MATHEMATICAL APPROACH TO MODELING DENDRITIC GROWTH

神经元过程的设计原理的知识是基本的 来理解神经元之间的功能性相互作用。 该研究旨在建立两个统一的数学模型， 树枝状生长称为树型和树生长分支 过程模型 将实施的定量特征 这些模型包括树枝状树的几何分支模式， 枝条的长度、直径和发育时间 这些特征。 估计数学模型的参数并检验预测 这个参数化模型与真实的树突树的观察结果的对比， 从发育中的大鼠收集树突树的数据库， 成年大鼠和成年恒河猴。 将收集树突状数据 从海马和齿状回在体外和体内。 用于体内 大鼠树突生长的研究，锥体神经元 海马和齿状回的颗粒细胞将在 出生后第5、10、15、24、48和90天。 对于体外研究， 在接种后第2天测量海马神经元的树突， 4、6、8和12。 数学模型将问题的复杂性降低到几个模型 参数 模型建立后，只有参数 对每个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数量。 的 拟议中的研究应能增进对枝晶生长的理解， 行为，有助于促进计算神经元模型的设计， 并发展数学和统计方法， 不同环境下树枝状生长的比较。

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.