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Bindschadler and Sneyd (2001), Coupled Calcium Oscillators

April 2007, model of the month by Melanie Stefan
Original model: BIOMD0000000058

In a variety of tissues, coordination between neighbouring cells is mediated by waves of intercellular calcium (reviewed in [1]). But beyond their obvious biological interest, the nonlinear behaviour of intercellular calcium waves lends itself to thorough mathematical analysis (reviewed in [2]). It is therefore not surprising that a number of models have been developed to inverstigate the mechanisms of calcium oscillations (see [3], [4] - BIOMD0000000043, BIOMD0000000044, and BIOMD0000000045, [5], [6], [7] - BIOMD0000000039, [8] - BIOMD0000000059).

The model by Bindschadler and Sneyd [9] examines calcium oscillations in acinar cells of the pancreas. These cells secrete digestive enzymes, a process which is controlled by calcium. The release of calcium from intracellular stores is mediated by inositol trisphosphate (IP-3) (reviewed in [10]). In the model presented here, while each cell is an oscillator by itself, neighbouring cells are coupled through the diffusion of calcium between them [9]. Based on an earlier model of calcium oscillations in acinar cells [11], the authors examined the behaviour of calcium waves in two coupled neighbouring cells. The model includes IP-3 receptor opening, closing, and subsequent desensitation as functions of calcium concentration, as well as calcium entering and leaving the cytoplasm, and calcium diffusion between two neighbouring cells.

antiphase oscillations in identical cells

Figure 1: Same-amplitude antiphase oscillations in identical cells. Results of a simulation reproducing Figure 5b of [9]. Simulation result obtained from MathSBML.

multiperiodic oscillations in different cells

Figure 2: Multiperiodic oscillation behaviour in different cells. From [9].

The authors observed a range of different possible behaviours, depending on IP-3 concentration and diffusion coefficient. Two identical cells, when coupled, can show synchronised oscillation, nearly in-phase oscillations of different amplitudes, and antiphase oscillations. Figure 1 shows an example of same-amplitude antiphase oscillations in identical neighbouring cells. If both cells are different, the picture is less simple. The authors have examined this case using cells with different IP-3 receptor densities. Emerging behaviours were more complex, and included multiperiodic solutions, as shown in figure 2.

Although the model does not go into much biological detail, it has served to explore what types of behaviour are possible for neighbouring cells. It has also shown how a wide range of behaviours can be explained by the same common mechanism, with variations in a small number of parameters. Efforts on further elucidating the dynamics of calcium waves in coupled cells are still ongoing, with more recent work considering the diffusion of not only calcium, but also IP-3 between adjacent cells (e.g. [12], [13]).

Bibliographic References

  1. M.J. Sanderson, A.C. Charles, S. Boitano, and E.R. Dirksen. Mechanisms and function of intercellular calcium signaling. Mol Cell Endocrinol, 98(2):173-187, Jan 1994. [SRS@EBI]
  2. J. Sneyd, J. Keizer, and M.J. Sanderson. Mechanisms of calcium oscillations and waves: a quantitative analysis. FASEB J, 9(14):1463-1472, Nov 1995. [SRS@EBI]
  3. A. Goldbeter, G. Dupont, M.J. Berridge. Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci U S A, 87(4):1461-1465, Feb 1990. [SRS@EBI]
  4. J.M. Borghans, G. Dupont, and A. Goldbeter. Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms.Biophys Chem, 66(1):25-41, May 1997. [SRS@EBI]
  5. T. Höfer. Model of intercellular calcium oscillations in hepatocytes: synchronization of heterogeneous cells. Biophys J, 77(3):1244-1256, Sep 1999. [SRS@EBI]
  6. G. Dupont, T. Tordjmann, C. Clair, S. Swillens, M. Claret, and L. Combettes. Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes. FASEB J, 14(2):279-289, Feb 2000. [SRS@EBI]
  7. 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, Jul 2000. [SRS@EBI]
  8. L.E. Fridlyand, N. Tamarina, and L.H. Philipson. Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores. Am J Physiol Endocrinol Metab, 285(1):E138-E154, Jul 2003. [SRS@EBI]
  9. M. Bindschadler and J. Sneyd. A bifurcation analysis of two coupled calcium oscillators. Chaos, 11(1):237-246, Mar 2001. [SRS@EBI]
  10. J.A. Williams. Regulation of pancreatic acinar cell function. Curr Opin Gastroenterol, 22(5):498-504, Sep 2006. [SRS@EBI]
  11. A.P. LeBeau, D.I. Yule, G.E. Groblewski, and J. Sneyd. Agonist-dependent phosphorylation of the inositol 1,4,5-trisphosphate receptor: A possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells. J Gen Physiol, 113(6):851-872, Jun 1999. [SRS@EBI]
  12. D. Wu, Y. Jia, X. Zhan, L. Yang, and Q. Liu. Effects of gap junction to Ca(2+) and to IP(3) on the synchronization of intercellular calcium oscillations in hepatocytes. Biophys Chem, 113(2):145-154, Feb 2005. [SRS@EBI]
  13. G. Ullah, P. Jung, and A.H. Cornell-Bell. Anti-phase calcium oscillations in astrocytes via inositol (1, 4, 5)-trisphosphate regeneration. Cell Calcium, 39(3):197-208, Mar 2006. [SRS@EBI]