Reconciling Competing Models: A Case Study of Wine Fermentation Kinetics

Mathematical models of wine fermentation kinetics promise early diagnosis of stuck or sluggish winemaking processes as well as better matching of industrial yeast strains to specific vineyards. The economic impact of these challenges is significant: worldwide losses from stuck or sluggish fermentations are estimated at 7 billion € annually, and yeast starter production is a highly competitive market estimated at 40 million € annually. Additionally, mathematical models are an important tool for studying the biology of wine yeast fermentation through functional genomics, and contribute to our understanding of the link between genotype and phenotype for these important cell factories. We have developed an accurate combined model that best matches experimental observations over a wide range of initial conditions. This model is based on mathematical analysis of three competing ODE models for wine fermentation kinetics and statistical comparison of their predictions with a large set of experimental data. By classifying initial conditions into qualitative intervals and by systematically evaluating the competing models, we provide insight into the strengths and weaknesses of the existing models, and identify the key elements of their symbolic representation that most influence the accuracy of their predictions. In particular, we can make a distinction between main effects and secondary quadratic effects, that model interactions between cellular processes. We generalize our methodology to the common case where one wishes to combine competing models and refine them to better agree with experimental data. The first step is symbolic, and rewrites each model into a polynomial form in which main and secondary effects are conveniently expressed. The second step is statistical, classifying the match of each model's predictions with experimental data, and identifying the key terms in its equations. Finally, we use a combination of those terms to instantiate the combined model expressed in polynomial form. We show that this procedure is feasible for the case of wine fermentation kinetics, allowing predictions which closely match experimental observations in normal and problematic fermentation.