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2016 | OriginalPaper | Buchkapitel

3. Basic Modelling Principles: Deterministic Models

verfasst von : Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Erschienen in: Models of Calcium Signalling

Verlag: Springer International Publishing

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Abstract

The task of combining toolbox components into an overall model is neither simple nor easy.

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Literatur
Zurück zum Zitat Backx PH, de Tombe P, Van Deen J, Mulder BJM, ter Keurs H (1989) A model of propagating calcium-induced calcium release mediated by calcium diffusion. J Gen Physiol 93:963–77, DOI: 10.1085/jgp.93.5.963 CrossRef Backx PH, de Tombe P, Van Deen J, Mulder BJM, ter Keurs H (1989) A model of propagating calcium-induced calcium release mediated by calcium diffusion. J Gen Physiol 93:963–77, DOI: 10.​1085/​jgp.​93.​5.​963 CrossRef
Zurück zum Zitat van Breemen C, Fameli N, Evans AM (2013) Pan-junctional sarcoplasmic reticulum in vascular smooth muscle: nanospace Ca2+ transport for site- and function-specific Ca2+ signalling. J Physiol 591(8):2043–54, DOI: 10.1113/jphysiol.2012.246348 CrossRef van Breemen C, Fameli N, Evans AM (2013) Pan-junctional sarcoplasmic reticulum in vascular smooth muscle: nanospace Ca2+ transport for site- and function-specific Ca2+ signalling. J Physiol 591(8):2043–54, DOI: 10.​1113/​jphysiol.​2012.​246348 CrossRef
Zurück zum Zitat Britton N (1986) Reaction-Diffusion Equations and their Applications to Biology. Academic Press, LondonMATH Britton N (1986) Reaction-Diffusion Equations and their Applications to Biology. Academic Press, LondonMATH
Zurück zum Zitat De Young GW, Keizer J (1992) A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci USA 89(20):9895–9, DOI: 10.1073/pnas.89.20.9895 CrossRef De Young GW, Keizer J (1992) A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci USA 89(20):9895–9, DOI: 10.​1073/​pnas.​89.​20.​9895 CrossRef
Zurück zum Zitat Dupont G, Swillens S (1996) Quantal release, incremental detection, and long-period Ca2+ oscillations in a model based on regulatory Ca2+-binding sites along the permeation pathway. Biophys J 71(4):1714–22, DOI: 10.1016/s0006-3495(96)79373-6 CrossRef Dupont G, Swillens S (1996) Quantal release, incremental detection, and long-period Ca2+ oscillations in a model based on regulatory Ca2+-binding sites along the permeation pathway. Biophys J 71(4):1714–22, DOI: 10.​1016/​s0006-3495(96)79373-6 CrossRef
Zurück zum Zitat Dupont G, Koukoui O, Clair C, Erneux C, Swillens S, Combettes L (2003) Ca2+ oscillations in hepatocytes do not require the modulation of InsP3 3-kinase activity by Ca2+. FEBS Lett 534(1–3):101–5, DOI: 10.1016/s0014-5793(02)03789-4 CrossRef Dupont G, Koukoui O, Clair C, Erneux C, Swillens S, Combettes L (2003) Ca2+ oscillations in hepatocytes do not require the modulation of InsP3 3-kinase activity by Ca2+. FEBS Lett 534(1–3):101–5, DOI: 10.​1016/​s0014-5793(02)03789-4 CrossRef
