Evaluation of bifurcation phenomena in a modified Shen–Larter model for intracellular \[\hbox {Ca}^{\varvec{2+}}\] bursting oscillations

• Published in: Nonlinear dynamics 2016-05, Vol.84 (3), p.1281-1288
• Main Authors: Ji, Quanbao, Zhou, Yi, Yang, Zhuoqin, Meng, Xiangying
• Format: Article
• Language: English
• Subjects: Bifurcations; Bursting; Calcium; Calcium ions; Endoplasmic reticulum; Mathematical models; Oscillations; Receptors; Stimulation; Subsystems; Time lag
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-015-2566-3

The present work describes an evaluation of the bifurcation phenomena in a modified Shen–Larter model based on calcium-induced calcium release and inositol triphosphate \[(\hbox {IP}_{3})\] crosscoupling for calcium ion \[(\hbox {Ca}^{2+})\] bursting oscillations. A time delay for negative \[\hbox {Ca}^{2+}\] feedback on the \[(\hbox {IP}_{3})\] receptor is added to the original Shen–Larter model, by introducing the proportion of receptors not inactivated by \[\hbox {Ca}^{2+}\] as a new variable. Compared with the original model, the number of chaotic regions for a stimulation level r is significantly reduced, and regions of \[\hbox {Ca}^{2+}\] oscillations (particularly bursting) appear to become slightly enlarged. Different topological types of bursting oscillations in this modified model are classified by fast/slow dynamical analysis and codimension-2 bifurcations of fast subsystem, when choosing better of two slow variables the free \[\hbox {Ca}^{2+}\] concentration in the endoplasmic reticulum and the \[\hbox {IP}_{3}\] concentration in the cytosol. Furthermore, classification and transition mechanisms of bursting \[\hbox {Ca}^{2+}\] oscillations could help to understand or detect more distinctive oscillatory behaviors of real cells in response to different levels of stimulation.