  Neuronal and glial cells release diverse proteoglycans and glycoproteins,
which aggregate in the extracellular space and form the extracellular matrix
(ECM) that may in turn regulate major cellular functions. Brain cells also
release extracellular proteases that may degrade the ECM, and both synthesis
and degradation of ECM are activity-dependent. In this study we introduce a
mathematical model describing population dynamics of neurons interacting with
ECM molecules over extended timescales. It is demonstrated that depending on
the prevalent biophysical mechanism of ECM-neuronal interactions, different
dynamical regimes of ECM activity can be observed, including bistable states
with stable stationary levels of ECM molecule concentration, spontaneous ECM
oscillations, and coexistence of ECM oscillations and a stationary state,
allowing dynamical switches between activity regimes.
