### 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) |
---|---|

Article number | 125976 |

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

DOIs | |

State | 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)

### Cite this

**Neuron model with conductance-resistance symmetry.** / Deng, Bo.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Neuron model with conductance-resistance symmetry

AU - Deng, Bo

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Conductance-resistance symmetry

KW - FitzHugh-Nagumo equations

KW - Hodgkin-Huxley equations

KW - Opening probability for ion transport channel

KW - Opening probability for protein gating channel

KW - Spontaneous firing

UR - http://www.scopus.com/inward/record.url?scp=85072175446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072175446&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2019.125976

DO - 10.1016/j.physleta.2019.125976

M3 - Article

AN - SCOPUS:85072175446

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

M1 - 125976

ER -