### Abstract

This paper is to derive a mathematical model for neuron by imposing only a principle of symmetry that two modelers must obtain the same model when one models the conductances of ion channels and the other models the channels' resistances. Conductance-voltage characteristics for ion transport channels and protein gating channels are both derived. They are expressed as products of maximal conductances and opening probabilities for both types of channel. It gives an explanation to the role of spontaneous firing of individual channel pores and to the origin of leak current. The model has a better fit to a classical data than the Hodgkin-Huxley model does. It can also be reduced to a 2-dimensional model qualitatively similar to the FitzHugh-Nagumo equation and be expanded to a model of three ion channels capable of spike bursts.

Original language | English (US) |
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Article number | 125976 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

DOIs | |

Publication status | Accepted/In press - Jan 1 2019 |

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### Keywords

- Conductance-resistance symmetry
- FitzHugh-Nagumo equations
- Hodgkin-Huxley equations
- Opening probability for ion transport channel
- Opening probability for protein gating channel
- Spontaneous firing

### ASJC Scopus subject areas

- Physics and Astronomy(all)