Robustness of the Dorsal morphogen gradient with respect to morphogen dosage

Abstract

In multicellular organisms, the timing and placement of gene expression in a developing tissue assigns the fate of each cell in the embryo in order for a uniform field of cells to differentiate into a reproducible pattern of organs and tissues. This positional information is often achieved through the action of spatial gradients of morphogens. Spatial patterns of gene expression are paradoxically robust to variations in morphogen dosage, given that, by definition, gene expression must be sensitive to morphogen concentration. In this work we investigate the robustness of the Dorsal/NF-κB signaling module with respect to perturbations to the dosage of maternally-expressed dorsal mRNA. The Dorsal morphogen gradient patterns the dorsal-ventral axis of the early Drosophila embryo, and we found that an empirical description of the Dorsal gradient is highly sensitive to maternal dorsal dosage. In contrast, we found experimentally that gene expression patterns are highly robust. Although the components of this signaling module have been characterized in detail, how their function is integrated to produce robust gene expression patterns to variations in the dorsal maternal dosage is still unclear. Therefore, we analyzed a mechanistic model of the Dorsal signaling module and found that Cactus, a cytoplasmic inhibitor for Dorsal, must be present in the nucleus for the system to be robust. Furthermore, active Toll, the receptor that dissociates Cactus from Dorsal, must be saturated. Finally, the vast majority of robust descriptions of the system require facilitated diffusion of Dorsal by Cactus. Each of these three recently-discovered mechanisms of the Dorsal module are critical for robustness. These mechanisms synergistically contribute to changing the amplitude and shape of the active Dorsal gradient, which is required for robust gene expression. Our work highlights the need for quantitative understanding of biophysical mechanisms of morphogen gradients in order to understand emergent phenotypes, such as robustness.

Fig 1. The protein Dorsal patterns the DV axis of the Drosophila embryo.

(A) An antibody staining against Dorsal in an NC 14 embryo. (B) mRNA expression of a variety of the Dorsal target genes sna and sog. (C) Illustration of the borders of gene expression. We use these borders to quantify and compare the extent of domain of Dl target genes. Embryo cross-sections are oriented so that ventral is down.

Fig 2. Theoretical consideration of the sensitivity coefficient.

(A) Testing whether a lower value of the parameter b could result in a lower sensitivity. (B) The empirical prediction shows that 1x embryos completely lose sna expression, while 4x embryos have an overexpanded domain of sna, and lose dpp completely. (C) The prediction when lower b values were used.

Fig 3. Varying the maternal dl dose influences gene expression.

(A) Box-and-violin plot of the ventral border of sog. (B) Box-and-violin plot of the dorsal border of sog. (C) Box-and-violin plot of the of the dorsal border of sna. The numbers above or below distributions indicate sample size (numbers of embryos imaged). Numbers between distributions indicate p-value; n.s. = “not significant”. Plus signs indicate statistical outliers. (D) Abundance of dl mRNA relative to wildtype, measured by qPCR. Red curve indicates expectation of y = 0.5x. Circles indicate weighted mean and errorbars indicate weighted standard error of the mean (see Methods). Numbers indicate sample size, including both biological and technical replicates (see Methods).

Fig 4. Varying the maternal dl dose influences the Dl gradient.

(A) Averaged and normalized Dl gradients in 1x, 2x, and 4x embryos. Averaged from n > 30 embryos each (see Methods). (B) Box-and-violin plot of the width of the Dorsal gradient in the genotypes shown in (A). Numbers below distributions indicate sample size. Numbers above indicate p-values. The width of the 1x gradient was modified, as the shape was non-Gaussian (see Supplementary Methods). (C) Dl gradient plot in 1x, 2x, and 4x embryos in the dosage-scaling model showing the effect of higher width in 4x embryos and lower width in 1x embryos. (D) Graph of Dl gradients with best-fit amplitudes for the 1x and 4x gradients, with respect to the 2x gradient set to amplitude of one. (E) Contour plot of the SSE with respect to the amplitude of the 1x gradient (α_1x) and that of the 4x gradient α_4x. Red dot: the set of best-fit amplitudes. Red curves show the contours of the objective function landscape. Dimmed portion of the α_1x,α_4x plane: infeasible region, as realistically, α_1x cannot be greater than 1, and α_4x cannot be less than one.

Fig 5. Computational results.

(A) Concentration distribution of free Dl for one of the robust parameter sets for dosage 1x,2x and 4x. (B) Cumulative distribution plot for length scale ratio (ρ). (C) Cumulative distribution plot of the Michaelis Menten constant (κ). (D) Histogram of amplitude ratios. (E) Plot of amplitude ratio 1x/2x against length scale ratio. (F) Plot of amplitude ratio 4x/2x against length scale ratio. (G) Plot of amplitude ratio 1x/2x against κ. (H) Plot of amplitude ratio 4x/2x against κ.

Fig 6. The effect of dl dosage on gradient amplitude in live embryos.

(A) Cross sectional view of a live Drosophila embryo, showing the accumulation of Dl-GFP in the ventral nuclei during late nc 14. (B) Quantification of Dl gradient in live embryos 25 minutes after the start of nc 14. (C) A quantification of the gradient amplitude over time from nc 12 to 14. A canonical curve of gradient amplitude dynamics during nc 14 is plotted in orange. (D) Plot of gradient amplitude (corresponding to the max amplitude during nc 14; see part (C)) of 1x, 2x, and 4x live embryos. The ratios are average plus/minus standard deviation, which were calculated by bootstrap. Whole numbers next to average data points indicate sample sizes. (E) Distributions of amplitude ratios calculated by bootstrap. The normal distributions with the same mean and standard deviation are plotted on top in dashed curves. Mean and standard deviation are depicted on the histogram as dot with errorbars. (F) Comparison of distributions of amplitude ratios obtained computationally (see Fig 5D) and experimentally (dashed black curves; from part (E)). The probability that the experimental 1x:2x amplitude ratio falls between 0.4 and 1 is 0.79 (shaded blue area). The probability that the experimental 4x:2x amplitude ratio falls between 1 and 1.5 is 0.27 (shaded red area).