Quantitative Analysis of Bacterial Migration in Chemotaxis

A user’s guide to PDE models for chemotaxis

“…With this version, we obtain the minimal model as β → ∞, while for β = 0 we obtain the "logistic" chemotactic sensitivity mentioned briefly above. Although the logistic sensitivity has inherent problems, amplified on below, its prominent employment both in specific applications [3,5,21,46] and mathematical analyses (for a review, see Sect. 6.1.1 of Horstmann's paper [40]) merits its consideration here.…”

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

“…They discussed the importance of solutions involving chemotaxis matching with experimental observations and posed the question "If after choosing a suitable χ , theory does not match experiment, then is it the choice of χ or the model itself which is inadequate?" Further work (Lapidus and Schiller, 1976) noted that the earlier work of Segel and Jackson (1973), Nossal and Weis (1973) and Lapidus and Schiller (1974) using the original K-S formulation did not successfully predict all of the experiments observed by Dahlquist et al (1972). Noting this and considering the experimental work of Mesibov et al (1973) and Brown and Berg (1974), Lapidus and Schiller (1976) suggested a revised chemotactic coefficient of the form…”

“…We note here that given the difference in timescales of the experiments (capillary assays are of the order of minutes or hours whereas swarm plate assays can be carried out over days) growth terms can in the case of capillary assays be neglected, whereas they may be important when modeling swarm plates. Segel and Jackson (1973), Nossal and Weis (1973), and Lapidus and Schiller (1974) formulated K-S models to explain the experimental observations of Dahlquist, Lovely, and Koshland (DLK) (Dahlquist et al, 1972) regarding chemotaxis of Salmonella typhimurium in an assay analogous to that of the capillary assay. Segel and Jackson (1973) considered the relative strengths of diffusion and chemotaxis on model solutions compared to the DLK experiments.…”

“…Here, the focus was the findings of Dahlquist et al (1972) (see Section 2.2 for earlier models and details) where steep and smooth attractant gradients were considered. Ford and Lauffenburger (1991a) qualitatively assessed the effect that varying diffusion and chemotactic motility parameters had on the shape of the attractant and bacterial profiles.…”

“…Difficulties with this assay method include the inability to control the attractant gradient, counting the number of bacteria which have entered the capillary and the large variations in the number of bacteria entering the capillary between measurements. • Dahlquist et al (1972) used a laser densitometer assay to study the effect that varying profiles of attractant (exponential, step, and linear) have on the response of the bacterial colony. A helium-neon laser was used to detect the change in density of the bacterial population as it moved through the chamber.…”