Evaluation of a Stochastic Inactivation Model for Heat-Activated Spores of Bacillus spp

Abstract

Heat activates the dormant spores of certain Bacillus spp., which is reflected in the "activation shoulder" in their survival curves. At the same time, heat also inactivates the already active and just activated spores, as well as those still dormant. A stochastic model based on progressively changing probabilities of activation and inactivation can describe this phenomenon. The model is presented in a fully probabilistic discrete form for individual and small groups of spores and as a semicontinuous deterministic model for large spore populations. The same underlying algorithm applies to both isothermal and dynamic heat treatments. Its construction does not require the assumption of the activation and inactivation kinetics or knowledge of their biophysical and biochemical mechanisms. A simplified version of the semicontinuous model was used to simulate survival curves with the activation shoulder that are reminiscent of experimental curves reported in the literature. The model is not intended to replace current models to predict dynamic inactivation but only to offer a conceptual alternative to their interpretation. Nevertheless, by linking the survival curve's shape to probabilities of events at the individual spore level, the model explains, and can be used to simulate, the irregular activation and survival patterns of individual and small groups of spores, which might be involved in food poisoning and spoilage.Heat inactivation kinetics of bacterial spores is a wellresearched field. Much of the work on its relation to foods has focused on the heat-resistant spores of Clostridia, particularly those of Clostridium botulinum, which to this date serves as the reference organism in sterility calculations of low-acid foods (8, 32). The thermal resistance of Bacilli spores, although also extensively studied, has received less attention in the literature on food preservation. This is primarily because they are unlikely to germinate and produce cells that will survive and divide under the anaerobic conditions in a sterilized food container. Yet the mere possibility of viable Bacillus spores being present in processed foods has become an issue of food safety and a security concern. For this reason, there is a renewed interest in these spores' heat resistance (2,3,6,7,16,30). One of the peculiarities of certain Bacillus spores, like those of Bacillus sporothermodurans or Bacillus stearothermophilus, is that many of them can remain dormant unless activated by heat. The result is a survival curve that exhibits an "activation shoulder," as shown schematically in Fig. 1 and with published data in Fig. 2. Thus, modeling this survival pattern, where the number of spores initially grows rather than declines, must account for the heat's dual role of being a lethal agent and activator at the same time.Traditionally, the thermal inactivation of both Clostridia and Bacilli spores has been thought to follow first-order kinetics (9, 12, 31), an assumption that has been frequently challenged in recent years (18,21,33,35). The most p...

Maturation of Released Spores Is Necessary for Acquisition of Full Spore Heat Resistance during Bacillus subtilis Sporulation

“…High spore wet heat resistance is acquired late in sporulation, largely in parallel with the uptake of DPA by the developing forespore and the final decrease in spore core water content. However, the precise time of acquisition of full spore heat resistance during sporulation is not completely clear because (i) precise measurements of wet heat resistance are usually carried out only on purified spores; (ii) analysis of acquisition of wet heat resistance can be carried out only with spore populations, and the lack of precise synchrony in sporulation of cell populations can complicate kinetic analysis of events in sporulation; and (iii) the specific conditions in sporulating cultures, including the composition of the medium and the environment in the mother cell surrounding the developing spore, may change during sporulation, and such changes could modify spore wet heat resistance compared to that of purified spores in water.It is also clear that the wet heat resistance of individuals in spore populations can vary significantly (1,3,9,13,19,27,34,36). Indeed, analyses of spore killing by wet heat as a function of time often suggest that there is a significant level of more wet-heat-resistant spores in populations (27).…”

Modeling of Fungal and Bacterial Spore Germination under Static and Dynamic Conditions

“…Figure 10 shows the germination pattern of initially dormant spores in assemblies of 10, 30, 100, and 500. As expected (20,21), as the group size rises, the assembly's germination curve becomes smoother and more deterministic. The role of the germination probability rate function is revealed in Fig.…”

“…In the simplest model that can describe such a situation, the germination probability rate function, P g (t), would have to be accompanied by the spores' inactivation probability rate function and the probability rate functions of the vegetative cells' mortality and of their division, all determined by the organism, its temperature history, and the medium in which these processes occur. We say the "simplest" because to accurately account for spore inactivation and cell mortality and division, one might need to consider different probability rate functions for the different branches of the probabilities tree (21). Discussion and mathematical description of such general scenarios is outside the scope of the present work.…”

“…Or, in the case of dynamic germination, at least in principle one can compare the resulting curve produced by the stochastic model with the solution of equation 8 or 9. As in growth and inactivation (19)(20)(21), the stochastic model's structure is the same regardless of whether the temperature is constant or varies with time. The difference will be manifested in the probability rate function, P g (t) or P g (i), which would be affected by the changing temperature, but not in the model's mathematical structure, which will remain the same.…”

“…The asymptotic germination level in this case would depend on the peak's location and height. Although not attempted in this work, it is possible to determine the probability rate function from germination data obtained with large spore populations (20,21). Once determined, this probability function could be used to simulate and examine the germination patterns of small groups of spores, and even individual ones, under circumstances relevant to food safety or infection.…”