Fig 1.
Examples of equilibrium curves corresponding to Eqs (4)–(6) in the (Z, Q) phase plane for the case of (top) excitatory ECM-neuron interaction and (bottom) inhibitory ECM-neuron interaction.
Both panels show the existence of bistable solutions regardless of the polarity of ECM-neuron interactions. The intersections of the nullclines determine the equilibria of the system: blue points are stable, red points are unstable.
Fig 2.
Nullclines Zˆ(Z,P) = 0 and Pˆ(Z,P) = 0 for three different values of the ECM production threshold θZ: (a) θZ = 5.68, (b) θZ = 6 and (c) θZ = 6.4.
The intersections of the nullclines determine the equilibria of the system: green (focus) and blue (node) points are stable, red (saddle) and purple (focus) are unstable. Biologically meaningless areas are indicated as shaded domains. Other parameters are given in Table 1.
Table 1.
Fig 3.
(a) Bifurcation diagram of the system (4)–(7) for varied ECM production threshold value θZ. (b) Differences ΔZ = Zmax–Zmin and ΔP = Pmax–Pmin as functions of θZ. (c)-(j) Phase portraits of the system for various values of θZ. Other parameters are given in Table 1.
Fig 4.
Simulated ECM concentration trace under the conditions when the ECM-protease system exhibits coexistence of a stable limit cycle and a stable stationary state.
Application of an external stimulus (e.g. a spontaneous increase or decrease in neural activity) may induce dynamical switches between activity states. This is an imposed change in neural activity. Parameter value for θZ = 3.75. Other parameters are given in Table 1.