NON-LINEAR MODELING OF KEFIR GRAINS GROWTH CURVE
Integration of life sciences & engineering
Design, Analysis & Control of Fermentation Processes (T5-2)
Keywords: kefir grains, batch propagation, growth models, statistical analysis
Marko Tramšek, Andreja Goršek*
University of Maribor, Faculty of Chemistry and Chemical Engineering,
Smetanova 17, SI–2000 Maribor, Slovenia, tel: +386 2 22 94 453,
*e-mail: andreja.gorsek@uni-mb.si
ABSTRACT
Kefir grains consist of complex symbiotic microflora, containing more than 35 probiotic bacteria which are entrapped in a water-insoluble polysaccharide matrix and have proven highly beneficial to humans. They are primarily used as natural culture starters in traditional large scale kefir fermentation processes. Over recent years, it has been established that their variegated microbial composition also enables applications in bread production as baker’s yeast, volatile aroma compounds production and ethanol production using immobilized kefir yeast cells. Owing to their potential commercial applications, special attention should be focused on their production, using traditional batch cultivation in milk with low biomass increase. Kefir grains batch propagation is a inherently very complex process, thus it is of critical importance for its further improvement, (optimization, monitoring and controlling) to develop models that provide an accurate description of kefir grains growth curve.
Therefore, the aim of the present study was to model a growth curve during kefir grains batch propagation using traditional cultivation in fresh high temperature pasteurized (HTP) whole fat cow’s milk. Several non-linear sigmoidal growth models (Logistic, Gompertz and Richards) and values of their biological parameters were compared to describe the growth curve using experimental data regarding time-dependent kefir grains increase. These experiments were performed in an RC1 reaction calorimeter under selected bioprocess conditions (temperature 24 °C, rotational frequency of the stirrer, 90 (1/min), initial kefir grains mass concentration, 75 g/L and glucose mass concentration 20 g/L). The models were compared statistically by using six statistical indicators, i.e. standard error, SE, coefficient of the variation, CV, adjusted coefficient of the determination, Radj2, root mean squared error, variance ratio, F, predicted residual error sum of squares, PRESS, and t-statistic value, t-st.
The graphical results of change in the logarithm of relative kefir grains mass versus batch propagation time, show that all the proposed models have a good predictive ability and, therefore, satisfactorily fit the data obtained from the experimental measurements. The maximum specific growth rates and asymptotic values proposed by all three models are very similar, meanwhile, lag phase times and batch propagation times at maximum specific growth rate are markedly different. Statistically, the Radj2 values were almost equal (variation +/-0.4 %) for all models . Therefore, this statistic indicator can not be used as a single criterion for kefir grains growth model ranking. Furthermore, the RMSE and PRESS values of the Logistic model are smaller, compared to the Gompertz and Richards ones. Therefore, it is statistically less reliable for describing the kefir grains growth curve. Further comparison shows that Gompertz, compared to the Richards model has greater F value. The relative difference is more than 63 %. Moreover, it also has greater t-st values for all kefir grains growth’s biological parameters. Finally, on the basis of the applied statistical indicators, we established that the kefir grains growth curve during traditional batch propagation in fresh HTP whole fat cow’s milk, under selected bioprocess conditions, can be statistically described most successfully by the Gompertz growth model.
The presented results are specific for the selected bioprocess conditions, for used propagation medium and initial kefir grains culture. It is also well-known that microbial compositions of milk and kefir grains vary considerably over time and are dependent on age and storage conditions. Therefore, these conclusions cannot be presented as general for all kinds of batch kefir grains propagations. In spite of this, the experimental and statistical procedure given in this paper can be used to find the best model describing batch kefir grains growth under different experimental and propagation setups.
See the full pdf manuscript of the abstract.
Presented Thursday 20, 11:18 to 11:36, in session Design, Analysis & Control of Fermentation Processes (T5-2).
