Hodgkin-Huxley network

Replacing Ip by F(Jj + Jj ) where is the linearized version of (5.70) and is its Na -counterpart, directly leads to the Hodgkin-Huxley equation (2.34). The scheme of the complete Hodgkin-Huxley network is shown in Fig. 9. 

US to quite different excitation models, namely, a molecular model in the following section and a dissipative one in Section 6.2. We will come back to the Hodgkin-Huxley model in Section 5.6 in context with a generalized network language. 

The whole excitation phenomenon travels along the axon membrane. Within the framework of our brief representation in this section, we restrict ourselves to a local description of the phenomenon which has been given by Hodgkin and Huxley in the form of a network shown in Fig. 5. 

The important point of this model description is the appearance of a feedback coupling from the membrane voltage V to the conductivities gj, gj indicated as dotted lines in Fig. 5. If such a feedback coupling were not present, the system would behave like an ordinary electric network and relax exponentially into its steady state but never show excitability. Hodgkin and Huxley have shown that this necessary feedback coupling can be represented by three different kinds of charged particles which control the values of gj and gj. Let p, P2 and p the probabilities of the particles to be present in the membrane at the positions of the channels. It is found now that the K -channel is activated by the first particle in a fourth-order chemical reaction but independent on the second and third particle, whereas the Na -channel is independent on the first particle but activated by the second particle in a trimolecular reaction and inhibited by the third particle in a unimole-cular reaction such that... 

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