Run and tumble dynamics as Levy flights in orientation: Theory and Experiment*

Many microorganisms exhibit run and tumble dynamics. This behavior is usually modeled as smooth runs followed by discrete random tumble events. However, in the lab, we see a wide spectrum of tumbling behavior. We offer a new model that may explain this wide variety of tumbling behavior, not as discrete tumbling events, but as a continuum of random reorientations that follow a Lorentzian (or Cauchy) distribution. This means microbes undergo Levy flights in their angular dynamics. The corresponding Fokker Planck equation for a stochastic differential equation with Lorentzian noise is exactly solvable. We construct the time evolution of a probability distribution from experimental data and show it closely matches the modified Fokker Planck equation for Lorentzian noise. We also extract the noise strength of the Lorentzian distribution for several populations of microbes (all with different behaviors), and run Monte Carlo simulations that closely reproduce the statistics. This is strong evidence that run and tumble dynamics can be modeled as Levy flights in orientation.