Mathematical Sciences: Modeling Cellular Control Systems

本研究将继续研究元胞控制系统和延迟微分方程。有三个主要的研究领域。第一个领域是与J. W. Zyskind博士合作完成的关于大肠杆菌开始复制的建模的跨学科研究，开发数学模型以帮助我们理解DNA开始复制的实验观察。第二个项目使用解析和数值方法研究大小和分区对具有扩散和延迟的元胞控制模型稳定性的影响。建立了动态增长模型，并与实验数据进行了比较。第三部分用解析和数值方法探讨了一类双时滞线性微分方程的稳定性。找到了分岔曲面，并研究了将其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。

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.