Differentiation of vegetative cells into spores: A kinetic model applied to Bacillus subtilis

Abstract

Spore-forming bacteria are natural contaminants of food raw materials, and sporulation can occur in many environments from farm to fork. In order to characterize and to predict spore formation over time, we developed a model that describes both the kinetics of growth and the differentiation of vegetative cells into spores. The model is based on a classical growth model and enables description of the kinetics of sporulation with the addition of three parameters specific to sporulation. Two parameters are related to the probability of each vegetative cell to commit to sporulation and to form a spore, and the last one is related to the time needed to form a spore once the cell is committed to sporulation. The goodness of fit of this growth-sporulation model was assessed using growth-sporulation kinetics at various temperatures in laboratory medium or in whey for Bacillus subtilis, Bacillus cereus, and Bacillus licheniformis. The model accurately describes the kinetics in these different conditions, with a mean error lower than 0.78 log10 CFU/ml for the growth and 1.08 log10 CFU/ml for the sporulation. The biological meaning of the parameters was validated with a derivative strain of Bacillus subtilis 168 which produces green fluorescent protein at the initiation of sporulation. This model provides physiological information on the spore formation and on the temporal abilities of vegetative cells to differentiate into spores and reveals the heterogeneity of spore formation during and after growth.