AUTHOR=Lobo-Cabrera Francisco Javier , Navarro Tomás , Iannini Antonella , Casares Fernando , Cuetos Alejandro 

TITLE=Quantitative Relationships Between Growth, Differentiation, and Shape That Control Drosophila Eye Development and Its Variation

JOURNAL=Frontiers in Cell and Developmental Biology

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/cell-and-developmental-biology/articles/10.3389/fcell.2021.681933

DOI=10.3389/fcell.2021.681933

ISSN=2296-634X

ABSTRACT=The size of organs is critical for their function and often a defining trait of a species. Still, how organs reach a species-specific size or how this size varies during evolution are problems not yet solved. Here, we have investigated the conditions that ensure growth termination, variation of final size and the stability of the process for developmental systems that grow and differentiate simultaneously. Specifically, we present a theoretical model for the development of the Drosophila eye, a system where a wave of differentiation sweeps across a growing primordium. This model, which describes the system in a simplified form, predicts universal relationships linking final eye size and developmental time to a single parameter which integrates genetically-controlled variables, the rates of cell proliferation and differentiation, with geometrical factors. We validate the theoretical model by finding a good  qualitative agreement between its predictions and previously published experimental results. We also develop a new computational model that recapitulates the process more realistically and find a good agreement between this model when the primordium is circular and the theory as well. However, when the piomordium is elliptical both models show discrepancies. We explain this difference by the mechanical interactions between cell, an aspect that is not included in the theoretical model. Globally, our work defines the quantitative relationships between rates of growth and differentiation and organ primordium size that ensure growth termination (and, thereby, specify final eye size) and determine the duration of the process; identifies geometrical dependence on both size and developmental time; and uncovers potential instabilities of the system which might constraint developmental strategies to evolve eyes of different size.