A Kinetic Model for Single-Yeast Sour Beer Fermentation

The math model of González-Hernández, et al. [1], was adapted as the starting point of our model. The key feature of the present model is a switch function that controls the change in metabolism from lactic acid to ethanol during a fermentation. Utilizing the existing rate equations and stoichiometric coefficients within the model, we were able to construct a rate expression for lactic acid and integrate it into the model proposed [1,2] and extended the model to describe the use of maltose and maltotriose as primary substrates [2].

We conducted four trials, fermenting Philly Sour yeast with increasing initial glucose concentrations. We calibrated our model to specific gravity and pH data, and then data from one trial was used to estimate model parameters using optimization. Results were then applied to the other three trials to assess the capability of the model. We accomplished this through the switch function model approach [1] using parameters to control each unique component, including lactic acid production, and used optimisation algorithms to best match our modeled behavior to data.

Our model coincides well with experimental data when comparing our modeled specific gravity and pH to measurements taken over time. The switch function captures essential features of the specific gravity and pH data. Our model also provides plausible component curves which capture key features of how sour yeasts metabolize sugars in this process. For example, our model demonstrates lactic acid production coinciding with cell mass growth causing an early pH decrease to about 3.2, after which a change in metabolism converts the remaining sugar into ethanol. Predictions comparing our model with fitted parameters to non-calibration trials was encouraging.

The switch function model is effective in modeling complex changes in metabolism in this setting. Our results show that this model captured the change in metabolism from acid production to ethanol production. We recommend that more detailed experiments measuring composition of individual components should be used to improve the performance of the model and the accuracy of its parameters.

[1] González-Hernández, Y., Michiels, E., Perré, P. A Comprehensive Mechanistic Yeast Model Able to Switch Metabolism According to Growth Conditions. Fermentation 2022 (8), 710. doi.org/10.3390/fermentation8120710.
[2] Gee DA, Ramirez WF. Optimal temperature control for batch beer fermentation. Biotechnol Bioeng. 1988 31(3),224-34. doi: 10.1002/bit.260310308.