Traveling concentration pulses of bacteria in a generalized Keller–Segel model

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.

Chemotaxis strategies of bacteria with multiple run modes

“…Note in this context that the bias of run times may, in principle, depend on other motion characteristics, such as the speed in the respective run state. This may occur, for example, if the underlying model for the run-time bias relies on a memory kernel ( 16 , 20 – 24 ), but it is also observed in alternative models describing navigation of active particles in concentration gradients ( 25 ).…”

Chemotactic Migration of Bacteria in Porous Media

“…Implementation of numerical simulations. To numerically solve the continuum model, we use an Adams-Bashforth-Moulton predictor corrector method (49) where the order of the predictor and corrector are 3 and 2, respectively. Since the predictor corrector method requires past time points to inform future steps, the starting time points must be found with another method; we choose the Shanks starter of order 6 as described previously (75,76).…”

Migration and accumulation of bacteria with chemotaxis and chemokinesis

“…5. The reduced pulse also travels slower than the pulse of the chemotactic population at elevated speed V = 1 + η because the front speed scales with the number of bacteria in the pulse [35]. This observation might explain why in agar plate experiments testing for chemotaxis, chemokinetic species such as Sinorhizobium meliloti lack the sharp bands [8,36], which are known to be a hallmark of chemotaxis for other species, e.g.…”