Switching from Simple to Complex Oscillations in Calcium Signaling

Abstract

We present a new model for calcium oscillations based on experiments in hepatocytes. The model considers feedback inhibition on the initial agonist receptor complex by calcium and activated phospholipase C, as well as receptor type-dependent self-enhanced behavior of the activated G(alpha) subunit. It is able to show simple periodic oscillations and periodic bursting, and it is the first model to display chaotic bursting in response to agonist stimulations. Moreover, our model offers a possible explanation for the differences in dynamic behavior observed in response to different agonists in hepatocytes.

Different types of bursting calcium oscillations in non-excitable cells

“…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]. In the present paper, we provide a comparative mathematical classification of bursting types for all four recently proposed mathematical models [28][29][30][31] that account for complex intracellular calcium oscillations in non-excitable cells.…”

“…[23]) as well as in nonexcitable cells [24][25][26][27]. Trying to explain the mechanism of bursting Ca 2þ oscillations, several mathematical models for complex Ca 2þ oscillations in excitable [23] as well as in non-excitable cells [28][29][30][31] were proposed. Here, we focus on the models that describe bursting Ca 2þ oscillations in non-excitable cells [28][29][30][31].…”

“…Trying to explain the mechanism of bursting Ca 2þ oscillations, several mathematical models for complex Ca 2þ oscillations in excitable [23] as well as in non-excitable cells [28][29][30][31] were proposed. Here, we focus on the models that describe bursting Ca 2þ oscillations in non-excitable cells [28][29][30][31]. The first model, describing bursting Ca 2þ oscillations in non-excitable cells, was proposed by Shen and Larter [28].…”

“…Another CICR based model with the same set of model variables as in the previous model [28] was proposed by Borghans et al [29], however, with focusing on the effect of cytosolic calcium on the degradation of inositol trisphosphate (for equations see Model 2 in Appendix A). Another modelling approach represent models proposed by Marhl et al [30] and Kummer et al [31]. In the model by Marhl et al [30], the important role of mitochondria [35] and cytosolic Ca 2þ binding proteins [36,37] is taken into account.…”

“…The three main variables that describe the dynamics of the model system are: free Ca 2þ concentration in the cytosol (Ca cyt ), free Ca 2þ concentration in the ER (Ca er ), and the free Ca 2þ concentration in the mitochondria (Ca m ) (for equations see Model 3 in Appendix A). The model proposed by Kummer et al [31] incorporates the feedback inhibition on the initial agonist receptor complex by Ca 2þ and activated phospholipase C (PLC), as well as receptor type-dependent self-enhanced behaviour of the activated G a subunit. Consequently, the three main variables are: the concentration of the active G a subunit (G a ), the concentration of the active PLC (PLC) and the free Ca 2þ concentration in the cytosol (Ca cyt ) (for equations see Model 4 in Appendix A).…”