Computational Analysis of Morphogensis

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。最近的许多实验和理论研究表明，大多数形态因子系统比预期的要复杂得多：反馈回路、分泌抑制剂、形态因子之间的合作相互作用以及具有复杂边界条件的高空间维度共同作用，产生强大而复杂的形态因子模式。该项目涉及果蝇胚胎发育过程中两个系统中复杂相互作用的数学和计算研究。该项目的第一部分是研究dally样蛋白的作用，dally样蛋白是一种膜结合的非扩散蛋白，在无翼形态素分布和成像翼盘的信号传导中起作用。该项目的第二部分是研究某些反馈回路在早期发育中在背-腹模式中锐化形态梯度和降噪中的作用。此外，研究人员将开发有效和准确的数值方法与自适应网格细化刚性反应-扩散方程在复杂的几何形状，以满足在这种复杂的生物系统的数学模型中出现的计算挑战。在发育过程中，细胞和组织组织的许多模式都是由形态因子的梯度决定的，形态因子是指示细胞在不同空间位置采取不同命运的物质。该工作旨在通过数学建模和计算分析，更好地了解胚胎组织的模式和形态梯度的形成。这些模型是基于已知的实验观察，它们明确地结合了关键的形态因子、它们的调节因子，以及从实验中已知的影响形态因子介导的模式的重要过程。该项目研究了强大的胚胎组织模式是如何从许多成分和过程的复杂相互作用中产生的，以及胚胎形状如何影响形态细胞介导的模式，因为胚胎发育通常发生在三维空间几何中。这项研究需要开发新的计算工具，能够有效地处理由胚胎发育建模产生的复杂方程组。开发的框架和模型将广泛适用于不同动物模型的各种形态系统。形态发生的定量理论建立在与实验紧密结合的机制模型的基础上，将促进我们对胚胎发育的理解。这些研究可能导致更好地理解和治疗出生缺陷和其他与胚胎异常发育有关的人类疾病。该研究项目是跨学科的，因此将加强与该项目相关的学生在数学和生物学界面上的跨学科培训。

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.