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Neuronal Model Reduction

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Encyclopedia of Computational Neuroscience

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Definition

The act of reducing the complexity of a mathematical neuron model while preserving its essential features.

Detailed Description

The biophysical description of ion channels distributed on a three-dimensional neuron membrane is a typical example of a complex mathematical neuron model. In such models, the voltage dependence of ion channels follows the formalism of Hodgkin and Huxley. Therefore, each patch of membrane is characterized by the membrane potential, x 1, and the state of activation/inactivation for every ion channel type, x 2, … , x n . These state variables evolve according to a differential equation arising from biophysics and biochemistry. The equations are typically of first order in time, but nonlinear. Given the nonlinear functions f 1, f 2, …, f n , the evolution of n state variables follows:

$$ \begin{array}{c}\frac{d{x}_1}{ dt}={f}_1\left({x}_1,{x}_2,\dots, {x}_n,{y}_1,{y}_2,\dots, {y}_k\right)\\ {}\frac{d{x}_2}{ dt}={f}_2\left({x}_1,{x}_2,\dots,...

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Further Reading

  • Gerstner W, Kistler W, Naud R, Paninski L (2014) Neuronal dynamics. Cambridge University Press, Cambridge

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Authors and Affiliations

  1. Department of Physics, University of Ottawa, 150 Louis Pasteur, K1N 6N5, Ottawa, ON, Canada

    Richard Naud

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  1. Richard Naud
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Correspondence to Richard Naud .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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© 2014 Springer Science+Business Media New York

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Naud, R. (2014). Neuronal Model Reduction. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_166-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_166-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

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