Thermodynamic Limits of Sperm Swimming Precision

Sperm swimming is crucial to fertilize the egg, in nature and in assisted reproductive technologies. Modelingthe sperm dynamics involves elasticity, hydrodynamics, internal active forces, and out-of-equilibrium noise. Herewe give experimental evidence in favor of the relevance of energy dissipation for sperm beating fluctuations. Foreach motile cell, we reconstruct the time evolution of the two main tail's spatial modes, which together tracea noisy limit cycle characterized by a maximum level of precision pmax. Our results indicate pmax ~ 102 s-1,remarkably close to the estimated precision of a dynein molecular motor actuating the flagellum, which isbounded by its energy dissipation rate according to the thermodynamic uncertainty relation. Further experimentsunder oxygen deprivation show that pmax decays with energy consumption, as it occurs for a single molecularmotor. Both observations are explained by conjecturing a high level of coordination among the conformationalchanges of dynein motors. This conjecture is supported by a theoretical model for the beating of an idealflagellum actuated by a collection of motors, including a motor-motor nearest-neighbor coupling of strengthK: When K is small the precision of a large flagellum is much higher than the single motor one. On the contrary,when K is large the two become comparable. Based upon our strong-motor-coupling conjecture, old and newdata coming from different kinds of flagella can be collapsed together on a simple master curve.