A material-balance approach for modeling bacterial chemotaxis to a consumable substrate in the capillary assay

A mathematical model was developed to simulate the movement of chemotactic bacteria into and within a capillary tube containing a metabolizable chemoattractant. The model was based on a material balance that accounts for the transport of bacteria and chemoattractant as well as consumption of the substrate throughout the capillary assay system. By solving the model with a numerical method, it was possible to predict the concentration of substrate and bacteria at points within the capillary and throughout the chamber. The model was tested for its ability to simulate the results of capillary assay experiments performed with Pseudomonas putida G7 and one of its chemoattractants, naphthalene, under conditions wherein naphthalene consumption was expected to affect the flux of bacteria into the capillary. While variations in the chemotactic responses were evident among different experiments, the model could simulate the accumulation of cells in the capillary using previously determined parameters, including the chemotactic sensitivity and random motility coefficients, chi(0) and mu. In particular, model predictions were consistent with the experimental observation that the chemotactic response in the capillary is diminished under conditions wherein consumption would be expected to be significant.