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.IMPORTANCE The growth-sporulation model describes the progressive transition from vegetative cells to spores with sporulation parameters describing the sporulation potential of each vegetative cell. Consequently, the model constitutes an interesting tool to assess the sporulation potential of a bacterial population over time with accurate parameters such as the time needed to obtain one resistant spore and the probability of sporulation. Further, this model can be used to assess these data under various environmental conditions in order to better identify the conditions favorable for sporulation regarding the time to obtain the first spore and/or the concentrations of spores which could be reached during a food process.

Keywords: Spore-forming bacteria; cellular heterogeneity; growth modeling; sporulation.

FIG 1

Fluorescence and probability kinetics (a, c, and e) and growth and sporulation kinetics (b, d, and f) of B. subtilis at 27°C (a and b), 40°C (c and d), and 49°C (e and f). The values of fluorescence (diamonds) were fitted with the normal density function (solid gray lines in a, c and e) and the corresponding probability densities (black dashed lines in a, c and e) with the three sporulation parameters of equation 4: P_max, t_max, and σ. The concentration of total cells (circles) and the concentration of spores (squares) over time were fitted with the growth and sporulation model in equations 1, 2, and 3 (b, d, and f). The time between the fluorescence curve (log₁₀ AU on the right scale in b, d, and f) and the sporulation curve (log₁₀ CFU/ml on the left scale in b, d, and f) corresponded to the time to form a spore t_f (indicated on the time scale) fitted with equation 6.

FIG 2

Growth and sporulation kinetics of three Bacillus species. B. subtilis BSB1 was grown in whey medium at 25°C, 37°C, and 48°C. B. licheniformis Ad978 was grown in Hageman medium supplemented with 1% BHI at 45°C and at 20°C and pH 7.2. B. cereus AH187 was grown in MODS medium in aerobiosis (24). The kinetics of total cells (circles) and the spores were fitted (solid lines) with the growth (equation 1) and sporulation model (equations 2 and 3). The probability to sporulate over time (equation 2) is indicated in gray dashed lines.