doi:10.1016/j.bpc.2005.10.010 
Copyright © 2005 Elsevier B.V. All rights reserved.
Metabolic response to exogenous ethanol in yeast: An in vivo NMR and mathematical modelling approach
Silvia Martinia, c, Maso Riccia, Fiora Bartolinia, Claudia Bonechia, Daniela Braconib, Lia Milluccib, Annalisa Santuccib and Claudio Rossia, 
, 
aDipartimento di Scienze e Tecnologie Chimiche e dei Biosistemi, Università di Siena Via Aldo Moro, 2-53100 Siena, Italy
bDipartimento di Biologia Molecolare, Università di Siena Via Fiorentina, 1-53100 Siena, Italy
cPolo Universitario di Colle di Val D'Elsa Viale Matteotti, 12-53034-Colle di Val D'Elsa, Siena, Italy
Received 10 June 2005;
revised 10 October 2005;
accepted 14 October 2005.
Available online 28 November 2005.
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Abstract
The understanding of the metabolic behaviour of complex systems such as eukaryotic cells needs the development of new approaches that are able to deal with the complexity due to a large number of interactions within the system. In this paper, we applied an approach based on the combined use of in vivo NMR experiments and mathematical modelling in order to analyze the metabolic response to ethanol stress in a wild-strain of Saccharomyces cerevisiae. Considering the cellular metabolic processes resulting from activation, inhibition, and feed-back activities, we developed a model able to describe the modulation of the whole system induced by an external stress due to increasing concentrations of exogenous ethanol. This approach was able to interpret the experimental results in terms of metabolic response to exogenous ethanol in the yeast. The robustness and flexibility of the model enables it to work correctly at different initial exogenous ethanol concentrations.
Keywords: Saccharomyces cerevisiae; Metabolism; Mathematical modelling; Inhibition; In vivo NMR
Fig. 1. 13C-NMR spectra obtained at 20 min intervals during glucose fermentation by S. cerevisiae.
Fig. 2. (a) Data comparison of glucose (●) and ethanol () concentration collected in the presence of increasing exogenous ethanol concentrations. Experiments were performed with 0 g/l of exogenous ethanol (blue data), 20 g/l of exogenous ethanol (red), 50 g/l of exogenous ethanol (green) and 75 g/l of exogenous ethanol (pink). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. Energy System Diagram of the model of fermentative process in the presence of exogenous ethanol. The diagram is composed by a few compartments representing glucose concentration (G), total ethanol concentration which involves two distinct compartments referring to exogenous and endogenous ethanol concentrations (Eexo and Eendo, respectively), cellular activity (C) and inhibited cells (I) (not included in the set of differential equations). The fluxes and interactions among the compartments are symbolized by arrrows. The dynamics of glucose metabolisation was assumed to be the result of an autocatalytic process which depends on the concentration of the available carbon source and the cellular activity. The presence of the sugar promotes an energy flow to the active cells which allows the cell culture to grow. The interaction between the total ethanol and the number of actual active cells takes into account the inhibition effects which produced the amount of inhibited cells during the fermentation.
Fig. 4. Experimental time course of ethanol () and glucose (●) compared with model simulation (continuous line). (a) In the absence of exogenous ethanol (blue data); (b) in the presence of 20 g/l of ethanol (red); (c) in the presence of 20 g/l of ethanol (green); (d) in the presence of 75 g/l of ethanol (pink). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Cellular activity curves simulated by the model: in the absence of exogenous ethanol (blue), at 20, 50 and 75 g/l of exogenous ethanol (red, green and pink lines, respectively). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Plot of endogenous ethanol vs. consumed glucose concentration for the fermentation process of 100 g/l of glucose: (blue) in the absence of exogenous ethanol, (red) in the presence of 20 g/l of ethanol, (green) in the presence of 50 g/l of ethanol and (pink) in the presence of 75 g/l of ethanol. The slope of each line calculated by linear regression of experimental data is also reported as EMY0, EMY20, EMY50 and EMY75. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. Calculated metabolic yield (
) in relation to exogenous ethanol concentration and data fitting.
Fig. 8. Simulation of glucose degradation and ethanol formation during the fermentative process in the presence of 0, 10, 20, 30, 40, 50, 60, 70, 75 g/l of exogenous ethanol. The coloured line plots are calculated by fitting the experimental data, the black ones are simulated by the model.
Fig. 9. (a) 3D plot of cellular activity vs. time and exogenous ethanol concentration and (b) simulation of the cellular activity vs. time.
Table 1.
Estimated values and coefficient of variation (CV) of the kinetics parameters
Table 2.
Experimental metabolic yield (EMY) and metabolic yield calculated from the model (YM)
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