Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration

Abstract

In this work, we consider a mathematical model describing spontaneous calcium signaling in astrocytes. Based on biologically relevant principles, this model simulates experimentally observed calcium oscillations and can predict the emergence of complicated dynamics. Using analytical and numerical analysis, various attracting sets were found and investigated. Employing bifurcation theory analysis, we examined steady state solutions, bistability, simple and complicated periodic limit cycles and also chaotic attractors. We found that astrocytes possess a variety of complex dynamical modes, including chaos and multistability, that can further provide different modulations of neuronal circuits, enhancing their plasticity and flexibility.

Global and multistable dynamics in calcium oscillations model

“…Therefore, the high sensitivity of the calcium oscillation model to the variation of the initial condition is demonstrated and validated by the previous investigation. In the work of the authors, such as Pankratova et al [34], the author investigated the bistability of the calcium oscillation. That bistability involves the coexistence of a steady state (point attractor) and an oscillatory mode.…”

Finite volume simulation of calcium distribution in a cholangiocyte cell

“…The effects of calcium-dependent protein and flux through the sodium-calcium exchanger were incorporated in the model [59]. Pankratova et al employed bifurcation theory analysis and examined steady-state solutions, bistability, simple and complicated periodic limit cycles and also chaotic attractors for calcium variation in astrocytes [54]. Tarifa et al demonstrated that preferential calcium release near the sarcolemma is key to a higher spatiotemporal distribution of sparks and amplitude of post-depolarizations in atrial myocytes from patients with atrial fibrillation using mathematical model [57].…”