  Despite evidence for a hydrodynamic origin of flagellar synchronization
between different eukaryotic cells, recent experiments have shown that in
single multi-flagellated organisms, coordination hinges instead on direct basal
body connections. The mechanism by which these connections leads to
coordination, however, is currently not understood. Here we focus on the model
biflagellate {\it Chlamydomonas reinhardtii}, and propose a minimal model for
the synchronization of its two flagella as a result of both hydrodynamic and
direct mechanical coupling. A spectrum of different types of coordination can
be selected, depending on small changes in the stiffness of intracellular
couplings. These include prolonged in-phase and anti-phase synchronization, as
well as a range of multistable states induced by spontaneous symmetry breaking
of the system. Linking synchrony to intracellular stiffness could lead to the
use of flagellar dynamics as a probe for the mechanical state of the cell.
