Isoelectric Fractionation, Analysis, and Characterization of Ampholytes in Natural pH Gradients. I. The Differential Equation of Solute Concentrations at a Steady State and its Solution for Simple Cases.

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Abstract
The properties of natural pH gradients formed by stationary electrolysis are analyzed and compared with those of artificial pH gradients. The pH of a pure ampholyte solution is calculated, and the difference between this and its isoelectric pH is used to prove that a stationary state is characterized by mutually balancing diffusional and electric mass flows. The differential equation of the concentration of a component contributing to a natural pH gradient is formulated. It is shown that such components have to be defined as acids, bases, or ampholytes, and that the mobilities or transference numbers entering the differential equations must be ascribed to those ion constituents of the protolytes which are not H+ or OH-. Solutions to the differential equation are presented for a one-component system and for a trace component present in a large excess of other components. The practical significance of the results for fractionation and characterization of ampholytes is discussed. Thus it is proved that the pH at the concentration maximum of an ampholyte is identical with its isoelectric point, which should be of value for direct measurement of isoelectric points. The concentrations of acids and bases or, more generally, of the most acidic and the most basic components present in the system, are shown to increase steadily towards the anode and cathode, respectively, without developing maxima in the mathematical sense. It is shown that the electrokinetic properties of proteins make them especially suitable to isoelectric fractionation, whereas simple ampholytes are extremely useful as "carrier electrolytes" in work and proteins. By a proper choice of simple ampholytes and their concentrations, it is possible in principle to obtain pH gradients of any desired extension and shallowness, but for the present a sufficient number of suitable simple ampholytes is not available.

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