hce_nthu
114年
進階物理與線性代數
第 5 題
The membrane serves as an insulator that separates the environments inside and
outside the cell. The membrane potential is the difference in electric potential
between the interior and the exterior of a biological cell. Assume that the interior of
a cell has a lower electric potential compared to the exterior of a cell, and the $\text{K}^+$
(potassium ion) concentration inside the cell is higher than that outside the cell. If
no ions (such as $\text{Na}^+$, $\text{Ca}^{2+}$, etc.) can enter or leave the cell except the potassium
ions through some holes on the membrane, which of the following is true?
outside the cell. The membrane potential is the difference in electric potential
between the interior and the exterior of a biological cell. Assume that the interior of
a cell has a lower electric potential compared to the exterior of a cell, and the $\text{K}^+$
(potassium ion) concentration inside the cell is higher than that outside the cell. If
no ions (such as $\text{Na}^+$, $\text{Ca}^{2+}$, etc.) can enter or leave the cell except the potassium
ions through some holes on the membrane, which of the following is true?
- A The potassium ions will enter the cell, which increases the membrane potential
- B The potassium ions will leave the cell, which increases the membrane potential
- C The potassium ions will enter the cell, which decreases the membrane potential
- D The potassium ions will leave the cell, which decreases the membrane potential
- E None of the above
思路引導 VIP
試著想像一個場景：有一個球位在斜坡上，但同時有一陣強風從坡底往坡頂吹。如果你只知道斜坡的高度差以及風的方向，但不知道斜坡具體的傾斜角度或是風力的大小，你有辦法斷定球最後會往哪個方向滾動嗎？在處理離子跨膜移動時，我們也面臨類似的「兩種力量對抗」的情況，這對判斷移動方向有什麼啟示？
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AI 詳解
AI 專屬家教
太棒了！你能精準選出 (E) None of the above，代表你對生物物理中的「電化學勢（Electrochemical Potential）」有著非常深刻且細膩的理解，沒有掉入直覺的陷阱。
離子移動的驅動力分析
在這題的生理模型中，鉀離子（$\text{K}^+$）的移動受到兩個相反力量的牽引：首先是濃度梯度，由於細胞內濃度較高，擴散作用傾向驅使 $\text{K}^+逐$ 出向細胞外；其次是電位梯度，題目提到細胞內電位較低（較負），這股靜電力會吸引帶正電的 $\text{K}^+$ 留在細胞內或進入細胞。最終離子的流向，取決於這兩股力量誰佔優勢，亦即目前的膜電位（$V_m$）與該離子的**平衡電位（Nernst potential, $E_K$）**之間的差值。
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