Zurück zum Zitat Endo M, Tanaka M, Ogawa Y (1970) Calcium-induced release of calcium from the sarcoplasmic reticulum of skinned skeletal muscle fibres. Nature 228:34–6, DOI: 10.1038/228034a0 CrossRef Endo M, Tanaka M, Ogawa Y (1970) Calcium-induced release of calcium from the sarcoplasmic reticulum of skinned skeletal muscle fibres. Nature 228:34–6, DOI: 10.​1038/​228034a0 CrossRef
Zurück zum Zitat Fabiato A, Fabiato F (1978) Calcium-induced release of calcium from the sarcoplasmic reticulum of skinned cells from adult human, dog, cat, rabbit, rat, and frog hearts and from fetal and new-born rat ventricles. Ann N Y Acad Sci 307:491–522, DOI: 10.1111/j.1749-6632.1978.tb41979.x CrossRef Fabiato A, Fabiato F (1978) Calcium-induced release of calcium from the sarcoplasmic reticulum of skinned cells from adult human, dog, cat, rabbit, rat, and frog hearts and from fetal and new-born rat ventricles. Ann N Y Acad Sci 307:491–522, DOI: 10.​1111/​j.​1749-6632.​1978.​tb41979.​x CrossRef
Zurück zum Zitat Fameli N, van Breemen C, Kuo KH (2007) A quantitative model for linking Na+/Ca2+ exchanger to SERCA during refilling of the sarcoplasmic reticulum to sustain [Ca2+] oscillations in vascular smooth muscle. Cell Calcium 42(6):565–75, DOI: 10.1016/j.ceca.2007.02.001 CrossRef Fameli N, van Breemen C, Kuo KH (2007) A quantitative model for linking Na+/Ca2+ exchanger to SERCA during refilling of the sarcoplasmic reticulum to sustain [Ca2+] oscillations in vascular smooth muscle. Cell Calcium 42(6):565–75, DOI: 10.​1016/​j.​ceca.​2007.​02.​001 CrossRef
Zurück zum Zitat Fife P (1979) Mathematical aspects of reacting and diffusing systems, Springer Lecture Notes in Biomathematics, vol 28. Springer-Verlag, Berlin, DOI: 10.1007/978-3-642-93111-6 Fife P (1979) Mathematical aspects of reacting and diffusing systems, Springer Lecture Notes in Biomathematics, vol 28. Springer-Verlag, Berlin, DOI: 10.​1007/​978-3-642-93111-6
Zurück zum Zitat FitzHugh R (1969a) Impulses and physiological states in theoretical models of nerve membrane. In: Schwan HP (ed) Biological Engineering, McGraw-Hill, New York, pp 445–66 FitzHugh R (1969a) Impulses and physiological states in theoretical models of nerve membrane. In: Schwan HP (ed) Biological Engineering, McGraw-Hill, New York, pp 445–66
Zurück zum Zitat FitzHugh R (1969b) Mathematical models of excitation and propagation in nerve. In: Schwan H (ed) Biological Engineering, McGraw-Hill, New York, pp 1–85 FitzHugh R (1969b) Mathematical models of excitation and propagation in nerve. In: Schwan H (ed) Biological Engineering, McGraw-Hill, New York, pp 1–85
Zurück zum Zitat Gaspers LD, Bartlett PJ, Politi A, Burnett P, Metzger W, Johnston J, Joseph SK, Höfer T, Thomas AP (2014) Hormone-induced calcium oscillations depend on cross-coupling with inositol 1,4,5-trisphosphate oscillations. Cell Rep 9(4):1209–18, DOI: 10.1016/j.celrep.2014.10.033 CrossRef Gaspers LD, Bartlett PJ, Politi A, Burnett P, Metzger W, Johnston J, Joseph SK, Höfer T, Thomas AP (2014) Hormone-induced calcium oscillations depend on cross-coupling with inositol 1,4,5-trisphosphate oscillations. Cell Rep 9(4):1209–18, DOI: 10.​1016/​j.​celrep.​2014.​10.​033 CrossRef
Zurück zum Zitat Glass L, Mackey M (1988) From Clocks to Chaos. Princeton University Press, PrincetonMATH Glass L, Mackey M (1988) From Clocks to Chaos. Princeton University Press, PrincetonMATH
