Diffusion and scaling during early embryonic pattern formation - PubMed (original) (raw)

Diffusion and scaling during early embryonic pattern formation

Thomas Gregor et al. Proc Natl Acad Sci U S A. 2005.

Abstract

Development of spatial patterns in multicellular organisms depends on gradients in the concentration of signaling molecules that control gene expression. In the Drosophila embryo, Bicoid (Bcd) morphogen controls cell fate along 70% of the anteroposterior axis but is translated from mRNA localized at the anterior pole. Gradients of Bcd and other morphogens are thought to arise through diffusion, but this basic assumption has never been rigorously tested in living embryos. Furthermore, because diffusion sets a relationship between length and time scales, it is hard to see how patterns of gene expression established by diffusion would scale proportionately as egg size changes during evolution. Here, we show that the motion of inert molecules through the embryo is well described by the diffusion equation on the relevant length and time scales, and that effective diffusion constants are essentially the same in closely related dipteran species with embryos of very different size. Nonetheless, patterns of gene expression in these different species scale with egg length. We show that this scaling can be traced back to scaling of the Bcd gradient itself. Our results, together with constraints imposed by the time scales of development, suggest that the mechanism for scaling is a species-specific adaptation of the Bcd lifetime.

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Figures

Fig. 1.

Fig. 1.

Diffusion of inert molecules in the Drosophila embryo. (A) Two-photon image of a wild-type D. melanogaster embryo 8 min after injection of fluorescently labeled dextran molecules at the mid-plane of the embryo. The tip of the glass micropipette used for the injection is located at the anterior pole (black asterisk on the left side of the image). Colored discs show areas where fluorescence intensity was analyzed. (B) Changes in the fluorescence intensity with time for the six color-corresponding discs in A, extracted from a time series of images taken with a frame rate of 8 s. Solid lines represent the time courses computed from the best fit of a numerical 3D diffusion model. Note that 18 curves (6 per focal plane) are fit by the solutions of the same diffusion equation, with only a single free parameter, the diffusion constant D. (C) Diffusion coefficients of dextran molecules of different hydrodynamic radii (red dots). The solid line represents diffusion coefficients expected from the modified Stokes–Einstein relation (10), D = k_B_T/(6π η_R_) + b, with a viscosity η = 4.1 ± 0.4 cP and b = 6.2 ± 1.0 μm2/s; dashed line is at the value of b.

Fig. 2.

Fig. 2.

Immunofluorescence stainings for products of the gap and pair-rule genes in higher diptera. (A) Immunofluorescence staining of L. sericata (upper embryos) and D. melanogaster (lower embryos) for Hunchback (green) and Giant (red) in the left column, and for Paired (green) and Runt (red) in the right column. (B) Anti-Hunchback (green) and anti-Runt (red) immunofluorescence staining of D. melanogaster (upper embryo) and D. busckii (lower embryo). (Scale bars: 100 μm.)

Fig. 3.

Fig. 3.

Scaling of Bcd profiles. (A) Typical confocal images of Bcd immunofluorescence staining for L. sericata (top), D. melanogaster (middle), and D. busckii (bottom). The focal plane is at mid-embryo and top-embryo in the left and right columns, respectively. (Scale bar: 100 μm.) (B) Intensity profiles of Bcd fluorescence of 27 L. sericata (blue), 35 D. melanogaster (red), and 18 D. busckii (green) embryos. The abscissa in Upper is absolute; the abscissa in Lower is relative to egg length. (C) Length constants λ as a function of egg length for L. sericata (blue), D. melanogaster (red), and D. busckii (green). (D) Cumulative probability distributions of length constants λ for L. sericata (blue), D. melanogaster (red), and D. busckii (green). Asterisks indicate the means of the three distributions.

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