Abstract
We can improve our understanding of biological processes through the use of computational and mathematical modeling. One such morphogenetic process (ommatidia formation in the Drosophila eye imaginal disc) provides us with an opportunity to demonstrate the power of this approach. We use a high-resolution image that catches the spatially- and temporally-dependent process of ommatidia formation in the act. This image is converted to quantitative measures and models that provide us with new information about the dynamics and geometry of this process. We approach this by addressing four computational hypotheses, and provide a publicly-available repository containing data and images for further analysis. Potential spatial patterns in the morphogenetic furrow and ommatidia are summarized, while the ommatidia cells are projected to a spherical map in order to identify higher-level spatiotemporal features. In the conclusion, we discuss the implications of our approach and findings for developmental complexity and biological theory.
Highlights
To advance the development and use of computational representations and models in developmental neuroscience, we require a well-characterized biological system that yields fairly unambiguous information regarding the differentiation process
This furrow produces 800 ommatidia structures present in the adult compound eye by inducing proneural states during its movement through undifferentiated cells (Chanut and Heberlein, 1995). The cells in this epithelium commit to a neuronal fate as they receive signals triggered by the passing of the morphogenetic furrow and its proximity to/recruitment by an ommatidia founder (R8) cell (Brennan and Moses, 2000; Dokucu et al, 1996)
Various molecular pathways interact with progression of the furrow during differentiation of various cells in a single ommatidium (Davis and Rebay, 2018; Greenwood and Struhl, 1999). These patterns of differentiation may be due to a phenomenon we have defined as single-cell differentiation waves (Gordon and Gordon, 2016; Gordon, 1999)
Summary
To advance the development and use of computational representations and models in developmental neuroscience, we require a well-characterized biological system that yields fairly unambiguous information regarding the differentiation process. Biological noise) in terms of the positioning and fate of specific cells within the disc (Heberlein and Moses, 1995; Tare et al, 2013) (for a definition of biological noise, see Elowitz et al (2002)) While these data are representative, they by no means capture the variation inherent in the differentiation process. A morphogenetic furrow marks the boundary between a population of isotropic and presumably undifferentiated cells to a structured population of ommatidia cells and background cells We use both mathematical and computational techniques to uncover patterns, features, and geometric relationships previously not characterized in the literature. We will address these hypotheses using a variety of methods These can be stated as follows: H1: the size distributions of cells representing three components of the eye imaginal disc (furrow, differentiated background, and ommatidia) will yield differences. H4: animations of the spherical map as a series of time slices will reveal a process analogous to anatomical differentiation
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