Skip to main content
SpringerLink
Log in

Nonlinear statistical data assimilation for HVC\(_{\mathrm{RA}}\) neurons in the avian song system

  • Original Article
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

With the goal of building a model of the HVC nucleus in the avian song system, we discuss in detail a model of HVC\(_{\mathrm{RA}}\) 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 \(V_\mathrm{s}(t)\) 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Sterratt D, Graham B, Gillies A, Willshaw D (2011) Principles of computational modeling in neuroscience. Cambridge University Press, Cambridge

    Book  Google Scholar 

  2. Johnston D, Wu SMS (1995) Foundations of cellular neurophysiology. MIT Press, Cambridge

    Google Scholar 

  3. Hahnloser RHR, Kozhevnikov AA, Fee MS (2002) An ultra-sparse code underlies the generation of neural sequences in a songbird. Nature 419(6902):65 (Erratum)

  4. Konishi M (1985) Birdsong: from behavior to neuron. Ann Rev Neurosci 8(1):125

    Article  CAS  PubMed  Google Scholar 

  5. Abarbanel HDI (2013) Predicting the future: completing models of observed complex systems. Springer, New York

    Book  Google Scholar 

  6. Toth BA, Kostuk M, Meliza CD, Margoliash D, Abarbanel HDI (2011) Dynamical estimation of neuron and network properties I: variational methods. Biol Cybern 105(3–4):217

    Article  PubMed  Google Scholar 

  7. Kostuk M, Toth BA, Meliza CD, Margoliash D, Abarbanel HDI (2012) Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods. Biol Cybern 106(3):155

    Article  PubMed  Google Scholar 

  8. Meliza CD, Kostuk M, Huang H, Nogaret A, Margoliash D, Abarbanel HD (2014) Estimating parameters and predicting membrane voltages with conductance-based neuron models. Biol Cybern 108(4):495

    Article  PubMed  Google Scholar 

  9. Abarbanel HDI, Bryant P, Gill PE, Kostuk M, Rofeh J, Singer Z, Toth B, Wong E (2011) Dynamical parameter and state estimation in neuron models. In: Ding M, Glanzman DL (eds) The dynamic brain: an exploration of neuronal variability and its functional significance. Oxford University Press, New York

    Google Scholar 

  10. Ye J, Rozdeba PJ, Morone UI, Daou A, Abarbanel HD (2014) Estimating the biophysical properties of neurons with intracellular calcium dynamics. Phys Rev E 89(6):062714

    Article  CAS  Google Scholar 

  11. Rey D, Eldridge M, Kostuk M, Abarbanel HDI, Schumann-Bischoff J, Parlitz U (2014) Accurate state and parameter estimation in nonlinear systems with sparse observations. Phys Lett A 378(11):869

    Article  CAS  Google Scholar 

  12. Ye J, Kadakia N, Rozdeba PJ, Abarbanel HDI, Quinn JC (2015) Improved variational methods in statistical data assimilation. Nonlinear Process Geophys 22:205

    Article  Google Scholar 

  13. Ye J, Rey D, Kadakia N, Eldridge M, Morone UI, Rozdeba PJ, Abarbanel HDI, Quinn JC (2015) Systematic variational method for statistical nonlinear state and parameter estimation. Phys Rev E 92(12):052901

  14. Vanier MC, Bower JM (1999) A comparative survey of automated parameter-search methods for compartmental neural models. J Comput Neurosci 7(2):149

    Article  CAS  PubMed  Google Scholar 

  15. Keren N, Peled N, Korngreen A (2005) Constraining compartmental models using multiple voltage recordings and genetic algorithms. J Neurophysiol 94(6):3730

    Article  PubMed  Google Scholar 

  16. Buhry L, Pace M, Saïghi S (2012) Global parameter estimation of an Hodgkin Huxley formalism using membrane voltage recordings: application to neuro-mimetic analog integrated circuits. Neurocomputing 81:75

  17. Gibb L, Gentner TQ, Abarbanel HDI (2009) Inhibition and recurrent excitation in a computational model of sparse bursting in song nucleus HVC. J Neurophysiol 102:1748

