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

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 find that the predictions of the theoretical model show good agreement with previously published experimental results. We also develop a new computational model that recapitulates the process more realistically and find concordance between this model and theory as well, but only when the primordium is circular. However, when the primordium is elliptical both models show discrepancies. We explain this difference by the mechanical interactions between cells, 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 dependencies of both size and developmental time; and uncovers potential instabilities of the system which might constraint developmental strategies to evolve eyes of different size.

EyeVolve, a modular PYTHON based model for simulating developmental eye type diversification

“…Regardless of when cell division occurs, the size of the eye field sets the stage for 'how much eye' can be developed. In D. melanogaster, the proliferation rate (and therefore size) of this tissue is under the precisely regulated, region-specific control of well-known molecular cascades, including the growth-promoting Notch signaling (dorso-ventral axis) and JAK/ STAT pathways (Baonza and Freeman, 2005;Domínguez and Casares, 2005), and differences in the size and shape of the precursor epithelium have already been recognized as important factors (Lobo-Cabrera et al, 2021). Altering the proliferation rate of progenitors in the precursor epithelium is one option for size regulation, as has been shown in mutant flies with the transmembrane protein Crumbs.…”

“…Indeed, some important aspects have already been modeled and could be incorporated into the broader but simpler model presented here. This includes factors that influence the precursor epithelium, such as cell proliferation (Amore and Casares, 2010;Lobo-Cabrera et al, 2021) and transcription factor activity (Fried et al, 2016;Gavish et al, 2016;Jörg et al, 2019). Other processes that have been modeled include MF dynamics, Delta-Notch-dependent lateral inhibition during R8 selection (Formosa-Jordan et al, 2013;Fried et al, 2016) and subsequent cellular patterning (Graham et al, 2010;Larson et al, 2010;Lubensky et al, 2011).…”

Feedback control of organ size precision is mediated by BMP2-regulated apoptosis in the Drosophila eye

“…To ensure that the target, species-specific final eye size is reached with precision, the rates of growth and of differentiation need to be coordinated within the eye primordium [ 6 , 19 , 20 ]. For example, a transient halt of the differentiation wave would produce some excess of progenitor cells and a concomitant deviation from the target size—unless this halt were communicated to the progenitors as a negative feedback on their rate of growth.…”

Feedback control of organ size precision is mediated by BMP2-regulated apoptosis in theDrosophilaeye

“…To ensure that the target, species-specific final eye size is reached with precision, the rates of growth and of differentiation need to be coordinated within the eye primordium (Casares and McGregor, 2020;Fried et al, 2016;Lobo-Cabrera et al, 2021). For example, a transient halt of the differentiation wave would produce some excess of progenitor cells and a concomitant deviation from the target size -unless this halt were communicated to the progenitors as a negative feedback on their rate of growth.…”