Skip to main content

Advertisement

SpringerLink
Log in

Efficient fitting of conductance-based model neurons from somatic current clamp

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

Estimating biologically realistic model neurons from electrophysiological data is a key issue in neuroscience that is central to understanding neuronal function and network behavior. However, directly fitting detailed Hodgkin–Huxley type model neurons to somatic membrane potential data is a notoriously difficult optimization problem that can require hours/days of supercomputing time. Here we extend an efficient technique that indirectly matches neuronal currents derived from somatic membrane potential data to two-compartment model neurons with passive dendrites. In consequence, this approach can fit semi-realistic detailed model neurons in a few minutes. For validation, fits are obtained to model-derived data for various thalamo-cortical neuron types, including fast/regular spiking and bursting neurons. A key aspect of the validation is sensitivity testing to perturbations arising in experimental data, including sampling rates, inadequately estimated membrane dynamics/channel kinetics and intrinsic noise. We find that maximal conductance estimates and the resulting membrane potential fits diverge smoothly and monotonically from near-perfect matches when unperturbed. Curiously, some perturbations have little effect on the error because they are compensated by the fitted maximal conductances. Therefore, the extended current-based technique applies well under moderately inaccurate model assumptions, as required for application to experimental data. Furthermore, the accompanying perturbation analysis gives insights into neuronal homeostasis, whereby tuning intrinsic neuronal properties can compensate changes from development or neurodegeneration.

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

Similar content being viewed by others

Notes

  1. The square bracket notation denotes that I[V(t)] depends on the time course of V(t), as represented by a solution to a set of differential equations, rather than just the value of V at the time t.

References

  • Achard, P., & De Schutter, E. (2006). Complex parameter landscape for a complex neuron model. PLoS Computational Biology, 2(7), e94.

    Article  PubMed  Google Scholar 

  • Achard, P., & De Schutter, E. (2008). Calcium, synaptic plasticity and intrinsic homeostasis in Purkinje neuron models. Frontiers in Computational Neuroscience, 2, 8.

    Article  PubMed  Google Scholar 

  • Booth, V., & Rinzel, J. (1995). A minimal, compartmental model for a dendritic origin of bistability of motoneuron firing patterns. Journal of Computational Neuroscience, 2(4), 299–312.

    Article  PubMed  CAS  Google Scholar 

  • Bower, J. M., & Beeman, D. (1998). The book of GENESIS. New York: Springer.

    Book  Google Scholar 

  • Bush, K., Knight, J., & Anderson, C. (2005). Optimizing conductance parameters of cortical neural models via electrotonic partitions. Neural Networks, 18(5–6), 488–496.

    Article  PubMed  Google Scholar 

  • Connors, B. W., & Gutnick, M. J. (1990). Intrinsic firing patterns of diverse neocortical neurons. Trends in Neurosciences, 13(3), 99–104.

    Article  PubMed  CAS  Google Scholar 

  • Davis, G. W. (2006). Homeostatic control of neural activity: From phenomenology to molecular design. Annual Review of Neuroscience, 29, 307–323.

    Article  PubMed  CAS  Google Scholar 

  • Druckmann, S., Banitt, Y., Gidon, A., Schurmann, F., Markram, H., & Segev, I. (2007). A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data. Frontiers in Neuroscience, 1(1), 7.

    Article  PubMed  Google Scholar 

  • Druckmann, S., Berger, T. K., Hill, S., Schurmann, F., Markram, H., & Segev, I. (2008). Evaluating automated parameter constraining procedures of neuron models by experimental and surrogate data. Biological Cybernetics, 99(4), 371–379.

    Article  PubMed  Google Scholar 

  • Edelman, G. M., & Gally, J. A. (2001). Degeneracy and complexity in biological systems. Proceedings of the National Academy of Sciences of the United States of America, 98(24), 13763.

    Article  PubMed  CAS  Google Scholar 

  • Gerstner, W., & Naud, R. (2009). Neuroscience. how good are neuron models? Science, 326(5951), 379–80.

