Abstract
We present a scheme for systematically reducing the number of differential equations required for biophysically realistic neuron models. The techniques are general, are designed to be applicable to a large set of such models and retain in the reduced system as high a degree of fidelity to the original system as possible. As examples, we provide reductions of the Hodgkin-Huxley system and the A-current model of Connor et al. (1977).
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References
Abbott LF, Kepler TB (1990) Model neurons: from Hodgkin-Huxley to Hopfield. In: Garrido L (ed) Statistical mechanics of neural networks. Springer, Berlin Heidelberg New York
Buchholtz F, Golowasch J, Epstein IR, Marder E (1992) The contribution of individual ionic currents to the activity of a model stomatogastric ganglion neuron J Neurophysiol (in press)
Connor JA, Walter D, McKown R (1977) Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons. Biophys J 18:81–102
FitzHugh R (1961) Impulses and physiological states in models of nerve membrane. Biophys J 1:445–466
Golowasch J, Buchholtz F, Epstein IR, Marder E (1992) A mathematical model of an identified stomatogastric ganglion neuron J Neurophysiol (in press)
Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296:162–164
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500
Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci79:2554
Krinskii VI and Kokoz YM (1973) Analysis of equations of excitable membranes — 1. Reduction of the Hodgkin-Huxley equations to a second-order system. Biofizika 18:506–511
Lapicque L (1907) Recherches quantitatives sur l'excitation électrique des nerfs traitée comme une polarization. J Physiol Pathol Gen 9:620–635
McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:114–133
Rinzel J (1985) Excitation dynamics: insights from simplified membrane models. Fed Proc 44:2944–2946
Rose RM, Hindmarsh JL (1989) The assembly of ionic currents in a thalamic neuron I. The three-dimensional model. Proc R Soc Lond 237:267
Yamada WM, Koch C, Adams PR (1989) Multiple channels and calcium dynamics. In methods of neuronal modeling. In: Koch C, Segev I (eds) From synapses to networks. MIT Press, Cambridge
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Kepler, T.B., Abbott, L.F. & Marder, E. Reduction of conductance-based neuron models. Biol. Cybern. 66, 381–387 (1992). https://doi.org/10.1007/BF00197717
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DOI: https://doi.org/10.1007/BF00197717