Zurück zum Zitat Goldbeter A, Dupont G, Berridge M (1990) Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci USA 87:1461–5, DOI: 10.1073/pnas.87.4.1461 CrossRef Goldbeter A, Dupont G, Berridge M (1990) Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci USA 87:1461–5, DOI: 10.​1073/​pnas.​87.​4.​1461 CrossRef
Zurück zum Zitat Grindrod P (1991) Patterns and Waves: the Theory and Application of Reaction-Diffusion Equations. Clarendon Press, OxfordMATH Grindrod P (1991) Patterns and Waves: the Theory and Application of Reaction-Diffusion Equations. Clarendon Press, OxfordMATH
Zurück zum Zitat Guevara MR, Shrier A, Glass L (1986) Phase resetting of spontaneously beating embryonic ventricular heart cell aggregates. Am J Physiol 251(6):H1298–305 Guevara MR, Shrier A, Glass L (1986) Phase resetting of spontaneously beating embryonic ventricular heart cell aggregates. Am J Physiol 251(6):H1298–305
Zurück zum Zitat Harootunian AT, Kao JP, Tsien RY (1988) Agonist-induced calcium oscillations in depolarized fibroblasts and their manipulation by photoreleased Ins(1,4,5)P3, Ca2+, and Ca2+ buffer. Cold Spring Harb Symp Quant Biol 53:935–43, DOI: 10.1101/sqb.1988.053.01.108 CrossRef Harootunian AT, Kao JP, Tsien RY (1988) Agonist-induced calcium oscillations in depolarized fibroblasts and their manipulation by photoreleased Ins(1,4,5)P3, Ca2+, and Ca2+ buffer. Cold Spring Harb Symp Quant Biol 53:935–43, DOI: 10.​1101/​sqb.​1988.​053.​01.​108 CrossRef
Zurück zum Zitat Harvey E, Kirk V, Osinga HM, Sneyd J, Wechselberger M (2010) Understanding anomalous delays in a model of intracellular calcium dynamics. Chaos 20(4):045,104, DOI: 10.1063/1.3523264 Harvey E, Kirk V, Osinga HM, Sneyd J, Wechselberger M (2010) Understanding anomalous delays in a model of intracellular calcium dynamics. Chaos 20(4):045,104, DOI: 10.​1063/​1.​3523264
Zurück zum Zitat Hassinger T, Guthrie P, Atkinson P, Bennett M, Kater S (1996) An extracellular signaling component in propagation of astrocytic calcium waves. Proc Natl Acad Sci USA 93:13,268–73, DOI: 10.1073/pnas.93.23.13268 Hassinger T, Guthrie P, Atkinson P, Bennett M, Kater S (1996) An extracellular signaling component in propagation of astrocytic calcium waves. Proc Natl Acad Sci USA 93:13,268–73, DOI: 10.​1073/​pnas.​93.​23.​13268
Zurück zum Zitat Hirose K, Kadowaki S, Tanabe M, Takeshima H, Iino M (1999) Spatiotemporal dynamics of inositol 1,4,5-trisphosphate that underlies complex Ca2+ mobilization patterns. Science 284(5419):1527–30CrossRef Hirose K, Kadowaki S, Tanabe M, Takeshima H, Iino M (1999) Spatiotemporal dynamics of inositol 1,4,5-trisphosphate that underlies complex Ca2+ mobilization patterns. Science 284(5419):1527–30CrossRef
Zurück zum Zitat Höfer T, Venance L, Giaume C (2002) Control and plasticity of intercellular calcium waves in astrocytes: a modeling approach. J Neurosci 22(12):4850–9 Höfer T, Venance L, Giaume C (2002) Control and plasticity of intercellular calcium waves in astrocytes: a modeling approach. J Neurosci 22(12):4850–9
