Bifurcation Scenarios of a Modified Mathematical Model for Intracellular Ca<sup>2<em>+</sup></em> Oscillations

doi:10.1088/0256-307X/32/5/050501

Chin. Phys. Lett.

2015, Vol. 32

Issue (5): 050501 DOI: 10.1088/0256-307X/32/5/050501

GENERAL

Bifurcation Scenarios of a Modified Mathematical Model for Intracellular Ca²⁺ Oscillations

JI Quan-Bao¹, ZHOU Yi¹, YANG Zhuo-Qin², MENG Xiang-Ying^3**

¹School of Mathematics and Computational Science, Huainan Normal University, Huainan 232038
²School of Mathematics and Systems Science and LMIB, Beihang University, Beijing 100191
³Department of Biology, University of Maryland, College Park, Maryland 20742, USA

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JI Quan-Bao, ZHOU Yi, YANG Zhuo-Qin et al 2015 Chin. Phys. Lett. 32 050501

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Abstract The contribution of this work is the modification of a mathematical model for bursting Ca²⁺ oscillations by introducing the proportion of receptors not inactivated by Ca²⁺ as a new variable. Generation mechanisms of different oscillatory patterns in this modified model are investigated and classified, based on fast/slow dynamical analysis. It is shown that periodic oscillations appear around the original chaotic regions. Moreover, two new types of oscillatory phenomena are observed at the sustaining region. The results may be instructive for understanding the difference between direct observation of dynamical behavior in real cells and theoretical explanations under a variety of stimulus conditions.

Received: 04 December 2014 Published: 01 June 2015

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	82.40.Bj	(Oscillations, chaos, and bifurcations)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/32/5/050501 OR https://cpl.iphy.ac.cn/Y2015/V32/I5/050501

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	JI Quan-Bao
	ZHOU Yi
	YANG Zhuo-Qin
	MENG Xiang-Ying

[1] Berridge M J, Bootman M D and Lipp P 1998 Nature 395 645
[2] Matrosov V V and Kazantsev V 2011 Chaos 21 023103
[3] Domijan M, Murray R and Sneyd J 2006 J. Nonlinear Sci. 16 483
[4] Kashir J, Jones C and Coward K 2012 Adv. Exp. Med. Biol. 740 1095
[5] Izhikevich E M 2000 Int. J. Bifurcation Chaos Appl. Sci. Eng. 10 1171
[6] Perc M and Marhl M 2003 Chaos Solitons Fractals 18 759
[7] Borghans J A M, Dupont G and Goldbeter A 1997 Biophys. Chem. 66 25
[8] Zhang F, Lu Q S and Su J Z 2009 Chaos Solitons Fractals 41 2285
[9] Ji Q B and Lu Y 2013 Int. J. Bifurcation Chaos Appl. Sci. Eng. 23 1350033
[10] Zhang F, Lu Q S and Duan L X 2007 Chin. Phys. Lett. 24 3344
[11] Meng P and Lu Q S 2010 Chin. Phys. Lett. 27 010502
[12] Gu H G, Pan B B and Xu J 2014 Europhys. Lett. 106 50003
[13] Li X H and Bi Q S 2013 Chin. Phys. Lett. 30 070503
[14] Li X H and Bi Q S 2013 Chin. Phys. Lett. 30 010503
[15] Wu X B, Mo J, Yang M H, Zheng Q H, Gu H G and Ren W 2008 Chin. Phys. Lett. 25 2799

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