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Main Title: Traveling concentration pulses of bacteria in a generalized Keller–Segel model
Author(s): Seyrich, Maximilian
Palugniok, Andrzej
Stark, Holger
Type: Article
Language Code: en
Abstract: We formulate a Markovian response theory for the tumble rate of a bacterium moving in a chemical field and use it in the Smoluchowski equation. Based on a multipole expansion for the one-particle distribution function and a reaction-diffusion equation for the chemoattractant field, we derive a polarization extended model, which also includes the recently discovered angle bias. In the adiabatic limit we recover a generalized Keller–Segel equation with diffusion and chemotactic coefficients that depend on the microscopic swimming parameters. Requiring the tumble rate to be positive, our model introduces an upper bound for the chemotactic drift velocity, which is no longer singular as in the original Keller–Segel model. Solving the Keller–Segel equations numerically, we identify traveling bacterial concentration pulses, for which we do not need a second, signaling chemical field nor a singular chemotactic drift velocity as demanded in earlier publications. We present an extensive study of the traveling pulses and demonstrate how their speeds, widths, and heights depend on the microscopic parameters. Most importantly, we discover a maximum number of bacteria that the pulse can sustain—the maximum carrying capacity. Finally, by tuning our parameters, we are able to match the experimental realization of the traveling bacterial pulse.
Issue Date: 1-Oct-2019
Date Available: 22-Nov-2019
DDC Class: 530 Physik
Subject(s): Keller–Segel model
maximum carrying capacity
collective active matter
bacterial pulse
Sponsor/Funder: DFG, 87159868, GRK 1558: Kollektive Dynamik im Nichtgleichgewicht: in kondensierter Materie und biologischen Systemen
DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berlin
Journal Title: New Journal of Physics
Publisher: IOP
Publisher Place: London
Volume: 21
Article Number: 103001
Publisher DOI: 10.1088/1367-2630/ab4522
EISSN: 1367-2630
Appears in Collections:FG Statistische Physik weicher Materie und biologischer Systeme » Publications

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