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The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiac myocytes, and hence it is a continuous time model, unlike the Rulkov map for example. Alan Lloyd Hodgkin and Andrew Huxley described the model in 1952 to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon. They received the 1963 Nobel Prize in Physiology or Medicine for this work. ==Basic components== The typical Hodgkin–Huxley model treats each component of an excitable cell as an electrical element (as shown in the figure). The lipid bilayer is represented as a capacitance (Cm). Voltage-gated ion channels are represented by electrical conductances (''g''''n'', where ''n'' is the specific ion channel) that depend on both voltage and time. Leak channels are represented by linear conductances (''g''''L''). The electrochemical gradients driving the flow of ions are represented by voltage sources (''E''''n'') whose voltages are determined by the ratio of the intra- and extracellular concentrations of the ionic species of interest. Finally, ion pumps are represented by current sources (''I''''p''). The membrane potential is denoted by ''Vm''. Mathematically, the current flowing through the lipid bilayer is written as : and the current through a given ion channel is the product : where is the reversal potential of the ''i''-th ion channel. Thus, for a cell with sodium and potassium channels, the total current through the membrane is given by: : where ''I'' is the total membrane current per unit area, ''C''''m'' is the membrane capacitance per unit area, ''g''''K'' and ''g''''Na'' are the potassium and sodium conductances per unit area, respectively, ''V''''K'' and ''V''''Na'' are the potassium and sodium reversal potentials, respectively, and ''g''''l'' and ''V''''l'' are the leak conductance per unit area and leak reversal potential, respectively. The time dependent elements of this equation are ''V''''m'', ''g''''Na'', and ''g''''K'', where the last two conductances depend explicitly on voltage as well. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hodgkin–Huxley model」の詳細全文を読む スポンサード リンク
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