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With the goal of building a model of the HVC nucleus in the avian songsystem, we discuss in detail a model of HVC$_{\text{RA}}$ projection neuronscomprised of a somatic compartment with fast Na$^+$ and K$^+$ currents and adendritic compartment with slower Ca$^{2+}$ dynamics. We show this modelqualitatively exhibits many observed electrophysiological behaviors. We thenshow in numerical procedures how one can design and analyze feasible laboratoryexperiments that allow the estimation of all of the many parameters andunmeasured dynamical variables, given observations of the somatic voltage$V_s(t)$ alone. A key to this procedure is to initially estimate the slowdynamics associated with Ca, blocking the fast Na and K variations, and thenwith the Ca parameters fixed, estimate the fast Na and K dynamics. Thisseparation of time scales provides a numerically robust method for completingthe full neuron model, and the efficacy of the method is tested by predictionwhen observations are complete. The simulation provides a framework for theslice preparation experiments and illustrates the use of data assimilationmethods for the design of those experiments.

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