Katz, membrane potential

Equation (3) suggests that the membrane potential in the presence of sufficient electrolytes in Wl, W2, and LM is primarily determined by the potential differences at two interfaces which depend on charge transfer reactions at the interfaces, though the potential differences at interfaces are not apparently taken into account in theoretical equations such as Nernst-Planck, Henderson, and Goldman-Hodgkin-Katz equations which have often been adopted in the discussion of the membrane potential. 

Fig. 6.19 Time dependence of excitation current pulses (1) and membrane potential A0. (2) The abrupt peak is the spike. (According to B. Katz)...

This Goldman-Hodgkin-Katz voltage equation is often used to determine the relative permeabilities of ions from experiments where the bathing ion concentrations are varied and changes in the membrane potential are recorded [5],... 

An equation (also referred to as the constant field equation, the Goldman-Hodgkin-Katz equation, and the GHK equation) which relates the membrane potential (Ai/r) to the individual permeabilities of the ions (and their concentrations) on both sides of the membrane. Thus,... 

Around 1970, some clues as to individual channel action emerged. Katz and Miledi (1972) discovered that the end-plate membrane potential becomes markedly noisy in the presence of acetylcholine, and they interpreted this as a series of elementary events produced by the opening and closing of individual channels as they bound and released acetylcholine molecules. This led to a series of studies by Stevens and others using techniques of fluctuation analysis to gain information about the size and duration of these events. 

If the permeability is significant for both potassium and sodium, the Nernst equation is not a good predictor of membrane potential, but the Goldman-Hodgkin-Katz equation may be used. 

Thus, one can artificially change the concentrations of Na+, K+, and Cl on either side of the membrane. Then, one can go back to the Hodgkin-Katz equation (14.5) and ask what change in potential these artificial changes of ionic concentrations should bring about. There is found (Jahn, 1962) to be a poor match between theory and experiment. Ionic concentration differences alone, then, do not completely determine membrane potentials in living systems. 

Figure 16.2 Illustration of the squid giant axon action potential and its dependence on external Na+. The resting membrane potential (Em) is about -60 mV. Following stimulation (S), the initial Na+-dependent depolarization phase of the action potential that rises above 0 mV (overshoot) is gradually reduced in amplitude and delayed in time with reduction in extracellular Na+. Similar experiments were originally conducted by Hodgkin, Huxley, and Katz in the 1930s/1950s using the voltage clamp technique (Section 16.5.1.1).

Figure 26. Membrane potential profiles (A) Goldman-Hodgkin-Katz constant field model (diffusion potential-dominated) (B) fixed-charge membrane model with positive fixed charges.

The membrane potential in biology came to prominence in the days in which electrode phenomena were treated exclusively in terms of equilibrium thermodynamics. Between 1892 (Nernst ) and 1911 (Donnan " ), three treatments were given of membrane potentials. They form such a durable part of electrochemistry, not because of their importance per se, or even of their direct relevance to biological phenomena, but because one of them was the origin of the best-known of bioelectrochemical theories, the Hodgkin-Huxley-Katz mechanism for the passage of electricity through nerves. 

S. Ohki, Membrane Potential of Squid Axons Comparison between the Goldman-Hodgkin-Katz Equation and the Diffusion/Surface Potential Equation, in Charge and Field Effects in Biosystems (M. J. Allen and P. N. R. Usherwood, eds.), pp. 147-156, Abacus Press, Tunbridge Wells (1984). 

With whole-cell configuration, the series resistance plays an important role in the control of the voltage of the cell membrane. The series resistance problem has been described for the first time by Hodgkin, Huxley and Katz [31]. It produces a double effect on the voltage-clamp A passive filtering of the voltage pulses applied to the membrane, and a drop of the applied membrane potential when a current is flowing... 

Quantal analysis defines the mechanism of release as exocytosis. Stimulation of the motor neuron causes a large depolarization of the motor end plate. In 1952, Fatt and Katz [11] observed that spontaneous potentials of approximately 1 mV occur at the motor endplate. Each individual potential change has a time course similar to the much larger evoked response of the muscle membrane that results from electrical stimulation of the motor nerve. These small spontaneous potentials were therefore called... 

In general, the process of vesicular release can be summarized as follows During or after the biosynthesis of the neurotransmitter, the substance is packaged into synaptic vesicles at the nerve terminals. Here the transmitter is stored until the nerve terminal is depolarized by the appearance of an action potential, at which time Ca " enters the cell and permits the exocytotic process that involves the apparent fusion of vesicular membranes with the plasmalemma. Such fusion allows for the release of the transmitter that is packaged within the vesicle. Regulatory mechanisms that are not presently clear then lead to the recycling of the vesicle within the nerve ending. In-depth reviews of release processes can be found in Cooke et al. (1973), Krnjevic (1974), Katz (1969), Rubin (1970), Zimmerman (1979), and Kelly et al. (1979). 

When an action potential traveling down the axon of a motoneuron reaches the myoneural endplate, a process occurs that releases acetylcholine into the synaptic cleft and consequently depolarizes the postsynaptic membrane. A similar process probably occurs at cholinergic synapses in the central nervous system. In 1950 Fatt and Katz discovered a spontaneous subthreshold activity (MEPP) of motor nerve endings and were thereby led to the concept that acetylcholine is released in definite units (quanta) of 10 to 10 molecules. Electron microscopy subsequently revealed characteristic vesicles about 40 nm in diameter, clustered near presynaptic membranes. Subcellular fractionation procedures were devised by Whittaker and de Robertis for the isolation of these vesicles from brain homogenates in sucrose density gradients, and it was soon demonstrated that they were indeed concentrated reservoirs of acetylcholine. The hypothesis that the vesicles discharge the quanta of transmitter became irresistible. 

Assuming that the membrane is homogeneous and neutral, and that the gradient of the electrical potential is constant across the membrane, Eqn. 25 may be directly integrated. Goldman [5] made these assumptions and Hodgkin and Katz [6] used it to analyse results concerning ion flux. The first assumption is used to relate the concentrations at both surfaces... 

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