The Role of Neuronal Ionic Current Correlations and Level Sets in Network Activity

神经元产生驱动行为的活动是由于电流通过几个不同但高度特定的通道流过它们的膜。这些通道是由每个细胞合成的特殊蛋白质形成的，并嵌入细胞膜中。如果这些通道蛋白的数量不同，人们可以从这些细胞中记录到的活动（如有节奏的振荡）预计也会发生变化。然而，已经观察到相同类型的神经元表达的每种通道蛋白类型的数量变化极大，因此流过它们膜的电流变化很大，对它们的活动（例如，它们的振荡频率）的影响相对较小。它们的存在是否保证了这些细胞的活动是相似的，以及它们对网络功能的影响是什么，这些在很大程度上仍不清楚。这个项目的总体目标是研究神经元活动的哪些特征是由电流相关性调节的，这些活动的特征是否会传播到它们组成的网络中，以及这些关系遵循什么普遍原则或机制。该项目的研究成果将对数学生物学的各个领域产生影响，并将通过参与研究促进本科生和研究生的跨学科培养。在许多制剂中观察到相同神经元表达的离子电导水平的高度可变性。在一些相同的制剂中，已经确定了一些离子电导率的共变趋势。这种共变表现为神经元群体中这些电流的相关性，这被认为导致了非常相似类型的活动的产生，尽管单个电流的可变性，在这些电流的一种稳态缩放中。这个项目将测试这样一个假设，即离子电流子集之间的相关性决定了神经元活动的稳定和强大，并且这种影响会传播到网络的水平。受这些相关性影响的活动特征预计将接近振荡属性（例如，频率、幅度、占空比）的所谓活动水平集。水平集的数学概念仅在单个神经元的水平上有限地应用于动态神经元系统。项目团队将研究水平集的生成机制，特别是与已知神经网络（甲壳类幽门神经网络）的单个神经元中离子电流相关性的存在有关。本项目将(i)扩展这一点，以确定它们的存在对网络动力学的影响，（ii）确定是否存在通用机制，可以理解为离子电流性质的类别，而不是单个电流性质，决定水平集的出现，以及（iii）调查除了电导的幅度之外，还有哪些其他因素决定了水平集的存在。研究生和本科生将接受神经系统特性的多学科研究训练，包括计算、动力系统理论和实验。

Neurons generate the activity that drives behaviors thanks to electrical currents that flow across their membranes through several different but highly specific channels. These channels are formed by specialized proteins synthesized by each cell and embedded in their membranes. The activity that one can record from these cells (such as rhythmic oscillations) is expected to vary if the number of these channel-proteins varies. Yet, neurons of the same type have been observed to express extremely variable numbers of each channel-protein type, and thus extremely variable electrical currents flowing across their membranes, with relatively minimal effects on their activity (e.g., their oscillation frequency). Whether their existence ensures that the activity of these cells will be similar, and what the consequences for network function are, remains largely unclear. The general goal of this project is to examine what features of neuronal activity are regulated by electrical current correlations, whether these features of activity are propagated to the networks they form part of, and what universal principles or mechanisms these relationships obey. The results of this project are expected to have impact in various areas of mathematical biology, and the project will promote interdisciplinary training of undergraduate and graduate students through involvement in the research.High variability in the levels of ionic conductance expressed by identical neurons have been observed in a number of preparations. In some of the same preparations, a tendency of some of the ionic conductances to co-vary has been identified. This co-variation appears as correlations of these currents in populations of neurons, which are thought to lead to the generation of very similar types of activity despite the variability of individual currents, in a sort of homeostatic scaling of these currents. This project will test the hypothesis that the existence of correlations among subsets of ionic currents determines a stable and robust neuronal activity, and that this effect propagates to the level of the networks. The features of activity affected by these correlations are expected to lie close to so-called level sets of activity for the oscillation attributes (e.g., frequency, amplitude, duty cycle). The mathematical concept of level sets has been applied to dynamical neuronal systems to a limited degree and only at the level of single neurons. The project team will investigate the mechanisms of generation of level sets, particularly related to the existence of ionic current correlations, in single neurons of a well-known neuronal network (the crustacean pyloric network). This project will (i) extend this to determine the consequences of their existence for network dynamics, (ii) determine if there are universal mechanisms, understandable in terms of classes of ionic current properties rather than individual current properties, that determine the emergence of level sets, and (iii) investigate what other factors determine the existence of level sets besides the amplitude of the conductances. Graduate and undergraduate students will be trained in a multidisciplinary investigation of the properties of neuronal systems, including computations, dynamical systems theory, and experiments.