Mathematical Sciences: Model Mechanisms for the Formation and Spatial Patterning of Teeth Primordia

数学科学：牙齿原基形成和空间图案的模型机制

• 批准号: 9106848
• 负责人: James Murray
• 金额: $ 16.5万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1996-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106848&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Model; Mechanisms; Formation

The Principal Investigator will study possible mechanisms involved in the formation and spatial distribution of tooth primordia. The preliminary model will be closely based on experimental evidence from alligators Alligator mississippiensis and the known properties of cells. The case for the alligator as a model for research in craniofacial development is convincingly made by Ferguson (1981). In particular the PI's aim to reproduce a specific pattern, namely the positions and initiation sequence of the first seven teeth in the right half lower jaw of the alligator. The model will be a quantitative realization of a caricature of the descriptive model for tooth formation in Alligator mississippiensis described by Westergaard and Ferguson (1987). The mathematical model will involve a system of nonlinear coupled partial differential equations describing both the mechanical properties of the epithelial and mesenchymal cells as well as the reaction and diffusion of various chemicals. Thus, the model will include elements of both the reaction-diffusion and the mechanochemical approaches to pattern formation, and will incorporate tissue interaction processes. In the modelling the emphasis will be on the greatest possible biological realism at the expense of mathematical simplicity.

主要研究者将研究可能的机制 参与牙齿的形成和空间分布 原基 初步模型将紧密基于 短吻鳄的实验证据 和细胞的已知特性。 鳄鱼的案子 颅面发育的研究模型令人信服地 Ferguson（1981） 特别是PI的目的是复制 一种特定的模式，即位置和启动序列 在右下颌的前七颗牙齿中， 鳄鱼。 该模型将是一个量化的实现， 牙齿形成描述模型的漫画， 密西西比短吻鳄，Westergaard和Ferguson描述 （1987年）。 数学模型将涉及一个非线性系统， 耦合的偏微分方程描述了 上皮细胞和间充质细胞的机械性能， 以及各种化学物质的反应和扩散。 因此，在本发明中， 该模型将包括反应-扩散 和机械化学方法来形成图案， 结合组织相互作用过程。 在建模中， 重点将是最大可能的生物现实主义， 数学简单性的代价。