Oscillations and Waves in Conductance-Based Neuronal Network Models

该研究者开发并应用数学技术来研究基于非传导的神经网络模型的活动模式，这些模型结合了诸如连续耦合、扩散相互作用和参数值的异质性等特征，这些特征在这些系统的先前数学工作中很大程度上被忽视了。许多数学结果涉及到在不同时间尺度上捕获动态方程的子系统的推导和后续分析。这项工作的一个挑战是，考虑到的附加功能阻止了已知方法的应用，这些方法可以用来减少子系统的大小，从而促进分析。被研究的特定活动模式是持续的，丘脑中参与睡眠节律和跟踪头部方向的细胞群的局部活动；波在非均匀神经元介质（如分支、增厚或受损神经元）中的传播、阻滞和反射；以及脑干中异质呼吸起搏器细胞群的周期性和混沌振荡。虽然这项工作是由特定的神经系统驱动的，但它提供了具有广泛相关性的新步骤。因此，该项目的结果对模式形成和选择机制产生了深入的了解，这些模式形成和选择机制适用于特定的神经元环境，但也构成了更普遍发生的现象。中枢神经系统的神经网络通常可以表现出多种类型的节律性活动，从同步振荡的周期性爆发到活动的行进波，再到更无组织的模式。这些活动的许多形式似乎与基本的神经元过程有关。研究者的总体目标是在数学上研究在某些神经网络模型中产生的振荡种群节律和波传播，这些模型基于涉及诸如导航、呼吸和睡眠节律产生等不同任务的系统。这项工作阐明了允许这些网络支持不同活动模式并在不同活动模式之间进行调节的机制。这些结果得出了关于各种生物物理参数在形成网络动力学中的作用的结论，其中个体的贡献以一种可能很难用纯粹的实验方法实现的方式分开。这些发现可以作为未来生物和计算实验的指南。

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.