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Reliability of spike and burst firing in thalamocortical relay cells

Journal of Computational Neuroscience volume 35, pages 317–334 (2013)Cite this article

Abstract

The reliability and precision of the timing of spikes in a spike train is an important aspect of neuronal coding. We investigated reliability in thalamocortical relay (TCR) cells in the acute slice and also in a Morris-Lecar model with several extensions. A frozen Gaussian noise current, superimposed on a DC current, was injected into the TCR cell soma. The neuron responded with spike trains that showed trial-to-trial variability, due to amongst others slow changes in its internal state and the experimental setup. The DC current allowed to bring the neuron in different states, characterized by a well defined membrane voltage (between −80 and −50 mV) and by a specific firing regime that on depolarization gradually shifted from a predominantly bursting regime to a tonic spiking regime. The filtered frozen white noise generated a spike pattern output with a broad spike interval distribution. The coincidence factor and the Hunter and Milton measure were used as reliability measures of the output spike train. In the experimental TCR cell as well as the Morris-Lecar model cell the reliability depends on the shape (steepness) of the current input versus spike frequency output curve. The model also allowed to study the contribution of three relevant ionic membrane currents to reliability: a T-type calcium current, a cation selective h-current and a calcium dependent potassium current in order to allow bursting, investigate the consequences of a more complex current-frequency relation and produce realistic firing rates. The reliability of the output of the TCR cell increases with depolarization. In hyperpolarized states bursts are more reliable than single spikes. The analytically derived relations were capable to predict several of the experimentally recorded spike features.

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Notes

  1. Note that Badel et al. (2008) use the membrane current \(I_{m} (t)=I_{in}(t)-C_{m} \frac {d V_{m}}{dt}\) in their I–V curve, whereas we use the input current \(I_{in}(t)\).

References

  • Badel, L., Lefort, S., Brette, R., Petersen, C.C.H., Gerstner, W., Richardson, M.J.E. (2008). Journal of Neurophysiology, 99, 656.

    Article  PubMed  Google Scholar 

  • Bernander, O., Douglas, R., Martin, K.A.C., Koch, C. (1991). Proceedings of the National Academy of Sciences of the United States of America, 88, 11569.

    Google Scholar 

  • Bryant, H.L., & Segundo, J.P. (1976). Spike initiation by transmembrane current: a white-noise analysis. The Journal of Physiology, 260, 279–314.

    PubMed  CAS  Google Scholar 

  • Cafaro, J., & Rieke, F. (2010). Nature, 468, 964.

  • Chacron, M.J., Longtin, A., Maler, L. (2004). Journal of Computational Neuroscience, 17(2), 127.

    Article  PubMed  Google Scholar 

  • de Ruyter van Steveninck, R.R., Lewen, G.D., Strong, S.P., Koberle, R., Bialek, W. (1997). Science, 275, 1805.

    Article  PubMed  CAS  Google Scholar 

  • Destexhe, A., Babloyantz, A., Sejnowski, T.J. (1993). Biophysical Journal, 65, 1538.

    Article  PubMed  CAS  Google Scholar 

  • Dyhrfjeld-Johnsen, J., Morgan, R.J., Földy, C., Soltesz, I. (2008). Frontiers in Cellular Neuroscience, 2(2).

  • Fellous, J.M., Tiesinga, P.H.E., Thomas, P.J., Sejnowski, T.J. (2004). The Journal of Neuroscience, 24(12), 2989.

    Article  PubMed  CAS  Google Scholar 

  • George, M.S., Abbott, L.F., Siegelbaum, S.A. (2009). Nature Neuroscience, 12(5), 577.

    Article  PubMed  CAS  Google Scholar 

  • Goldberg, J.M., Smith, C.E., Fernandez, C. (1984). Journal of Neurophysiology, 51(6), 1236.

    PubMed  CAS  Google Scholar 

  • Golding, N.L., Kath, W.L., Spruston, N. (2001). Journal of Neurophysiology, 86, 2998.

    PubMed  CAS  Google Scholar 

  • Gutkin, B.S., & Ermentrout, B. (1998). Neural Computation, 10, 1047.

    Article  PubMed  CAS  Google Scholar 

  • Gutkin, B.S., Ermentrout, B., Rudolph, M. (2003). Journal of Computational Neuroscience, 15, 91.

    Article  PubMed  Google Scholar 

  • Hodgkin, A.L. (1948). The Journal of Physiology, 107, 165.

    PubMed  CAS  Google Scholar 

  • Huguenard, J.R., & McCormick, D.A. (1992). Journal of Neurophysiology, 68(4), 1373.

    PubMed  CAS  Google Scholar 

  • Hunter, J.D., & Milton, J.G. (2003). Journal of Neurophysiology, 90, 387.

    Article  PubMed  Google Scholar 

  • Hunter, J.D., Milton, J., Thomas, P. (1998). Journal of Neurophysiology, 80, 1427.

