How do flagella propel protozoans through water?

Protozoans, which are eukaryotic organisms, utilize flagella that function through coordinated microtubule sliding powered by adenosine triphosphate (ATP). These organelles propel the organism through water using three primary forms of movement, all involving contraction waves that travel along the flagellum:123

• Planar waves: These S-shaped, sinusoidal waves move along a single plane, similar to the swimming motion of an eel. This motion typically causes the protozoan to rotate on its longitudinal axis and follow a helical path.2
• Oarlike beating: This planar movement involves a wide, asymmetrical side-to-side swing, often used when the protozoan moves with the flagellum at its forward end.2
• Three-dimensional waves: The flagellum rotates in a conical configuration while asymmetrical waves pass from base to tip. This motion acts like an airplane propeller, forcing water backward and pushing the organism forward.2

The specific direction and speed of this propulsion depend on factors such as the organism's size, the medium's viscosity, and the flagellum's length and position.3