Modeling of fungal and bacterial spore germination under static and dynamic conditions.

Isothermal germination curves, sigmoid and nonsigmoid, can be described by a variety of models reminiscent of growth models. Two of these, which are consistent with the percent of germinated spores being initially zero, were selected: one, Weibullian (or "stretched exponential"), for more or less symmetric curves, and the other, introduced by Dantigny's group, for asymmetric curves (P. Dantigny, S. P.-M. Nanguy, D. Judet-Correia, and M. Bensoussan, Int. J. Food Microbiol. 146:176-181, 2011). These static models were converted into differential rate models to simulate dynamic germination patterns, which passed a test for consistency. In principle, these and similar models, if validated experimentally, could be used to predict dynamic germination from isothermal data. The procedures to generate both isothermal and dynamic germination curves have been automated and posted as freeware on the Internet in the form of interactive Wolfram demonstrations. A fully stochastic model of individual and small groups of spores, developed in parallel, shows that when the germination probability is constant from the start, the germination curve is nonsigmoid. It becomes sigmoid if the probability monotonically rises from zero. If the probability rate function rises and then falls, the germination reaches an asymptotic level determined by the peak's location and height. As the number of individual spores rises, the germination curve of their assemblies becomes smoother. It also becomes more deterministic and can be described by the empirical phenomenological models.