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A Mathematical Model to Optimize Fermentation in Xanthomonas campestris*
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A Mathematical Model to Optimize Fermentation in Xanthomonas campestris* Enrique Rodriquez INTEVEP, S.A., P.O. Box 7 6 3 4 3 , Caracas 1070-A, Venezuela Abstract This work presents a mathematical model to control and optimize the production of xanthan gum by Xanthomonas campestris by fermentation of the waste from lactic industrial processes as nutrients instead of saccharose; the clone of X. campestris used was developed at INTEVEP, S.A. Our main objective was to incorporate the model parameters that can be set up in the bioreactor, such as the stirring velocity and temperatures, to get an optimum final concentration of xantham gum in the least time. To achieve this goal, several mathematical approaches were developed to model the effect of each parameter. Several mathematical fermentation models were formulated depending on the representation chosen for each parameter; all the models are based on the description of bacterial growth by a logistic representation, andxanthanproduction and lactose consumptionby Luedeking-Piret equations, where the coefficients depend on the fermentor’s parameters. The models were evaluated using data obtained from fermentation experiments, and then compared with the aims of statistics estimators. In another experiment, the growth in complexity of the final model showed a significant number of known parameters; to do that, a particular strategy of estimation that combined empirical and least square methods was applied. The comparison with real data shows that the mathematical model selected described very well the fermentation process under the different conditions.
*Because of Patent considerations, only the Abstract of the paper is included in this publication.
A Mathematical Model to Optimize Fermentation in Xanthomonas campestris* Enrique Rodriquez INTEVEP, S.A., P.O. Box 7 6 3 4 3 , Caracas 1070-A, Venezuela Abstract This work presents a mathematical model to control and optimize the production of xanthan gum by Xanthomonas campestris by fermentation of the waste from lactic industrial processes as nutrients instead of saccharose; the clone of X. campestris used was developed at INTEVEP, S.A. Our main objective was to incorporate the model parameters that can be set up in the bioreactor, such as the stirring velocity and temperatures, to get an optimum final concentration of xantham gum in the least time. To achieve this goal, several mathematical approaches were developed to model the effect of each parameter. Several mathematical fermentation models were formulated depending on the representation chosen for each parameter; all the models are based on the description of bacterial growth by a logistic representation, andxanthanproduction and lactose consumptionby Luedeking-Piret equations, where the coefficients depend on the fermentor’s parameters. The models were evaluated using data obtained from fermentation experiments, and then compared with the aims of statistics estimators. In another experiment, the growth in complexity of the final model showed a significant number of known parameters; to do that, a particular strategy of estimation that combined empirical and least square methods was applied. The comparison with real data shows that the mathematical model selected described very well the fermentation process under the different conditions.
*Because of Patent considerations, only the Abstract of the paper is included in this publication.