Simulation and modelling of the effect of small inoculum size on time to spoilage by Bacillus stearothermophilus

Mathematical models developed in predictive food microbiology typically use large (approx. 10⁵cfu ml⁻¹) inoculum sizes. Real food systems may contain low microbial loads (1–10 cfu ml⁻¹) introducing an additional uncertainty unaccounted for by model predictions. This research investigated the effects of very low inoculum sizes on the time to spoilage of Bacillus stearothermophilus ATCC 12980 spores. Microtiter plates (96-well) were filled with tryptic soy broth and inoculated with various concentrations of B. stearothermophilus spores. Time to spoilage was defined as colour change of the medium containing bromcresol purple (corresponding to c. 10⁸cfu ml⁻¹) from purple to yellow. A Poisson distribution best described the number of spores in a well. Spoilage times showed maximum variability (7·25–17 h) at 1 spore well⁻¹, and negligible variability (c. 6·5 h) at 500 spores well⁻¹. A simplified Gompertz function described spoilage kinetics. Mathematical modelling and simulation approaches were used to study spoilage times. The modelling approach had a fail-safe bias in its predictions and provided greater accuracy than the simulation, which was fail-dangerous. The simulation approach provided potentially greater mechanistic insight into the causes of spoilage time variability, and supported the notion that the effects of biovariability and interactions among individual spores manifest at very low inoculum sizes.