    Article  PubMed  CAS  Google Scholar 

  • Goldman, M. S., Golowasch, J., Marder, E., & Abbott, L. F. (2001). Global structure, robustness, and modulation of neuronal models. Journal of Neuroscience, 21(14), 5229.

    PubMed  CAS  Google Scholar 

  • Golowasch, J., Goldman, M. S., Abbott, L. F., & Marder, E. (2002). Failure of averaging in the construction of a conductance-based neuron model. Journal of Neurophysiology, 87(2), 1129.

    PubMed  Google Scholar 

  • Gunay, C., Edgerton, J. R., & Jaeger, D. (2008). Channel density distributions explain spiking variability in the globus pallidus: A combined physiology and computer simulation database approach. Journal of Neuroscience, 28(30), 7476.

    Article  PubMed  CAS  Google Scholar 

  • Herz, A. V. M., Gollisch, T., Machens, C. K., & Jaeger, D. (2006). Modeling single-neuron dynamics and computations: A balance of detail and abstraction. Science, 314(5796), 80–85.

    Article  PubMed  CAS  Google Scholar 

  • Hines, M. (1984). Efficient computation of branched nerve equations. International Journal of Bio-Medical Computing, 15(1), 69–76.

    Article  PubMed  CAS  Google Scholar 

  • Hobbs, K. H., & Hooper, S. L. (2008). Using complicated, wide dynamic range driving to develop models of single neurons in single recording sessions. Journal of Neurophysiology, 99(4), 1871.

    Article  PubMed  Google Scholar 

  • Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology (London), 117, 500–544.

    CAS  Google Scholar 

  • Huys, Q. J. M., Ahrens, M. B., & Paninski, L. (2006). Efficient estimation of detailed single-neuron models. Journal of Neurophysiology, 96(2), 872–890.

    Article  PubMed  Google Scholar 

  • Huys, Q. J. M., & Paninski, L. (2009). Smoothing of, and parameter estimation from, noisy biophysical recordings. PLoS Computational Biology, 5(5), e1000379.

    Article  PubMed  Google Scholar 

  • Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6), 1569–1572.

    Article  PubMed  CAS  Google Scholar 

  • Keren, N., Peled, N., & Korngreen, A. (2005). Constraining compartmental models using multiple voltage recordings and genetic algorithms. Journal of neurophysiology, 94(6), 3730.

    Article  PubMed  Google Scholar 

  • Kita, T., Kita, H., & Kita, S. T. (1984). Passive electrical membrane properties of rat neostriatal neurons in an in vitro slice preparation. Brain Research, 300, 129–139.

    Article  PubMed  CAS  Google Scholar 

  • Lander, E. S., Linton, L. M., Birren, B., Nusbaum, C., Zody, M. C., Baldwin, J., et al. (2001). Initial sequencing and analysis of the human genome. Nature, 409(6822), 860–921.

    Article  PubMed  CAS  Google Scholar 

  • LeMasson, G., & Maex, R. (2001). Introduction to equation solving and parameter fitting. In Computational neuroscience: Realistic modelling for experimentalists (pp. 1–25).

  • Lepora, N. F., Overton, P., & Gurney, K. (2009). Efficient current-based optimization techniques for parameter estimation in multi-compartment neuronal models. BMC Neuroscience, 10(Suppl 1), 347.

    Article  Google Scholar 

  • Lindau, M., & Neher, E. (1988). Patch-clamp techniques for time-resolved capacitance measurements in single cells. Pflügers Archiv European Journal of Physiology, 411(2), 137–146.

    Article  PubMed  CAS  Google Scholar 

  • Llano, I., Marty, A., Armstrong, C. M., & Konnerth, A. (1991). Synaptic-and agonist-induced excitatory currents of Purkinje cells in rat cerebellar slices. The Journal of Physiology, 434(1), 183.

