Figure 14.

Positional error for a single gene and a pair of genes. (A) The mean hb profile and standard deviation across $\mathcal{N}=24$ embryos of data set A, as a function of fractional egg length. The inset shows a close-up with the positional error σ_x determined geometrically from the mean $\overline{g}\left(x\right)$ and the variability σ_g of the profiles. (B) Positional error for hb, computed using Equation 17 (dashed line corresponds to σ_x = 0.01). Error bars are obtained by bootstrapping 10 times over $\mathcal{N}/2$ embryo subsets. (C and D) Plots analogous to A and B for Kr. (E) Three-dimensional representation of hb and Kr profiles from A and C as a function of position x. The mean and standard deviations of the gene expression levels are shown in the {hb, Kr} plane in a gray curve with error bars; cf. the joint distribution of hb and Kr expression levels in Figure 11A. The black curve that extends through the cube volume shows the average expression “trajectory” as a function of position x. (F) Positional error computed using Equation 21 for the {hb, Kr} pair.