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# Project C.2: From trajectories to an understanding of chemotactic response: theory

We will first choose an appropriate formulation of the tumbling bacterium. In a stochastic equation tumbles are initiated by shot noise with Poissonian distributed tumble times which gives additional rate terms in a Smoluchowski equation. The mean tumble rate appears here as parameter. It depends on the chemical field at earlier times and thus on the bacterial trajectory. We will investigate if this non-Markovian stochastic process can be mapped on coupled Markov processes.

We will then simulate the bacterial trajectories in a constant chemical gradient using some ansatz for the chemotactic response function R. With these data we will explore how one can extract the response function from experimental trajectories. For example, on can think of an adaptive method that refines the estimate for R during the analysis of the trajectories. We will also explore other protocols for the applied chemical field. For example, an oscillating uniform field gives a local response in frequency space. Ultimately, we will apply our findings to the experiments of project C.1.

At a later stage of the project, we will also investigate collective phenomena in bacterial populations, such as the traveling concentration wave which occurs in a chemical field dynamically generated by the migrating population itself.**Project leaders: ****Prof. Dr. H. Stark**, **Prof. Dr. C. Beta**