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Sperm modulate their flagellar symmetry to navigate through complexphysico-chemical environments and achieve reproductive function. Yet it remainselusive how sperm swim forwards despite the inherent asymmetry of severalcomponents that constitutes the flagellar engine. Despite the criticalimportance of symmetry, or the lack of it, on sperm navigation and itsphysiological state, there is no methodology to date that can robustly detectthe symmetry state of the beat in free-swimming sperm in 3D.How does symmetricprogressive swimming emerge even for asymmetric beating, and how can beating(a)symmetry be inferred experimentally? Here, we numerically resolve the fluidmechanics of swimming around asymmetrically beating spermatozoa. This revealsthat sperm spinning critically regularizes swimming into persistently symmetricpaths in 3D, allowing sperm to swim forwards despite any imperfections on thebeat. The sperm orientation in three-dimensions, and not the swimming path, caninform the symmetry state of the beat, eliminating the need of tracking theflagellum in 3D. We report a surprising correspondence between the movement ofsperm and spinning-top experiments, indicating that the flagellum drives''spinning-top'' type rotations during sperm swimming, and that this parallelis not a mere analogy. These results may prove essential in future studies onthe role of (a)symmetry in spinning and swimming microorganisms andmicro-robots, as body orientation detection has been vastly overlooked infavour of swimming path detection. Altogether, sperm rotation may provide afoolproof mechanism for forward propulsion and navigation in nature that wouldotherwise not be possible for flagella with broken symmetry.

Swimming by spinning: spinning-top type rotations regularize sperm swimming into persistently symmetric paths in 3D