Figure 1.
Drosophila germarium system and data.
A) Diagram of Wild Type germarium structure with anterior to the left, showing cap cells (CC), germline stem cells (GSC), cystoblasts (CB), and cysts. Below, a color-matched schematic of the 1 dimensional model used in this study. B) Diagram of signaling in the anterior germarium, showing the internal regulatory state of the GSC (left), and CB (right). Yellow and blue boxes refer to differentiation- and self-renewal-promoting elements, respectively. C) Examples of typical images (upper) and qualitative interpretations (lower) comprising available data. Qualitative interpretations are mappings of relative intensity (fluorescent, colorimetric, etc.) and original author interpretations to the 1-D model, indicated at bottom. Relevant color channels per image are (from left to right): pMad in red, Nos in red, Bam in green, Phenotype showing spectrosomes in red. Images reproduced/adapted from [57] (1st from left), [58] (2nd and 3rd from left), and [59] (right).
Figure 2.
Estimation of representative parameters.
A) Diagram of fitness quantification by Optimal Scaling. Images are mapped to qualitative data (left, image reproduced/adapted from [58]). Surrogate data (blue ) are chosen to best fit model outputs (green line) within intervals that match data (shaded boxes). Intervals are additionally constrained by minimum gaps and sizes. B) Diagram of the global optimization procedure. (Left) Parameter space is screened by sparse grid (
) and pseudo-random sampling (
)A. Color indicates cost (blue: low, red: high). (Right) Multiple gradient-based searches are started from the best samples (blue
), and find local minima (blue
). Finding all minima is not guaranteed (no solution in upper right quadrant). C) Diagram of the multiobjective optimization procedure. (Left and center) Example Pareto fronts (solid line) for objectives
and
, showing Anchor points (
and
), and Utopian points (
). (Right) Example solution via the modified NNC method, showing: Anchor points (
), Utopian (
), gradient search starts (
), normal constraints (dashed line), gradient solutions (
).
Table 1.
Table of data employed to fit models.
Figure 3.
Parameter estimation in the Core network.
A) Solved Pareto front for the Core network, showing the 3-D front (left) and projections (right 3 plots). Plotted in log space to accentuate small errors, showing: Pareto front (blue line), local solutions (red ), Pareto optimal solutions (
), Anchor points (
), and Utopian point (
). Projection views are bounded by the relevant Anchor points, so many solved points may not be visible and scales vary (e.g. Wild Type and Behavioral values are very similar and produce a negligible front with no Pareto points other than the Anchors, 3rd from left). B) Sample of model outputs and optimally scaled surrogate data for the Pareto point closest to the Utopian, indicated by black arrows in A. Plot titles indicate measurement: experiment; relative error (
). Notation as in Figure 2A.
Figure 4.
Yellow and blue boxes refer to differentiation- and self-renewal-promoting elements, respectively.
Figure 5.
A) Solved Pareto fronts for naively generated networks, superimposed for comparison. Insets enlarge view near Utopian point. B) Examples of model fitness, comparing the Core network with the two closest alternatives (based on Pareto front placement) and a poor alternative. Only Alt1 remains similar to the Core on examination. Simulated from Pareto points closest to the Utopian, black arrows in A. Notation as in Figures 3 and 2A.
Figure 6.
A) Informed hypothetical networks, each adding elements to the Core network. * indicates an indirect interaction, potentially involving many intermediaries. Coloring as previously, with white boxes where effects are not conceptually clear. B) Solved Pareto fronts for informed hypothetical networks, including Alt1 which performs similarly to the Core. Arrows indicate the only distinguishable feature among them, where Ago1 improves over other networks, though only at one point.
Figure 7.
A) Heatmaps showing relative information gain expected from qualitative data, with experiments on the ordinate and species to measure on the abscissa. Darker boxes indicate greater information (i.e. a more preferable experiment), via expected prediction variance among models (upper), dissimilarity of Representative prediction distributions (center), or variance among Representatives (lower). B) Heatmaps showing experiment design for quantitative data. Based on local sensitivity to a parameter affecting the indicated system feature (ordinate), and ranked by variance among models of mean sensitivity (upper) or variance among Representatives (lower).
Figure 8.
Simulated experiments designed for qualitative data.
Example simulated results for recommended experiments, showing for each model: qualitative interpretations (upper) and quantitative model outputs for all Representatives, normalized by the mean value to visualize all curves (lower). A) Simulations for experiments recommended directly for model discrimination. B) Simulations for an experiment recommended to first refine acceptable parameter estimates in each model.