# Nonlinear Statistical Data Assimilation for HVCRA Neurons in the Avian Song System

arXiv: https://arxiv.org/abs/1608.04005 · HTML: https://mlsanity.com/paper/1608.04005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2016.

## Built on by (most cited first, 1 of 1)

- [Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.08742/) (2026)

## Abstract (arXiv)

With the goal of building a model of the HVC nucleus in the avian song system, we discuss in detail a model of HVCRA projection neurons comprised of a somatic compartment with fast Na^+ and K^+ currents and a dendritic compartment with slower Ca2+ 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 Vs(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.