    PubMed  CAS  Google Scholar 

  • London, M., & Hausser, M. (2005). Dendritic computation. Annual Review of Neuroscience, 28(1), 503–532.

    Article  PubMed  CAS  Google Scholar 

  • Mainen, Z. F., & Sejnowski, T. J. (1996). Influence of dendritic structure on firing pattern in model neocortical neurons. Nature, 382(6589), 363–366.

    Article  PubMed  CAS  Google Scholar 

  • Marder, E., & Goaillard, J. M. (2006). Variability, compensation and homeostasis in neuron and network function. Nature Reviews Neuroscience, 7(7), 563–574.

    Article  PubMed  CAS  Google Scholar 

  • Marder, E., & Prinz, A. A. (2002). Modeling stability in neuron and network function: The role of activity in homeostasis. Bioessays, 24(12), 1145–1154.

    Article  PubMed  CAS  Google Scholar 

  • Markram, H. (2006). The blue brain project. Nature Reviews Neuroscience, 7(2), 2153–2160.

    Article  Google Scholar 

  • Mennerick, S., Que, J., Benz, A., & Zorumski, C. F. (1995). Passive and synaptic properties of hippocampal neurons grown in microcultures and in mass cultures. Journal of neurophysiology, 73(1), 320.

    PubMed  CAS  Google Scholar 

  • Moore, E. H. (1920). On the reciprocal of the general algebraic matrix. Bulletin of the American Mathematical Society, 26, 394–395.

    Google Scholar 

  • Morse, T. M., Davison, A. P., & Hines, M. (2001). Parameter space reduction in neuron model optimization through minimization of residual voltage clamp current. In 31st Annual Meeting of the Society for Neuroscience, San Diego, CA, USA, 10–15 November 2001. Society for Neuroscience Abstracts (Vol. 27).

  • Penrose, R. (1955). A generalized inverse for matrices. Proceedings of the Cambridge Philosophical Society, 51, 406–413.

    Article  Google Scholar 

  • Pinsky, P. F., & Rinzel, J. (1994). Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. Journal of Computational Neuroscience, 1(1), 39–60.

    Article  PubMed  CAS  Google Scholar 

  • Pospischil, M., Toledo-Rodriguez, M., Monier, C., Piwkowska, Z., Bal, T., Frégnac, Y., et al. (2008). Minimal Hodgkin–Huxley type models for different classes of cortical and thalamic neurons. Biological Cybernetics, 99(4), 427–441.

    Article  PubMed  Google Scholar 

  • Prinz, A. A., Billimoria, C. P., & Marder, E. (2003). Alternative to hand-tuning conductance-based models: Construction and analysis of databases of model neurons. Journal of Neurophysiology, 90(6), 3998.

    Article  PubMed  Google Scholar 

  • Rall, W. (1960). Membrane potential transients and membrane time constant of motoneurons. Experimental Neurology, 2, 503–532.

    Article  PubMed  CAS  Google Scholar 

  • Rall, W. (1969). Time constants and electrotonic length of membrane cylinders and neurons. Biophysics Journal, 9(12), 1483–1508.

    Article  CAS  Google Scholar 

  • Schulz, , D. J., Goaillard, J. M., & Marder, E. (2006). Variable channel expression in identified single and electrically coupled neurons in different animals. Nature Neuroscience, 9(3), 356–362.

    Article  PubMed  CAS  Google Scholar 

  • Swensen, A. M., & Bean, B. P. (2005). Robustness of burst firing in dissociated purkinje neurons with acute or long-term reductions in sodium conductance. Journal of Neuroscience, 25(14), 3509.

    Article  PubMed  CAS  Google Scholar 

  • Tabak, J., Murphey, C. R., & Moore, L. E. (2000). Parameter estimation methods for single neuron models. Journal of Computational Neuroscience, 9(3), 215–236.

