Abstract
Calcium ions are an important second messenger in living cells. A fundamental approach for studying calcium signalling is the combination of state-of-the-art experimental techniques with spatiotemporal mathematical models of calcium regulation. Extensive modelling work on calcium oscillations and waves consists of a variety of theoretical/computational methods and models of different complexity. Some models can be assigned to a category of biologically realistic, detailed models, analysis of which is restricted to numerical methods. Other models can be placed in a category of simplified, minimal models susceptible to mathematical analysis. In this chapter, we provide an overview of a number of models for intracellular calcium dynamics belonging to both categories. Both types of models complement each other nicely and are vital for a better understanding of the complex mechanisms involved in cellular calcium signalling.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berridge MJ (2005) Unlocking the secrets of cell signalling. Ann Rev Physiol 67:1–21
Berridge MJ (2009) Inositol trisphosphate and calcium signalling mechanisms. Biochimica et Biophysica Acta 1793:933–940
Berridge MJ, Lipp P, Bootman MD (2000) The versatility and universality of calcium signalling. Nat Rev Mol Cell Biol 1:11–21
Berridge MJ, Bootman MD, Roderick HL (2003) Calcium signalling: dynamics, homeostasis and remodelling. Nat Rev Mol Cell Biol 4:517–529
Bezprozvanny I, Watras J, Ehrlich BE (1991) Bell-shaped calcium-response curves of Ins(1,4,5)P\(_3\)-and calcium-gated channels from endoplasmic reticulum of cerebellum. Nature 351:751–754
Boitano S, Dirksen ER, Sanderson MJ (1992) Intercellular propagation of calcium waves mediated by inositol trisphosphate. Science 258:292–294
Bootman MD, Berridge MJ, Putney JW, Roderick HL (eds) (2011) Calcium signaling. Cold Spring Harbor Laboratory Press, New York
Carafoli E (2002) Calcium signaling: a tale for all seasons. Proc Natl Acad Sci USA 99(3):1115–1122
Cheng H, Lederer WJ (2008) Calcium sparks. Physiol Rev 88:1491–1545
Clapham DE (2007) Calcium signaling. Cell 131:1047–1058
Combettes L, Dupont G, Parys JB (2004) New mechanisms and functions in Ca\(^{2+}\) signalling. Biol Cell 96:1–2
Coombes S (2001) The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of Ca\(^{2+}\) release. Bull Math Biol 63:1–20
Coombes S, Timofeeva Y (2003) Sparks and waves in a stochastic fire-diffuse-fire model of calcium release. Phys Rev E 68(021):915
Coombes S, Hinch R, Timofeeva Y (2004) Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release. Prog Biophys Mol Biol 85:197–216
Cornell-Bell AH, Finkbeiner SM, Cooper MS, Smith SJ (1990) Glutamate induces calcium waves in cultured astrocytes: long-range glial signaling. Science 247(4941):470–473
Dupont G, Tordjmann T, Clair C, Swillens S, Claret M, Combettes L (2000) Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes. FASEB J 14(2):279–289
Dupont G, Combettes L, Leybaert L (2007) Calcium dynamics: spatio-temporal organization from the subcellular to the organ level. Int Rev Cytol 261:193–245
Dupont G, Falcke M, Kirk V, Sneyd J (2016) Models of calcium signalling. Springer, Interdisciplinary Applied Mathematics
Endo M, Tanaka M, Ogawa Y (1970) Calcium induced release of calcium from the sarcoplasmic reticulum of skinned skeletal muscle fibres. Nature 228:34–36
Ermentrout GB (2002) Simulating, analysing, and animating dynamical systems: a guide to XPPAUT for researchers and students. SIAM, Philadelphia
Falcke M (2003) Deterministic and stochastic models of intracellular Ca\(^{2+}\) waves. New J Phys 5:96.1–96.28
Falcke M (2004) Reading the patterns in living cells - the physics of Ca\(^{2+}\) signaling. Adv Phys 53(3):255–440
Falcke M, Tsimring L, Levine H (2000) Stochastic spreading of intracellular Ca\(^{2+}\) release. Phys Rev E 62:2636–2643
FitzHugh R (1961) Impulses and physiological states in models of nerve membrane. Biophys J 1:445–466
Goldbeter A (1996) Biochemical oscillations and cellular rhythms: the molecular bases of periodic and chaotic behaviour. Cambridge University Press, Cambridge
Goldbeter A, Dupont G, Berridge MJ (1990) Minimal model for signal-induced Ca\(^{2+}\) oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci USA 87:1461–1465
Goldbeter A, Gérard C, Gonze D, Leloup J, Dupont G (2012) Systems biology of cellular rhythms. FEBS Lett 586:2955–2965
Harris J, Timofeeva Y (2010) Intercellular calcium waves in the fire-diffuse-fire framework: green’s function for gap-junctional coupling. Phys Rev E 82(051):910
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544
Izu LT, Wier WG, Balke CW (2001) Evolution of cardiac waves from stochastic calcium sparks. Biophys J 80:103–120
Jaffe LF (1993) Classes and mechanisms of calcium waves. Cell Calcium 14:736–745
Kaneko T, Tanaka H, Oyamada M, Kawata S, Takamatsu T (2000) Three distinct types of Ca\(^{2+}\) waves in Langendorff-perfused rat heart revealed by real-time confocal microscopy. Circ Res 86:1093–1099
Keizer JE, Smith GD (1998) Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes. Biophys Chem 72:87–100
