This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
Many recent experimental and theoretical studies have shown that most morphogen systems are far more complex than had been expected: Feedback loops, secreted inhibitors, cooperative interactions among morphogens, and high spatial dimensions with complex boundary conditions act together to produce robust and complex patterns of morphogens. This project is concerned with a mathematical and computational investigation of such complex interactions in two systems during Drosophila embryonic development. The first part of the project is to investigate roles of the Dally-like protein, a membrane bound and non-diffusive protein, on Wingless morphogen distribution and signaling in the imaginal wing disc. The second part of the project is to investigate roles of certain feedback loops in sharpening morphogen gradients and noise reduction during dorsal-ventral patterning in early development. In addition, the investigator will develop efficient and accurate numerical methods with adaptive mesh refinement for stiff reaction-diffusion equations in complex geometries, in order to meet the computational challenges arising in the mathematical models of such complex biological systems.
Many patterns of cell and tissue organization are specified during development by gradients of morphogens, substances that instruct cells to adopt different fates at different spatial locations. The work seeks to provide better understanding on embryonic tissue patterning and formation of morphogen gradients through mathematical modeling and computational analysis. The models are based on known experimental observations, and they explicitly incorporate the key morphogens, their regulators, and the important processes that are known from experiments to influence morphogen-mediated patterning. The project addresses how robust embryonic tissue patterns arise from complex interactions of many components and processes, and how the embryo shape affects morphogen-mediated patterning as embryonic development usually occurs in three-dimensional spatial geometries. The study requires development of new computational tools that can efficiently handle complex systems of equations arising from modeling embryonic development. The developed framework and models will be applicable broadly to various morphogen systems in different animal models. Quantitative theories of morphogenesis, based on mechanistic models with close integration with experiments, will advance our understanding of embryonic development. Such studies may lead to better understanding and treatment of birth defects and other human diseases related to abnormal embryonic development. The research project is interdisciplinary and hence will enhance interdisciplinary training at the interface between mathematics and biology for the students associated with the project.
