Modelling Saccharomyces cerevisiae for the production of fermented beverages

Authors

Paul A. Valle, Yolocuauhtli Salazar, Luis N. Coria, Nicolas O. Soto-Cruz, Jesus B. Paez-Lerma

Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnologico Nacional de Mexico/IT Tijuana, Blvd. Alberto Limon Padilla s/n, Tijuana 22454, Mexico

Postgraduate Program in Engineering, Tecnologico Nacional de Mexico/IT Durango, Blvd. Felipe Pescador 1830 Ote., Durango 34080, Mexico

Departament Chemical and Biochemical Engineering, Tecnologico Nacional de Mexico/IT Durango, Blvd. Felipe Pescador 1830 Ote., Durango 34080, Mexico

Abstract

Mezcal is a traditional distilled spirit beverage from the state of Durango, Mexico, which is obtained by the fermentation of Agave duranguensis sugars. In this work, we formulate a mechanistic model consisting of three first-order Ordinary Differential Equations (ODEs) to describe ethanol production for mezcal by the Saccharomyces cerevisiae yeast using glucose and fructose as substrates. These equations were fitted to three different sets of experimental data, representing the concentrations of glucose [x(t)], fructose [y(t)], and ethanol [z(t)] in g/L per hour. A nonlinear regression algorithm was designed in MATLAB to fit the model to each set of experimental data where values of parameters were estimated with a 95% confidence interval. The goodness of fit of the model was evaluated both quantitatively and qualitatively by means of the coefficient of determination (R-squared), the Akaike Information Criterion (AIC), and numerical simulations that illustrate data approximation and prediction in the short-term. Furthermore, conditions for the existence of a localizing domain in the nonnegative octant as well as sufficient conditions for asymptotic stability of the unique biologically feasible equilibrium point of the system were derived by means of the Localization of Compact Invariant Sets method and Lyapunov's Stability theory for nonlinear autonomous systems.

Keywords

Alcoholic fermentation; Asymptotic stability; Biostatistcs; In silico experimentation; Mechanistic modelling; Ordinary Differential Equations.

Experimental data

The S. cerevisiae strain ITD-00185 was obtained from the yeast collection of the Microbial Biotechnology Laboratory at the Durango Institute of Technology. Fermentation kinetics were conducted in triplicate using Agave duranguensis juice with an initial sugar concentration of 1294.7 g/L (12% glucose and 88% fructose) and a C/N ratio of 73 g C/g N as substrate. Fermentation kinetics were carried out in glass tubes (20150 mm), each containing 15 mL of agave juice inoculated with 110^8 cells/mL. These tubes were then incubated at 28C for 72 hours. Samples were analyzed every 8 hours using high-performance liquid chromatography (HPLC) to determine the concentrations of glucose, fructose, and ethanol.

Acknowledgements

This research was fulfilled within the TecNM projects Estrategias in silico integradas con biomatemticas y sistemas dinmicos no lineales para el modelizado, anlisis y control de sistemas biolgicos [19377.24-P], Modelizado de sistemas no lineales para procesos de fermentacin basados en la dinmica de crecimiento de microorganismos: parte 2 [19805.24-P], the academic research group Project Sistemas dinmicos no lineales ITIJ-CA-10, and the RICCA Red Internacional de Control y Cmputo Aplicados.

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