Goldman diffusion equation

Equation (5.2) implies that when summation of all the fluxes (Ji) of charged species (Zi) across the membrane leading to charging of the membrane capacity has concluded a quasi-equilibrium with a (approximately) constant Vm or Aij/ is attained. Its value depends on the difference in chemical potential Afj, ) of all transported species and on the affinities of coupled chemical reactions. This is embodied in the so-called Goldman diffusion equation but these relations are essentially transcendental with their explicit solution tractable only under defined conditions. If only one species permeates through the membrane, for example, a true equilibrium state is reached and the resulting transmembrane electrical potential difference is described by an expression known as the Nemst equation... 

In this expression, there are no jumps in values of electrical potential and ionic concentration at the phase boundary. Although Eqs. (122) and (123) have a quite complex form, this equation can be reduced easily to the Nernst diffusion equation and the constant field equation (Goldman ), by assuming proper physical conditions. The former, the Nernst diffusion equation [Eq. (119)], can be obtained from Eqs. (122) and (123) for the case of solutions containing only a single salt (such as NaCl) and the latter, the constant field... 

In the Goldman equation use the diffusion coefficients in question 1 in place of permeation coefficients. The rate of permeation is -D(dc/dx). The dx is essentially the membrane thickness and its neglect will cancel out of the equation (cf. the Goldman equation), (c) Is this flux consistent with actual radiotracer measurements of the movement concerned (In the Hodgkin-Huxley and Katz work, arbitrary values were used for the P s to ensure that the equation replicated the experiment. This, of course, makes it difficult to check its validity. Assume the starting concentration of ions on either side of the membrane is that shown in the text. The average internal diameter of a squid axon is about 1 mm.)... 

In certain cases, all of the quantities in Equation 3.20 —namely, the permeabilities and the internal and the external concentrations of K+, Na+, and Cl- —have been measured. The validity of the Goldman equation can then be checked by comparing the predicted diffusion potential with the actual electrical potential difference measured across the membrane. 

Thus, we expect the cytosol to be electrically negative with respect to the external bathing solution, as is indeed the case. In fact, the measured value of the electrical potential difference across the plasma membrane of N. translucens is —138 mV at 20°C (Table 3-1). This close agreement between the observed electrical potential difference and that calculated from the Goldman equation supports the contention that the membrane potential is a diffusion potential. This can be checked by varying the external concentration of K+, Na+, and/or Cl and seeing whether the membrane potential changes in accordance with Equation 3.20. 

Joslin and Goldman [105] in 1992 studied this problem by using the Diffusive Quantum Monte Carlo Methods. By resorting to the hard spherical box model, they performed calculations, not only on the ground state of helium atom, but also for H- and Li+. In this method the Schrodinger equation is... 

The diffusion potential within the membrane may be expressed by the Goldman and Hodgkin and Katz equation [Eq. (126)] as follows ... 

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). 

Part of the system reacts "classically and can be described by the Goldman-Hodgkin-Katz equation for transmembrane diffusion of ions. We believe that our earlier measurements were done on chloroplasts which completely fit such a system description (fig. 3A). Such chloroplasts revealed only monophasic decay kinetics (reaction 1) after the light was turned off. 

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