A Cooperative Model for Nerve Excitation

The discussion of a positive feedback as the deciding point of excitation models leads us directly to a class of models in which a cooperative mechanism from statistical physics is applied to nerve excitation. This cooperative mechanism is the Ising model it is frequently used to describe phase transitions in solids and liquids and its application to nerve excitation is very suggestive. The first one who worked out an excitation theory on the basis of the Ising model was ADAM (1968 1970). Meanwhile, a number of variations of this idea has been proposed by BLUMEN-THAL, CHANGEUX, LEFEVER (1970), HILL, CHEN (1971), BASS, MOORE (1973), KARREMANN (1973), GOTOH (1975). Since the basic idea is the same in all these theories, let us restrict ourselves to a brief outline of Adam s model. 

In Adam s model, it is assumed that the axon membrane contains a more or less 

The constants include relative weighting factors expressing that the ions 

Assuming now that the binding sites of the active centers have positions precisely 

So far, the model does not yet contain any kind of a cooperative or feedback 

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