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On the Classification of Experimental Data Modeled Via a Stochastic Leaky Integrate and Fire Model Through Boundary Values

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Abstract

We present a computational algorithm aimed to classify single unit spike trains on the basis of observed interspikes intervals (ISI). The neuronal activity is modeled with a stochastic leaky integrate and fire model and the inverse first passage time method is extended to the Ornstein-Uhlenbeck (OU) process. Differences between spike trains are detected in terms of the boundary shape. The proposed classification method is applied to the analysis of multiple single units recorded simultaneously in the thalamus and in the cerebral cortex of unanesthetized rats during spontaneous activity. We show the existence of at least three different firing patterns that could not be classified using the usual statistical indices.

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References

  • Abeles, M., 1982. Local Cortical Circuits: An Electrophysiological Study. Springer Verlag, Berlin.

    Google Scholar 

  • Abeles, M., 1991. Corticonics: Neural Circuits of the Cerebral Cortex. Cambridge Univiversity Press, Cambridge.

    Google Scholar 

  • Bertram, R., Butte, M.J., Kiemel, T., Sherman, A., 1995. Topological and phenomenological classification of bursting oscillations. Bull. Math. Biol. 57(3), 413–439.

    MATH  Google Scholar 

  • Bulsara, A.R., Elston, T.C., Doering, C.R., Lowen, S.B., Lindenberg, K., 1996. Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics. Phys. Rev. E 53(4), 3958–3969.

    Article  Google Scholar 

  • Capocelli, R.M., Ricciardi, L.M., 1971. Diffusion approximation and first passage time problem for a model neuron. Kybernetik 8(6), 214–223.

    Article  MathSciNet  Google Scholar 

  • Celletti, A., Villa, A.E.P., 1996. Low dimensional chaotic attractors in the rat brain. Biol. Cybern. 74, 387–394.

    Article  Google Scholar 

  • Del Prete, V., Martignon, L., Villa, A.E.P., 2004. Detection of syntonies between multiple spike trains using a coarse-grain binarization of spike count distributions. Netw. Comput. Neural Syst. 15, 13–28.

    Article  Google Scholar 

  • Ditlevsen, S., Lansky, P., 2005. Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model. Phys. Rev. E 71(1), Art. No. 011907.

  • Eckhorn, R., Bauer, R., Jordan, W., Brosch, M., Kruse, W., Munk, M., Reitboeck, H.J., 1988. Coherent oscillations: A mechanism of feature linking in the visual cortex? Multiple electrode and correlation analyses in the cat. Biol. Cybern. 60, 121–130.

    Article  Google Scholar 

  • Fano, U., 1947. Ionization yield of radiations. II. The fluctuations of the number of ions. Phys. Rev. 72(1), 26–29.

    Article  MathSciNet  Google Scholar 

  • Feng, J.F., Brown, D., 2000. Integrate-and-fire models with nonlinear leakage. Bull. Math. Biol. 62(3), 467–481.

    Article  MathSciNet  Google Scholar 

  • Fortet, R., 1943. Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux dérivées partielles du type parabolique. J. Math. Pures Appl. 22, 177–243.

    MATH  MathSciNet  Google Scholar 

  • Fujii, H., Ito, H., Aihara, K., Ichinose, N., Tsukada, M., 1996. Dynamical cell assembly hypothesis—theoretical possibility of spatio-temporal coding in the cortex. Neural Netw. 9, 1303–1350.

    Article  MATH  Google Scholar 

  • Gray, C.M., Singer, W., 1995. Visual feature integration and the temporal correlation hypothesis. Annu. Rev. Neurosci. 18, 555–586.

    Article  Google Scholar 

  • Hopfield, J.J., Brody, C.D., 2000. What is a moment? “Cortical” sensory integration over a brief interval. Proc. Natl. Acad. Sci. U.S.A. 97, 13919–13924.

    Google Scholar 

  • Hopfield, J.J., Brody, C.D., 2001. What is a moment? Transient synchrony as a collective mechanism for spatiotemporal integration. Proc. Natl. Acad. Sci. U.S.A. 98, 1282–1287.

    Google Scholar 

  • Inoue, J., Sato, S., Ricciardi, L.M., 1995. On the parameter-estimation for diffusion-models of single neurons activities. 1. Application to spontaneous activities of mesencephalic reticular-formation cells in sleep and waking states. Biol. Cybern. 73(3), 209–221.

    Article  MATH  Google Scholar 

  • Lansky, P., Rodriguez, R., Sacerdote, L., 2004. Mean instantaneous firing frequency is always higher than the firing rate. Neur. Comp. 16(3), 477–489.

    Article  Google Scholar 

  • Lansky, P., Sacerdote, L., Tomassetti, F., 1995. On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity. Biol. Cyber. 73(5), 457–465.

    Article  MATH  Google Scholar 

  • Lindner, B., Longtin, A., Bulsara, A., 2003. Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise. Neur. Comp. 15(8), 1761–1788.

    Article  MATH  Google Scholar 

  • Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G., 1999. An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. Math. Japonica 50(2), 247–322.

    MATH  MathSciNet  Google Scholar 

  • Sacerdote, L., Sirovich, R., 2003. Multimodality of the interspike interval distribution in a simple jump-diffusion model. Sci. Math. Jpn. 58(2), 307–322.

