Stochastic Modelling of a Chemotactic Microswimmer

Abstract

Key to Escherichia coli (E-coli) bacteria survival is its ability to direct its movement to greener pasture and flee harmful environment - also known as chemotaxis. This thesis focuses on the modelling of E-coli chemotaxis in two- dimensions with emphasis on trying to understand the basic physics of how such a tiny microswimmer swim up a concentration gradient despite the enormous thermal fluctuations in its environment. E-coli strategically employs near straight swimming (also known as run) often interrupted by random reorientations (also known as tumble). How often this interruptions happens is the swimmer tumbling frequency. This chemotaxis strategy is here modeled as random telegraph process, which is a dichotomous stochastic process. The swimmer tumbling frequency is represented as the transition rate from run phase to tumble phase. The transition rate is a function of swimmer specific trait (known as response kernel) and the environmental condition - concentration profile. Furthermore, the random telegraph process is coupled to the swimmer Langevin equations in which the system was solved analytically making judicious approximations. Important chemotaxis parameter expres- sion was obtained for a swimmer with arbitrary trait and a simple swimmer case scenario analyzed. Even though, this framework describes E-coli chemo- taxis excellently, it can as well serve as a base framework for study of other interesting models that exhibit two state swimming strategy.