臺灣博碩士論文加值系統

神經元自發火現象是個在神經科學上重要且有趣的現象。本文藉著研究霍奇金-赫胥黎模型之分歧分析發現提高鈉離子通道之最大電導，或降低鉀離子通道之最大電導，或提高細胞外鉀離子濃度均可發生自發性振動，意即使得神經元產生自律性。提高細胞外鉀離子濃度會導致神經元自發火現象業已由實驗證實且為一普為人知的現象。但改變離子通道之最大電導，亦即改變離子通道之通透性，亦可導致神經元自發火現象則尚未經實驗證實。吾人希望未來的實驗可以驗證本文之發現。

Automatic neuron firing is an important and interesting research subject in neuroelectrophysiology. Through the original Hodgkin-Huxley model, we investigate its codimension 1 bifurcations along maximum conductance of sodium channel, maximum conductance of potassium channel, and extracellular potassium concentration. We find that increasing maximum conductance of sodium channel, or decreasing maximum conductance of potassium channel, or increasing extracellular potassium concentration will all cause spontaneous oscillation without any external stimulus current. The effect that increasing extracellular potassium concentration will cause repetitive neuron firing has been verified by experiments, but the effect of changing channel maximum conductance will cause automatic neuron firing is first analyzed in the current paper but not yet verified by experiments. We hope the experiment can be done in the future by using sodium channel activator and potassium channel blocker.

Contents

1. Introduction ……………………………………………...1

2. Mathematical Model and Numerical Method………….3

3. Results and Discussions……………………………….....6
3.1 Bifurcation along maximum conductance of sodium channel………………………………….....6
3.2 Bifurcation along maximum conductance of potassium channel……………………………..…10
3.3 Bifurcation along extracelluar potassium concentration ………………………………….....13

4. Conclusions……………………………………………..17

References………………………………………………18

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