The molecular basis of the run-and-tumble motility of Escherichia coli has been studied extensively. However, the quantitative spatiotemporal characterization of a swimming population remains challenging because of the broad range of relevant length and time scales. Here, we characterize the full spatiotemporal gait of populations of swimming E. 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 controlled by 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 the small-scale directed swimming and macroscopic diffusion. Moreover, we extend our theory to analytically study a minimal model of a chemotactic agent and provide a spatiotemporal characterization of the underlying dynamics.
[1] C Kurzthaler, Y Zhao et al. Phys. Rev. Lett. 132 (2024)
[2] Y Zhao, C Kurzthaler et al. Phys. Rev. E 109 (2024)