Keizer JE, Smith GD, Dawson SP, Pearson J (1998) Saltatory propagation of Ca\(^{2+}\) waves by Ca\(^{2+}\) sparks. Biophys J 75:595–600
Krebs J, Michalak M (eds) (2007) Calcium: a matter of life or death, New comprehensive biochemistry, vol 41. Elsevier Science
Kupferman R, Mitra PP, Hohenberg PC, Wang SSH (1997) Analytical calculation of intracellular calcium wave characteristics. Biophys J 72:2430–2444
Lechleiter J, Girard S, Peralta E, Clapham D (1991) Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. Science 252:123–126
Leybaert L, Sanderson MJ (2012) Intercellular Ca\(^{2+}\) waves: mechanisms and function. Physiol Rev 92:1359–1392
Li YX, Rinzel J (1994) Equations for InsP\(_3\) receptor-mediated [Ca\(^{2+}\)] oscillations derived from a detailed kinetic model: a hodgkin-huxley like formalism. J Theor Biol 166:461–473
Lipp P, Niggli E (1993) Microscopic spiral waves reveal positive feedback in subcellular calcium signaling. Biophys J 65:2272–2276
Marchant JS, Parker I (2001) Role of elementary Ca\(^{2+}\) puffs in generating repetitive Ca\(^{2+}\) oscillations. EMBO J 20:65–76
Mikoshiba K (2007) IP\(_3\) receptor/Ca\(^{2+}\) channel: from discovery to new signaling concepts. J Neurochem 102:1426–1446
Miyazaki S (2006) Thirty years of calcium signals at fertilization. Semin Cell Dev Biol 17:233–243
Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulation nerve axon. Proc IRE 50:2061–2070
Paemeleire K, Martin PEM, Coleman SL, Fogarty KE, Carrington WA, Leybaert L, Tuft RA, Evans WH, Sanderson MJ (2000) Intercellular calcium waves in HeLa cells expressing GFP-labeled connexin 43, 32, or 26. Mol Biol Cell 11(5):1815–1827
Parekh AB (2011) Decoding cytosolic Ca\(^{2+}\) oscillations. Trends Biochem Sci 36(2):78–87
Parker I, Ivorra I (1990) Inhibition by Ca\(^{2+}\) of inositol trisphosphate-mediated Ca\(^{2+}\) liberation: a possible mechanism for oscillatory release of Ca\(^{2+}\). Proc Natl Acad Sci USA 87:260–264
Petersen OH, Michalak M, Verkhratsky A (2005) Calcium signalling: past, present and future. Cell Calcium 38:161–169
Rizzuto R, Pozzan T (2006) Microdomains of intracellular ca\(^{2+}\): molecular determinants and functional consequences. Physiol Rev 86:369–408
Røttingen JA, Iversen JG (2000) Ruled by waves? Intracellular and intercellular calcium signalling. Acta Physiol Scand 169:203–219
Scemes E, Giaume C (2006) Astrocyte calcium waves: what they are and what they do. Glia 54:716–725
Schuster S, Marhl M, Höfer T (2002) Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling. Eur J Biochem 269:1333–1355
Slepchenko BM, Schaff JC, Choi YS (2000) Numerical approach to fast reactions in reaction-diffusion systems: application to buffered calcium waves in bistable models. J Comput Phys 162:186–218
Sneyd J, Falcke M (2005) Models of the inositol trisphosphate receptor. Prog Biophys Mol Biol 89:207–245
Sneyd J, Tsaneva-Atanasova K (2003) Understanding calcium dynamics: experiments and theory, Springer, chap Modeling calcium waves, pp 179–199
Sneyd J, Dale P, Duffy A (1998) Traveling waves in buffered systems: applications to calcium waves. SIAM J Appl Math 58:1178–1192
Sneyd J, LeBeau A, Yule D (2000) Traveling waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis. Phys D 145:158–179
Stokes DL, Green NM (2003) Structure and function of the calcium pump. Ann Rev Biophys Biomol Struct 32:445–468
Takamatsu T, Wier WG (1990) Calcium waves in mammalian heart: quantification of origin, magnitude, waveform, and velocity. FASEB J 4:1519–1525
Thomas AP, Renard DC, Rooney TA (1991) Spatial and temporal organization of calcium signalling in hepatocytes. Cell Calcium 12:111–126
Thul R, Coombes S, Roderick HL, Bootman MD (2012) Subcellular calcium dynamics in a whole-cell model of an atrial myocyte. Proc Natl Acad Sci USA 109(6):2150–2155
Timofeeva Y, Coombes S (2003) Wave bifurcation and propagation failure in a model of calcium release. J Math Biol 47:249–269
Toma I, Bansal E, Meer EJ, Kang JJ, Vargas SL, Peti-Peterdi J (2008) Connexin 40 and ATP-dependent intercellular calcium wave in renal glomerular endothelial cells. Am J Physiol - Regul Integr Comp Physiol 294(6):R1769–R1776
Wagner J, Keizer J (1994) Effects of rapid buffers on Ca\(^{2+}\) diffusion and Ca\(^{2+}\) oscillations. Biophys J 67:447–456
Wang Z, Haydon PG, Yeung ES (2000) Direct observation of calcium-independent intercellular ATP signaling in astrocytes. Anal Chem 72(9):2001–2007
Young GD, Keizer J (1992) A single pool IP\(_3\)-receptor based model for agonist-stimulated Ca\(^{2+}\) oscillations. Proc Natl Acad Sci USA 89:9895–9899
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Timofeeva, Y. (2019). Intracellular Calcium Dynamics: Biophysical and Simplified Models. In: De Pittà , M., Berry, H. (eds) Computational Glioscience. Springer Series in Computational Neuroscience. Springer, Cham. https://doi.org/10.1007/978-3-030-00817-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-00817-8_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00815-4
Online ISBN: 978-3-030-00817-8
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)