神經科學 1952

膜電流的定量描述

艾倫·霍奇金與安德魯·赫胥黎

把神經衝動寫成方程：電壓門控的離子，發放一記「全或無」的尖峰。

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In depth · the introduction

你的每一個念頭、每一次心跳、每一下抽動，都是一記微小的電脈衝——而 1952 年，兩位科學家寫下了讓它發放的精確方程。

核心想法

一個神經細胞靜息時，內部比外部約負 65 毫伏，像一節充好電的電池，靠兩側鈉、鉀離子數量的不均等來維持。所謂神經衝動，就是這個電壓一次突然的、行進著的反轉。霍奇金與赫胥黎指出，這是因為膜上帶著一些極小的、受電壓控制的門：當電壓升過一個閾值，鈉門驟然打開、鈉湧入，把電壓猛地頂上去；一瞬之後牠們又砰地關上，鉀門打開，讓鉀流出、把電壓復位。

他們的成就，是精確測出這些門如何開合，並把它凝成寥寥幾個方程——精確到足以預言整個脈衝：它的高度、它的速度，乃至神經再次能夠發放之前那段短暫的「死時間」。

它是如何誕生的

這項工作仰仗一位不太可能的主角：槍烏賊的巨軸突——一根粗到（可達一毫米）能往裡穿電線的神經纖維。在劍橋與普利茅斯的海洋實驗室，艾倫·霍奇金與安德魯·赫胥黎，還有伯納德·卡茨，發明了「電壓鉗」：一個反饋電路，把膜固定在選定的電壓上，並讀出電流。第二次世界大戰曾讓一切中斷數年。

歸來之後，他們極盡細緻地測量了鈉電流與鉀電流，又因為沒有電子電腦可用，花了幾週時間用手搖一台機械桌上計算器來求解方程。算出的神經衝動，連同它的形狀與速度，都與真實的那一記吻合。他們分享了 1963 年的諾貝爾獎。

它為何重要

一個活生生的訊號，第一次被化簡為你能求解、又能信賴的數學。它表明生物學連到毫伏一級都服從物理，也為「為任何帶電活動的細胞建模」立下了範本——神經元、心肌、分泌激素的細胞。今天的腦模擬、心臟藥物測試與神經假體，全都承自這組方程。

一個可以想像的畫面

想像一排能自己重新站起來的多米諾骨牌。只輕輕一碰第一張——那個刺激——什麼也不會發生，它晃一晃又穩住了。可一旦把它推過某個角度，它就倒下，撞倒下一張、再下一張：一道擋不住的波，而且無論你推得多用力，它的大小始終如一。這就是「全或無」。鈉門是那場倒下；鉀門則是把每張骨牌重新扶正的機關——歇上一小會兒，便又能再次發放。

它的位置

1780 年代，伽伐尼發現電能驅動肌肉；約 1902 年，伯恩斯坦猜想衝動是一種離子效應。霍奇金與赫胥黎把猜想變成了精確、可檢驗的方程——這與一年後沃森和克里克為遺傳所做的、從「描述」到「機制」的跨越如出一轍。從這裡，一條線通向今天原子級的通道結構、光遺傳學，以及大規模腦模擬背後那些基於電導的模型。

The original document

Original source text

A. L. Hodgkin & A. F. Huxley · J. Physiol. 117 (1952): 500–544

This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkin, Huxley & Katz, 1952; Hodgkin & Huxley, 1952 a–c). Its general object is to discuss the results of the preceding papers (Part I), to put them into mathematical form (Part II) and to show that they will account for conduction and excitation in quantitative terms (Part III).

Part I — The components of the membrane current

Current can be carried through the membrane either by charging the membrane capacity or by movement of ions through the resistances in parallel with the capacity. The ionic current is divided into components carried by sodium and potassium ions (I_Na and I_K), and a small 'leakage current' (I_l) made up by chloride and other ions.

Voltage-clamp records (from the preceding papers in the series) show that when the membrane is suddenly depolarised, the sodium conductance rises fast and then falls even though the depolarisation is maintained, while the potassium conductance rises later along an S-shaped curve and stays up. These two voltage- and time-dependent conductances, riding on a constant leak, are the whole of the ionic current.

Part II — Mathematical description of the membrane current

The total current is written as a capacitive term plus three ionic currents, each an Ohmic conductance times its driving force (V − E). The variable conductances are built from dimensionless gating variables m, h (sodium) and n (potassium), each between 0 and 1 and each obeying a first-order rate equation dx/dt = αₓ(V)(1−x) − βₓ(V)x. Fitting the clamp data gives g_Na = ḡ_Na·m³h and g_K = ḡ_K·n⁴, with the rate constants αₓ, βₓ expressed as functions of voltage.

Part III — Reconstruction of conduction and excitation

With no further assumptions, the equations are solved to reconstruct the action potential, the threshold, the refractory period, anode-break excitation, and — coupled to cable theory — the propagated impulse and its conduction velocity, all computed numerically by hand on a mechanical calculator and compared point-by-point with the measured records.

[ … ]

Physiological Laboratory, Cambridge · received 10 March 1952