Re-parameterization of the asymmetric model for fungal spore germination

The asymmetric model (Dantigny et al., 2011, A new model for germination of fungi, International Journal of Food Microbiology, 146, 176-181) is capable to fit both symmetric and asymmetric curves of fungal spore germination. However, the shape parameter in the asymmetric model must be derived from a regression of the model with experimental data of fungal spore germination, thus the asymmetric model can fit spore germination under tested conditions only. In this paper, to solve this limitation, the previously proposed shape parameter-based asymmetric model has been replaced by using the pure biological parameter-based asymmetric model as: P = P-max.[1-1/1+(t/tau)(4 tau.mu/Pmax)], where P is the percentage of germinated spores at time t, P-max is the maximum percentage of germinated spores, tau is the germination time (the time that P = 0.5P(max)), and p is the slope of fungal spore germination at t = tau, representing the rate of fungal spore germination. The modified asymmetric model was validated against the germination data of six fungal species collected from the literature. The results showed that the modified asymmetric model described the spore germination of all fungi studied well. Moreover, the tau and mu in the modified asymmetric model at various environmental conditions were estimated properly via the Cardinal Model with Inflection. This solved the limitation of the previous asymmetric model. So, it can be concluded that the modified asymmetric model is an improvement over the previous asymmetric model for predicting fungal spore germination.