A Model of the Spatio-temporal Dynamics of Drosophila Eye Disc Development

Abstract

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 Drosophila 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.

Critical Point in Self-Organized Tissue Growth

“…centration. This growth rule in conjunction with an expander mechanism for gradient scaling can account for the homogeneous growth observed in the wing imaginal disc [2,35] and may also apply to other tissues [37,44]. It has further been suggested that the temporal growth rule by itself could yield gradient scaling, without the need of an additional expander mechanism [35].…”

Growth and size control during development

“…Growth and proliferation are mainly restricted to the tissue anterior to the morphogenetic furrow (MF) [ 87 ]. The regulatory interactions between Hedgehog (Hh), which is expressed only behind the MF, Dpp, which is expressed in the MF activated by Hh, and Homothorax (Hth), which is expressed only in front of the MF, result in a travelling wave that propels the MF from the posterior to the anterior side of the eye disc ( figure 3 b ) [ 85 , 88 , 89 ]. Once the MF reaches the anterior-most side of the eye disc, growth terminates.…”

“…Green, posterior area; yellow, MF; dashed lines, growth within the next time step. Picture and legend in ( b ) were adapted and reproduced with permission from Fried et al [ 85 ] (Copyright © 2016 Public Library of Science). The pictures in ( c–e ) and the legend for ( e ) were adapted from Vollmer et al [ 86 ].…”

Growth control in theDrosophilaeye disc by the cytokine Unpaired

“…We followed the same approach as Fried et al (2016) and we provide a copy of the description in supplementary Materials and Methods. In short, the region of interest (ROI; Fig.…”