Mathematical modeling of a single-cell enzyme assay

A quantitative assay of beta-galactosidase activity in single cells of Saccharomyces cerevisiae has been developed using a fluorogenic substrate and flow cytometry [reported in Wittrup & Bailey, Cytometry, 9,394 (1988)]. The beta-galactosidase activity is expressed in yeast from the Escherichia coli lacZ gene under the control of the yeast GAL10 promoter, and is used as a marker for multicopy plasmid content. A nonfluorescent fluorogenic substrate is enzymatically cleaved by intracellular beta-galactosidase to form a fluorescent product. The accumulation of fluorescent product in single cells was found to depend on bulk substrate concentration and single-cell enzyme activity in a fashion that could not be described by a Michaelis-Menten kinetic rate form. It has been demonstrated that diffusion limitation rather than enzyme activity can determine the level of single-cell fluorescence under certain assay conditions, and a mathematical model has; been formulated which accounts for substrate and product diffusion. Guided by the mathematical model, the assay conditions were modified to allow measurement of single-cell enzyme activity rather than diffusion rates.