Constant field equation,

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,... 

Q.23.3 (a) What are the assumptions in the Goldman-Hodgkin-Katz constant field equation (b) Under what circumstances does the equation tend to fail (c) Choose one assumption and hypothesize a specific situation that it might not be applicable. 

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... 

Hodgkin and Katz modified the above constant field equation, introducing partition coefficients for ions between the aqueous and membrane phases. The expression is as follows ... 

We next explored the fit of the data to a more detailed relationship than that forming the basis of Nernst equation. We wrote the Goldman constant field equation (3) in the form used by Hodgkin and Katz (4) in the exponential form shown here as equation 3. 

Figure 2 shows the plot for atrium. The solid line is the least squares straight line. It has a slope of about 30 mv. The dash line is calculated from the constant field equation using the values of A and B derived from the exponential plot. Obviously the values of a do not extend over a large enough range of values to make it possible to say that one curve fits the data better than the other. It is convenient therefore to simply say that the data are fit by the constant field equation. 

Figure 3 shows the plot of the same relationships for sinus venosus. The solid line is the straight line with about a 30 mv slope and the dash line is calculated from the constant field equation. 

TABLE II. Values of the permeability ratios a and 3 estimated from the constant field equation fitted to the intracellular potassium data. 

The solid line is the least squares linear regression. The dashed line is the constant field equation fit to the data. 

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