Growth of bacteria in 3-d colonies

TL;DR

This study develops and validates a 3D mathematical model for bacterial colony growth that incorporates spatial heterogeneity and nutrient diffusion, revealing distinct growth regimes and colony dynamics compared to liquid cultures.

Contribution

The paper introduces a novel 3D model extending the Monod model to account for spatial heterogeneity and validates it with experimental data on E.coli colonies in soft agar.

Findings

Colony growth exhibits a diffusion-limited, sub-exponential regime.

Colonies produce approximately 2.5 times more cells than liquid cultures from the same nutrients.

Non-monotonic relationship between colony number and total cell count due to competition and cell death.

Abstract

The dynamics of growth of bacterial populations has been extensively studied for planktonic cells in well-agitated liquid culture, in which all cells have equal access to nutrients. In the real world, bacteria are more likely to live in physically structured habitats as colonies, within which individual cells vary in their access to nutrients. The dynamics of bacterial growth in such conditions is poorly understood, and, unlike that for liquid culture, there is not a standard broadly used mathematical model for bacterial populations growing in colonies in three dimensions (3-d). By extending the classic Monod model of resource-limited population growth to allow for spatial heterogeneity in the bacterial access to nutrients, we develop a 3-d model of colonies, in which bacteria consume diffusing nutrients in their vicinity. By following the changes in density of E.coli in liquid and embedded in glucose-limited soft agar, we evaluate the fit of this model to experimental data. The model accounts for the experimentally observed presence of a sub-exponential, diffusion-limited growth regime in colonies, which is absent in liquid cultures. The model predicts and our experiments confirm that, as a consequence of inter-colony competition for the diffusing nutrients and of cell death, there is a non-monotonic relationship between total number of colonies within the habitat and the total number of individual cells in all of these colonies. This combined theoretical-experimental study reveals that, within 3-d colonies, E.coli cells are loosely packed, and colonies produce about 2.5 times as many cells as the liquid culture from the same amount of nutrients. Our model provides a baseline description of bacterial growth in 3-d, deviations from which can be used to identify phenotypic heterogeneities and inter-cellular interactions that further contribute to the structure of bacterial communities.