Biological Cybernetics

, Volume 108, Issue 4, pp 495–516 | Cite as

Estimating parameters and predicting membrane voltages with conductance-based neuron models

  • C. Daniel Meliza
  • Mark Kostuk
  • Hao Huang
  • Alain Nogaret
  • Daniel Margoliash
  • Henry D. I. Abarbanel
Original Paper

Abstract

Recent results demonstrate techniques for fully quantitative, statistical inference of the dynamics of individual neurons under the Hodgkin–Huxley framework of voltage-gated conductances. Using a variational approximation, this approach has been successfully applied to simulated data from model neurons. Here, we use this method to analyze a population of real neurons recorded in a slice preparation of the zebra finch forebrain nucleus HVC. Our results demonstrate that using only 1,500 ms of voltage recorded while injecting a complex current waveform, we can estimate the values of 12 state variables and 72 parameters in a dynamical model, such that the model accurately predicts the responses of the neuron to novel injected currents. A less complex model produced consistently worse predictions, indicating that the additional currents contribute significantly to the dynamics of these neurons. Preliminary results indicate some differences in the channel complement of the models for different classes of HVC neurons, which accords with expectations from the biology. Whereas the model for each cell is incomplete (representing only the somatic compartment, and likely to be missing classes of channels that the real neurons possess), our approach opens the possibility to investigate in modeling the plausibility of additional classes of channels the cell might possess, thus improving the models over time. These results provide an important foundational basis for building biologically realistic network models, such as the one in HVC that contributes to the process of song production and developmental vocal learning in songbirds.

Keywords

Data assimilation Neuronal dynamics Ion channel properties Song system 

Notes

Acknowledgments

B. Toth contributed software used to generate IPOPT code. We acknowledge many productive conversations with P. E. Gill on numerical optimization, and we thank A. Daou for conversations about neuron classes in HVC. Support from the US Department of Energy (Grant DE-SC0002349 ) and the National Science Foundation (Grants IOS-0905076, IOS-0905030, and PHY-0961153) is gratefully acknowledged. Partial support from the NSF sponsored Center for Theoretical Biological Physics is also appreciated.

Supplementary material

422_2014_615_MOESM1_ESM.zip (6.6 mb)
Supplementary material 1 (zip 6779 KB)
422_2014_615_MOESM2_ESM.pdf (301 kb)
Supplementary material 2 (pdf 300 KB)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • C. Daniel Meliza
    • 1
    • 2
  • Mark Kostuk
    • 3
  • Hao Huang
    • 1
  • Alain Nogaret
    • 4
  • Daniel Margoliash
    • 1
  • Henry D. I. Abarbanel
    • 5
  1. 1.Department of Organismal Biology and AnatomyUniversity of ChicagoChicagoUSA
  2. 2.Department of PsychologyUniversity of VirginiaCharlottesvilleUSA
  3. 3.Department of PhysicsUniversity of California, San DiegoLa JollaUSA
  4. 4.Department of PhysicsUniversity of BathBathUK
  5. 5.Department of Physics and Marine Physical Laboratory (Scripps Institution of Oceanography), Center for Theoretical Biological PhysicsUniversity of California, San DiegoLa JollaUSA

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