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Fig. 6.21 Joint application of patch-clamp and voltageclamp methods to the study of a single potassium channel present in the membrane of a spinal-cord neuron cultivated in the tissue culture. The values indicated before each curve are potential differences imposed on the membrane. The ion channel is either closed (C) or open (O). (A simplified drawing according to B. Hille)
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Fig. 6.22 A function model of the sodium channel. P denotes protein, S the potential sensitive sensor and H the gate. The negative sign marks the carboxylate group where the guanidine group of tetrodotoxin can be attached. (According to B. Hille)
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(0.5 x 0.4 nm in size) controlling the entrance of ions with a definite radius. The rate of transport of sodium ions through the channel is considerable: when polarizing the membrane with a potential difference 4- 60 mV a current of approximately 1.5 pA flows through the channel which corresponds to 6 x 106 Na+ ions per second practically the same value as with the gramicidin A channel. The sodium channel is only selective but not specific for sodium transport. It shows approximately the same permeability to lithium ions, whereas it is roughly ten times lower than for potassium. The density of sodium channels varies among different animals, being only 30 fim~2 in the case of some marine animals and 330 jurn"2 in the squid axon, reaching 1.2 x 104 fj,m~2 in the mammalian nodes of Ranvier (see Fig. 6.17). The potassium channel mentioned above (there are many kinds) is more specific for K+ than the sodium channel for Na+ being almost impermeable to Na + .
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Fig. 6.23 Single-channel currents flowing across the membrane between the protoplast and vacuole of Chara corallina. Among several channels with different conductivity the recordings of the 130 pS channel are recorded here. The zero line is at the top of each curve. (By courtesy of F. Homble)
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461 The stochastic nature of membrane phenomena originating in channel opening and closing is not restricted to excitable cells. Figure 6.23 shows the time dependence of currents flowing through a patch of the membrane between the tonoplast (protoplasma) and the vacuole in the isolated part of a cell of the freshwater alga, Chara corallina. In this membrane there are three types of potassium channels with different conductivity and the behaviour of the 130 pS channel is displayed in the figure. D. E. Goldman, A. L. Hodgkin, A. P. Huxley and B. Katz (A. L. H. and A. P. H., Nobel Prize for Physiology and Medicine, 1963, B.K., 1970) developed a theory of the resting potential of axon membranes, based on the assumption that the strength of the electric field in a thin membrane is constant and that ion transport in the membrane can be described by the Nernst-Planck equations. It would appear that this approach does not correspond to reality it has been pointed out that ions are transported through the membrane in channels that are specific for a certain kind of ion. Thus, diffusion is not involved, but rather a jumping of the ions through the membrane, that must overcome a certain energy barrier. In deriving a relationship for the resting potential of the axon membrane it will be assumed that, in the vicinity of the resting potential, the frequency of opening of a definite kind of ion channel is not markedly dependent on the membrane potential. The transport of ions through the membrane can be described by the same equations as the rate of an electrode reaction in Section 5.2.2. It will be assumed that the resting potential is determined by the transport of potassium, sodium and chloride ions alone. The constants fcp are functions of the frequency of opening and closing of the gates of the ion-selective channels. The solution to this problem will be based on analogous assumptions to those employed for the mixed potential (see Section 5.8.4). The material fluxes of the individual ions are given by the equations
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