Oscillations and Waves in Conductance-Based Neuronal Network Models

Rubin 0108857这位研究人员开发并应用了数学技术来研究基于电导的神经网络模型中的活动模式，该模型包含了一些特征，如连续耦合、扩散相互作用和参数值的异质性，这些特征在以前关于这些系统的数学工作中被很大程度上忽略了。许多数学结果涉及到对捕捉不同时间尺度上的动态的方程的子系统的推导和随后的分析。这项工作中的一个挑战是，所考虑的附加特征阻止了已知方法的应用，否则这些方法可以用来减小子系统的大小，从而促进分析。所研究的特殊活动模式包括：参与睡眠节律和跟踪头部方向的丘脑细胞群持续的、局部的活动；波在非均质神经元介质中的传播、阻断和反射，如分支、增厚或受损的神经元；以及脑干中不同种类的呼吸起搏细胞群中的周期性和混沌振荡。虽然这项工作是由特定的神经系统推动的，但它提供了具有广泛相关性的间接新步骤。因此，这个项目的结果提供了对模式形成和选择机制的洞察，这些机制适用于特定的神经元环境，但也构成了更普遍的现象。中枢神经系统的神经元网络通常可以显示多种类型的节律活动，范围从周期性的同步振荡爆发到活动的行波，再到更杂乱无章的模式。许多这种形式的活动似乎与基本的神经过程有关。研究人员的总体目标是对某些神经网络模型中出现的振荡群体节律和波传播进行数学研究，这些模型基于参与导航、呼吸和睡眠节律生成等不同任务的系统。这项工作阐明了允许这些网络支持不同活动模式并在它们之间进行调节的机制。这些结果导致了关于各种生物物理参数在塑造网络动力学中的作用的结论，个人贡献被梳理成一种纯粹的实验方法可能很难实现的方式。这些发现可以作为未来生物和计算实验的路标。

Rubin0108857 This investigator develops and applies mathematicaltechniques for the study of activity patterns inconductance-based neuronal network models incorporating features,such as continuous coupling, diffusive interactions, andheterogeneity in parameter values, that have largely beenneglected in previous mathematical work on these systems. Manyof the mathematical results relate to the derivation andsubsequent analysis of subsystems of equations capturing dynamicson disparate time scales. One challenge in this endeavor is thatthe additional features considered prevent the application ofknown methods that could otherwise be used to reduce thesubsystem sizes and thereby facilitate analysis. The particularactivity patterns that are investigated are sustained, localizedactivity of cell populations in the thalamus involved in sleeprhythms and in tracking head direction; wave propagation, block,and reflection in inhomogeneous neuronal media such as branching,thickening, or damaged neurons; and periodic and chaoticoscillations in a heterogeneous population of respiratorypacemaker cells in the brain stem. While this work is motivatedby particular neuronal systems, it provides new steps indirections with broad relevance. Thus, the results of thisproject yield insight into pattern formation and selectionmechanisms that apply in specific neuronal contexts but that alsoconstitute more generally occurring phenomena. Neuronal networks of the central nervous system cantypically display multiple types of rhythmic activity, rangingfrom periodic bursts of synchronized oscillations to travelingwaves of activity to more disorganized patterns. Many of theseforms of activity appear to be relevant to fundamental neuronalprocesses. The overall goal of the investigator is to studymathematically the oscillatory population rhythms and wavepropagation arising in certain models of neuronal networks, basedon systems involved in such disparate tasks as navigation,respiration, and the generation of sleep rhythms. This workelucidates the mechanisms that allow these networks to support,and to modulate between, distinct activity patterns. Theseresults lead to conclusions about the roles of variousbiophysical parameters in shaping network dynamics, withindividual contributions teased apart in a way that may be quitedifficult to achieve with a purely experimental approach. Suchfindings can then serve as guideposts for future biological andcomputational experiments.