A novel image segmentation algorithm with applications on confocal microscopy analysis

Motivation: Developing cells change their gene expression profiles dynamically upon induction by proper triggers, typically diffusible morphogens that are spatially distributed (1). These changes impact cell cycle and apoptosis regulators differentially, eventually determining the final structure and size of the mature organs (2). A quantitative model that links gene regulation and tissue growth must be provided with precise experimental data at cell resolution level in order to proceed to its validation, which in some cases is essential for model screening (i.e. reverse ingineering methods). Image analysis from laser confocal microscopy (LCM) has already been used to address modelling problems in developmental tissues such as these (3). However current methods for LCM segmentation rely upon watershed algorithms that show variable efficiency, relatively high parametrization and oversegmentation problems that are critical on very aggregated objects (4). Here we present a different segmentation method based on the maximum complementary n-ball set (MCnB set) concept. The segmentation algorithm takes a full MCnB set as a starting graph representation of the whole stack, which is later contracted using a parallel implementation approach.Results: We assayed the performance by segmenting a randomly generated set of spheres with different resolutions, signal aggregation levels and densities, and compared to the results delivered by a common segmentation free software, (i.e. Vaa3D), which is based on watersheds (5). We also applied this comparison on DAPI stained samples from Drosophila eye-antenna imaginal discs. The results indicate that the mean square displacement of detected spheres centroids is higher in the 3D watershed implementation results than when our method is applied. The same results are obtained when the number of sets or their size are checked instead.Conclusions: The results indicate that our method is adequate enough for image segmentation in three dimensions. It makes no assumptions on what the shape or signal features of the objects are, and does not require any calibration since it can proceed with no specific user parameters. Moreover it beats at least one segmentation method that has already been set up for counting and segmentation. Since the shape of the voxel aggregates is not critical, we sugget that further implementations could be potentially applied in higher dimension samples with interesting applications in developmental biology (i.e. 4D 'movies' segmentation). However one major drawback is that at least one operation runs with a O(n^2) time complexity, which is time (and memory) consuming for very big images

A Toggle-Switch and a Feed-Forward Loop Engage in the Control of the Drosophila Retinal Determination Gene Network

Dipterans show a striking range of eye sizes, shapes, and functional specializations. Their eye is of the compound type, the most frequent eye architecture in nature. The development of this compound eye has been most studied in Drosophila melanogaster. The early development of the Drosophila eye is under the control of a gene regulatory network of transcription factors and signaling molecules called the retinal determination gene network (RDGN). Nodes in this network have been found to be involved not only in the development of different eye types in invertebrates and vertebrates, but also of other organs. Here we have analyzed the network properties in detail. First, we have generated quantitative expression profiles for a number of the key RDGN transcription factors, at a single-cell resolution. With these profiles, and applying a correlation analysis, we revisited several of the links in the RDGN. Our study uncovers a new link, that we confirm experimentally, between the transcription factors Hth/Meis1 and Optix/Six3 and indicates that, at least during the period of eye differentiation, positive feedback regulation from Eya and Dac on the Pax6 gene Ey is not operating. From this revised RDGN we derive a simplified gene network that we model mathematically. This network integrates three basic motifs: a coherent feedforward loop, a toggle-switch and a positive autoregulation which, together with the input from the Dpp/BMP2 signaling molecule, recapitulate the gene expression profiles obtained experimentally, while ensuring a robust transition from progenitor cells into retinal precursors.MINECOFEDER (BFU2012-34324, BFU2015-66040-P)Agencia Estatal de Investigacion (AEI) of Spai

Growth control in the Drosophila eye disc by the cytokine Unpaired

A fundamental question in developmental biology is how organ size is controlled. We have previously shown that the area growth rate in the eye primordium declines inversely proportionally to the increase in its area. How the observed reduction in the growth rate is achieved is unknown. Here, we explore the dilution of the cytokine Unpaired (Upd) as a possible candidate mechanism. In the developing eye, expression is transient, ceasing at the time when the morphogenetic furrow first emerges. We confirm experimentally that the diffusion and stability of the JAK/STAT ligand Upd are sufficient to control eye disc growth via a dilution mechanism. We further show that sequestration of Upd by ectopic expression of an inactive form of the receptor Domeless (Dome) results in a substantially lower growth rate, but the area growth rate still declines inversely proportionally to the area increase. This growth rate-to-area relationship is no longer observed when Upd dilution is prevented by the continuous, ectopic expression of Upd. We conclude that a mechanism based on the dilution of the growth modulator Upd can explain how growth termination is controlled in the eye disc

A Model of the Spatio-temporal Dynamics of <i>Drosophila</i> Eye Disc Development

