Bifurcation analysis of multistability and oscillation emergence in a model of brain extracellular matrix

Abstract

Neurons release diverse molecules including proteoglycans and glycoproteins, which can aggregate in the extracellular space and form the so-called extracellular matrix (ECM). The ECM represents an active medium that may regulate major cellular functions including signal generation and transmission. There are also extracellular proteases that may degrade the ECM. It is important that both synthesis and degradation of ECM are activity-dependent connected with neuronal firing. In this study we apply rigorous bifurcation analysis to nonlinear dynamical system describing the ECM activation. We found that the ECM can have both multistable and oscillatory dynamics. Specifically, there are different types of bistability including coexistence of two stationary states for the concentration of ECM molecules or coexistence of a limit cycle and a fixed point. We also found parameters when three attractors exist simultaneously. The attractors of the ECM model can be further treated as specific modulation modes of neuronal circuits being immersed into active ECM medium.