The load-response of the flagellar beat

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 \emph{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 chemo-mechanical efficiency of the flagellar beat and its ability to synchronize to oscillatory flows.