Saccharomyces cerevisiae and S. kudriavzevii Synthetic Wine Fermentation Performance Dissected by Predictive Modeling

Wineries face unprecedented challenges due to new market demands and climate change effects on wine quality. New yeast starters including non-conventional Saccharomyces species, such as S. kudriavzevii, may contribute to deal with some of these challenges. The design of new fermentations using non-conventional yeasts requires an improved understanding of the physiology and metabolism of these cells. Dynamic modeling brings the potential of exploring the most relevant mechanisms and designing optimal processes more systematically. In this work we explore mechanisms by means of a model selection, reduction and cross-validation pipeline which enables to dissect the most relevant fermentation features for the species under consideration, Saccharomyces cerevisiae T73 and Saccharomyces kudriavzevii CR85. The pipeline involved the comparison of a collection of models which incorporate several alternative mechanisms with emphasis on the inhibitory effects due to temperature and ethanol. We focused on defining a minimal model with the minimum number of parameters, to maximize the identifiability and the quality of cross-validation. The selected model was then used to highlight differences in behavior between species. The analysis of model parameters would indicate that the specific growth rate and the transport of hexoses at initial times are higher for S. cervisiae T73 while S. kudriavzevii CR85 diverts more flux for glycerol production and cellular maintenance. As a result, the fermentations with S. kudriavzevii CR85 are typically slower; produce less ethanol but higher glycerol. Finally, we also explored optimal initial inoculation and process temperature to find the best compromise between final product characteristics and fermentation duration. Results reveal that the production of glycerol is distinctive in S. kudriavzevii CR85, it was not possible to achieve the same production of glycerol with S. cervisiae T73 in any of the conditions tested. This result brings the idea that the optimal design of mixed cultures may have an enormous potential for the improvement of final wine quality.

We formulated several candidate models which account for the relevant process variables (biomass growth, sugars, ethanol, glycerol, acetate) based on different mechanisms described in literature. Exact formulations are described in the Main text.
All candidate models consist of a set of ordinary differential equations whose solution depends on the given initial conditions, process temperature and the value of a number of unknown parameters.
A multi-experiment data fitting approach was applied to compute unknown adjustable parameters for all models. Results are summarized in the sequel.
Tables include the step reduction number, the least squares value achieved, the number of data used, the number of unknown parameters, the Akaike criterion value and the name of the file including the model in the supplementary code distribution.
Step 2 (Reject): We assume the transport of glucose and fructose are affected equally by temperature. Two parameters from the φ T expression (one per strain) are removed. In this model the impact is big and AIC increases. Move back to step 1.
Step 3 (Reject): We assume glucose and fructose and glucose are affected equally by ethanol. Two parameters from the φ E expression (one per strain) are removed. In this model the impact is big and AIC increases. Move back to step 1.
Step Step 4 (Accept): We assume the affinity constants form the Michaelis Menten type kinetics used to describe the transport are unnecessary to describe transport in the operating range. Thus we reduce the model to mass action type kinetics. The AIC improves. The model is accepted. Four parameters are eliminated, two affinity constants (glucose and fructose) per strains.
Step 5 (Accept): We assume mass action type kinetics is sufficient to describe ethanol production (v F6P→E ) in the operating range of the model. Two affinity constants are removed (one per strain).

S.1.2. Models N2, R2 and intermediates
Step  Table 2. Path followed in the iterative procedure to reduce the model N2 to R2 based on the AIC.
Step: step reduction number, RSS: best least squares value, #Data: number of data,#Pars: number of unknown parameters, AIC: Akaike criterion value at optimum and File: name of the file including the model in the supplementary code distribution.
Step 2 (Accept) : We assume the transport of glucose and fructose are affected equally by temperature. Six parameters from the φ T expression (3 per strain) are removed.
Step 3 (Accept) : We assume φ T,A , with constant nitrogen data, is able to explain the temperature effect on the transport of hexoses without the need of ν H .
Step 4 (Accept) : We assume mass action type kinetics is sufficient to describe ethanol production (v F6P→E ) in the operating range of the model. Two affinity constants are removed (one per strain).
Step 5 (Accept: We assume mass action type kinetics is sufficient to describe ethanol production (v F6P→E ) in the operating range of the model. Two affinity constants are removed (one per strain).
Step 2 (Accept) : We assume the transport of glucose and fructose are affected equally by temperature. Two parameters from the φ T expression (one per strain) are removed.
Step  Table 3. Path followed in the iterative procedure to reduce model N3 to R3 based on the AIC.
Step: step reduction number, RSS: best least squares value, #Data: number of data,#Pars: number of unknown parameters, AIC: Akaike criterion value at optimum and File: name of the file including the model in the supplementary code distribution.
Step 3 (Accept) : We assume the affinity constants form the Michaelis Menten type kinetics used to describe the transport are unnecessary to describe transport in the operating range. Thus we reduce the model to mass action type kinetics. The AIC improves. The model is accepted. Four parameters are eliminated, two affinity constants (glucose and fructose) per strains.
Step 4 (Accept) : We assume glucose and fructose and glucose are affected equally by ethanol. Two parameters from the φ E expression (one per strain) are removed.
Step 5 (Reject) : We assume mass action type kinetics is sufficient to describe ethanol production (v F6P→E ) in the operating range of the model. Two affinity constants are removed (one per strain). In this model the impact is big and AIC increases. Move back to step 4.

S2. Ensemble of parameter values for the reduced model R3
Following figures present the ensemble of parameters as normalized to their mean values for the sake of comparing their relative confidence intervals.

S3. Correlation analysis of ensemble reduced model R3
The following figure presents the correlation as computed by pairs of parameters. Results reveal that several pairs of parameters are rather correlated (C r ij > 0.9). This is the case of the parameters that define specific growth rate as a function of temperature µ(T ); and parameters related to transport ν Glx and ν F . The correlation among ν Glx and ν F translates into significant confidence intervals for both parameters since their bounds could not be precisely estimated from the data.

S4. Code to reproduce the computational analysis
Model files, experimental data and scripts to reproduce results can be found in a public repository: http://doi.org/10.5281/zenodo.1115605.