Resultados de investigación

Simplifications in the formalization of some biological processes and how these have been modeled., Peer reviewed

Using our computational model, sets of 1,000 eye sizes were simulated for each condition and from these, samples of equal size to the experimental samples were taken to calculate the medians of rE (a) and interindividual FA (FAn) (b). The sampling was repeated 1,000 times to generate the distribution of medians shown in the graphs, where each point in gray corresponds to the median of one of those 1,000 samples (“Computational data”). The triangles represent the medians of the experimental results (“Real data”) of all genotypes. The computational data were scaled such that the median rE of experimental control coincides with the center of the distribution for the computational control group. The experimental medians for both metrics fall within the respective computational distributions for all genotypes. This is especially striking for the rE medians, for which the experimental medians coincide almost perfectly with the most probable value of the computational median distributions. This fact indicates that the model captures the process of eye development in those different genotypes very accurately (See S1 Statistical Methods for further details). (c) If apoptosis is blocked in the computational model (by strongly reducing the apoptotic rate of progenitors, equivalent to optix>RHGRI), eye size increases more rapidly than in the other 2 genotypes, in which apoptosis is allowed, until noise is too high (beyond 102), point at which allowing apoptosis or not becomes irrelevant. Computational results. Data for each point is from 200 simulations per genotype. The horizontal axis represents 1/Vp (see S1 Mathematical Model supporting information file). The data used in the graphs shown in the figure can be found in “Fig 4A,4B_data” in the Supporting information file S1 Raw Data., Peer reviewed

(a) Schematics of the process. R cells stimulate the differentiation process (by expressing Hh). Rn cells negatively regulate apoptosis (by producing Dpp). G cells can divide, die, or progress further into differentiation by transiting to Rn. (b) This process, schematized in space. MF: morphogenetic furrow is the differentiation wave-front that moves (arrow) from posterior (right) to anterior (left). LA, LP are the maximum distances anterior and posterior to the MF, respectively. The Lp can be used as a proxy for developmental time: As the MF moves with constant speed, Lp increases as time passes. LA corresponds to G cells. Lp comprises Rn (orange bar) + R cells. (c) “Qualitative” model. (d) Typical temporal profiles of all populations as predicted by the model. (e) Fit of the model to experimental data (LAP as minor axis of elliptical fits of eye primordia (blue points) and LA = LAP − Lp (orange points)). Each curve is an independent realization produced with the optix>+ parameter set (see main text and S1 Materials for details), differences between curves are an effect of the stochastic nature of the model., Peer reviewed

Lateral views of adult eyes (a-c) and L3 eye discs, stained with Dcp-1 (and counterstained with rhodamine phalloidin, “actin”) (a’-c’) of the indicated genotypes. (d) Distribution of apoptosis intensity in L3 discs of the indicated genotypes. Blocking apoptosis driving the UAS-RHG-RNAi reduces the apoptosis caused by tkv attenuation (optix>tkvRI + RHGRI). The statistical analysis corresponding to these data can be found in S2 Table. (*): p < 0.05; (**): p < 0.01; (***): p < 0.001. The data underlying the graphs shown in the figure can be found in “Fig 2_data” in the Supporting information file S1 Raw Data., Peer reviewed

The eye primordium ((a) “E”, outlined) develops into the adult eye (b) through the action of a differentiation wave that sweeps across it (arrow). (a) Eye primordium (“E”) of a Hh:GFP; dpp-Z larva. The differentiation wave-front expresses dpp-Z. Posterior to it further differentiated photoreceptors lose dpp expression and express hh. (b) Lateral view of an adult Drosophila eye. (c) The recruitment of proliferative progenitor cells (“G”) into early differentiating (dpp-expressing) retinal cells (“Rn”) and then into terminally differentiating (non-dpp-expressing) retinal cells (“R”) is controlled by 2 signaling molecules, Hh and Dpp. (e-h) Frontal views of female heads of the indicated genotypes, with the eyes colored for better visualization. (e) Control, optix>+, (f) optix>tkvRNAi, (g) optix>tkvRNAi + dadRNAi, (h) Bar (B) mutant. See main text for details. (i, j) rE (i) and sFAi (j) distributions of the indicated genotypes. Each violin plot includes the male (left) and female (right) distributions, which were not significantly different from each other in any genotype. The median of each distribution is indicated (solid and dashed line: male and female, respectively). The predicted rE median for each genotype and the statistical model from which they are derived can be found in S1 Table. The variances of each genotype were compared against the variance in the control group (optix>+) in rE and sFAi (S1 Table). (*): p < 0.05; (**): p > 0.01; (***): p < 0.001. Eye area is measured relative to the total head area and expressed as a percentage in this and subsequent figures. The data underlying the graphs shown in the figure can be found in “Fig 1_S6Fig 1_data” in the Supporting information file S1 Raw Data., Peer reviewed

Full mathematical model including its deterministic and stocastic versions, the analysis of effects of noise on the different variables of the model, and a sensitivity analysis., Peer reviewed

This file describes in detail the statistical methods used for data analysis., Peer reviewed

Each genotype effect on %Apop median, their p.values, and the predicted median for each of them are shown (see main text, Materials and methods section)., Peer reviewed

First block shows each genotype’s effect on the rE median, their p.values, and the predicted median for each of them. The second and third blocks show the standard deviation of each group for rE and sFAi, respectively, and the result of the comparison of variances of each group against the optix>+ reference group., Peer reviewed

(a, b) Heads from GMR>+ (a) and GMR>Upd (b) adult males; frontal view. While the median eye size (rE: c) of GMR>Upd flies is approximately 1.4 times that of control (GMR>+) ones (statistically significant), the fluctuating asymmetry index (“precision”) (FAi: d) is indistinguishable between the 2 genotypes. Female (F) and male (M) distributions are shown. (e, f) Eye primordia stained for the apoptotic marker Dcp-1. Apoptotic signal is observed in both GMR>Upd as well as in GMR>+ control primordia. The data used in the graphs shown in the figure can be found in “S1_Fig 4_data” in the Supporting information file S1 Raw Data., Peer reviewed