  Using a geometric feedback model of the flagellar axoneme accounting for
dynein motor kinetics, we study elastohydrodynamic phase synchronization in a
pair of spontaneously beating filaments with waveforms ranging from sperm to
cilia and Chlamydomonas. Our computations reveal that both in-phase and
anti-phase synchrony can emerge for asymmetric beats while symmetric waveforms
go in-phase, and elucidate the mechanism for phase slips due to biochemical
noise. Model predictions agree with recent experiments and illuminate the
crucial roles of hydrodynamics and mechanochemical feedback in synchronization.
