In-phase and anti-phase flagellar synchronization by waveform compliance and basal coupling

Cilia and flagella exhibit regular bending waves that perform mechanical work on the surrounding fluid,
to propel cellular swimmers and pump fluids inside organisms. Here, we quantify a force-velocity
relationship of the beating flagellum, by exposing flagellated Chlamydomonas cells to controlled
microfluidic flows. A simple theory of flagellar limit-cycle oscillations, calibrated by measurements in
the absence of flow, reproduces this relationship quantitatively. We derive a link between the energy
efficiency of the flagellar beat and its ability to synchronize to oscillatory flows.