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A note on stochastic modeling of shunting inhibition

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Abstract

Stochastic modeling of a neuron with a shunting inhibition is considered. The shunting inhibition divides a neuron potential, and in this case, the neuron has a state-dependent noise. The effect of this state-dependency is discussed by means of a comparison with a subtractive inhibition which was treated in a previous paper. Attention is focused on the firing statistics of both inhibitions described by the first passage time of a neuron potential. These statistics differ depending on the reset value of the potential. This is due to the fact that the shunting inhibition is effective when the potential is close to a threshold. Numerical examples illustrating this effect are given.

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References

  • Büttner, U., Glüsser, O.J.: Quantitative Untersuchungen der räumlichen Erregungssummation im rezeptiven Feld retinaler Neurone der Katze. Kybernetik 4, 81–94 (1968)

    Google Scholar 

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

    Google Scholar 

  • Furman, G.G.: Comparison of models for subtractive and shunting lateral inhibition in receptor neuron fields. Kybernetik 2, 257–274 (1965)

    Google Scholar 

  • Gerstein, G.L., Mandelbrot, B.: Random walk model for the spike activity of single neurons. Biophys. J. 4, 41–68 (1964)

    Google Scholar 

  • Gluss, B.: A model for neuron firing with exponential decay of potential resulting in diffusion equation for probability density. Bull. Math. Biophys. 29, 233–243 (1967)

    Google Scholar 

  • Johannesma, P.I.M.: Diffusion models for the stochastic activity of neurons. In: Neural networks. Ed.: Caianiello, E.R. Berlin-Heidelberg-New York: Springer 1968

    Google Scholar 

  • Kiang, N.Y-S., Watanabe, T., Thomas, E.C., Clark, L.F.: Discharge patterns of single fibers in cat's auditory nerve. Cambridge, Mass.: M.I.T. Press 1965

    Google Scholar 

  • Lettvin, J.Y.: Form-function relations in neurons. Q.P.R. of M.I.T., Electronics 66, 333 (1962)

    Google Scholar 

  • Matsuyama, Y., Shirai, K., Akizuki, K.: On some properties of stochastic information processes in neurons and neuron populations. Kybernetik 15, 127–145 (1974)

    Google Scholar 

  • Ten Hoopen, M.: Probilistic firing of neurons considered as a first passage time problem. Biophys. J. 6, 435–451 (1965)

    Google Scholar 

  • Weiss, T.F.: A model of peripheral auditory system. Kybernetik 3, 153–175 (1966)

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Stanford University, Stanford, CA, USA

    Y. Matsuyama

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  1. Y. Matsuyama
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Matsuyama, Y. A note on stochastic modeling of shunting inhibition. Biol. Cybernetics 24, 139–145 (1976). https://doi.org/10.1007/BF00364116

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  • DOI: https://doi.org/10.1007/BF00364116

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