Hydrodynamic phase entrainment drives synchronization of sperm flagella

Synchronization of sperm flagella may enhance reproductive fitness and offers an accessible model for studying biological coordination. However, a fundamental debate persists: while hydrodynamic models predict that fluid coupling alone can synchronize adjacent flagella, experiments on freely swimming sperm suggest that direct mechanical contact is required. This discrepancy likely reflects both idealized theoretical assumptions that neglect physiological heterogeneity and experimental limitations that preclude isolation of the hydrodynamic contribution. To resolve this, we developed a microfluidic trap array that immobilizes pairs of sperm cells while preserving their natural flagellar beating, enabling long-duration, high-precision measurements of phase dynamics under controlled hydrodynamic conditions. By analyzing the synchronization dynamics through the Adler equation-which accommodates the intrinsic frequency detuning of biological oscillators-we reveal that under head-fixed conditions, pure hydrodynamic coupling is sufficient to drive robust flagellar synchronization. Furthermore, we find that the coupling strength decays approximately linearly with interflagellar distance over physiologically relevant scales, and that flagellar phase fluctuations are dominated by low-frequency colored noise, challenging the ubiquitous white-noise approximation in active matter models. Going beyond the conventional phenomenological use of the Adler equation, we derive a phase-response function that traces its coupling term directly to the measured hydrodynamic flow field, thereby grounding the abstract phase dynamics in its physical basis in fluid mechanics. These results reconcile the theoretical-experimental divide regarding flagellar synchronization and establish a transferable framework for investigating collective behavior in diverse systems of nonidentical biological oscillators.