A stochastic model for chemotactic motion of micro-beads propelled by attached bacteria

This work presents a stochastic model for the motion of 10 μm beads propelled by an ensemble of attached flagellated bacteria in a chemical attractant gradient. Population scale stochastic models normally adopted when studying biological systems may not be an effective approach for cases in which a small number of agents are exposed to different boundary conditions and are interacting in a complex manner. The stochastic model presented here simulates the swimming behavior of each of the 44 bacteria assembled on a 10 μm bead and propel the bead in a transient chemo-attractant field. The concentration of the chemo-attractant as a function of location and time is calculated and the run and tumble rates of the attached bacteria are adjusted accordingly. Chemotactic motility of the micro-beads is modeled for timescales significantly shorter than its randomization time to capture directed propulsion behavior of the system. It is shown that the motion of the bead is a function of the chemo-attractant gradient field the micro-bead resides within. The simulation results are compared with previously reported experimental data to validate the model. The stochastic model demonstrates a 56.6% enhancement in the displacement to distance ratio of the micro-bead when traveled in a chemo-attractant gradient field; thus, proving the feasibility of achieving autonomous directed motion of bio-hybrid microrobots using chemotaxis.