DYNAMIC PATTERN IN CHEMICALLY-REACTING SYSTEMS

这项研究的长期目标是加深对 相互作用的细胞聚集体的动力学行为，并应用于 对发育生物学中模式形成问题的认识 以及生理学方面的问题。拟议的研究分为三个部分 主要类别：(1)信号检测、自适应和 盘基网柄藻的聚集，(2)同步化的研究， 耦合单元中的锁相等现象，以及(3)对 广义图灵系统中的模式形成。其中的具体目标 (1)将盘基网柄菌的适应模型推广到 结合循环GMP网络的动态行为，以 在信号传递和趋化作用模型中结合了适应和传递， 并开发聚集的连续统描述。中的目标 (2)了解耦合细胞的动力学，包括受迫和 不受强迫，在各种耦合模式下，并分析一个现实的模型 以期了解起搏细胞的简单模型 心源性心律失常。(3)的目的是研究反应扩散。 具有调制扩散系数的方程以确定 这种模式中的空间格局形成对变化的敏感性 发育中组织的大小和形状。 解决这些问题的方法如下。首先是相关的 将对实验文献进行分析，以提供指导 数学模型的制定。接下来，控制方程将 被分析以发展对模型及其 参数敏感度。最后进行必要的分析和数值计算 将开发求解方程的技术，并将数值计算 将进行相关的模拟。 信号传递和适配方面的工作将有助于更好地理解 盘基网柄菌信号转导、趋化和聚集的研究 其他系统的趋化性，以及钙循环的动力学 核苷酸网络。对花纹形成的研究将有助于 对生物正常发育和异常发育的认识 系统，特别是了解反馈控制是如何 细胞间的相互作用影响细胞的稳定性和大小不变性 开发系统中的前置模式。网络中的同步问题分析 蜂窝网络应该提供对某些类型的起源的洞察 心律失常的作用，并可能阐明不同类型的 癫痫发生中的细胞-细胞相互作用。

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.