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

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Abstract

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.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 11202083 and 11372017).

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Authors and Affiliations

  1. School of Finance, Huainan Normal University, Huainan, 232038, China

    Quanbao Ji & Yi Zhou

  2. School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China

    Zhuoqin Yang

  3. Department of Biology, University of Maryland, College Park, MD, 20742, USA

    Xiangying Meng

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  1. Quanbao Ji
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  2. Yi Zhou
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  4. Xiangying Meng
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Correspondence to Zhuoqin Yang.

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Ji, Q., Zhou, Y., Yang, Z. et al. Evaluation of bifurcation phenomena in a modified Shen–Larter model for intracellular \(\hbox {Ca}^{\varvec{2+}}\) bursting oscillations. Nonlinear Dyn 84, 1281–1288 (2016). https://doi.org/10.1007/s11071-015-2566-3

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  • DOI: https://doi.org/10.1007/s11071-015-2566-3

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