The electrophoretic hemolytic plaque assay -- theory

We use the mathematical theory of plaque qrowth to determine if there is merit in performing a hemolytic plaque assay in the presence of an external electric field. In particular, we study the effects of an electric field on the transport of antibodies secreted by a single lymphocyte and on the size and shape of the plaques they produce. Our results indicate that in the presence of an applied electric field: (1) The mobility of the antibodies produced by the antibody forming cell can be determined from the plaque shape. (In the electric field the plaques are no longer circular, but cigar shaped.) (2) By changing the magnitude or direction of the applied electric field more than one plaque can be generated by a single AFC. Thus changes in mobility or the rate of antibody secretion can be assayed. (3) Plaques will reach a steady state size; for good emitters (cells that secrete antibodies at a high rate or that secrete high affinity antibodies) this steady state will be achieved rapidly. Equations are given which describe both the temporal development and steady state plaque size and shape. From the equations, computer generated plots of plaques produced by typical antibody forming cells are presented. These plots are then used to show how pictures of plaques formed in an electric field can be analyzed to determine the antibody mobility.