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␘f 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 105 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.
Malakar, P. K., Martens, D. E., van Breukelen, W., Boom, R. M., Zwietering, M. H., & van 't Riet, K. (2002). Modeling in the interactions of Lactobacillus curvatus colonies in solid medium : consequences for food quality an safety. Applied and Environmental Microbiology, 68(7), 3432-3441. https://doi.org/10.1128/AEM.68.7.3432-3441.2002