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

标题： Nonlinear Statistical Data Assimilation for HVC 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\textsubscript{RA}投射神经元模型，体细胞区包含快速的Na$^+$和K$^+$电流，树突区包含较慢的Ca$^{2+}$动态。 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，我们通过数值方法展示如何设计和分析可行的实验室实验，以估计所有许多参数和未测量的动力学变量，仅给出体细胞电压$V_s(t)$的观测值。 此过程的关键是首先估计与Ca相关的慢动态，阻断快速的Na和K变化，然后在Ca参数固定的情况下，估计快速的Na和K动态。 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，并通过当观测完整时的预测来测试该方法的有效性。 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\textsubscript{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, give 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.