The Principle ofElectrical Neutrality

In arriving at -58 mV for the chloride equilibrium potential in Figure 4-2, we used 1.0 M and 0.1 M for [Cl-]1 and [Cl-]2. These are the initial concentrations in the two compartments, even though in our qualitative analysis we said that Cl- moved from compartment 1 to 2, producing an excess of negative charge in compartment 2 and giving rise to the electrical potential. This would seem to suggest that [Cl-] changes from its initial value, invalidating our sample calculation. It is legitimate to use initial concentrations, however, because the increment in the electrical gradient caused by the movement of a single charged particle from compartment 1 to 2 is very much larger than the decrement in concentration gradient resulting from movement of that same particle. Thus, only a very small number of charges need accumulate in order to counter even a large concentration gradient.

In Figure 4-2, for example, it is possible to calculate that if the volume of each compartment were 1 ml and if the barrier between compartments were 1 cm2 of the same material as found in cell membranes, it would require less than one-billionth of the chloride ions of side 1 to move to side 2 in order to reach the equilibrium potential of -58 mV. (The basis of this calculation is explained below.) Clearly, such a small change in concentration would produce an insignificant difference in the result calculated according to Equation (3-2), and we can safely ignore the movement of chloride necessary to achieve equilibrium.

This leads to an important principle that will be useful in the examples following in this chapter. This principle, called the principle of electrical neutrality, states that under biological conditions, the bulk concentration of cations within any compartment must be equal to the bulk concentration of anions in that compartment. This is an acceptable approximation because the number of charges necessary to reach transmembrane potentials of the magnitude encountered in biology is insignificant compared with the total numbers of cations and anions in the intracellular and extracellular fluids.

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