Bifurcations and Ca2+ oscillations dynamics in a reduced Tsodyks-IP3-Li-Rinzel astrocyte network

Abstract A tripartite synapse always links two neuronsand an astrocyte, while this astrocyte regulatessynaptic signal transmission between neurons by modulatingthe release of neurotransmitters through the oscillationof intracellular calcium ion (Ca2+). To investigateastrocytic network Ca2+ signaling regulation, thisstudy combines the Li-Rinzel Ca2+ oscillation model,Volman-Ben-Jacob’s inositol 1,4,5-trisphosphate (IP3)generation model, and the Li-Rinzel model to design asimplified Tsodyks-IP3-Li-Rinzel (TILR) astrocyte network.Using slow-fast dynamics method and comparison analysis of time series graphs of relevant variablesbefore and after dimensionality reduction, we parameterizeinactive neurotransmitter proportions via peakvalleyaveraging for boosting computational efficiency. Based on bifurcation theory, our TILR astrocyte networkundergoes two supercritical Hopf bifurcations withcodimension-one bifurcation parameter IP3 generationrate (rip3). Our simulations also reveal that the Ca2+ concentration ([Ca2+]) changes from a resting state toa decaying state oscillation and then to a sustainedlarge-amplitude oscillation when rip3 is near these twobifurcation thresholds. Furthermore, codimension-twobifurcation analysis in the (rip3, rL)-plane identifies aBogdanov-Takens (BT) point, which acts as an organizingcenter with three canonical bifurcation curve representationsmediating the global bistability-oscillationtransition. Moreover, simulations reveal that, under identicalconditions, low-frequency stimulation fails to generate Ca2+ oscillations, medium-frequency induces stable Ca2+ oscillations, while high-frequency increases theaverage [Ca2+] but disrupts the persistence of oscillations.Therefore, Ca2+ signal transduction is co-regulatedby rip3, rL and stimulation frequency. This proposedmulti-scale astrocyte network offers a theoretical frameworkfor translating computational data into neuropatho-logical interventions.