The effect of indicator layer thickness on the interpretation of hemolytic plaque results

Abstract

Mathematical theories of hemolytic plaque growth have all previously assumed that the assay is performed in layers of infinite thickness or in layers sufficiently thin that diffusion perpendicular to the layer can be neglected. Here we discuss the results of a general theory valid for any layer thickness and show under what conditions the approximate results for two-dimensional or infinitely thick layers apply. In commonly used procedures the thickness h can vary more than six hundred fold, i.e. 1 × 10 −3 cm ⩽ h ⩽ 6.5 × 10 −1 cm. We show that such variation in h will cause significantly different kinetics of plaque growth and change the sensitivity of the plaque assay. We establish that for typical direct plaque experiments of one hour duration the two-dimensional limit will be valid when h ⩽ 3 × 10 −3 cm, whereas the infinite thickness results will be valid when h ⩽ 3 × 10 −1 cm. For intermediate thicknesses the interpretation of plaque results is considerably more difficult and this range of layer thickness should be avoided if one is interested in doing more than simply counting plaque forming cells. For the limiting cases of very thin and very thick layers we compare the expected time development of a plaque, we compute the number of antibodies needed to produce a detectable plaque, and establish the range of times for which the plaque growth follows the limiting mathematical solutions. At very short times all layers appear thick while at long times all layers appear thin.