Nonlinear Dynamics of Electrophysiological Neural Models

研究者和他的同事研究了神经动力学分支和神经元电生理特征之间的关系。人们对分岔在神经元动力学中的作用有了越来越多的了解。事实上，在不了解电生理细节的情况下，对神经元模型中所有分支的了解可以解释神经元活动的一些特征，如振荡电位的存在、同步、爆发、兴奋性等。然而，人们对电生理与神经动力学分岔之间的关系了解甚少。例如，为什么某些离子电流或它们的组合会导致andronov - hopf分叉，而不是极限环分叉上的鞍节点？（这两种类型的分叉描述了霍奇金对可兴奋神经元的分类。）超过100种不同的可识别的分叉导致了活动的爆发模式。一个关键的问题是，对于一种给定的爆发活动，人们是否能够确定必须（或不必须）涉及何种离子电流组合。研究者和他的同事在这里介绍了最小电生理模型的概念，这些模型分为电压门控、第二信使门控和可变能势。他们将这种分类映射到神经动力学中现有的分岔机制分类上。这使我们对电生理系统的非线性动力学有了更深的理解。大脑是如何编码和处理信息的？迄今为止，数学在这个问题的研究中发挥了重要作用，它创造了分析生命科学和医学研究人员获得的结果的方法。关于神经组织如何利用离子电流维持和传播电活动，已经有了完善的电生理学理论。与此同时，有一种基于分支规范模型的新兴数学理论，分支是生物制剂对刺激的反应中可观察到的变化。该项目通过将动力系统（数学结构）与电生理学相一致的术语进行分类，将这两条研究线结合在一起。结果是对电生理系统中的非线性现象有了更深的理解。

Hoppensteadt0109001 The investigator and his colleague study the relationbetween bifurcations in neural dynamics and electrophysiologicalfeatures of neurons. There is growing understanding of the roleof bifurcations in neuron dynamics. Indeed, knowledge of allbifurcations in a neuron model can explain some features ofneuron activity, such as the existence of oscillatory potentials,synchronization, bursting, excitability, etc., without knowingelectrophysiological details. However, there is littleunderstanding of the relationship between electrophysiology andbifurcations in neural dynamics. For example, why do certainionic currents or combinations of them result in an Andronov-Hopfbifurcation but not a saddle-node on limit cycle bifurcation?(These two types of bifurcations describe Hodgkin'sclassification of excitable neurons.) Over 100 different kindsof recognizable bifurcations result in bursting patterns ofactivity. A key question is whether or not one can determine fora given type of bursting activity what combinations of ioniccurrents must (or must not) be involved. The investigator and hiscolleague introduce here a notion of minimal electrophysiologicalmodels classified by voltage gated, second messenger gated, andvariable Nernst potentials. They map this classification onto theexisting classification of bifurcation mechanisms in neurondynamics. This yields a deeper understanding of nonlineardynamics of electrophysiological systems. How does a brain encode and process information?Mathematics has played an important role in studies of thisproblem to date by creating methods for analyzing resultsobtained by life science and medical researchers. There is awell-developed electrophysiological theory of how neural tissuecan sustain and propagate electrical activity using ioniccurrents. At the same time there is an emerging mathematicaltheory based on canonical models of bifurcations, which areobservable changes in a biological preparation in response tostimulation. This project brings these two lines of inquirytogether by classifying dynamical systems (mathematicalstructures) in terms that are consistent with electrophysiology.The result is a deeper understanding of nonlinear phenomena inelectrophysiological systems.