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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. Here we introduce a general stochastic dynamics model for these cases, namely a chiral active particle with an Ornstein-Uhlenbeck process for torque, which implies a finite correlation time for internal noise. 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. We finally provide an experimental example by analyzing imaging data for malaria parasites that glide through hydrogels on helical trajectories.

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