Swimming cells typically move along a helical path or undergo longitudinal rotation as they swim, arising from chiral asymmetry in hydrodynamic drag or propulsion bending the swimming path into a helix. Helical paths are beneficial for some forms of chemotaxis, but why asymmetric shape is so prevalent when a symmetric shape would also allow highly directional swimming is unclear. Here, I analyse the swimming of the insect life cycle stages of two human parasites; Trypanosoma brucei and Leishmania mexicana. This showed quantitatively how chirality in T. brucei cell shape confers highly directional swimming. High speed videomicrographs showed that T. brucei, L. mexicana and a T. brucei RNAi morphology mutant have a range of shape asymmetries,...