Zurück zum Zitat Jafri M, Keizer J (1994) Diffusion of inositol 1,4,5-trisphosphate, but not Ca2+, is necessary for a class of inositol 1,4,5-trisphosphate-induced Ca2+ waves. Proc Natl Acad Sci USA 91:9485–89, DOI: 10.1073/pnas.91.20.9485 CrossRef Jafri M, Keizer J (1994) Diffusion of inositol 1,4,5-trisphosphate, but not Ca2+, is necessary for a class of inositol 1,4,5-trisphosphate-induced Ca2+ waves. Proc Natl Acad Sci USA 91:9485–89, DOI: 10.​1073/​pnas.​91.​20.​9485 CrossRef
Zurück zum Zitat Keener JP (2000) Principles of Applied Mathematics: Transformation and Approximation, 2nd edn. Perseus Books, Cambridge, Mass.MATH Keener JP (2000) Principles of Applied Mathematics: Transformation and Approximation, 2nd edn. Perseus Books, Cambridge, Mass.MATH
Zurück zum Zitat Lallouette J, De Pittà M, Ben-Jacob E, Berry H (2014) Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks. Front Comput Neurosci 8:45, DOI: 10.3389/fncom.2014.00045 CrossRef Lallouette J, De Pittà M, Ben-Jacob E, Berry H (2014) Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks. Front Comput Neurosci 8:45, DOI: 10.​3389/​fncom.​2014.​00045 CrossRef
Zurück zum Zitat Li YX, Keizer J, Stojilković SS, Rinzel J (1995a) Ca2+ excitability of the ER membrane: an explanation for IP3-induced Ca2+ oscillations. Am J Physiol 269(5):C1079–92 Li YX, Keizer J, Stojilković SS, Rinzel J (1995a) Ca2+ excitability of the ER membrane: an explanation for IP3-induced Ca2+ oscillations. Am J Physiol 269(5):C1079–92
Zurück zum Zitat Mak DOD, McBride S, Foskett J (2001) Regulation by Ca2+ and inositol 1,4,5-trisphosphate (InsP3) of single recombinant type 3 InsP3 receptor channels: Ca2+ activation uniquely distinguishes types 1 and 3 InsP3 receptors. J Gen Physiol 117:435–46, DOI: 10.1085/jgp.117.5.435 CrossRef Mak DOD, McBride S, Foskett J (2001) Regulation by Ca2+ and inositol 1,4,5-trisphosphate (InsP3) of single recombinant type 3 InsP3 receptor channels: Ca2+ activation uniquely distinguishes types 1 and 3 InsP3 receptors. J Gen Physiol 117:435–46, DOI: 10.​1085/​jgp.​117.​5.​435 CrossRef
Zurück zum Zitat Means S, Smith AJ, Shepherd J, Shadid J, Fowler J, Wojcikiewicz RJH, Mazel T, Smith GD, Wilson BS (2006) Reaction diffusion modeling of calcium dynamics with realistic ER geometry. Biophys J 91(2):537–57, DOI: 10.1529/biophysj.105.075036 CrossRef Means S, Smith AJ, Shepherd J, Shadid J, Fowler J, Wojcikiewicz RJH, Mazel T, Smith GD, Wilson BS (2006) Reaction diffusion modeling of calcium dynamics with realistic ER geometry. Biophys J 91(2):537–57, DOI: 10.​1529/​biophysj.​105.​075036 CrossRef
Zurück zum Zitat Naraghi M, Neher E (1997) Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of [Ca2+] at the mouth of a calcium channel. J Neurosci 17(18):6961–73 Naraghi M, Neher E (1997) Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of [Ca2+] at the mouth of a calcium channel. J Neurosci 17(18):6961–73
Zurück zum Zitat Nash MS, Young KW, Challiss RA, Nahorski SR (2001) Intracellular signalling. Receptor-specific messenger oscillations. Nature 413(6854):381–2, DOI: 10.1038/35096643 CrossRef Nash MS, Young KW, Challiss RA, Nahorski SR (2001) Intracellular signalling. Receptor-specific messenger oscillations. Nature 413(6854):381–2, DOI: 10.​1038/​35096643 CrossRef
