Energy-Based Dynamic Model for Variable Temperature Batch Fermentation by Lactococcus lactis

Abstract

We developed a mechanistic mathematical model for predicting the progression of batch fermentation of cucumber juice by Lactococcus lactis under variable environmental conditions. In order to overcome the deficiencies of presently available models, we use a dynamic energy budget approach to model the dependence of growth on present as well as past environmental conditions. When parameter estimates from independent experimental data are used, our model is able to predict the outcomes of three different temperature shift scenarios. Sensitivity analyses elucidate how temperature affects the metabolism and growth of cells through all four stages of fermentation and reveal that there is a qualitative reversal in the factors limiting growth between low and high temperatures. Our model has an applied use as a predictive tool in batch culture growth. It has the added advantage of being able to suggest plausible and testable mechanistic assumptions about the interplay between cellular energetics and the modes of inhibition by temperature and end product accumulation.A number of models have been developed to predict the growth of bacteria in foods (3,21,24). Several common types of these growth models, including the logistic, Gompertz, and Richards curves, have been shown to be special cases of a more general model (2, 27, 28). These models may be classified as empirical models; they are sigmoidal functions that approximate bacterial growth over time. It has been argued, however, that the usefulness of empirical models is limited and that a more fundamental understanding of the changes taking place during batch growth of bacteria will require the use of mechanistic models (2,20,31). A drawback of most of the above models is the assumption of a constant environment during growth, where growth is limited by a time-or cell densitydependent function. From a mechanistic point of view, this is clearly incorrect, as environmental variables, lack of nutrients, and accumulation of end products are the controlling factors in cell growth and death. Both the Monod equation (19), where growth is limited by substrate concentration, and the Levenspiel modification (15), to include end product inhibition, address this issue. These models for the growth of a single organism include a simplifying assumption, however, of a constant relationship between cell numbers, substrate utilization, and inhibitory end product production.Mechanistic models may be developed from theoretical or experimentally determined data describing the cause or mechanism behind the dynamic changes observed in an experimental system. Several researchers have used dynamic models to investigate the effects of various temperatures on the specific growth rates or lag times of bacterial cultures (3,4,9,29,30).In all cases, some parameter values in these models were allowed to vary with temperature. Van Impe et al. (29) used temperature-dependent adjustment functions for modifying the parameters for specific growth rate, asymptotic level of (maximum) growth, and lag time wi...

Isothermal and Non-isothermal Kinetic Models of Chemical Processes in Foods Governed by Competing Mechanisms

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“…[Even microbial growth and mortality in a closed habitat can be viewed as a peaked process, despite the fact that its "reactants" are cells rather than molecules [see, e.g., Dougherty et al (18)]. ] The same can be said about the growth of certain tissue cultures [see, e.g., Liu et al (19) and Sitton and Srienc (20)].…”

Probabilistic Model of Microbial Cell Growth, Division, and Mortality

“…Such growth/inactivation and inactivation/growth scenarios entail influences of temperature on the division and mortality rates and the manner in which these rates change with time. In the model outlined above, this implies that the coefficients of P d (t) and P m (t), defined by equations 13 For almost all realistic nonisothermal temperature histories or profiles, especially when both heating and cooling are involved, the integral in equation 12 cannot be solved analytically. However, the integral can be solved numerically to produce the corresponding growth/inactivation curve.…”

Μελέτη παραμέτρων που διέπουν την ανάπτυξη του μικροοργανισμού Listeria monocytogenes σε χαμηλές θερμοκρασίες

“…Μεταξύ άλλων προσεγγίσεων που έχουν διατυπωθεί για την έκφραση της επίδρασης της μεταβολής της θερμοκρασίας στη μικροβιακή ανάπτυξη, αξίζει να αναφερθεί η μελέτη των Dougherty et al (2002). Οι ερευνητές προσπάθησαν να συγχωνεύσουν τις επιδράσεις της μεταβολής της θερμοκρασίας και των ανασταλτικών τελικών προϊόντων σε ένα δυναμικό μοντέλο που βασίζεται στην ενεργειακή μορφή που αποκτούν αυτές οι μεταβολές, περιγράφοντας όλο το εύρος της μικροβιακής ανάπτυξης.…”

“…Σύμφωνα με αυτή τη μηχανιστική προσέγγιση, είναι οι ενεργειακές απώλειες κατά την προσαρμογή στη μεταβολή της θερμοκρασίας που προκαλούν τη λανθάνουσα φάση. Όλες οι μεταβλητές επηρεάζονταν και εξαρτιόνταν από την ενέργεια του κυττάρου (Dougherty et al, 2002).…”