Bursting, Chaos and Birhythmicity Originating from Self-modulation of the Inositol 1,4,5-trisphosphate Signal in a Model for Intracellular Ca2+Oscillations

Abstract

We investigate the various types of complex Ca2+ oscillations which can arise in a model based on the mechanism of Ca2+-induced Ca2+ release (CICR), that takes into account the Ca2+-stimulated degradation of inositol 1,4,5-trisphosphate (InsP3) by a 3-kinase. This model was previously proposed in the course of an investigation of plausible mechanisms capable of generating complex Ca2+ oscillations. Besides simple periodic behavior, this model for cytosolic Ca2+ oscillations in nonexcitable cells shows complex oscillatory phenomena like bursting or chaos. We show that the model also admits a coexistence between two stable regimes of sustained oscillations (birhythmicity). The occurrence of these various modes of oscillatory behavior is analysed by means of bifurcation diagrams. Complex oscillations are characterized by means of Poincaré sections, power spectra and Lyapounov exponents. The results point to the role of self-modulation of the InsP3 signal by 3-kinase as a possible source for complex temporal patterns in Ca2+ signaling.

Ca2+-induced delayed afterdepolarizations are triggered by dyadic subspace Ca2+ affirming that increasing SERCA reduces aftercontractions

“…These approaches did not reflect the fact that DADs are a general phenomenon of atrial, Purkinje, and ventricular cells across species, as shown by the respective findings in the mouse, rat, guinea pig, ferret, rabbit, feline, canine, calf, sheep, and human (40, 56, 69, 77, 84, 87, 94 -96, 103, 105). Ca 2ϩ oscillations have also been found in sinoatrial node cells, pancreatic ␤-cells, astrocytes, and others (5,29,45,46,55,64,72) (see also Table 1).…”

“…These approaches did not reflect the fact that DADs are a general phenomenon of atrial, Purkinje, and ventricular cells across species, as shown by the respective findings in the mouse, rat, guinea pig, ferret, rabbit, feline, canine, calf, sheep, and human (40, 56, 69, 77, 84, 87, 94 -96, 103, 105). Ca 2ϩ oscillations have also been found in sinoatrial node cells, pancreatic ␤-cells, astrocytes, and others (5,29,45,46,55,64,72) (see also Table 1).In this work, we focused on investigating the properties and underlying mechanisms of DADs in 37 different mathematical cell models of Purkinje, atrial, and ventricular cells from the human, dog, guinea pig, rabbit, rat, and mouse (see Tables 2 and 3). This broad range helped to ensure that the results were not model dependent (in regard to species or model formulation) while they reflected the summarized knowledge from many different experimental results.…”

Computation and stability analysis of Hopf Bifurcation in biophysical system model of cells

“…Based on calciuminduced calcium release (CICR) and the inositol trisphosphate cross-coupling (ICC), Shen et al gave an early theoretical study of complex Ca 2+ oscillations trying to describe bursting Ca 2+ oscillations in nonexcitable cells [11]. A more detailed study of different mechanisms explaining the Ca 2+ oscillations in non-excitable cells have been given by Borghans [2] and further mathematically analyzed by Houart, et al [3,4,7,12]. Synchronization behaviors of non-excitable cells by gap junction coupling were explored by Huo and Zhou, and the threshold values of synchronization for identical and un-identical oscillators were computed numerically [8].…”

Different types of bursting calcium oscillations in non-excitable cells

“…Although the models for bursting Ca 2þ oscillations in non-excitable cells were present for several years, different types of bursting Ca 2þ oscillations appearing in these models were studied only moderately [29,[38][39][40][41]. Several bursting patterns, including simple duplets, entangled regular as well as chaotic bursting Ca 2þ oscillations were found.…”

“…Several bursting patterns, including simple duplets, entangled regular as well as chaotic bursting Ca 2þ oscillations were found. Additionally, the occurrence of birhythmicity [39] as well as trirhythmicity and intermittency for chaotic bursting Ca 2þ oscillations [40] was examined. However, a mathematical classification of different types of bursting was made only for the model proposed by Kummer et al [31,41].…”