标题： 非线性统计数据同化用于鸟类鸣叫系统中的HVC$_{\text{RA}}$神经元 显示英文标题

标题： Nonlinear Statistical Data Assimilation for HVC$_{\text{RA}}$ Neurons in the Avian Song System

摘要： 为了构建鸟类鸣叫系统中HVC核的模型，我们详细讨论了一个由体细胞区和树突区组成的HVC$_{\text{RA}}$投射神经元模型，体细胞区包含快速钠离子$^+$和钾离子$^+$电流，树突区包含较慢的钙离子$^{2+}$动力学。 我们展示了该模型定性地表现出许多观察到的电生理行为。 然后，我们通过数值方法说明如何设计和分析可行的实验室实验，从而在仅观察体细胞电压$V_s(t)$的情况下估计所有参数和未测量的动力学变量。 此过程的关键是首先估计与钙相关的慢动力学，阻断快速钠和钾的变化，然后在钙参数固定的情况下，估计快速钠和钾的动力学。 时间尺度的分离为完成完整的神经元模型提供了一种数值上稳健的方法，当观测完整时，该方法的有效性通过预测进行了测试。 模拟提供了一个切片制备实验的框架，并说明了数据同化方法在这些实验设计中的应用。 显示英文摘要

摘要： With the goal of building a model of the HVC nucleus in the avian song system, we discuss in detail a model of HVC$_{\text{RA}}$ projection neurons comprised of a somatic compartment with fast Na$^+$ and K$^+$ currents and a dendritic compartment with slower Ca$^{2+}$ dynamics. We show this model qualitatively exhibits many observed electrophysiological behaviors. We then show in numerical procedures how one can design and analyze feasible laboratory experiments that allow the estimation of all of the many parameters and unmeasured dynamical variables, given observations of the somatic voltage $V_s(t)$ alone. A key to this procedure is to initially estimate the slow dynamics associated with Ca, blocking the fast Na and K variations, and then with the Ca parameters fixed, estimate the fast Na and K dynamics. This separation of time scales provides a numerically robust method for completing the full neuron model, and the efficacy of the method is tested by prediction when observations are complete. The simulation provides a framework for the slice preparation experiments and illustrates the use of data assimilation methods for the design of those experiments.