) axis of the embryo. The positions of the central and posterior domains of Krüppel (Kr), knirps (kni), giant (gt) and hunchback (hb) are shown diagrammatically, indicating the two pairs of staggered, mutually complementary domains along the AP axis (anterior, left). Cross-repressive feedback between complementary gap genes stabilises and sharpens these patterns (thick T-bars). A second layer of cross-repression with posterior dominance (thin T-bars) leads to anterior shifts in expression domain boundaries (indicated by coloured arrows). (B) Feedback between signalling ligands (morphogens) and their receptors or downstream pathways in the Drosophila wing disc. (Left) Hedgehog (Hh) signalling upregulates Patched (Ptc) receptor expression, which inhibits Hh movement by sequestering it extracellularly. (Centre) Wingless (Wg) signalling downregulates expression of its receptor Frizzled2 (Fz2) close to the Wg source. High levels of Fz2 away from the source stabilise the Wg protein. (Right) Decapentaplegic (Dpp) signalling downregulates expression of its receptor Thickveins (Tkv) close to its source. Tkv in turn sensitises cells away from the source to low levels of Dpp signalling. (C) Sonic Hedgehog (Shh) in the vertebrate neural tube (NT) is regulated by multiple levels of feedback. Shh (blue circles) up-regulates expression of its receptor Ptc1 (red), which inhibits signalling by repressing the co-receptor Smoothened (Smo, orange circles). This desensitises cells in the region of the gradient where ligand is limiting (in the dorsal NT, right) and alters the shape of the gradient (indicated by different blue shading). Yellow stars indicate signalling events. Brief Shh signalling activity induces expression of the target gene Olig2 (white). Maintained levels of Shh induce Nkx2.2 (blue), which in turn represses Olig2 (T-bar). Red indicates dorsal (Class I) Shh target genes, such as Irx3 and Pax6. (D) Dorsoventral patterning in the Drosophila embryo. Dpp/Scw heterodimers diffuse dorsally in a complex with Twisted Gastrulation (Tsg) and Short Gastrulation (Sog). They are captured and enriched at the dorsal midline by a surface bound ligand binding protein (SBP), whose expression is upregulated by Dpp signalling. This leads to the sharpening and narrowing of the dorsal stripe of Dpp activity (measured as the concentration of phosphorylated MAD, pMAD) through bistability in the cellular response.

 

Figure 4
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Fig. 3. Logical structure of conceptual frameworks for positional specification. (A) Classical: strictly feed-forward flow of information from the morphogen gradient, which specifies a static spatial metric that is imposed on the target tissue. The activity profile of the target cells has no influence on the metric. An example is the French flag model. (B) Semi-classical: feedback between target genes alters the metric over time without affecting the morphogen gradient itself. An example is the Drosophila gap gene system. (C) General relativistic: multiple levels of feedback exist between the cellular response (activity profile) and the metric, the morphogen profile and potentially also the morphogen source. See Fig. 2B-D for examples. (D) Logical structure of classical versus general relativistic positional information (GRPI). Compare with B in Box 1 for conceptual parallels to classical versus relativistic physics.

 

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© The Company of Biologists Ltd 2008