  Beating flagella exhibit a variety of synchronization modes. This synchrony
has long been attributed to hydrodynamic coupling between the flagella.
However, recent work with flagellated algae indicates that a mechanism internal
to the cell, through the contractile fibres connecting the flagella basal
bodies, must be at play to actively modulate flagellar synchrony. Exactly how
basal coupling mediates flagellar coordination remains unclear. Here, we
examine the role of basal coupling in the synchronization of the model
biflagellate \textit{Chlamydomonas reinhardtii} using a series of mathematical
models of decreasing level of complexity. We report that basal coupling is
sufficient to achieve inphase, antiphase, and bistable synchrony, even in the
absence of hydrodynamic coupling and flagellar compliance. These modes can be
reached by modulating the activity level of the individual flagella or the
strength of the basal coupling. We observe a slip mode when allowing for
differential flagellar activity, just as in experiments with live cells. We
introduce a dimensionless ratio of flagellar activity to basal coupling that is
predictive of the mode of synchrony. This ratio allows us to query biological
parameters which are not yet directly measurable experimentally. Our work shows
a concrete route for cells to actively control the synchronization of their
flagella.
