DYNAMIC PATTERN IN CHEMICALLY-REACTING SYSTEMS

这项研究的长期目标是进一步了解 相互作用的细胞聚集体的动力学行为，并应用 这些知识对于发育生物学中模式形成的问题 以及生理学上的问题 拟议的研究分为三个福尔斯 主要类别：（1）信号检测、自适应和 在盘基网柄藻中的聚集，（2）同步化研究， 锁相和其他现象的耦合细胞，和（3）研究 广义图灵系统中的模式形成 具体目标是 (1)将盘基网柄藻的适应模型扩展到 结合环GMP网络的动力学行为， 在信号和趋化性模型中结合适应和中继， 并发展聚合的连续描述。 的目标而 (2)是为了了解耦合细胞的动力学， 在各种耦合模式下，分析一个现实的模型 起搏细胞的研究，以期了解 心脏心律失常 （3）的目的是研究反应扩散 方程与调制扩散系数，以确定 在这种模式中，空间格局形成对环境变化的敏感性 发育组织的大小和形状。 解决这些问题的方法如下。 有限公司的相关 实验文献将进行分析，以提供指导， 建立数学模型。 接下来，控制方程将 进行分析，以发展对模型及其 参数灵敏度 最后，必要的分析和数值 解决方程的技术将得到发展，数值 将进行相关模拟。 信号中继和适应方面的工作将有助于更好地理解 的信号，趋化性和聚集， 在其他系统中的趋化性，以及钙循环的动力学 核苷酸网络 图案形成的研究将有助于 对生物学中正常和异常发育的理解 系统，特别是了解如何反馈控制， 细胞之间的相互作用影响细胞的稳定性和大小不变性， 在开发系统中的预模式。 系统的同步分析 蜂窝网络应该提供对某些类型的起源的深入了解 心律失常，并可能阐明各种类型的作用， 癫痫发生中的细胞间相互作用

The long range objectives of this research are to further the understanding of the dynamical behavior of aggregates of interacting cells, and to apply this knowledge to problems of pattern formation in developmental biology and to problems in physiology. The proposed research falls into three major categories: (1) studies on signal detection, adaptation and aggregation in Dictyostelium discoideum, (2) studies on synchronization, phase-locking and other phenomena in coupled cells, and (3) studies on pattern formation in generalized Turing systems. The specific aims in (1)\are to extend a model of adaptation in Dictyostelium discoideum to incorporate the dynamical behavior of the cyclic GMP network, to incorporate adaptation and relay in a model for signaling and chemotaxis, and to develop continuum descriptions of aggregation. The objectives in (2) are to understand the dynamics of coupled cells, both forced and unforced, under various modes of coupling, and to analyze a realistic model of pacemaker cells with a view toward understanding simple models of caridac arrhythmias. The aim in (3) is to study reaction-diffusion equations with modulated diffusion coefficients to determine the sensitivity of spatial pattern formation in such models to changes in the size and shape of the developing tissue. The approach to these problems will be as follows. First the relevant experimental literature will be analyzed to provide guidance in the formulation of the mathematical models. Next the governing equations will be analyzed to develop a qualitative understanding of the model and its parametric sensitivity. Finally the necessary analytical and numerical techniques for solving the equations will be developed, and the numerical simulations involved will be done. The work on signal relay and adaptation will lead to a better understanding of signaling, chemotaxis and aggregation in Dictyostelium discoideum, of chemotaxis in other systems, and of the dynamics of calcium-cyclic nucleotide networks. The studies on pattern formation will contribute to the understanding of both normal and abnormal development in biological systems, and in particular, to the understanding of how feedback control of interactions between cells affects the stability and size-invariance of prepatterns in developing systems. The analysis of synchronization in cellular networks should provide insight into the origin of certain types of cardiac arrhythmias, and may elucidate the role of various types of cell-cell interactions in epileptogenesis.