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BP: Fachverband Biologische Physik
BP 21: Microswimmers (joint session BP/CPP/DY)
BP 21.3: Vortrag
Mittwoch, 14. März 2018, 15:45–16:00, H 1028
The bacterial soliton in a nutrient field – re-examined — •Andrzej Palugniok2, Maximilian Seyrich1, and Holger Stark1 — 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany — 2Worcester College, University of Oxford, Walton Street, OX1 2HB Oxford, United Kingdom
The gut bacterium E. coli with its run-and-tumble walk is a well-studied model swimmer in the active-matter field. One of the various interesting collective phenomena is a bacterial soliton or a traveling concentration pulse of bacteria [1]. It develops when bacteria start to consume a nutrient in an initially uniform field, in which they also perform chemotaxis.
To describe such a situation, we start from a Smoluchowski equation of a run-and-tumble particle in a chemotactic field. A Markovian tumble rate is derived from the usual linear response theory. We perform a multipole expansion to derive equations for the bacterial density and the local polar order decribed by the bacterial polarization. On times longer than the typical relaxation time for the polarization, one recovers the Keller-Segel equation. Solving it together with the diffusion equation for the nutrient, we are able to reproduce the bacterial soliton. Thereby, we demonstrate that one does not need a second, signalling chemical field as introduced in Ref. [1] nor a singular chemotactic drift term as demanded in Ref. [2].
[1] J. Saragosti et al., PNAS 108, 39 (2011).
[2] E.F. Keller and L.A. Segel, J. Theor. Biol., 30, 2 (1971).