Mathematical Sciences: Dynamics of a Small Neural System

这个项目将探索一个小型神经网络的动力学。该项目有三个主要方面：1.将神经网络建模为一个非线性微分方程组，并对网络中每个神经元的离子通道进行显式表示；2.用于提供输入的刺龙虾口胃神经节幽门回路的实验。用于模型参数值的数据和测试模型的预测3.数学研究以开发算法，该算法将导致模型内几何特征的显式计算工具一种名为dstool的数学软件包，康奈尔大学为探索动力系统而开发的，将被使用，并将把算法的进步融入到这个环境中。最初的重点将是电路中的起搏神经元。Guckenheimer将研究它的反应如何依赖于其环境的多参数变化，这些变化来自通道阻滞剂和神经调节剂的应用，以及细胞外离子浓度的变化。以前对突触效能及其对胺的依赖性的研究数据将用于对网络内神经元的相互作用进行建模。

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.