Mathematical analysis of dynamic activity patterns in neuronal network models

鲁宾 研究者开发和应用数学技术，用于研究基于电导的神经元网络模型中的活动模式，其中包括生物病理学相关的时间尺度和参数，以及基于活动的模型，其中神经元群体累积活动的时间变化用单个方程跟踪。 分析的模型包括功能，如空间连续耦合，随时间变化的inputpatterns，和参数值的异质性，在以前的数学工作中被忽视，但这是相关的在广泛的神经系统。 开发的数学方法涉及到子系统的推导和随后的分析方程捕捉动态在不同的时间尺度。 此外，生物药理学为基础的模型的研究是一个新的和广泛适用的逆向方法，其中网络动态的观察是用来约束可能的模式，在网络中的细胞之间的连接的情况下，这种连接尚未实验确定的发展补充。 在这个项目中，神经元网络模型的数学研究的动机是关于正常和帕金森病条件之间神经元节律变化的实验数据;参与导航的神经元群的活动;以及帮助驱动呼吸的神经元的行为。 在每一种情况下，神经元网络通过参与有组织的放电模式并在这些模式之间切换来执行特定的任务。 相应地，本项目阐明了允许相关网络支持特定活动模式并在特定活动模式之间进行调节的机制。 这些分析结果导致了关于各种组件如何联合收割机来塑造神经元网络动力学的一般性结论，它们的特殊贡献以一种纯实验方法难以实现的方式分开。 所获得的理解非常适合指导未来的生物和计算实验。 特别是，该项目促进了与J. Smith在NIH的实验室的跨学科合作，该实验室允许直接访问实验数据和测试模型预测。 从事这项工作的学生在数学和生物学都感兴趣的一个重要领域接受跨学科培训。

Rubin The investigator develops and applies mathematical techniques forthe study of activity patterns in conductance-based neuronal networkmodels, which include biophysically relevant time scales andparameters, and in activity-based models, in which the temporalvariation in the cumulative activity of a neuronal population istracked with a single equation. The models analyzed include features,such as spatially continuous coupling, temporally varying inputpatterns, and heterogeneity in parameter values, that have largelybeen neglected in previous mathematical work yet which are relevant ina wide range of neuronal systems. The mathematical methods developedrelate to the derivation and subsequent analysis of subsystems ofequations capturing dynamics on disparate time scales. Further, thestudy of biophysically-based models is complemented by the developmentof a new and broadly applicable inverse approach, in whichobservations of network dynamics is used to constrain possiblepatterns of connections between cells in the network in cases wherethis connectivity has not been experimentally determined. The mathematical study of neuronal network models in this projectis motivated by experimental data on changes in neuronal rhythmsbetween normal and parkinsonian conditions; by activity of neuronalpopulations involved in navigation; and by the behavior of neuronsthat help to drive respiration. In each of these settings, networksof neurons perform particular tasks by engaging in, and switchingbetween, organized firing patterns. Correspondingly, this projectelucidates the mechanisms that allow the relevant networks to support,and to modulate between, particular modes of activity. Theseanalytical results lead to general conclusions about how variouscomponents combine to shape neuronal network dynamics, with theirparticular contributions teased apart in a way that would be difficultto achieve with a purely experimental approach. The understandinggained is well suited to guide future biological and computationalexperiments. In particular, this project promotes aninterdisciplinary partnership with J. Smith's lab at NIH, which allowsfor direct access to experimental data and testing of modelpredictions. Students engaged in the work receive interdisciplinarytraining in an important area of interest to both mathematics andbiology.