  Under mass-action kinetics, biochemical reaction networks give rise to
polynomial autonomous dynamical systems whose parameters are often difficult to
estimate. We deal in this paper with the problem of identifying the kinetic
parameters of a class of biochemical networks which are abundant, such as
multisite phosphorylation systems and phosphorylation cascades (for example,
MAPK cascades). For any system of this class we explicitly exhibit a single
species for each connected component of the associated digraph such that the
successive total derivatives of its concentration allow us to identify all the
parameters occurring in the component. The number of derivatives needed is
bounded essentially by the length of the corresponding connected component of
the digraph. Moreover, in the particular case of the cascades, we show that the
parameters can be identified from a bounded number of successive derivatives of
the last product of the last layer. This theoretical result induces also a
heuristic interpolation-based identifiability procedure to recover the values
of the rate constants from exact measurements.
