[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

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

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

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.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

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

Similar content being viewed by others

References

  • Abarbanel HDI (2009) Effective actions for statistical data assimilation. Phys Lett A 373:4044–4048

    Article  CAS  Google Scholar 

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

    Book  Google Scholar 

  • Abarbanel HDI, Creveling D, Jeanne J (2008) Estimation of parameters in nonlinear systems using balanced synchronization. Phys Rev E 77(016):208

    Google Scholar 

  • Abarbanel HDI, Creveling DR, Farsian R, Kostuk M (2009) Dynamical state and parameter estimation. SIAM J Appl Dyn Syst 8(4):1341–1381

    Article  Google Scholar 

  • Abarbanel HDI, Kostuk M, Whartenby W (2010) Data assimilation with regularized nonlinear instabilities. Q J Meteor Soc 136(648):769–783

    Google Scholar 

  • 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: Glanzman D, Ding M (eds) The dynamic brain: an exploration of neuronal variability and its functional significance, chap 8. Oxford University Press, New York

  • Achard P, Schutter ED (2006) Complex parameter landscape for a complex neuron model. PLoS Comput Biol 2(7):e94. doi:10.1371/journal.pcbi.0020094

    Article  PubMed Central  PubMed  Google Scholar 

  • Amador A, Perl YS, Mindlin GB, Margoliash D (2013) Elemental gesture dynamics are encoded by song premotor cortical neurons. Nature 495(7439):59–64. doi:10.1038/nature11967

    Article  CAS  PubMed  Google Scholar 

  • Ayali A, Lange AB (2010) Rhythmic behaviour and pattern-generating circuits in the locust: key concepts and recent updates. J Insect Physiol 56(8):834–843. doi:10.1016/j.jinsphys.2010.03.015

    Article  CAS  PubMed  Google Scholar 

  • Baldi P, Vanier MC, Bower JM (1998) On the use of Bayesian methods for evaluating compartmental neural models. J Comput Neurosci 5:285–314

    Article  CAS  PubMed  Google Scholar 

  • Bean BP (2007a) The action potential in mammalian central neurons. Nat Rev Neurosci 8(6):451–465. doi:10.1038/nrn2148

    Article  CAS  PubMed  Google Scholar 

  • Bean BP (2007b) The action potential in mammalian central neurons. Nat Rev Neurosci 8(6):451–465. doi:10.1038/nrn2148

    Article  CAS  PubMed  Google Scholar 

  • Briggman KL, Abarbanel HDI, Kristan WB (2005) Optical imaging of neuronal populations during decision-making. Science 307:896–901

    Article  CAS  PubMed  Google Scholar 

  • Buhry L, Pace M, Saighi S (2012) Global parameter estimation of an Hodgkin–Huxley formalism using membrane voltage recordings: application to neuro-mimetic analog integrated circuits. Neurocomputing 81:75–85. doi:10.1016/j.neucom.2011.11.002

    Article  Google Scholar 

  • Cerda O, Trimmer JS (2010) Analysis and functional implications of phosphorylation of neuronal voltage-gated potassium channels. Neurosci Lett 486(2):60–7. doi:10.1016/j.neulet.2010.06.064

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Clewley R (2011) Inferring and quantifying the role of an intrinsic current in a mechanism for a half-center bursting oscillation: a dominant scale and hybrid dynamical systems analysis. J Biol Phys 37(3):285–306

    Article  PubMed Central  PubMed  Google Scholar 

  • Daou A, Ross M, Johnson F, Hyson RL, Bertram R (2013) Electrophysiological characterization and computational models of HVC neurons in the zebra finch. J Neurophysiol. doi:10.1152/jn.00162.2013

    PubMed  Google Scholar 

  • Druckmann S, Banitt Y, Gidon A, Schürmann F, Markram H, Segev I (2007) A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data. Front Neurosci 1(1):7–18. doi:10.3389/neuro.01.1.1.001.2007

    Article  PubMed Central  PubMed  Google Scholar 

  • Druckmann S, Berger TK, Hill S, Schürmann F, Markram H, Segev I (2008) Evaluating automated parameter constraining procedures of neuron models by experimental and surrogate data. Biol Cybern 99(4–5):371–9. doi:10.1007/s00422-008-0269-2

    Article  PubMed  Google Scholar 

  • Dutar P, Vu HM, Perkel DJ (1998) Multiple cell types distinguished by physiological, pharmacological, and anatomic properties in nucleus HVc of the adult zebra finch. J Neurophysiol 80(4):1828 –1838

  • Fortune ES, Margoliash D (1995) Parallel pathways and convergence onto HVc and adjacent neostriatum of adult zebra finches (Taeniopygia guttata). J Comp Neurol 360(3):413–441. doi:10.1002/cne.903600305

