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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.

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 x 10-10 m2 s-1 with a standard deviation of 0.21 x 10-10 m2 s-1. 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.

Mixed cultures of Lactobacillus curvatus and Enterobacter cloacae were chosen as a model system to quantitatively study microbial interactions involved in food spoilage and food preservation. In this paper models were developed to predict the individual behaviour of L. curvatus and E. cloacae in pure suspension cultures as a function of the glucose and lactate concentration and the pH. In a second paper these models will be used to predict the moment of interaction in mixed suspension cultures and the cell concentrations at this moment. The effect of pH on the maximum specific growth rate could be described by a parabolic equation for L. curvatus and E. cloacae. E. cloacae is clearly more sensitive to a pH decrease than L. curvatus, as may be concluded from the theoretical minimum pH for growth of 5.6 for E. cloacae and 4.3 for L. curvatus. For both organisms no effect of glucose on the maximum specific growth rate could be detected and Monod kinetics with a low Monod constant was assumed. For L. curvatus the effect of lactate on the maximum specific growth rate at different initial pH values could be described by a linear relationship. For E. cloacae a slight effect of lactate on the maximum specific growth rate could only be detected at pH 7. However, this effect was negligible compared to the effect of the pH. For both organisms the lag time was modelled by the inverse of the specific growth rate. It can be concluded that, with regard to interactions between L. curvatus and E. cloacae, the pH is likely to be the most important factor in the case where L. curvatus is the dominant organism. Substrate limitation is likely to become important in the case where E. cloacae is the dominant organism or for media with a high buffer capacity.

Fluorescence ratio imaging is a non-invasive technique for studying the formation of microgradients in immobilised bacterial colonies. These gradients can be quantified easily when combined with the gel cassette system designed at the Institute of Food Research, Norwich, UK. Colonies of Lactobacillus curvatus were observed using this technique and relevant pH gradients were present when the colonies reached a diameter of about 100 μm. These pH gradients were due to production of lactic acid by L. curvatus cells in the colonies. The spatial resolution of the images was about 1.5 μm (scale of bacterial cells) and therefore very suitable for observing local effects in colonies which ranged in sizes from 1 to 500 μm. Copyright (C) 2000 Elsevier Science B.V.