Bifurcation analysis of calcium dynamics in nerve cell

Abstract

Communication between neurons and astrocytes involves numerous significant chemical transmissions. It has been established that $\textrm{Ca}^{2+}$ signaling is among the most adaptable second mediators in the majority of cell morphology and diverse cellular processes are regulated by complicated dynamical behaviors that range from random picking to well-ordered oscillations and periodic waves. Including muscular contraction, gene transcription, cell death, and neural activity. A significant regulator of intracellular $\textrm{Ca}^{2+}$ dynamics, including the voltage-gated $\textrm{Ca}^{2+}$ channels, the store-operated $\textrm{Ca}^{2+}$ channel (SOCC), and the receptor-operated $\textrm{Ca}^{2+}$ channel (ROCC), is the rate at which $\textrm{Ca}^{2+}$ enters cells through plasma membrane cells. In order to analyze the model’s dynamic behavior, we have solved the neuron–astrocyte model and conducted a bifurcation analysis. The consequences of changing certain parameters, specifically the bifurcation of numerous limit cycles, on the dynamics of $\textrm{Ca}^{2+}$ with changes in the signaling mechanism for distinct flows through the ER. Multiple limit cycle bifurcation, which may result in complicated dynamical behaviors, arises from the generalized coupling of mitochondria and NCX. It is further demonstrated that the parameter range for stable oscillations is determined by the fluctuation of the maximum flows for various calcium channels.