Locomotion of paired spermatozoa during flagellar synchronisation

Microorganisms, such as spermatozoa, exhibit rich behaviours when in close proximity to each other. However, their locomotion is not fully understood when coupled mechanically and hydrodynamically. In this study, we develop hydrodynamic models to investigate the locomotion of paired spermatozoa, predicting the fine structure of their swimming. Experimentally, sperm pairs are observed to transition between different modes of flagellar synchronisation: in-phase, anti-phase and lagged synchronisation. Using our models, we assess their swimming performances in these synchronisation modes in terms of average swimming speed, average power consumption, and swimming efficiency. The swimming performances of paired spermatozoa are shown to depend on their flagellar phase lag, flagellar waveforms, and the mechanical coupling between their heads.