鸟类鸣唱系统中HVC $_{\text{RA}}$神经元的非线性统计数据同化
Nonlinear Statistical Data Assimilation for HVC$_{\text{RA}}$ Neurons in the Avian Song System
摘要：
与建立一个模型的HVC核在鸟类的鸣叫系统的目标，我们详细讨论了模型的HVC $_{\text{RA}}$投射神经元组成的躯体隔间与快速Na $^+$和K $^+$电流和树突隔间与较慢的Ca $^{2+}$动力学。我们表明，该模型定性地表现出许多观察到的电生理行为。然后，我们展示了在数值程序如何可以设计和分析可行的实验室实验，允许所有的许多参数和不可测的动力学变量的估计，观察体细胞电压$V_s(t)$单独。该过程的关键是首先估计与Ca相关的慢动态，阻断快Na和K变化，然后在Ca参数固定的情况下估计快Na和K动态。这种时间尺度的分离提供了一种用于完成完整神经元模型的数值鲁棒性方法，并且当观测完成时，通过预测来测试该方法的功效。模拟提供了一个框架的切片制备实验，并说明了使用数据同化方法设计这些实验。
英文摘要：
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.
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