  Post-translational modification (PTM) of proteins plays a key role in signal
transduction, and hence significant effort has gone toward understanding how
PTM networks process information. This involves, on the theory side, analyzing
the dynamical systems arising from such networks. Which networks are, for
instance, bistable? Which networks admit sustained oscillations? Which
parameter values enable such behaviors? In this Perspective, we highlight
recent progress in this area and point out some important future directions.
Along the way, we summarize several techniques for analyzing general networks,
such as eliminating variables to obtain steady-state parametrizations, and
harnessing results on how incorporating intermediates affects dynamics.