<div><p>Patterning and growth are linked during early development and have to be tightly controlled to result in a functional tissue or organ. During the development of the <i>Drosophila</i> eye, this linkage is particularly clear: the growth of the eye primordium mainly results from proliferating cells ahead of the morphogenetic furrow (MF), a moving signaling wave that sweeps across the tissue from the posterior to the anterior side, that induces proliferating cells anterior to it to differentiate and become cell cycle quiescent in its wake. Therefore, final eye disc size depends on the proliferation rate of undifferentiated cells and on the speed with which the MF sweeps across the eye disc. We developed a spatio-temporal model of the growing eye disc based on the regulatory interactions controlled by the signals Decapentaplegic (Dpp), Hedgehog (Hh) and the transcription factor Homothorax (Hth) and explored how the signaling patterns affect the movement of the MF and impact on eye disc growth. We used published and new quantitative data to parameterize the model. In particular, two crucial parameter values, the degradation rate of Hth and the diffusion coefficient of Hh, were measured. The model is able to reproduce the linear movement of the MF and the termination of growth of the primordium. We further show that the model can explain several mutant phenotypes, but fails to reproduce the previously observed scaling of the Dpp gradient in the anterior compartment.</p></div

A toggle-switch and a feed-forward loop engage in the control of the Drosophila retinal determination gene network

© 2019 Sánchez-Aragón, Cantisán-Gómez, Luque, Brás-Pereira, Lopes, Lemos and CasaresDipterans show a striking range of eye sizes, shapes, and functional specializations. Their eye is of the compound type, the most frequent eye architecture in nature. The development of this compound eye has been most studied in Drosophila melanogaster. The early development of the Drosophila eye is under the control of a gene regulatory network of transcription factors and signaling molecules called the retinal determination gene network (RDGN). Nodes in this network have been found to be involved not only in the development of different eye types in invertebrates and vertebrates, but also of other organs. Here we have analyzed the network properties in detail. First, we have generated quantitative expression profiles for a number of the key RDGN transcription factors, at a single-cell resolution. With these profiles, and applying a correlation analysis, we revisited several of the links in the RDGN. Our study uncovers a new link, that we confirm experimentally, between the transcription factors Hth/Meis1 and Optix/Six3 and indicates that, at least during the period of eye differentiation, positive feedback regulation from Eya and Dac on the Pax6 gene Ey is not operating. From this revised RDGN we derive a simplified gene network that we model mathematically. This network integrates three basic motifs: a coherent feedforward loop, a toggle-switch and a positive autoregulation which, together with the input from the Dpp/BMP2 signaling molecule, recapitulate the gene expression profiles obtained experimentally, while ensuring a robust transition from progenitor cells into retinal precursors.This work was funded by MINECO and the Agencia Estatal de Investigacion (AEI) of Spain, co-financed by FEDER funds (EU) through grants BFU2012-34324 and BFU2015-66040-P to FC, MDM-2016-0687 in which FC is participant researcher, and TIN2017-89842 P in which MCL is participant researcher

Eye disc model can reproduce several mutant phenotypes.

<p>(a,b) Comparison of the MF movement (a) and the total area over time (b) between a simulation using the original parametrization (indicated by the black line) and a simulation using a reduced hh production rate (indicated by the red line). In the case of the simulation representing the hypomorphic hh mutant the MF is clearly slower and eventually stops (a), while the total area is overgrowing (b). (c) Simulation of a clone where the hh production rate is set to zero at t = 55h. Towards the center of the clone the tissue is not differentiated (blue color) despite residing within the posterior area (colored in orange). (d) Posterior (indicated by the black line) and total (indicated by the green line) eye disc sizes in relation to the wildtype (indicated by the dashed grey line) at different relative influxes of Hh from the posterior margin. (e,f) Comparison of the total area over time (e) and the movement of the MF (f) between a simulation using the original parametrization (black line) and a simulation using a reduced (red line) dpp production rate. In panel e an additional simulation with increased dpp production rate (blue line) is compared. (g) Simulation of a clone where the hth production rate is increased at t = 20h. The MF (indicated by orange color) shows a retardation in the clone. (h) Total area over time in a numerical simulation representing the wildtype phenotype (black line) and a simulation using a reduced (red line) or increased (blue line) hth production rate.</p

Eye disc model captures linear MF movement and growth termination.

<p>(a) Simulated progression of MF is approximately linear over time (black line). The speed of the MF movement is determined by a linear fit and is ≈3.4 μm h^-1. (b-d) Simulated total area (b), posterior area (c) and anterior area (d) over time in the eye disc model show growth termination towards the end of development.</p

Effects of parameter changes on MF speed, nonlinearity and final eye disc area.

<p>Blue bars indicate a 1% decrease and red bars a 1% increase in parameter values compared with the wildtype (black line). In panels a, c, and e, the absolute values for speed, nonlinearity and area of the resulting eye discs are shown whereas in b, d, and f, the same data is shown in relation to the wildtype values.</p

The simulated Dpp gradient is not scaling in the anterior compartment.

<p>(a,b) The simulated spatial profiles of Dpp (a) and pMad (b) in a developing eye disc at 20h (light blue), 40h (dark blue) and 60h (black). (c) Anterior length over time (black solid line). Vertical dashed lines indicate time points corresponding to (a,b).</p