Internal friction controls active ciliary oscillations near the instability threshold

Active filaments are prototypical engines of motility at the micron scale. Their motion in viscous fluids is determined by the balance of external drag and internal structural stress. The latter contains both active and passive components that, respectively, excite and relax motion. Knowledge of the passive internal and external stresses enables determination of the nature of the active component, which is a key step in the validation of mechanochemical models of activity. We simultaneously measure filament motion and external flow of an isolated and active Chlamydomonas cilium with high spatio-temporal resolution to unambiguously estimate the passive stresses. The measured flow field provides a self-consistent validation of the external drag force, which is found to be local and, surprisingly, negligibly small compared to internal elastic stresses. Consequently, there must exist other sources of friction within filament interior for it to exhibit stable driven oscillations. Incorporating internal dissipation as the sole source of friction and a generic spring-dashpot form of active stress, we show that an instability to oscillations takes place when active stresses are strain-softening and shear-thinning. This is in striking contrast with the conventional wisdom that external fluid friction plays an indispensable role in ciliary oscillations.