Three-dimensional chiral active Ornstein-Uhlenbeck model for helical motion of microorganisms

Active movement is essential for the survival of microorganisms like bacteria, algae and unicellular parasites. In three dimensions, both swimming and gliding microorganisms often exhibit helical trajectories. One such case are malaria parasites gliding through 3D hydrogels, for which we find that the internal correlation time for the stochastic process generating propulsion is similar to the time taken for one helical turn. Motivated by this experimental finding, here we theoretically analyze the case of finite internal correlation time for microorganisms with helical trajectories as chiral active particles with an Ornstein-Uhlenbeck process for torque. We present an analytical solution which is in very good agreement with computer simulations. We then show that for this type of internal noise, chirality and rotation increase the persistence of motion and results in helical trajectories that have a larger long-time mean squared displacement than straight trajectories at the same propulsion speed. Finally we provide experimental evidence for this prediction for the case of the malaria parasites.