Dynamic Pattern in Chemically Reacting Systems

DESCRIPTION (provided by applicant): The growth and development of tissues of the appropriate size, shape and spatial patterning in a developing organism requires appropriate balances between the output of signaling pathways for patterning, growth control and cell-cell interaction. Drosophila has proven to be an ideal model system for understanding the networks that control tissue development and homeostasis. Recent studies on the Drosophila wing disc have elucidated the signaling pathways used in patterning the disc, and results on the interaction of these pathways with the Hippo signaling pathway, which controls cell proliferation and apoptosis, have emerged. Our overall objective in the proposed work is to develop a comprehensive, geometrically-realistic computational model for use in understanding the experimentally-observed spatio-temporal evolution of growth and patterning as the output of the integrated pathways governing wing development in Drosophila. The component models we develop will be validated by matching wild-type patterning, and then used to make experimentally-testable predictions about the response to gene mis-expression and other interventions. Our first objective is to formulate a cell-based model of the Drosophila wing disc that correctly describes the shape of the columnar cells, and incorporates the signaling networks. The computational framework will be designed to allow for all the known transport steps in the wing, including cytonemes, diffusion modulated by binding to receptors and glypicans in the extracellular spaces, and transcytosis. The second aim is to develop a cell-based model of the growth control pathways that incorporates diffusive transport within cells and cell-cell signaling between cells. Our objective is to determine whether all or most of the numerous experimental results on growth patterns in various over- and under-expression mutants can be explained on the basis of the currently-defined gene control networks. The third aim is to develop an integrated model for the signaling pathways that incorporates the components in the first two aims and properly incorporates growth and mechanics. The resulting model will be used to investigate how signaling, growth and growth control, and mechanical properties of the tissue interact to produce the appropriate size tissue in a normal adult, what mechanisms account for the observed proper patterning of certain types of mutants that produce larger or smaller wings, and why the scaling of pattern to tissue size fails in certain circumstances. The proposed work represents the first attempt to understand the spatio-temporal evolution of growth and patterning as the output of the integrated pathways governing wing development in a geometrically-realistic environment, and we anticipate that it will provide significant new insights into the complex interactions that govern patterning and growth in the disc. The model should also prove to be a valuable adjunct to experimental work.