Swimming strategies of microorganisms must conform to the principles of self-propulsion at low Reynolds numbers. Here we relate the translational and rotational speeds to the surface motions of a swimmer and, for spheres, make evident novel constraints on mechanisms for propulsion. The results are applied to a cyanobacterium, an organism whose motile mechanism is unknown, by considering incompressible streaming of the cell surface and oscillatory, tangential surface deformations. Finally, swimming efficiency using tangential motions is related to the surface velocities and a bound on the efficiency is obtained.
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