Abstract
We explore the dynamic behavior of a model of calcium oscillations and wave propagation in the basal region of pancreatic acinar cells [Sneyd, J., et al., Biophys. J. 85: 1392–1405, 2003]. Since it is known that two principal calcium release pathways are involved, inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR), we study how the model behavior depends on the density of each receptor type. Calcium oscillations can be mediated either by IPR or RyR. Continuous increases in either RyR or IPR density can lead to the appearance and disappearance of oscillations multiple times, and the two receptor types interact via their common effect on cytoplasmic calcium concentration and the subsequent effect on the total amount of calcium inside the cell. Increases in agonist concentration can stimulate oscillations via the RyR by increasing calcium influx. Using a two time-scale approach, we explain these complex behaviors by treating the total amount of cellular calcium as a slow parameter. Oscillations are controlled by the shape of the slow manifold and where it intersects the nullcline of the slow variable. When calcium diffusion is included, the existence of traveling waves in the model equation is strongly dependent on the interplay between the total amount of calcium in the cell and membrane transport, a feature that can be experimentally tested. Our results help us understand the behavior of a model that includes both receptors in comparison to the properties of each receptor type in isolation.
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Albrecht, M.A., Colegrove, S.L., Friel, D.D., 2002. Differential regulation of ER calcium uptake and release rates accounts for multiple modes of Ca2+-induced Ca2+ release. J. Gen. Physiol. 119, 211–233.
Ashby, M.C., Craske, M., Park, M.K., Gerasimenko, O.V., Burgoyne, R.D., Petersen, O.H., Tepikin, A.V., 2002. Localized Ca2+ uncaging reveals polarized distribution of Ca2+-sensitive Ca2+ release sites: mechanism of unidirectional Ca2+ waves. J. Cell Biol. 158, 283–292.
Camello, P., Gardner, J., Petersen, O.H., Tepikin, A.V., 1996. Calcium dependence of calcium extrusion and calcium uptake in mouse pancreatic acinar cells. J. Physiol. 85, 490–593.
Cancela, J.M., Van Coppenolle, F., Galione, A., Tepikin, A.V., Petersen, O.H., 2002. Transformation of local Ca2+ spikes to global Ca2+ transients: The combinatorial roles of multiple Ca2+ releasing messengers. EMBO J. 21, 909–919.
Doedel, E., 1986. Software for continuation and bifurcation problems in ordinary differential equations. California Institute of Technology, California.
Dupont, G., Koukoui, O., Clair, C., Erneux, C., Swillens, S., Combettes, L., 2003. Ca2+ oscillations in hepatocytes do not require the modulation of InsP3-kinase activity by Ca2+. FEBS Lett. 534(1–3), 101–105.
Ermentrout, B., 2002. Simulating, Analyzing and Animating Dynamical Systems. SIAM, Philadelphia, PA. http://www.math.pitt.edu/~bard/xpp/xpp.html
Favre, C.J., Jacquet, J., Lew, D.P., Krause, K.H., 1996. Highly supralinear feedback inhibition of Ca2+ uptake by the Ca2+ load of intracellular stores. J. Biol. Chem. 271, 14925–14930.
Fogarty, K.E., Kidd, J.F., Tuft, D.A., Thorn, P., 2000. Mechanisms underlying InsP3-evoked global Ca2+ signals in mouse pancreatic acinar cells. J. Physiol. 526, 515–526.
Galione, A., McDougall, A., Busa, W.B., Willmott, N.,Gillot, I., Whitaker, M., 1993. Redundant mechanisms of calcium-induced calcium release underlying calcium waves during fertilization of sea urchin eggs. Science 261(5119), 348–352.
Gin, E., Kirk, V., Sneyd. J., 2006. A bifurcation analysis of calcium buffering, Bulletin of Mathematical Biology, in press.
Giovannucci, D.R., Bruce, J.I., Straub, S.V., Arreola, J., Sneyd, J., Shuttleworth, T.J., Yule, D.I., 2002. Cytosolic Ca2+ and Ca2+-activated Cl− current dynamics: Insights from two functionally distinct mouse exocrine cells. J. Physiol. 540, 469–484.
Goldbeter, A., 2002. Computational approaches to cellular rhythms. Nature 420, 238–245.
Kasai, H., 1995. Pancreatic calcium waves and secretion. Ciba Found. Symp. 188, 104–116.
Kasai, H., Li, Y.-X., Miyashita, Y., 1993. Subcellular distribution of Ca2+ release channels underlying Ca2+ waves and oscillations in exocrine pancreas. Cell. 74, 669–677.
Keener, J.P., Sneyd, J., 1998. Mathematical Physiology. Springer-Verlag, New York.
Keizer, J., Levine, L., 1996. Ryanodine receptor adaptation and Ca2+-induced Ca2+ release-dependent Ca2+ oscillations. Biophys. J. 71, 3477–3487.
LeBeau, A.P., Yule, D.I., Groblewski, G.E., Sneyd, J., 1999. 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, 851–872.
Leite, M.F., Burgstahler, A.D., Nathanson, M.H., 2002. Ca2+ waves require sequential activation on inositol trisphosphate receptors and ryanodine receptors in pancreatic acini. Gastroenterology 122, 415–427.
MacLennan, D.H., Rice, W.J., Green, N.M., 1997. The mechanism of Ca2+ transport by sarco(endo)plasmic reticulum Ca2+-ATPases. J. Biol. Chem. 272, 28815–28818.
