  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.