    Article  CAS  PubMed  Google Scholar 

  • Foster WR, Ungar LH, Schwaber JS (1993) Significance of conductances in Hodgkin–Huxley models. J Neurophysiol 70(6):2502–2518

    CAS  PubMed  Google Scholar 

  • Geit WV, Schutter ED, Achard P (2008) Automated neuron model optimization techniques: a review. Biol Cybern 99:241–251. doi:10.1007/s00422-008-0257-6

    Article  PubMed  Google Scholar 

  • Gill PE, Murray W, Wright MH (1981) Practical optimization. Academic Press, London

    Google Scholar 

  • Gleeson P, Crook S, Cannon RC, Hines ML, Billings GO, Farinella M, Morse TM, Davison AP, Ray S, Bhalla US, Barnes SR, Dimitrova YD, Silver RA (2010) NeuroML: a language for describing data driven models of neurons and networks with a high degree of biological detail. PLoS Comput Biol 6(6):e1000,815. doi:10.1371/journal.pcbi.1000815

    Article  Google Scholar 

  • Golowasch J, Goldman MS, Abbott LF, Marder E (2002) Failure of averaging in the construction of a conductance-based neuron model. J Neurophysiol 87(2):1129–31

    PubMed  Google Scholar 

  • Günay C, Edgerton JR, Jaeger D (2008) Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach. J Neurosci 28(30):7476–7491. doi:10.1523/JNEUROSCI.4198-07.2008

    Article  PubMed  Google Scholar 

  • Hahnloser RHR, Kozhevnikov AA, Fee MS (2002) An ultra-sparse code underlies the generation of neural sequences in a songbird. Nature 419:65–70

    Article  CAS  PubMed  Google Scholar 

  • Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97

    Article  Google Scholar 

  • Hendrickson EB, Edgerton JR, Jaeger D (2011) The use of automated parameter searches to improve ion channel kinetics for neural modeling. J Comput Neurosci 31(2):329–346. doi:10.1007/s10827-010-0312-x

    Article  PubMed  Google Scholar 

  • Herz AVM, Gollisch T, Machens CK, Jaeger D (2006) Modeling single-neuron dynamics and computations: a balance of detail and abstraction. Science 314(5796):80–85. doi:10.1126/science.1127240

    Article  CAS  PubMed  Google Scholar 

  • Hines ML, Carnevale NT (1997) The NEURON simulation environment. Neural Comput 9(6):1179–1209

    Article  CAS  PubMed  Google Scholar 

  • Hobbs KH, Hooper SL (2008) Using complicated, wide dynamic range driving to develop models of single neurons in single recording sessions. J Neurophysiol 99(4):1871–83. doi:10.1152/jn.00032.2008

    Article  PubMed  Google Scholar 

  • Hochberg D, Molina-París C, Pérez-Mercader J, Visser M (1999) Effective action of stochastic partial differential equations. Phys Rev E 60(6):6343–6360

    Article  CAS  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117(4):500–44

    CAS  Google Scholar 

  • Huijberts HJC, Lilge T, Nijmeijer H (2001) Nonlinear discrete-time synchronization via extended observers. Int J Bifurcat Chaos 11(7):1997–2006

    Article  Google Scholar 

  • Huys QJM, Paninski L (2009) Smoothing of, and parameter estimation from, noisy biophysical recordings. PLoS Comput Biol 5(5):e1000,379. doi:10.1371/journal.pcbi.1000379

    Article  Google Scholar 

  • Huys QJM, Ahrens MB, Paninski L (2006) Efficient estimation of detailed single-neuron models. J Neurophysiol 96(2):872–90. doi:10.1152/jn.00079.2006

    Article  PubMed  Google Scholar 

  • Jin D, Ramazanoğlu F, Seung H (2007) Intrinsic bursting enhances the robustness of a neural network model of sequence generation by avian brain area HVC. J Comput Neurosci 23(3):283–299

    Article  PubMed  Google Scholar 

  • Jin L, Han Z, Platisa J, Wooltorton JR, Cohen LB, Pieribone VA (2012) Single action potentials and subthreshold electrical events imaged in neurons with a fluorescent protein voltage probe. Neuron 75(5):779–785. doi:10.1016/j.neuron.2012.06.040

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Johnston J, Forsythe ID, Kopp-Scheinpflug C (2010) Going native: voltage-gated potassium channels controlling neuronal excitability. J Physiol (Lond) 588(Pt 17):3187–3200. doi:10.1113/jphysiol.2010.191973

    Article  CAS  Google Scholar 

  • Jolivet R, Lewis TJ, Gerstner W (2004) Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. J Neurophysiol 92(2):959–76. doi:10.1152/jn.00190.2004

    Article  PubMed  Google Scholar 

  • Jolivet R, Kobayashi R, Rauch A, Naud R, Shinomoto S, Gerstner W (2008a) A benchmark test for a quantitative assessment of simple neuron models. J Neurosci Methods 169(2):417–424. doi:10.1016/j.jneumeth.2007.11.006

