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Marhl et al. (2000), Calcium Oscillations

July 2008, model of the month by Lu Li
Original model: BIOMD0000000039

Calcium oscillations are important for intracellular signalling both in excitable and non-excitable cells. The endoplasmic reticulum (ER) is thought to be a major calcium store and responsible for sustained calcium oscillations. It is not clear, however, how other calcium stores, such as mitochondria, and calcium binding proteins (CBPs) cooperate with the ER in regulating this process.

Besides, many experimental results have shown that calcium always oscillates in a more complex manner: During the active phase the system exhibits bursting [1]. There have been several explanations for this form of complex oscillation [1-4], but none of them considers intracellular calcium stores other than the ER.

In this present paper ([5], BIOMD0000000039), Marhl et al. provide another possible mechanism for this complex oscillation. By setting up a three-compartment mathematical model (Fig. 1), including ER, mitochondria, and cytosol, they concluded that the complex calcium oscillations are the result of interplay between three calcium stores.

Three compartment model by Marhl et al.

Figure 1: Three compartment model used by Marhl et al., figure taken from [5].

Calcium spikes

Figure 2: Calcium spikes, figure taken from [5].

Phases of calcium release

Figure 3: Phases of calcium release, figure taken from [5].

Firstly, high frequency bursting oscillation and basic simple calcium spikes were observed (Fig. 2). Then, the authors analysed one cycle in detail. The first high amplitude calcium spike is the result of fast calcium release from the ER in phase I, as shown in Fig.3. In phase II, the fast exchange of calcium between ER and cytosol forms small, but fast bursting oscillations. Meanwhile, the slow release of calcium from mitochondria facilitates the steady binding of calcium to cytosolic buffer proteins. Finally, the silent phase (phase III) begins, during which the dissociation of calcium from cytosolic proteins is predominant. To summarise, calcium oscillation is driven by the exchange of calcium among the three calcium stores: ER, mitochondria, and cytosolic proteins. In addition, the kinetic properties of ER and cytosolic calcium binding proteins are crucial for the creation of high frequency calcium bursting oscillations.

In order to support the above conclusion, the authors further examined how the change of kch (a kinetic parameter describing calcium efflux from ER through calcium-induced calcium release (CICR)) affects the limit cycle and the frequency of bursting. When kch is 4100 (per second), there is only one cycle when plotting calcium in mitochondria against cytosol (Fig. 4); when kch is reduced to 4000 (per second), there is a two-fold limit cycle (Fig. 5). As a consequence, two different spiking patterns with different frequencies of bursting repeatedly appear, as shown in Fig. 6 (only two cycles are presented). When kch is further reduced to 2000 (per second), there is only one cycle and no bursting oscillations appear (Fig.7, 8). This indicates that when calcium cannot be released from the ER quickly, and thus cannot facilitate fast exchange between ER and cytosolic calcium binding proteins, there is no bursting but only simple oscillations appear (Fig. 4-8 were reproduced using XPPAUT).

One limit cycle at high kch values

Figure 4: Single limit cycle for kch=4100 s-1. Figure generated using XPPAUT

Two-fold limit cycle at intermediate kch values

Figure 5: Two-fold limit cycle for kch=4000 s-1. Figure generated using XPPAUT

intermediate kch values: time scale

Figure 6: Time scale shown for kch=4000 s-1. Figure generated using XPPAUT

One limit cycle at low kch values

Figure 7: Single limit cycle for kch=2000 s-1. Figure generated using XPPAUT

Figure 8

Figure 8: Time scale shown for kch=2000 s-1. Figure generated using XPPAUT

To summarise, Marhl et al. present a possible mechanism for complex calcium oscillations. Complementing other theories that do not consider mitochondria, authors emphasise the slow Ca release from mitochondria is important for complex oscillation, since it facilitates the fast calcium exchange between cytosolic calcium buffer proteins and ER.

Bibliographic References

  1. J. M. Borghans, G. Dupont, and A. Goldbeter. Complex intracellular calcium oscillations A theoretical exploration of possible mechanisms. Biophys Chem 66:25-41, 1997. [SRS@EBI]
  2. V. A. Golovina and M. P. Blaustein. Spatially and functionally distinct Ca2+ stores in sarcoplasmic and endoplasmic reticulum. Science 275:1643-1648, 1997. [SRS@EBI]
  3. G. Houart, G. Dupont, and A. Goldbeter. Bursting, chaos and birhythmicity originating from self-modulation of the inositol 1,4,5-trisphosphate signal in a model for intracellular Ca2+ oscillations. Bull Math Biol 61:507-530, 1999. [SRS@EBI]
  4. P. Shen and R. Larter. Chaos in intracellular Ca2+ oscillations in a new model for non-excitable cells. Cell Calcium 17:225-232, 1995. [SRS@EBI]
  5. M. Marhl, T. Haberichter, M. Brumen, and R. Heinrich. Complex calcium oscillations and the role of mitochondria and cytosolic proteins. Biosystems 57(2):75-86, 2000. [SRS@EBI]
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