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W = *2T.*cNa+(l) exp ( ^ y M ) - *lf.*CN.*(2) exp (^f) Jcr = *g c cr (l) exp ( ^ ) - *g-Ccr(2) exp
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At rest, no current passes through the membrane and thus the material flux of chloride ions compensates the material flux of sodium and potassium ions: W + . / K + =Ja(6.5.2) Equations (6.5.1) and (6.5.2) yield the membrane rest potential in the form
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* c K +(l) + * +cNa+( * c K+ (2) + ^ a + c N a + (
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462 Ion transport is characterized by conditional rate constants & +, k^a+ and &a- which can be identified with the permeabilities of the membrane for these ions. These relationships can be improved by including the effect of the electrical double layer on the ion concentration at the membrane surface (cf. page 444 and Section 5.3.2). Equation (6.5.3) is identical with the relationship derived by Hodgkin, Huxley and Katz. It satisfactorily explains the experimental values of the membrane rest potential assuming that the permeability of the membrane for K+ is greater than for Na+ and Cl~~, so that the deviation of A$ M from the Nernst potential for K+ is not very large. However, the permeabilities for the other ions are not negligible. In this way the axon at rest would lose potassium ions and gain a corresponding concentration of sodium ions. This does not occur because of the action of Na+,K+-ATPase, transferring potassium ions from the intercellular liquid into the axon and sodium ions in the opposite direction, through hydrolysis of ATP. When the nerve cells are excited by an electric impulse (either 'natural', from another nerve cell or another site on the axon, or 'artificial', from an electrode), the membrane potential changes, causing an increase in the frequency of opening of the gates of the sodium channels. Thus, the flux of sodium ions increases and the membrane potential is shifted towards the Nernst potential value determined by sodium ions, which considerably differs from that determined by potassium ions, as the concentration of sodium ions in the extracellular space is much greater than in the intracellular space, while the concentration ratio of potassium ions is the opposite. The potential shift in this direction leads to a further opening of the sodium gates and thus to 'autocatalysis' of the sodium flux, resulting in a spike which is stopped only by inactivation of the gates. In spite of the fact that the overall currents flowing across the cell membranes consist of tiny stochastic fluctuating components, the resulting dependences, as shown in Figs 6.19 and 6.20, are smooth curves and can be used for further analysis (the situation is, in fact, analogous to most of phenomena occurring in nature). Thus, the formation of a spike can be shown to be a result of gradual opening and closing of very many potassium and sodium channels (Fig. 6.24). According to Fig. 6.17 the nerve cell is linked to other excitable, both nerve and muscle, cells by structures called, in the case of other nerve cells, as partners, synapses, and in the case of striated muscle cells, motor endplates (neuromuscular junctions). The impulse, which is originally electric, is transformed into a chemical stimulus and again into an electrical impulse. The opening and closing of ion-selective channels present in these junctions depend on either electric or chemical actions. The substances that are active in the latter case are called neurotransmitters. A very important member of this family is acetylcholine which is transferred to the cell that receives the signal across the postsynaptic membrane or motor endplate through a
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Fig. 6.24 A hypothetic scheme of the time behaviour of the spike linked to the opening and closing of sodium and potassium channels. After longer time intervals a temporary hyperpolarization of the membrane is induced by reversed transport of potassium ions inside the nerve cell. Nernst potentials for Na+ and K+ are also indicated in the figure. (According to A. L. Hodgkin and A. F. Huxley)
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specific channel, the nicotinic acetylcholine receptor. This channel has been investigated in detail, because, among other reasons, it can be isolated in considerable quantities as the membranes of the cells forming the electric organ of electric fish are filled with this species. Acetylcholine, which is set free from vesicles present in the neighbourhood of the presynaptic membrane, is transferred into the recipient cell through this channel (Fig. 6.25). Once transferred it stimulates generation of a spike at the membrane of the recipient cell. The action of acetylcholine is inhibited by the enzyme, acetylcholinesterase, which splits acetylcholine to choline and acetic acid. Locomotion in higher organisms and other mechanical actions are made possible by the striated skeletal muscles. The basic structural unit of muscles is the muscle cell muscle fibre which is enclosed by a sarcoplasmatic membrane. This membrane invaginates into the interior of the fibre through transversal tubules which are filled with the intercellular liquid. The inside of the fibre consists of the actual sarcoplasm with inserted mitochondria, sarcoplasmatic reticulum and minute fibres called myofibrils, which are the organs of muscle contraction and relaxation. The membrane of the sarcoplasmatic reticulum contains Ca2+-ATPase, maintaining a concentration of calcium ions in the sarcoplasm of the relaxed muscle below 10~7mol dm~3. Under these conditions, the proteins, actin and myosin, forming the myofibrils lie in relative positions such that the muscle is relaxed. When a spike is transferred from the nerve fibre to the sarcoplasmatic membrane, another spike is also formed there which continues
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