Modelling the interactions between Lactobacillus curvatus and Enterobacter cloacae

Martens, Dirk E.; Béal, Catherine; Malakar, Pradeep K.; Zwietering, Marcel H.; Riet, K. van ’t

doi:10.1016/s0168-1605(99)00095-1

Cited by 27 publications

(16 citation statements)

References 23 publications

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“…It should be noted that these are not fits but predictions based on parameters from the literature and from earlier experiments (6,8,15). The lag time was the exception, as it was fitted by using data from the 100-CFU/ml experiments.…”

Section: Resultsmentioning

confidence: 90%

“…The specific growth rate of L. curvatus in broth culture, m (8), a function of S, pH, and P, can be described by m ϭ optͩ S K s ϩ S ͪ ͫ 4(pH Ϫ pH min )(pH max Ϫ pH) (pH max Ϫ pH min )…”

Section: Theorymentioning

confidence: 99%

“…Apart from the direct effect, P also indirectly influences the specific growth rate by decreasing the pH. The pH can be empirically related to the amount of P present by using the titration equation of Martens et al (8), which is expressed by…”

Section: Theorymentioning

confidence: 99%

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Modeling the Interactions of Lactobacillus curvatus Colonies in Solid Medium: Consequences for Food Quality and Safety

Malakar

Martens

Breukelen

et al. 2002

Appl Environ Microbiol

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The growth process of Lactobacillus curvatus colonies was quantified by a coupled growth and diffusion equation incorporating a volumetric rate of lactic acid production. Analytical solutions were compared to numerical ones, and both were able to predict the onset of interaction well. The derived analytical solution modeled the lactic acid concentration profile as a function of the diffusion coefficient, colony radius, and volumetric production rate. Interaction was assumed to occur when the volume-averaged specific growth rate of the cells in a colony was 90% of the initial maximum rate. Growth of L. curvatus in solid medium is dependent on the number of cells in a colony. In colonies with populations of fewer than 10 5 cells, mass transfer limitation is not significant for the growth process. When the initial inoculation density is relatively high, colonies are not able to grow to these sizes and growth approaches that of broth cultures (negligible mass transfer limitation). In foods, which resemble the model solid system and in which the initial inoculation density is high, it will be appropriate to use predictive models of broth cultures to estimate growth. For a very low initial inoculation density, large colonies can develop that will start to deviate from growth in broth cultures, but only after large outgrowth.The mathematical description of growth responses of microorganisms has a long history. In the recent 2 decades, however, a new family of these models has been developed for prediction of food quality and safety. These are usually multidimensional activator and inhibitor empirical models for predicting growth of microorganisms. The independent variables are the environmental conditions of the food in which these microorganisms grow. As the demand for minimally processed foods increases, these models will play an increasingly important role in ensuring the quality and safety of these foods.Almost all of these models are derived from experiments with liquid cultures, where the environmental conditions are homogeneous. However, there are many types of foods where this is not the case. One example is growth of microorganisms in sausages (4). Microorganisms grow as colonies or nests in these foods, and microgradients can occur in and around these colonies. The microgradients are caused by diffusive transport of substrate into the colonies and metabolic products out of the colonies. Microgradients of pH were detected in colonies of Salmonella enterica serovar Typhimurium with microelectrodes (14) and in colonies of Lactobacillus curvatus by the fluorescence ratio imaging technique (7). In time, these microgradients should produce a set of varying specific growth rates in a colony.These mass transfer effects can be important for predicting spoilage and safety. The strategy of controlling the growth of this pathogen in this heterogeneous system might be different from that used for the free-living species. The aim of this paper is to quantify these mass transfer effects in a model system. This model system ...

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Section: Resultsmentioning

confidence: 90%

Section: Theorymentioning

confidence: 99%

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Modeling the Interactions of Lactobacillus curvatus Colonies in Solid Medium: Consequences for Food Quality and Safety

Malakar

Martens

Breukelen

et al. 2002

Appl Environ Microbiol

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“…The pH effect on K S was probably not significant. Burgos-Rubio et al [43] reported a K S value of 3.36 g l −1 for L. bulgaricus, while Martens et al [38] did not observe any dependence of L. plantarum optS on the initial sugar concentration of the medium. For this reason they considered a K S value of 0.072 g l −1 , which is the general value for E. coli on glucose [44].…”

Section: Secondary Modelling Of Mmentioning

confidence: 94%

“…., f n ). This concept is generally called the -concept and has been extensively used to relate the bio-kinetic parameters describing cell growth (and in fewer cases primary or secondary metabolic activities) to the environmental conditions (usually pH or temperature) [11,16,[37][38][39][40]. Fig.…”

Section: Growth Modelsmentioning

confidence: 99%

Modelling and validation of Lactobacillus plantarum fermentations in cereal-based media with different sugar concentrations and buffering capacities

Charalampopoulos

Vázquez

Pandiella

2009

Biochemical Engineering Journal

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a b s t r a c tAn unstructured mathematical model is proposed to describe the fermentation kinetics of growth, lactic acid production, pH and sugar consumption by Lactobacillus plantarum as a function of the buffering capacity and initial glucose concentration of the culture media. Initially the experimental data of L. plantarum fermentations in synthetic media with different buffering capacity and glucose were fitted to a set of primary models. Later the parameters obtained from these models were used to establish mathematical relationships with the independent variables tested. The models were validated with 6 fermentations of L. plantarum in different cereal-based media. In most cases the proposed models adequately describe the biochemical changes taking place during fermentation and are a promising approach for the formulation of cereal-based probiotic foods.

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Diffusion of lactic acid in a buffered gel system supporting growth of Lactobacillus curvatus

Malakar

Zwietering²,

Boom

et al. 2002

J Sci Food Agric

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Diffusion of lactic acid in a buffered gel system was investigated using fluorescent ratio imaging. The range of pH studied was from 5.5 to 3.8, which included the minimum pH of growth of Lactobacillus curvatus (4.26). Diffusion of lactic acid in this pH range was found to be Fickian and the estimated effective diffusion coefficient of lactic acid at 20°C was 2.81 Â 10 À10 m 2 s À1 with a standard deviation of 0.21 Â 10 À10 m 2 s À1 . This effective diffusion coefficient was estimated by fitting the one-dimensional solution of the Fickian diffusion equation for infinite systems to a transformed experimental data set. The original data set as recorded by the fluorescent microscope consisted of concentration-distance curves at specific time intervals. This was transformed by realigning the distance scale of all the concentration-distance curves.

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Modelling the interactions between Lactobacillus curvatus and Enterobacter cloacae

Cited by 27 publications

References 23 publications

Modeling the Interactions of Lactobacillus curvatus Colonies in Solid Medium: Consequences for Food Quality and Safety

Modeling the Interactions of Lactobacillus curvatus Colonies in Solid Medium: Consequences for Food Quality and Safety

Modelling and validation of Lactobacillus plantarum fermentations in cereal-based media with different sugar concentrations and buffering capacities

Diffusion of lactic acid in a buffered gel system supporting growth of Lactobacillus curvatus

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