Flagellar ultrastructure suppresses buckling instabilities and enables mammalian sperm navigation in high-viscosity media

Eukaryotic flagellar swimming is driven by a slender motile unit, the axoneme, which possesses an internal structure that is essentially conserved in a tremendous diversity of sperm. Mammalian sperm, however, which are internal fertilizers, also exhibit distinctive accessory structures that further dress the axoneme and alter its mechanical response. This raises the following two fundamental questions. What is the functional significance of these structures? How do they affect the flagellar waveform and ultimately cell swimming? Hence we build on previous work to develop a mathematical mechanical model of a virtual human sperm to examine the impact of mammalian sperm accessory structures on flagellar dynamics and motility. Our findings demonstrate that the accessory structures reinforce the flagellum, preventing waveform compression and symmetry-breaking buckling instabilities when the viscosity of the surrounding medium is increased. This is in agreement with previous observations of internal and external fertilizers, such as human and sea urchin spermatozoa. In turn, possession of accessory structures entails that the progressive motion during a flagellar beat cycle can be enhanced as viscosity is increased within physiological bounds. Hence the flagella of internal fertilizers, complete with accessory structures, are predicted to be advantageous in viscous physiological media compared with watery media for the fundamental role of delivering a genetic payload to the egg.