Mogami, H., Tepikin, A.V., Petersen, O.H., 1998. Termination of cytosolic Ca2+ signals: Ca2+ reuptake into intracellular stores is regulated by the free Ca2+ concentration in the store lumen. EMBO J. 17, 435–442.
Murray, J.D., 1989. Mathematical Biology. Springer-Verlag, Berlin.
Nash, M.S, Kenneth, W.Y., Challiss, R.A.J., Nahorski, S.R., 2001. Receptor-specific messenger oscillations. Nature 413, 381–382.
Nathanson, M.H., Padfield, P.J., O'Sullivan, A.J., Burgstahler, A.D., Jamieson, J.D., 1992. Mechanism of Ca2+ wave propagation in pancreatic acinar cells. J. Biol. Chem. 267, 18118–18121.
Petersen, O.H., 2002. Calcium signal compartmentalization. Biol. Res. 35, 177–182.
Petersen, O.H., 1995. Local calcium spiking in pancreatic acinar cells. Ciba Found. Symp. 188, 85–103.
Petersen, O.H., Burdakov, D., Tepikin, A.V., 1999. Polarity in intracellular calcium signaling. Bioessays 21, 851–860.
Schuster, S., Marhl, M., Hofer, T., 2002. Modelling of simple and complex calcium james-dufouroscillations. From single-cell responses to intercellular signalling. Eur. J. Biochem. 269, 1333–1355.
Shuttleworth, T.J., 1999. What drives calcium entry during [Ca2+] i oscillations? Challenging the capacitative model. Cell Calcium 25, 237–246.
Simpson, D., Kirk, V., Sneyd, J., 2005. Complex oscillations and waves of calcium in pancreatic acinar cells. Physica D 200(3–4), 303–324.
Sneyd, J., Girard, S., Clapham, D., 1993. Calcium wave propagation by calcium-induced calcium release: an unusual excitable system. Bull. Math. Biol. 55, 315–344.
Sneyd, J., Tsaneva-Atanasova, K., Yule, D.I., Thompson, J.L., Shuttleworth, T.J., 2004. Control of calcium oscillations by membrane fluxes. Proc. Natl. Acad. Sci. USA 101(5), 1392–1396.
Sneyd, J., Tsaneva-Atanasova, K., Bruce, J.I.E., Straub, S.V., Giovannucci, D.R., Yule, D.I., 2003. A Model of Calcium Waves in Pancreatic and Parotid Acinar Cells. Biophys. J. 85, 1392–1405.
Sneyd, J., Dufour, J.F., 2002. A dynamic model of the type-2 inositol trisphosphate receptor. Proc. Natl. Acad. Sci. USA 99, 2398–2403.
Straub, S.V., Giovannucci, D.R., Yule, D.I., 2000. Calcium wave propagation in pancreatic acinar cells: functional interaction of inositol 1,4,5-trisphosphate receptors, ryanodine receptors, and mitochondria. J. Gen. Physiol. 116, 547–560.
Thorn, P., 1996. Spatial domains of Ca2+ signalling in secretory epithelial cells. Cell Calcium 20, 203–214.
Thorn, P., 1993. Spatial aspects of Ca2+ signalling in pancreatic acinar cells. J. Exp. Biol. 184, 129–144.
Thorn, P., Lawrie, A.M., Smith, P.M., Gallacher, D.V., Petersen, O.H., 1993a. Ca2+ oscillations in pancreatic acinar cells: Spatiotemporal relationships and functional implications. Cell Calcium 14, 746–757.
Thorn, P., Lawrie, A.M., Smith, P.M., Gallacher, D.V., Petersen, O.H., 1993b. Local and global cytosolic Ca2+ oscillations in exocrine cells evoked by agonists and inositol trisphosphate. Cell 74, 661–668.
Tsaneva-Atanasova, K., Shuttleworth, T.J., Yule, D.I., Thompson, J.L., Sneyd, J., 2004. Calcium oscillations and membrane transport: The importance of two time scales. SIAM J.Multiscale Model. Simul. 3, 245–264.
Wakui, M., Potter, B.V.L., Petersen, O.H., 1989. Pulsatile intracellular calcium release does not depend on fluctuations in inositol trisphosphate concentration. Nature 62, 339–358.
Xu, X., Zeng, W., Diaz, J., Muallem, S., 1996. Spatial compartmentalization of Ca2+ signaling complexes in pancreatic acini. J. Biol. Chem. 271, 24684–24690.
Yano, K., Petersen, O.H., Tepikin, A.V., 2004. Dual sensitivity of sarco-plasmic/endo-plasmic Ca2+-ATPase to cytosolic and endoplasmic reticulum Ca2+ as a mechanism of modulating cytosolic Ca2+ oscillations. Biochem J. 383, 353–356.
Yule, D.I., Stuenkel, E., Williams, J. A., 1996. Intercellular calcium waves in rat pancreatic acini: mechanism of transmission. Am. J. Physiol. 271, C1285–C1294.
Yule, D.I., Lawrie, A.M., Gallacher, D.V., 1991. Acetylcholine and cholecystokinin induce different patterns of oscillating calcium signals in pancreatic acinar cells. Cell Calcium. 12, 145–151.
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Ventura, A.C., Sneyd, J. Calcium Oscillations and Waves Generated by Multiple Release Mechanisms in Pancreatic Acinar Cells. Bull. Math. Biol. 68, 2205–2231 (2006). https://doi.org/10.1007/s11538-006-9101-0
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DOI: https://doi.org/10.1007/s11538-006-9101-0