Modeling the locomotion of the African trypanosome using multi-particle collision dynamics

The African trypanosome is a single flagellated micro-organism that causes the deadly sleeping sickness in humans and animals. We study the locomotion of a model trypanosome by modeling the spindle-shaped cell body using an elastic network of vertices with additional bending rigidity. The flagellum firmly attached to the model cell body is either straight or helical. A bending wave propagates along the flagellum and pushes the trypanosome forward in its viscous environment, which we simulate with the method of multiparticle collision dynamics. The relaxation dynamics of the model cell body due to a static bending wave reveals the sperm number from elastohydrodynamics as the relevant parameter. Characteristic cell body conformations for the helically attached flagellum resemble experimental observations. We show that the swimming velocity scales as the root of the angular frequency of the bending wave reminiscent of predictions for an actuated slender rod attached to a large viscous load. The swimming velocity for one geometry collapses on a single master curve when plotted versus the sperm number. The helically attached flagellum leads to a helical swimming path and a rotation of the model trypanosome about its long axis as observed in experiments. The simulated swimming velocity agrees with the experimental value.