The application of the WLF equation to predict lag time as a function of temperature for three psychrotrophic bacteria

Many mathematical models for microbial growth rates or lag times have been proposed. Most of these models either predict well, but are empirical and offer no insight into mechanism or they reflect mechanism but are too complex or do not fit the data adequately. The Williams-Landel-Ferry (WLF) equation (used by polymer chemists) is empirical, but shows some relation to first principles, and hence may offer some insight into mechanism. This model also has only three parameters and therefore a fairly simple form. The WLF equation was fit to lag times derived from three datasets previously developed in our laboratory. The fits obtained with the WLF equation were as good as the best fits obtained with other models (e.g Arrhenius, Davey, response surface and square root). The WLF model was able to account for 98 to 99% of the variance in the three datasets, indicating a very good fit overall. The parameter estimates of the WLF model were not as highly correlated as those of some of the other models. Many of the models, including the WLF equation did not predict well at very long lag times. Weighted least squares non-linear regression improved the fit for these long lag times.