Spatio-temporal structure of migrating chemotactic band of Escherichia coli. I. Traveling band profile

Abstract

We developed a rapid-scanning, light-scattering densitometer by which extensive measurements of band migration speeds and band profiles of chemotactic bands of Escherichia coli in motility buffer both with and without serine have been made. The purpose is to test the applicability of the phenomenological model proposed by Keller and Segel (J. Theor. Biol. 1971. 30:235) and to determine the motility (mu) and chemotactic (delta) coefficients of the bacteria. We extend the previous analytical solution of the simplified Keller-Segel model by taking into account the substrate diffusion which turns out to be significant in the case of oxygen. We demonstrate that unique sets of values of mu and delta can be obtained for various samples at different stages of migration by comparing the numerical solution of the model equation and the experimental data. The rapid-scanning technique also reveals a hitherto unobserved time-dependent fine structure in the bacterial band. We give a qualitative argument to show that the fine structure is an example of the dissipative structure that arises from a nonlinear coupling between the bacterial density and the oxygen concentration gradient. Implications for a further study of the dissipative structure in testing the Keller-Segel model of chemotaxis are briefly discussed.

Quantification of random motility and chemotaxis bacterial transport coefficients using individual‐cell and population‐scale assays

“…This likely stems from the multitude of specialized components (machined Plexiglas chamber, cold light source, stereomicroscope, CCD camera, computer with image-capture software) required for its use. Similar disadvantages are associated with the lightscattering densiometer (Holz and Chen, 1977), laser densiometer (Dahlquist et al, 1972), and fused capillary array (Berg and Turner, 1990). Thus, the most commonly used technique for quantifying bacterial random motility remains the capillary assay (Adler, 1973).…”

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations

“…Keller and Segel (1971b) noted this form of the chemotactic coefficient allows the model to predict band behavior (traveling wave solutions) in the bacterial density profiles when the concentration of s is such that a continuum description is no longer adequate, the only condition being that χ/μ > 1. Holz and Chen (1979) demonstrated that the model of Keller and Segel (1971b) provides an adequate description of bacterial migration in the bacterial response of E. coli to serine. They derived estimates for μ and χ when the chemotactic coefficient is of the form in Eq.…”

Traveling waves in a chemotactic model

“…But, by using laser techniques, in [5] it was found that the bands slowly changes their shape. [5] also mentioned about the necessity of performing a linear stability analysis to find out the region of instability and the wavenumber range where the instability occurs. Theorems 1.3 and 1.4, which are proved in Sect.…”

“…~ [3] and [10] have discussed the stability of the traveling wave solutions. When D >/0, Holz and Chen [5] have studied the band propagation both numerically and experimentally to test the applicability of the model. For further references see [ 12].…”