Transitions in the synchronization modes of elastic filaments through basal-coupling*

Cilia and flagella often beat in synchrony. They can also switch between different synchronization modes. However, the exact mechanisms responsible for such switching remain elusive. While previous evidence suggests that cilia coordination can be a result of hydrodynamic coupling, recent experimental findings show that defects in the intra-cellular basal coupling significantly affect the synchronization modes. Here, we account for basal coupling between two elastic filaments, driven by a geometric switch moment, by introducing a linear elastic spring that connects the two filaments.  We quantitatively examine the effects of this coupling on the synchrony of the filaments. We find that their coordination is strongly affected by the stiffness of the basal spring and the geometric switch parameters. Specifically, we observe a bistable region in the parameter space where the filaments could synchronize in either breast-stroke or free-style fashion depending on their initial conditions. We use the model to explain the transitions between various synchronization modes observed experimentally for the algae cells Chlamydomonas.