Inferring the Chemotactic Strategy of P. putida and E. coli Using Modified Kramers-Moyal Coefficients

Many bacteria perform a run-and-tumble random walk to explore their surrounding and to perform chemotaxis. In this article we present a novel method to infer the relevant parameters of bacterial motion from experimental trajectories including the tumbling events. We introduce a stochastic model for the orientation angle, where a shot-noise process initiates tumbles, and analytically calculate conditional moments, reminiscent of Kramers-Moyal coefficients. Matching them with the moments calculated from experimental trajectories of the bacteria E. coli and Pseudomonas putida, we are able to infer their respective tumble rates, the rotational diffusion constants, and the distributions of tumble angles in good agreement with results from conventional tumble recognizers. We also define a novel tumble recognizer, which explicitly quantifies the error in recognizing tumbles. In the presence of a chemical gradient we condition the moments on the bacterial direction of motion and thereby explore the chemotaxis strategy. For both bacteria we recover and quantify the classical chemotactic strategy, where the tumble rate is smallest along the chemical gradient. In addition, for E. coli we detect some cells, which bias their mean tumble angle towards smaller values. Our findings are supported by a scaling analysis of appropriate ratios of conditional moments, which are directly calculated from experimental data.DFG, 87159868, GRK 1558: Kollektive Dynamik im Nichtgleichgewicht: in kondensierter Materie und biologischen Systeme

Characterization and Control of the Run-and-Tumble Dynamics of Escherichia Coli

We characterize the full spatiotemporal gait of populations of swimming Escherichia coli using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlledby a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type E. coli, we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion

Statistical analysis of bacteria locomotion

Many bacteria swim by employing their helical appendages, the flagella. We studied the statistics of this locomotion. To obtain more natural and especially long trajectories compared to two-dimensional tracking strategies, we developed a measurement-setup suitable to track bacteria in three-dimensions.The main component of this setup is an electrically focus tunable lens (ETL), able to adapt it’s shape via an applied electrical current, resulting in a change of the current focal plane. This setup has no mechanical interaction with the sample to avoid adulteration of the measured trajectories. We found that for times smaller than the average running-time, the slope of the mean-squared displacement MSD of the tracked bacteria obeys a ballistic behavior, whereas for longer times we saw a clear diffusive behavior. To allow for a more efficient evaluation of the measured trajectories we introduce the Kalman-Filter. By using simulated trajectories we could show that the Kalman-Filter allows a more accurate determination of the rotational-diffusion coefficient than conventional methods. Furthermore we could show that evaluation of three-dimensional trajectories obeys slightly different statistics than the evaluation of projected two-dimensional trajectories due to missing information.Through the qualitative simulation of bacteria locomotion we could show that the flagella-positioning has a crucial impact on the tumbling dynamics.Viele Bakterien schwimmen durch Nutzung ihrer spiralförmigen Anhänge,den Flagellen. Wir untersuchten die Statistik dieser Bewegung. Um natürlichere und vor allem längere Trajektorien - verglichen mit konventionellen zweidimensionalen Trackingmethoden - zu erhalten, haben wir einen Messaufbau zum dreidimensionalen tracken von Bakterien entwickelt. Die Hauptkomponente dieses Setups ist eine elektrische, fokusanpassbare Linse (ETL),welche ihre Form durch Anlegen eines elektrischen Stroms ändern kann,was zu einer Änderung der Fokusebene führt. Dieser Messaufbau hat keine mechanischen Wechselwirkungen mit der Probe, wodurch Verfälschungender gemessenen Trajektorien verhindert werden. Wir konnten zeigen dassfür Zeiten kleiner als die durchschnittlicherunning-Zeit (dt.Renn-Zeit), die mittlere quadratische Verschiebung (MSD) der getrackten Bakterien ein ballistisches Verhalten zeigt, wohingegen für längere Zeiten ein diffusives Verhalten vorliegt. Um eine effizientere Auswertung der gemessenen Trajektorien zu erlauben, führten wir den Kalman-Filter ein. Durch Nutzung simulierterTrajektorien konnten wir zeigen dass der Kalman-Filter eine genauere Bestimmung des Rotations-Diffusionskoeffizienten - verglichen mit konventionellen Methoden - erlaubt.Weiterhin konnten wir zeigen, dass die Auswertung dreidimensionaler Trajektorien leicht andere Statistiken als die Auswertung zweidimensionaler Trajektorien liefert, was durch den Verlust an Information zu erklären ist. Durch die qualitative Simulation der Bewegung von Bakterien konnten wir zeigen, dass die Position der Flagellen einen wesentlichen Einfluss auf die Tumbling-Dynamik (dt.Taumel-Dynamik) hat