    PubMed  CAS  Google Scholar 

  • Izhikevich, E.M. (2005). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Cambridge: MIT Press.

    Google Scholar 

  • Jahnsen, H., & Llinás, R. (1984). The Journal of Physiology, 349, 227.

    PubMed  CAS  Google Scholar 

  • Johansson, R.S., & Birznieks, I. (2004). Nature Neuroscience, 7(2), 170.

    Article  PubMed  CAS  Google Scholar 

  • Jolivet, R., Rauch, A., Lüscher, H.R., Gerstner, W. (2006). Journal of Computational Neuroscience, 21, 35.

    Article  PubMed  Google Scholar 

  • Kepecs, A., & Lisman, J. (2003). Network: Computation in Neural Systems, 14(1), 103.

    Google Scholar 

  • Kistler, W.M., Gerstner, W., van Hemmen, J.L. (1997). Neural Computation, 9, 1015.

    Article  Google Scholar 

  • Kreuz, T., Haas, J.S., Morelli, A., Abarbanel, H.D.I., Politi, A. (2007). Journal of Neuroscience Methods, 165, 151.

    Article  PubMed  Google Scholar 

  • Kreuz, T., Chicharro, D., Greschner, M., Andrzejak, R.G. (2011). Journal of Neuroscience Methods, 195, 92.

    Article  PubMed  Google Scholar 

  • Kruskal, P., Stanis, J., McNaughton, B. (2007). Statistics in Medicine, 26, 3997.

    Article  PubMed  Google Scholar 

  • Kuznetsova, M.S., Higgs, M.H., Spain, W.J. (2008). The Journal of Neuroscience, 28(46), 11906.

    Article  PubMed  CAS  Google Scholar 

  • Lesica, N., & Stanley, G.B. (2004). The Journal of Neuroscience, 24(47), 10731.

    Article  PubMed  CAS  Google Scholar 

  • Lyttle, D., & Fellous, J.M. (2011). Journal of Neuroscience Methods, 199(2), 296.

    Article  PubMed  Google Scholar 

  • Maccaferri, G., Mangoni, M., Lazzari, A., DiFrancesco, D. (1993). Journal of Neurophysiology, 69(6), 2129.

    PubMed  CAS  Google Scholar 

  • Magee, J.C. (1998). The Journal of Neuroscience, 18(19), 7613.

    PubMed  CAS  Google Scholar 

  • Mainen, Z.F., & Sejnowski, T.J. (1995). Science, 268.

  • Mainen, Z.F., & Sejnowski, T.J. (1996). Nature, 382, 363.

    Article  PubMed  CAS  Google Scholar 

  • McCormick, D.A., & Huguenard, J.R. (1992). Journal of Neurophysiology, 68(4), 1384.

    PubMed  CAS  Google Scholar 

  • Migliore, M., Messineo, L., Ferrante, M. (2004). Journal of Computational Neuroscience, 16(1), 5.

    Article  PubMed  CAS  Google Scholar 

  • Morris, G., & Lecar, H. (1981). Biophysical Journal, 35(1), 193.

    Article  PubMed  CAS  Google Scholar 

  • Naud, R., Gerhard, F., Gerstner, W. (2011). Neural Computation, 23(12).

  • Oswald, A.M., Chacron, M.J., Doiron, B., Bastian, J., Maler, L. (2004). The Journal of Neuroscience, 24(18), 4351.

    Article  PubMed  CAS  Google Scholar 

  • Paiva, A.R., Park, I., Principe, J.C. (2010). Neural Computing & Applications, 19, 405.

    Article  Google Scholar 

  • Poirazi, P., Brannon, T., Mel, B.W. (2003). Neuron, 37, 977.

    Article  PubMed  CAS  Google Scholar 

  • Poolos, N.P., Migliore, M., Johnston, D. (2002). Nature Neuroscience, 5(8), 767.

    PubMed  CAS  Google Scholar 

  • Prescott, S.A., Ratté, S., De Koninck, Y., Sejnowski, T.J. (2006). The Journal of Neuroscience, 26(36), 9084.

    Article  PubMed  CAS  Google Scholar 

  • Prescott, S.A., De Koninck, Y., Sejnowski, T.J. (2008a). PLoS Computational Biology, 4(10), e1000198.

    Article  Google Scholar 

  • Prescott, S.A., Ratté, S., De Koninck, Y., Sejnowski, T.J. (2008b). Journal of Neurophysiology, 100, 3030.

    Article  Google Scholar 

  • Reinagel, P., & Reid, R.C. (2000). The Journal of Neuroscience, 20(14), 5392.

    PubMed  CAS  Google Scholar 

  • Reinagel, P., Godwin, D., Sherman, S.M., Koch, C. (1999). Journal of Neurophysiology, 81(5), 2558.

