A population balance model of enzymatic lysis of microbial cells

A model is proposed for enzymatic lysis of microbial cells based on number balances over the distribution of cell-wall mass in a population of cells. Analytical solutions to the population balance equations were obtained by the method of characteristics for simple reaction kinetics. The model has been used to analyze the following cases of lysis in a nonhomogeneous cell population: wall hydrolysis with cell rupture and product release, the effect of a distribution of lysis rates, and lysis of two-layer cell walls. Rate expressions for the reactions of lysis can be derived from bulk-phase experiments; the distributions of cell size and product content can be measured independently by flow cytometric techniques. The population model also provides an explanation for the initial lag seen in lysis kinetics for virtually any initial distribution. The model demonstrates patterns of lysis and product recovery for heterogeneous populations of cells and also applies to the more general problem of soluble-enzyme reactions with heterogeneous solid substrates.