Global constraints within the developmental program of the Drosophila wing
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, United States
- NSF-Simons Center for Quantitative Biology, Northwestern University, United States
- Department of Molecular Biosciences, Northwestern University, United States
Figures
Figure 1 with 4 supplements
Landmark-free morphometrics.
(a–c) Standard landmarks (red) for Procrustes analysis of a Drosophila wing (a), the beak of a Darwin finch (b), and the face of DaVinci’s Vitruvian Man (c). (d–f), The landmark-free method involves …
Figure 1—figure supplement 1
Procrustes alignment of landmarks.
(a) Image of a Drosophila wing with axes labeled. (b) Image of a wing with the 12 standard landmarks used in Procrustes analysis. (c) Positions of landmarks of outbred wildtype male and female wings …
Figure 1—figure supplement 2
Wing boundary identification.
(a) An example of a training layer for Ilastik classification. The model has four layers: wing bulk (yellow), veins (blue), bristles (red), and background (cyan). (b) Output of Ilastik. (c) Cleaning …
Figure 1—figure supplement 3
Structure and form of the Drosophila wing.
(a) Contrast-limited adaptive histogram equalization (CLAHE). The part of the histogram that exceeds the clip limit redistributes equally among all histogram bins. In contrast to ordinary histogram …
Figure 1—figure supplement 4
Conformal map representation.
(a–c) An example of the conformal map between a disc (a), a triangle (b), and a square (c) showing polar grids. (d–f) An example of the conformal map between a square (d), a disc (e), and for the …
Figure 2 with 3 supplements
Comparison of Procrustes and landmark-free phenotyping.
(a, b) Variation between ensembles of male and female wings from the outbred wildtype population. (a) Procrustes analysis with inset showing the landmark where L1 and L2 veins intersect. (b) …
Figure 2—figure supplement 1
Accounting for the variation in wings.
(a) Area distribution of wings from outbred wildtype females and males raised on a standard rich diet at 25°C. (b) Kullback–Leibler divergence between the male and female ensembles with single-pixel …
Figure 2—figure supplement 2
Mean wing conformal maps from animals raised under different conditions or with different genotypes.
(a) Mean wings from ensembles of outbred wildtype (WT) male and female flies raised under the diet and temperature conditions, as indicated. Differences between mean wings are subtle and require …
Figure 2—figure supplement 3
Alignment of axis of sexual dimorphism rotates as a function of environmental stress across 4 different conditions.
(panels a-d) and the degree of alignments betweeen the axis of sexual dimorphism and the top principal components of each of the conditions (panel e). As is apparent in the scatter plots in panels …
Figure 3 with 4 supplements
Variational analysis of genetic mutants.
(a) Schematic of hypothetical 3D phenotype space, with each cloud of points representing wings from an ensemble subject to a different treatment or condition. The principal component (PC)1 vector …
Figure 3—figure supplement 1
Radon transformation.
(a) A Radon transform maps f on the (x, y) domain to Rf (r, β) on the (r, β) domain. The function f is equal to 255 in the blue squares and 0 otherwise. This simulates an 8-bit image containing only …
Figure 3—figure supplement 2
Eigenvalue spectrum in wings.
For each ensemble of wings, we performed alignment to the reference wing and Radon transformation. For each population, we performed principal component analysis on a single population. As a result, …
Figure 3—figure supplement 3
Bootstrap for genetic ensemble.
(a) Bootstraped distributions for the degree of alignments in mutant conditions, for males and females. (b) Box whisker plots summarizing histograms in panels a. Alignment distributions of different …
Figure 3—figure supplement 4
Statistical significance (p-values) of alignments in genetic analyses relative to a shuffled label null distribution.
Figure 4 with 4 supplements
Variational analysis of environmental perturbations.
(a–c) Per-pixel intensity difference between wings from a test condition (described on left) and a reference condition (described on the right). Difference is measured at the center of each point …
Figure 4—figure supplement 1
Kullback–Leibler divergence between left and right wings for each populations of female flies.
(a) 25°C, low diet, (b) 25°C, (c) 29°C, (d) 18°C, and (e) 18°C random left-right label assignment for population of 18°C.
Figure 4—figure supplement 2
Eigenvalue spectrum in wings.
For each ensemble of wings, we performed alignment to the reference wing and Radon transformation. For each population, we performed principal component analysis on a single population. As a result, …
Figure 4—figure supplement 3
Bootstrap for environmental ensembles.
(a) Bootstraped distributions for the degree of alignments for the environmental ensembles. Variability is far greater in the stressed populations at 29c and low diet. (b) Box whisker plots …
Figure 4—figure supplement 4
Statistical significance (p-values) of alignments in environmental analyses relative to a shuffled label null distribution.
Figure 5 with 3 supplements
Geometric analysis of dominant variational mode.
(a) Schematic of a data manifold with a single dominant linear direction of variation, embedded in high-dimensional phenotype space. Variation orthogonal to the dominant direction is visualized with …
Figure 5—figure supplement 1
Geometric analysis of dominant mode.
We observe the expected increase in alignment between directions of variation and directions connecting distinct populations. We fitted power laws to the experimental value of the trigonometric …
Figure 5—figure supplement 2
Robustness of manifold geometry to perturbations in image analysis pipeline.
In each panel, sigma/R vs. R is plotted. (a) Original data, (b) random perturbation to location of origin, (c) random shift of hinge cut points, and (d) boundary perturbations. The schematics in …
Figure 5—figure supplement 3
Degree of alignment and analysis of global geometry of (a, b) log-transformed data and (c, d) log-transformed inverse data.
Representative images are included in (e–g).
Additional files
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Supplementary file 1
Description of inbred stock lines.
- https://cdn.elifesciences.org/articles/66750/elife-66750-supp1-v2.xlsx
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Supplementary file 2
Crossing scheme.
- https://cdn.elifesciences.org/articles/66750/elife-66750-supp2-v2.xlsx
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Transparent reporting form
- https://cdn.elifesciences.org/articles/66750/elife-66750-transrepform-v2.docx