    Article  PubMed  PubMed Central  Google Scholar 

  18. Kosche G, Vallentin D, Long MA (2015) Interplay of inhibition and excitation shapes a premotor neural sequence. J Neurosci 35(3):1217

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Dayan P, Abbott LF (2005) Theoretical neuroscience: computational and mathematical modeling of neural systems. MIT Press, Cambridge, Massachusetts

    Google Scholar 

  20. Ermentrout GB, Terman DH (2010) Interdisciplinary applied mathematics. In: Mathematical foundations of neuroscience. Springer

  21. Izhikevich EM (2007) Dynamical systems in neuroscience: the geometry of excitability and bursting. Comput Neurosci. MIT Press, Cambridge

  22. Fee MS, Kozhevnikov AA, Hahnloser RHR (2004) Neural mechanisms of vocal sequence generation in the songbird. Ann N Y Acad Sci 1016:153–170

    Article  PubMed  Google Scholar 

  23. Jin DZ, Ramazanoglu FM, Seung HS (2007) Neural mechanisms of vocal sequence generation in the songbird. J Comput Neurosci 23(3):283

    Article  PubMed  Google Scholar 

  24. Long MA, Jin DZ, Fee MS (2010) Support for a synaptic chain model of neuronal sequence generation. Nature 48(7322):394

    Article  CAS  Google Scholar 

  25. Daou A, Ross MT, Johnson F, Hyson RL, Bertram R (2013) Electrophysiological characterization and computational models of HVC neurons in the zebra finch. J Neurophysiol 110(5):1227

    Article  CAS  PubMed  Google Scholar 

  26. Kubota M, Taniguchi I (1998) Electrophysiological characteristics of classes of neuron in the HVc of the zebra finch. J Neurophysiol 80(2):914

    CAS  PubMed  Google Scholar 

  27. Mooney R, Prather JF (2005) The HVC microcircuit: the synaptic basis for interactions between song motor and vocal plasticity pathways. J Neurosci 25(8):1952

    Article  CAS  PubMed  Google Scholar 

  28. Kandel ER, Schwartz JH, Jessell TM (eds) (2000) Principles of neural science, 4th edn. McGraw-Hill, New York

    Google Scholar 

  29. Laplace, P (1774) Memoir on the probability of causes of events. Mémoires de Mathématique et de Physique Tome Sixième

  30. Zinn-Justin J (2002) Quantum field theory and critical phenomena. Oxford University Press, Oxford

    Book  Google Scholar 

  31. Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Progr 106(1):25

    Article  Google Scholar 

  32. Graber MH, Helmchen F, Hahnloser RHR (2013) Activity in a premotor cortical nucleus of zebra finches is locally organized and exhibits auditory selectivity in neurons but not in glia PLoS ONE 8(12):1

  33. Peh W, Roberts T, Mooney R (2015) Imaging auditory representations of song and syllables in populations of sensorimotor neurons essential to vocal communication. J Neurosci 35:5589

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of California, 9500 Gilman Drive, La Jolla, CA, 92903-0402, USA

    Nirag Kadakia, Daniel Breen & Uriel Morone

  2. BioCircuits Institute, University of California, 9500 Gilman Drive, La Jolla, CA, 92903-0328, USA

    Eve Armstrong

  3. Department of Organismal Biology and Anatomy, University of Chicago, 1027 E. 57th Street, Chicago, IL, 63607, USA

    Arij Daou & Daniel Margoliash

  4. Marine Physical Laboratory (Scripps Institution of Oceanography), Department of Physics, University of California, 9500 Gilman Drive, La Jolla, CA, 92903, USA

    Henry D. I. Abarbanel

Authors
  1. Nirag Kadakia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eve Armstrong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Breen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Uriel Morone
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Arij Daou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Daniel Margoliash
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Henry D. I. Abarbanel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nirag Kadakia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kadakia, N., Armstrong, E., Breen, D. et al. Nonlinear statistical data assimilation for HVC\(_{\mathrm{RA}}\) neurons in the avian song system. Biol Cybern 110, 417–434 (2016). https://doi.org/10.1007/s00422-016-0697-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-016-0697-3

Keywords

Search

Navigation