    MATH  MathSciNet  Google Scholar 

  • Sacerdote, L., Zucca, C., 2003a. Threshold shape corresponding to a Gamma firing distribution in an Ornstein-Uhlenbeck neuronal model. Sci. Math. Jpn. 58(2), 295–305.

    MATH  MathSciNet  Google Scholar 

  • Sacerdote, L., Zucca, C., 2003b. On the relationship between interspikes interval distribution and boundary shape in the Ornstein-Uhlenbeck neuronal model. In: Capasso, V. (Ed.), Mathematical Modelling & Computing in Biology and Medicine (Proceedings of the V Conference ECMTB2002). Esculapio, Bologna, pp. 161–168.

  • Segundo, J.P., 2003. Nonlinear dynamics of point process systems and data. Int. J. Bifurcation Chaos 13, 2035–2116.

    Article  MATH  MathSciNet  Google Scholar 

  • Shadlen, M.N., Newsome, W.T., 1998. The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. J. Neurosci. 18(10), 3870–3896.

    Google Scholar 

  • Singer, W., Gray, C., Engel, A., Konig, P., Artola, A., Brocher, S., 1990. Formation of cortical cell assemblies. Cold Spring Harb. Symp. Quant. Biol. 55, 939–952.

    Google Scholar 

  • Shimokawa, T., Pakdaman, K., Sato, S., 1999. Time-scale matching in the response of a leaky integrate-and-fire neuron model to periodic stimulus with additive noise. Phys. Rev. E 59(3), 3427–3443.

    Article  Google Scholar 

  • Shimokawa, T., Pakdaman, K., Takahata, T., Tanabe, S., Sato, S., 2000. A first-passage-time analysis of the periodically forced noisy leaky integrate-and-fire model. Biol. Cybern. 83(4), 327–340.

    Article  MATH  Google Scholar 

  • Shinomoto, S., Sakai, Y., Funahashi, S., 1999. The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex. Neur. Comp. 11(4), 935–951.

    Article  Google Scholar 

  • Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334–350.

    Google Scholar 

  • Tuckwell, H.C., 1988. Introduction to Theoretical Neurobiology: I. Cambridge University Press, Cambridge.

    Google Scholar 

  • Tuckwell, H.C., Wan, F.Y.M., Rospars, J.P., 2002. A spatial stochastic neuronal model with Ornstein-Uhlenbeck input current. Biol. Cybern. 86(2), 137–145.

    Article  MATH  Google Scholar 

  • Villa, A.E.P., Rouiller, E.M., Simm, G.M., Zurita, P., de Ribaupierre, Y., de Ribaupierre, F., 1991. Corticofugal modulation of information processing in the auditory thalamus of the cat. Exp. Brain Res. 86, 506–517.

    Article  Google Scholar 

  • Villa, A.E.P., Tetko, I.V., Hyland, B., Najem, A., 1999a. Spatiotemporal activity patterns of rat cortical neurons predict responses in a conditioned task. Proc. Natl. Acad. Sci. U.S.A. 96, 1006–1011.

  • Villa, A.E.P., Tetko, I.V., Dutoit, P., De Ribaupierre, Y., De Ribaupierre, F., 1999b. Corticofugal modulation of functional connectivity within the auditory thalamus of rat, guinea pig and cat revealed by cooling deactivation. J. Neurosci. Meth. 86(2), 161–178.

    Article  Google Scholar 

  • Villa, A.E.P., 2000. Empirical evidence about temporal structure in multi-unit recordings. In: Miller, R. (Ed.), Time and the Brain. Conceptual advances in brain research, vol. 2. Harwood Academic Publishers, New York, pp. 1–51.

    Google Scholar 

  • Von der Marlsburg, C., 1981. The correlation theory of brain function. Internal Report 81-2. Max-Planck-Institute for Biophysical Chemistry, Goettingen.

  • Zucca, C., Sacerdote, L., Peskir, G., 2003. On the inverse first-passage problem for a Wiener process. Quaderno 2/2003. Dipartimento di Matematica, Universitá di Torino.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Torino, Carlo Alberto 10, 10123, Torino, Italy

    L. Sacerdote & C. Zucca

  2. INSERM, U318, Laboratoire de Neurobiophysique, University Joseph Fourier, Grenoble, France

    A. E. P. Villa

  3. Neuroheuristic Research Group, Institute of Computer Science and Organization INFORGE, University of Lausanne, Lausanne, Switzerland

    A. E. P. Villa

Authors
  1. L. Sacerdote
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  2. A. E. P. Villa
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  3. C. Zucca
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Correspondence to L. Sacerdote.

Additional information

PACS: 87.19.La

MSC: 60K30, 60J60, 65C40, 62P10

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Sacerdote, L., Villa, A.E.P. & Zucca, C. On the Classification of Experimental Data Modeled Via a Stochastic Leaky Integrate and Fire Model Through Boundary Values. Bull. Math. Biol. 68, 1257–1274 (2006). https://doi.org/10.1007/s11538-006-9107-7

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  • DOI: https://doi.org/10.1007/s11538-006-9107-7

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