Calcium concentration in astrocytes: Emergence of complicated spontaneous oscillations and their cessation

Abstract

The purpose of this work is to show the mechanisms of transitions between different dynamic modes of spontaneous astrocytic calcium activity. With this aim, dynamics of recently introduced Lavrentovich–Hemkin mathematical model was examined by both analytical and numerical techniques. Methods. In order to obtain the conditions for the oscillations cessation, the linear stability analysis for the equilibrium point was carried out. Complicated dynamics was studied numerically by calculations of time traces and bifurcation diagrams. Results. The mechanisms of oscillatory mode development with the increase of the maximal calcium flux out of the SERCA pump in the presence of low and high level of extracellular calcium concentration were demonstrated. It was shown that emergence of oscillations occurs via supercritical Andronov–Hopf bifurcation, and the properties of the oscillatory mode with further increase of the maximal calcium flux out of the SERCA pump are highly dependent on the value of extracellular calcium concentration. Notably, emergence of chaotic spontaneous calcium oscillations for specific level of calcium ions outside the cell was revealed. Conclusion. Based on the analysis of various dynamical modes of spontaneous astrocytic chemical activity, the peculiarities in astrocyte-neuron interaction in complex multicellular systems can be further investigated.

Keywords

• mathematical modeling
• calcium concentration in astrocytes
• oscillatory mode
• stationary mode