Transient state isoelectric focusing: theory

Mathematical theory is developed to describe the transient state of isoelectric focusing (pH-gradient electrophoresis) in a linear pH gradient under highly idealized conditions. This theory makes it possible to predict the concentration profile (distribution) for the protein or other amphoteric species of interest as a function of time, when the sample is applied in a zone of infinitesimal thickness at one end of the column, or in a uniform distribution throughout the column. Further, the position of the centroid, and the second moment around the mean, σ², (square of the standard deviation of peak width) are described as a function of time, irrespective of the initial distribution of the protein in the column. Three arbitrary stages of the “focusing” experiment are considered: (1) Focusing, wherein the sample is applied to a preformed pH gradient; (2) Defocusing, which occurs when the electrical field is abolished after an arbitrary time (usually after the concentration profile has begun to approach its steady state) and diffusion is allowed to occur. (3) Refocusing, which occurs after the electrical field is reapplied. Although stages 1 and 3 are conceptually identical aside from the difference in initial conditions, they may differ in several important respects in practice, both with regard to technical problems of measurement, and with regard to the closeness of conditions to the stated assumptions.This theory should make it possible to predict the time necessary to achieve any desired degree of focusing, i.e., approach to the steady-state distribution. Further, this theory and the techniques of analytical scanning isoelectric focusing provide the basis for measurement of the apparent diffusion coefficient (D), the derivative of velocity with respect to position, and if the field strength is known, the slope of the mobility-pH curve at the isoelectric point, {$\text{dM}\text{d(}\text{pH}\text{)}$}.