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

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.