|
In neurophysiology, several mathematical models of the action potential have been developed, which fall into two basic types. The first type seeks to model the experimental data quantitatively, i.e., to reproduce the measurements of current and voltage exactly. The renowned Hodgkin–Huxley model of the axon from the ''Loligo'' squid exemplifies such models.〔 〕 Although qualitatively correct, the H-H model does not describe every type of excitable membrane accurately, since it considers only two ions (sodium and potassium), each with only one type of voltage-sensitive channel. However, other ions such as calcium may be important and there is a great diversity of channels for all ions. As an example, the cardiac action potential illustrates how differently shaped action potentials can be generated on membranes with voltage-sensitive calcium channels and different types of sodium/potassium channels. The second type of mathematical model is a simplification of the first type; the goal is not to reproduce the experimental data, but to understand qualitatively the role of action potentials in neural circuits. For such a purpose, detailed physiological models may be unnecessarily complicated and may obscure the "forest for the trees". The Fitzhugh-Nagumo model is typical of this class, which is often studied for its entrainment behavior. Entrainment is commonly observed in nature, for example in the synchronized lighting of fireflies, which is coordinated by a burst of action potentials; entrainment can also be observed in individual neurons. Both types of models may be used to understand the behavior of small biological neural networks, such as the central pattern generators responsible for some automatic reflex actions. Such networks can generate a complex temporal pattern of action potentials that is used to coordinate muscular contractions, such as those involved in breathing or fast swimming to escape a predator.〔Hooper, Scott L. "Central Pattern Generators." ''Embryonic ELS'' (1999) http://www.els.net/elsonline/figpage/I0000206.html (2 of 2) (11:42:28 AM ) Online: Accessed 27 November 2007 ().〕 ==Hodgkin–Huxley model== (詳細はAlan Lloyd Hodgkin and Andrew Huxley developed a set of equations to fit their experimental voltage-clamp data on the axonal membrane.〔 The model assumes that the membrane capacitance ''C'' is constant; thus, the transmembrane voltage ''V'' changes with the total transmembrane current ''I''tot according to the equation : In summary, the Hodgkin–Huxley equations are complex, non-linear ordinary differential equations in four independent variables: the transmembrane voltage ''V'', and the probabilities ''m'', ''h'' and ''n''. No general solution of these equations has been discovered. A less ambitious but generally applicable method for studying such non-linear dynamical systems is to consider their behavior in the vicinity of a fixed point. This analysis shows that the Hodgkin–Huxley system undergoes a transition from stable quiescence to bursting oscillations as the stimulating current ''I''ext is gradually increased; remarkably, the axon becomes stably quiescent again as the stimulating current is increased further still.〔 〕 A more general study of the types of qualitative behavior of axons predicted by the Hodgkin–Huxley equations has also been carried out.〔 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「Quantitative models of the action potential」の詳細全文を読む スポンサード リンク
|