    Article  PubMed  Google Scholar 

  • Jolivet R, Schürmann F, Berger TK, Naud R, Gerstner W, Roth A (2008b) The quantitative single-neuron modeling competition. Biol Cybern 99(4–5):417–426. doi:10.1007/s00422-008-0261-x

    Article  PubMed  Google Scholar 

  • Jouvet B, Phythian R (1979) Quantum aspects of classical and statistical fields. Phys Rev A 19(3):1350–1355

    Article  Google Scholar 

  • Kew JNC, Davies CH (eds) (2010) Ion channels: from structure to function. Oxford University Press, New York

    Google Scholar 

  • Kobayashi R, Tsubo Y, Shinomoto S (2009) Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold. Front Comput Neurosci 3:9. doi:10.3389/neuro.10.009.2009

    Article  PubMed Central  PubMed  Google Scholar 

  • Kole MH, Hallermann S, Stuart GJ (2006) Single Ih channels in pyramidal neuron dendrites: properties, distribution, and impact on action potential output. J Neurosci 26(6):1677–1687. doi:10.1523/JNEUROSCI.3664-05.2006

    Article  CAS  PubMed  Google Scholar 

  • 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):155–167. doi:10.1007/s00422-012-0487-5

    Article  PubMed  Google Scholar 

  • Kubota M, Saito N (1991) Sodium- and calcium-dependent conductances of neurones in the zebra finch hyperstriatum ventrale pars caudale in vitro. J Physiol (Lond) 440:131–142

    CAS  Google Scholar 

  • Kubota M, Taniguchi I (1998) Electrophysiological characteristics of classes of neuron in the HVc of the zebra finch. J Neurophysiol 80(2):914–923

    CAS  PubMed  Google Scholar 

  • Lepora NF, Overton PG, Gurney K (2011) Efficient fitting of conductance-based model neurons from somatic current clamp. J Comput Neurosci. doi:10.1007/s10827-011-0331-2

    PubMed  Google Scholar 

  • Long MA, Jin DZ, Fee MS (2010) Support for a synaptic chain model of neuronal sequence generation. Nature 468(7322):394–9. doi:10.1038/nature09514

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Marder E, Bucher D (2007) Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs. Annu Rev Physiol 69:291–316. doi:10.1146/annurev.physiol.69.031905.161516

    Article  CAS  PubMed  Google Scholar 

  • Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092

  • Mooney R (2000) Different subthreshold mechanisms underlie song selectivity in identified HVc neurons of the zebra finch. J Neurosci 20(14):5420–5436

    CAS  PubMed  Google Scholar 

  • Mooney R, Prather JF (2005) The HVC microcircuit: the synaptic basis for interactions between song motor and vocal plasticity pathways. J Neurosci 25(8):1952–1964. doi:10.1523/JNEUROSCI.3726-04.2005

    Article  CAS  PubMed  Google Scholar 

  • Nixdorf B, Davis S, DeVoogd T (1989) Morphology of Golgi-impregnated neurons in hyperstriatum ventralis, pars caudalis in adult male and female canaries. J Comp Neurol 284(3):337–349. doi:10.1002/cne.902840302

    Article  CAS  PubMed  Google Scholar 

  • Olypher AV, Calabrese RL (2007) Using constraints on neuronal activity to reveal compensatory changes in neuronal parameters. J Neurophysiol 98(6):3749–58. doi:10.1152/jn.00842.2007

    Article  PubMed  Google Scholar 

  • Pospischil M, Toledo-Rodriguez M, Monier C, Piwkowska Z, Bal T, Frégnac Y, Markram H, Destexhe A (2008) Minimal Hodgkin–Huxley type models for different classes of cortical and thalamic neurons. Biol Cybern 99(4–5):427–441. doi:10.1007/s00422-008-0263-8

    Article  PubMed  Google Scholar 

  • Prinz AA, Billimoria CP, Marder E (2003) Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. J Neurophysiol 90(6):3998–4015. doi:10.1152/jn.00641.2003

    Article  PubMed  Google Scholar 

  • Prinz AA, Bucher DEM (2004) Similar network activity from disparate circuit parameters. Nat Neurosci 7:1345–1352

    Article  CAS  PubMed  Google Scholar 

  • Ransdell J, Nair S, Schulz D (2013) Neurons within the same network independently achieve conserved output by differentially balancing variable conductance magnitudes. J Neurosci 33(24):9950–9956. doi:10.1523/JNEUROSCI.1095-13.2013

    Article  CAS  PubMed  Google Scholar 

  • Reid MS, Brown EA, DeWeerth SP (2007) A parameter-space search algorithm tested on a Hodgkin–Huxley model. Biol Cybern 96(6):625–634. doi:10.1007/s00422-007-0156-2

