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，大多数形态生物质系统比预期的要复杂得多：反馈回路、秘密抑制剂、形态生物质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，产生健壮而复杂的形态生物质形态。这个项目涉及对果蝇胚胎发育过程中两个系统中这种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，一种膜结合的非扩散蛋白，在想象的翼盘中无翼形态原分布和信号转导中的作用。该项目的第二部分是研究某些反馈环在早期发育的背腹模式中在锐化形态梯度和降低噪音方面的作用。此外，研究人员还将为复杂几何结构中的刚性反应扩散方程开发高效、准确的自适应网格加密数值方法，以应对此类复杂生物系统数学模型中出现的计算挑战。在发育过程中，许多细胞和组织组织模式是由指示细胞在不同空间位置采用不同命运的形态成因物质的梯度指定的。这项工作旨在通过数学建模和计算分析，更好地理解胚胎组织的图案和形态梯度的形成。这些模型是以已知的实验观察为基础的，它们明确地包含了关键的形态原、它们的调节器以及从实验中已知的影响形态原介导的图案形成的重要过程。该项目研究了许多成分和过程的复杂相互作用如何产生强大的胚胎组织模式，以及胚胎形状如何影响形态因子介导的模式，因为胚胎发育通常发生在三维空间几何图形中。这项研究需要开发新的计算工具，能够有效地处理因模拟胚胎发育而产生的复杂方程系统。所开发的框架和模型将广泛适用于不同动物模型中的各种形态生成系统。形态发生的定量理论建立在机理模型的基础上，并与实验紧密结合，将促进我们对胚胎发育的理解。这样的研究可能有助于更好地理解和治疗出生缺陷和其他与胚胎发育异常有关的人类疾病。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之间的跨学科培训。

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.