MATHEMATICAL APPROACH TO MODELING DENDRITIC GROWTH

了解神经元突起的设计原理是基础。 以了解神经元之间存在的功能相互作用。 建议的研究是建立两个统一的数学模型 树枝生长称为树型和树木生长分枝 流程模型。将在以下方面实施的量化特征 这些模型包括树枝状树的几何分枝模式， 枝条的长度和直径，以及时间发展 这些功能中。 估计数学模型的参数并检验预测 该参数化模型与真实树枝状树的观测结果相对照， 将从发育中的大鼠身上收集树枝状树的数据库， 成年老鼠和成年恒河猴。将收集树枝状数据 从体外和体内的海马体和齿状回中提取。用于活体内 大鼠树突状细胞生长的研究 海马体和齿状回颗粒细胞将在 出生后第5、10、15、24、48和90天。对于体外研究， 在电镀后第2天测量海马神经元树突， 4、6、8和12。 一个数学模型将一个问题的复杂性减少到几个模型 参数。一旦建立了模型，只有参数具有 对每一种新的实验情况进行估计。因此，这些 数学模型可以减少生物实验的次数。这个 拟议的研究应加强对树枝状生长的理解 行为，有助于促进计算神经元模型的设计 并制定可靠的数学和统计方法 不同环境中树枝状生长的比较。

A knowledge of the design principles of neuronal processes is fundamental to understanding the functional interactions that exist between neurons. The proposed study is to develop two unified mathematical models of dendritic growth called the tree-pattern and tree growth branching process models. The quantitative features which will be implemented in these models include the geometric branching pattern of dendritic trees, the lengths and the diameters of the branches, and the time development of these features. To estimate parameters of the mathematical models and to test predictions of this parameterized model against observations of real dendritic trees, a database of dendritic trees will be collected from developing rats, adults rats, and adult rhesus monkeys. Dendritic data will be collected from the hippocampus and dentate gyrus in vitro and in vivo. For in vivo studies of dendritic growth in the rats, pyramidal neurons of the hippocampus and granule cells of the dentate gyrus will be digitized at postnatal days 5, 10, 15, 24, 48, and 90. For in vitro studies, the dendrites of hippocampal neurons will be measured at postplating days 2, 4, 6, 8, and 12. A mathematical model reduces the complexity of a problem to a few model parameters. Once a model has been established, only the parameters have to be estimated for each new experimental situation. Thus, these mathematical models can reduce the number of biological experiments. The proposed studies should enhance the understanding of dendritic growth behavior, help facilitate the design of computational neuronal models, and develop mathematical and statistical methodology for reliable comparisons of dendritic growth in different environments.