    Article  PubMed  CAS  Google Scholar 

  • Taylor, A. L., Goaillard, J. M., & Marder, E. (2009). How multiple conductances determine electrophysiological properties in a multicompartment model. Journal of Neuroscience, 29(17), 5573.

    Article  PubMed  CAS  Google Scholar 

  • Taylor, A. L., Hickey, T. J., Prinz, A. A., & Marder, E. (2006). Structure and visualization of high-dimensional conductance spaces. Journal of Neurophysiology, 96(2), 891.

    Article  PubMed  Google Scholar 

  • Tien, J. H., & Guckenheimer, J. (2008). Parameter estimation for bursting neural models. Journal of Computational Neuroscience, 24(3), 358–373.

    Article  PubMed  Google Scholar 

  • Tobin, A. E., & Calabrese, R. L. (2006). Endogenous and half-center bursting in morphologically inspired models of leech heart interneurons. Journal of Neurophysiology, 96(4), 2089.

    Article  PubMed  Google Scholar 

  • Turrigiano, G. G., & Nelson, S. B. (2004). Homeostatic plasticity in the developing nervous system. Nature Reviews Neuroscience, 5(2), 97–107.

    Article  PubMed  CAS  Google Scholar 

  • Van Geit, W., Achard, P., & De Schutter, E. (2007). Neurofitter: A parameter tuning package for a wide range of electrophysiological neuron models. Frontiers in Neuroinformatics, 1, 1.

    PubMed  Google Scholar 

  • Van Geit, W., De Schutter, E., & Achard, P. (2008). Automated neuron model optimization techniques: A review. Biological Cybernetics, 99(4), 241–251.

    Article  PubMed  Google Scholar 

  • Vanier, M. C., & Bower, J. M. (1999). A comparative survey of automated parameter-search methods for compartmental neural models. Journal of Computational Neuroscience, 7(2), 149–171.

    Article  PubMed  CAS  Google Scholar 

  • Venter, J. C., Adams, M. D., Myers, E. W., Li, P. W., Mural, R. J., Sutton, G. G., et al. (2001). The sequence of the human genome. Science, 291(5507), 1304.

    Article  PubMed  CAS  Google Scholar 

  • Weaver, C. M., & Wearne, S. L. (2006). The role of action potential shape and parameter constraints in optimization of compartment models. Neurocomputing, 69(10–12), 1053–1057.

    Article  Google Scholar 

  • Weaver, C. M., & Wearne, S. L. (2008). Neuronal firing sensitivity to morphologic and active membrane parameters. PLoS Computational Biology, 4(1), e11.

    Article  PubMed  Google Scholar 

  • Wood, R., & Gurney, K. N. (2002). A new parametric search technique for biophysical models. A study in the rat neostriatal projection neuron. In 32nd annual meeting of the Society for Neuroscience, Orlando, FL, USA, 2–7 November 2002. Society for Neuroscience abstracts (Vol. 28).

  • Wood, R., Gurney, K. N., & Wilson, C. J. (2004). A novel parameter optimisation technique for compartmental models applied to a model of a striatal medium spiny neuron. Neurocomputing, 58–60, 1109–1116.

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank Darren Hoyland, Mark Humphries and Ric Wood for valuable advice and discussions. This work was supported by EPSRC (CARMEN: EP/E002331/1).

Author information

Authors and Affiliations

  1. Department of Psychology, University of Sheffield, Sheffield, S10 2TP, UK

    Nathan F. Lepora, Paul G. Overton & Kevin Gurney

Authors
  1. Nathan F. Lepora
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul G. Overton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kevin Gurney
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nathan F. Lepora.

Additional information

Action Editor: Erik De Schutter

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(PDF 7.64 MB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lepora, N.F., Overton, P.G. & Gurney, K. Efficient fitting of conductance-based model neurons from somatic current clamp. J Comput Neurosci 32, 1–24 (2012). https://doi.org/10.1007/s10827-011-0331-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-011-0331-2

Keywords

Search

Navigation