    Article  PubMed  Google Scholar 

  • Restrepo JM (2008) A path integral method for data assimilation. Physica D 237:14–27

    Article  Google Scholar 

  • Roberts TF, Klein ME, Kubke MF, Wild JM, Mooney R (2008) Telencephalic neurons monosynaptically link brainstem and forebrain premotor networks necessary for song. J Neurosci 28(13):3479–3489. doi:10.1523/JNEUROSCI.0177-08.2008

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Sarkar AX, Christini DJ, Sobie EA (2012) Exploiting mathematical models to illuminate electrophysiological variability between individuals. J Physiol (Lond) 590(Pt 11):2555–67. doi:10.1113/jphysiol.2011.223313

    Article  CAS  Google Scholar 

  • Schenk O, Bollhoefer M, Gärtner K (2008) On large-scale diagonalization techniques for the Anderson model of localization. SIAM Rev 50:91–112

    Article  Google Scholar 

  • Schulz DJ, Goaillard JM, Marder E (2006) Variable channel expression in identified single and electrically coupled neurons in different animals. Nat Neurosci 9(3):356–362. doi:10.1038/nn1639

    Article  CAS  PubMed  Google Scholar 

  • Shea SD, Koch H, Baleckaitis D, Ramirez JM, Margoliash D (2010) Neuron-specific cholinergic modulation of a forebrain song control nucleus. J Neurophysiol 103(2):733–745. doi:10.1152/jn.00803.2009

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Swensen AM, Bean BP (2005) Robustness of burst firing in dissociated Purkinje neurons with acute or long-term reductions in sodium conductance. J Neurosci 25(14):3509–20. doi:10.1523/JNEUROSCI.3929-04.2005

    Article  CAS  PubMed  Google Scholar 

  • Szendro IG, Rodríguez MA, López JM (2009) On the problem of data assimilation by means of synchronization. J Geophys Rev. doi:10.1029/2009JD012411

    Google Scholar 

  • Tomaiuolo M, Bertram R, Leng G, Tabak J (2012) Models of electrical activity: calibration and prediction testing on the same cell. Biophys J 103(9):2021–2032. doi:10.1016/j.bpj.2012.09.034

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Toth BA, Kostuk M, Meliza CD, Margoliash D, Abarbanel HDI (2011) Dynamical estimation of neuron and network properties I: variational methods. Biol Cybern 105:217–237. doi:10.1007/s00422-011-0459-1

    Article  PubMed  Google Scholar 

  • Trimmer J, Rhodes K (2004) Localization of voltage-gated ion channels in mammalian brain. Annu Rev Physiol 66(1):477–519. doi:10.1146/annurev.physiol.66.032102.113328

    Article  CAS  PubMed  Google Scholar 

  • Vanier MC, Bower JM (1999) A comparative survey of automated parameter-search methods for compartmental neural models. J Comput Neurosci 7(2):149–171. doi:10.1023/A:1008972005316

    Article  CAS  PubMed  Google Scholar 

  • Vavoulis DV, Straub VA, Aston JAD, Feng J (2012) A self-organizing state-space-model approach for parameter estimation in Hodgkin–Huxley-type models of single neurons. PLoS Comput Biol. doi:10.1371/journal.pcbi.1002401

  • Wächter A (2002) An interior point algorithm for large-scale nonlinear optimization with applications in process engineering. Phd thesis, Carnegie Mellon University

  • Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE T Evolut Comput 1(1):67–82

    Article  Google Scholar 

Download references

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.

Author information

Author notes

  1. C. Daniel Meliza

    Present address: Department of Psychology, University of Virginia, PO Box 400400, Charlottesville, VA, 22904, USA

Authors and Affiliations

  1. Department of Organismal Biology and Anatomy, University of Chicago, 1027 E 57th Street, Chicago, IL, 60637, USA

    C. Daniel Meliza, Hao Huang & Daniel Margoliash

  2. Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0402, USA

    Mark Kostuk

  3. Department of Physics, University of Bath, Claverton Down, Bath, UK

    Alain Nogaret

  4. Department of Physics and Marine Physical Laboratory (Scripps Institution of Oceanography), Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0374, USA

    Henry D. I. Abarbanel

Authors
  1. C. Daniel Meliza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark Kostuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hao Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alain Nogaret
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Daniel Margoliash
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Henry D. I. Abarbanel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Daniel Meliza.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (zip 6779 KB)

Supplementary material 2 (pdf 300 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meliza, C.D., Kostuk, M., Huang, H. et al. Estimating parameters and predicting membrane voltages with conductance-based neuron models. Biol Cybern 108, 495–516 (2014). https://doi.org/10.1007/s00422-014-0615-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-014-0615-5

Keywords

Search

Navigation