    PubMed  CAS  Google Scholar 

  • Rinzel, J., & Ermentrout, B. (1998). In C. Koch, & I. Segev, (Eds.), Methods in Neural Modelling: from synapses to networks, (pp. 251–292). Cambridge: MIT Press.

    Google Scholar 

  • Rubin, J.E., & Terman, D. (2004). Journal of Computational Neuroscience, 16, 211.

    Article  PubMed  Google Scholar 

  • Rudolph, M., & Destexhe, A. (2003). Journal of Computational Neuroscience, 14, 239.

    Article  PubMed  Google Scholar 

  • Schneider, A.D., Cullen, K.E., Chacron, M.J. (2011). PLoS Computational Biology, 7(7), e1002120.

    Article  PubMed  CAS  Google Scholar 

  • Schreiber, S., Fellous, J.M., Whitmer, D., Tiesinga, P.H.E., Sejnowski, T.J. (2003). Neurocomputing, 52–54, 925.

    Article  PubMed  Google Scholar 

  • Schreiber, S., Fellous, J.M., Tiesinga, P.H.E., Sejnowski, T.J. (2004). Journal of Neurophysiology, 91, 194.

    Article  PubMed  Google Scholar 

  • Schreiber, S., Samengo, I., Herz, A.V.M. (2009). Journal of neurophysiology, 101(5), 2239.

    Article  PubMed  Google Scholar 

  • Sherman, S.M. (2001). Trends in Neurosciences, 24(2), 122.

    Article  PubMed  CAS  Google Scholar 

  • Stein, R.B. (1967). Biophysical journal, 7(1), 37.

    Article  PubMed  CAS  Google Scholar 

  • Stein, R.B., Gossen, E.R., Jones, K.E. (2005). Nature Reviews Neuroscience, 6(5), 389.

    Article  PubMed  CAS  Google Scholar 

  • Steriade, M., & Llinás, R. (1988). Physiological Reviews, 68, 649.

    PubMed  CAS  Google Scholar 

  • Thomas, P.J., Tiesinga, P.H.E., Fellous, J.M., Sejnowski, T.J. (2003). Neurocomputing, 52–54, 955.

    Article  PubMed  Google Scholar 

  • Tiesinga, P.H.E., Fellous, J.M., Sejnowski, T.J. (2008). Nature Neuroscience, 9, 97.

    CAS  Google Scholar 

  • Tort, A.B., Rotstein, H.G., Dugladze, T., Gloveli, T., Kopell, N.J. (2007). Proceedings of the National Academy of Sciences of the United States of America, 104(33), 13490.

    Google Scholar 

  • Toups, J.V., Fellous, J.-M., Thomas, P.J., Sejnowski, T.J., Tiesinga, P.H. (2012). Multiple spike time patterns occur at bifurcation points of membrane potential dynamics. PLoS Comput Biol, 8(10), e1002615.

    Article  PubMed  CAS  Google Scholar 

  • van Rossum, M.C.W. (2001). Neural Computation, 13, 751.

    Article  PubMed  CAS  Google Scholar 

  • van Welie, I., van Hooft, J.A., Wadman, W.J. (2004). Proceedings of the National Academy of Sciences of the United States of America, 101(14), 5123.

    Article  PubMed  CAS  Google Scholar 

  • Victor, J.D., & Purpura, K.P. (1996). Journal of Neurophysiology, 76(2), 1310.

    PubMed  CAS  Google Scholar 

  • Victor, J.D., & Purpura, K.P. (1997). Network: Computation in Neural Systems, 8, 127.

    Article  Google Scholar 

  • Wan, F.Y.M., & Tuckwell, H.C. (1982). Journal of Theoretical Neurobiology, 1, 197.

    Google Scholar 

  • Zeldenrust, F. (2012). Neural coding with spikes and bursts: characterizing neurons and networks with noisy input. Ph.D. thesis, University of Amsterdam.

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Acknowledgments

We are very grateful to the extensive and constructive comments of one of our anonymous reviewers.

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Authors and Affiliations

  1. Swammerdam Institute for Life Sciences, Center for Neuroscience, University of Amsterdam, P.O. Box 94215, 1090, GE, Amsterdam, The Netherlands

    Fleur Zeldenrust, Pascal J. P. Chameau & Wytse J. Wadman

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  1. Fleur Zeldenrust
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  2. Pascal J. P. Chameau
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  3. Wytse J. Wadman
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Correspondence to Fleur Zeldenrust.

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Zeldenrust, F., Chameau, P.J.P. & Wadman, W.J. Reliability of spike and burst firing in thalamocortical relay cells. J Comput Neurosci 35, 317–334 (2013). https://doi.org/10.1007/s10827-013-0454-8

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  • DOI: https://doi.org/10.1007/s10827-013-0454-8

Keywords

  • Reliability
  • Precision
  • Morris-Lecar model
  • Thalamocortical relay cell
  • Coincidence factor
  • Hunter and Milton measure
  • Frozen noise