Mathematical Sciences: Dynamics of a Small Neural System

这个项目将探索一个小的神经动力学 网络 该项目有三个主要方面： 1.将神经网络建模为非线性系统， 离子显式微分方程 网络中每个神经元的通道 2.口胃幽门环路实验 多刺龙虾的神经节， 数据的参数值的模型和测试 模型预测 3.数学研究来开发算法， 几何特征的显式计算工具 在模型中 一个名为dstool的数学软件包， 康奈尔大学的动力系统的探索，将被使用， 并将算法的进步融入到这个环境中。 最初的重点将是起搏神经元内的 电路. Guckenheimer将调查其反应如何取决于 根据环境的多参数变化， 通道阻滞剂和神经调节剂的应用 细胞外离子浓度的变化。 数据从 以前的研究突触的功效和他们的依赖性， 胺将用于模拟神经元之间的相互作用， 在网络中。

This project will explore the dynamics of a small neural network. There are three major aspects to the project: 1. modelling the neural network as a system of nonlinear differential equations with explicit representation of ion channels for each neuron within the network 2. experiments on the pyloric circuit of the stomatogastric ganglion of spiny lobsters that will be used to provide input data for parameter values of the models and to test predictions of the models 3. mathematical research to develop algorithms that will lead to tools for the explicit computation of geometric features within the models A mathematical software package called dstool, developed at Cornell for the exploration of dynamical systems, will be used, and will incorporate algorithmic advances into this environment. The initial emphasis will be the pacemaker neuron within the circuit. Guckenheimer will investigate how its response depends upon multiparameter variations of its environment that come from application of channel blockers and neuromodulators and from changes in extracellular ionic concentrations. Data from previous studies of synaptic efficacy and their dependencies upon amines will be used in modelling the interactions of neurons within the network.