Mathematical Sciences: Modeling Cellular Control Systems

数学科学：细胞控制系统建模

• 批准号: 9007718
• 负责人: Joseph Mahaffy
• 金额: $ 5.69万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-08-01 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007718&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Modeling; Cellular; Control

This investigation will continue the study of cellular control systems and delay differential equations. There are three main areas of study. The first area is an interdisciplinary study done in collaboration with Dr. J. W. Zyskind on the modeling of initiation of replication in Escherichia coli, Mathematical models are developed to aid in our understanding of experimental observations on initiation of DNA replication. The second project uses analytical and numerical methods to study the effects of size and compartmentalization on the stability of cellular control models with diffusion and delays. Dynamic growth models are developed and compared to experimental data. The third area explores the stability of a linear differential equation with two delays using analytical and numerical methods. Bifurcation surfaces are found, and methods are investigated to connect their geometries to analytical results. The first two projects link mathematical studies to current biological problems. All three problems require the development of new techniques of analysis that can be applied to many modeling problems.

这项研究将继续对细胞控制系统和时滞微分方程组的研究。主要研究领域有三个。第一个领域是与J·W·齐斯金德博士合作进行的关于在大肠杆菌中启动复制的建模的跨学科研究，数学模型被开发来帮助我们理解关于DNA复制启动的实验观察。第二个项目使用解析和数值方法来研究大小和划分对具有扩散和时滞的细胞控制模型稳定性的影响。建立了动态生长模型，并与实验数据进行了比较。第三部分利用解析和数值方法研究了一类双时滞线性微分方程解的稳定性。找到了分叉曲面，并研究了将它们的几何形状与分析结果联系起来的方法。前两个项目将数学研究与当前的生物学问题联系起来。所有这三个问题都需要开发新的分析技术，这些技术可以应用于许多建模问题。