Zurück zum Zitat Nuccitelli R, Yim DL, Smart T (1993) The sperm-induced Ca2+ wave following fertilization of the Xenopus egg requires the production of Ins(1,4,5)P3. Dev Biol 158(1):200–12, DOI: 10.1006/dbio.1993.1179 CrossRef Nuccitelli R, Yim DL, Smart T (1993) The sperm-induced Ca2+ wave following fertilization of the Xenopus egg requires the production of Ins(1,4,5)P3. Dev Biol 158(1):200–12, DOI: 10.​1006/​dbio.​1993.​1179 CrossRef
Zurück zum Zitat Puglisi JL, Bers DM (2001) LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol 281(6):C2049–60 Puglisi JL, Bers DM (2001) LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol 281(6):C2049–60
Zurück zum Zitat Sanderson MJ, Charles AC, Dirksen ER (1990) Mechanical stimulation and intercellular communication increases intracellular Ca2+ in epithelial cells. Cell Regul 1(8):585–96, DOI: 10.1091/mbc.1.8.585 Sanderson MJ, Charles AC, Dirksen ER (1990) Mechanical stimulation and intercellular communication increases intracellular Ca2+ in epithelial cells. Cell Regul 1(8):585–96, DOI: 10.​1091/​mbc.​1.​8.​585
Zurück zum Zitat Sneyd J, Charles AC, Sanderson MJ (1994) A model for the propagation of intercellular calcium waves. Am J Physiol 266(1):C293–302 Sneyd J, Charles AC, Sanderson MJ (1994) A model for the propagation of intercellular calcium waves. Am J Physiol 266(1):C293–302
Zurück zum Zitat Sneyd J, Keizer J, Sanderson MJ (1995a) Mechanisms of calcium oscillations and waves: a quantitative analysis. FASEB J 9(14):1463–72 Sneyd J, Keizer J, Sanderson MJ (1995a) Mechanisms of calcium oscillations and waves: a quantitative analysis. FASEB J 9(14):1463–72
Zurück zum Zitat Sneyd J, Wetton BT, Charles AC, Sanderson MJ (1995b) Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dimensional model. Am J Physiol 268(6):C1537–45 Sneyd J, Wetton BT, Charles AC, Sanderson MJ (1995b) Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dimensional model. Am J Physiol 268(6):C1537–45
Zurück zum Zitat Sneyd J, Wilkins M, Strahonja A, Sanderson MJ (1998b) Calcium waves and oscillations driven by an intercellular gradient of inositol (1,4,5)-trisphosphate. Biophys Chem 72(1–2):101–9, DOI: 10.1016/s0301-4622(98)00126-4 Sneyd J, Wilkins M, Strahonja A, Sanderson MJ (1998b) Calcium waves and oscillations driven by an intercellular gradient of inositol (1,4,5)-trisphosphate. Biophys Chem 72(1–2):101–9, DOI: 10.​1016/​s0301-4622(98)00126-4
Zurück zum Zitat Sneyd J, Tsaneva-Atanasova K, Reznikov V, Bai Y, Sanderson MJ, Yule DI (2006) A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations. Proc Natl Acad Sci USA 103(6):1675–80, DOI: 10.1073/pnas.0506135103 CrossRef Sneyd J, Tsaneva-Atanasova K, Reznikov V, Bai Y, Sanderson MJ, Yule DI (2006) A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations. Proc Natl Acad Sci USA 103(6):1675–80, DOI: 10.​1073/​pnas.​0506135103 CrossRef
Zurück zum Zitat Tanimura A, Morita T, Nezu A, Tojyo Y (2009) Monitoring of IP3 dynamics during Ca2+ oscillations in HSY human parotid cell line with FRET-based IP3 biosensors. J Med Invest 56 Suppl:357–61, DOI: 10.2152/jmi.56.357 CrossRef Tanimura A, Morita T, Nezu A, Tojyo Y (2009) Monitoring of IP3 dynamics during Ca2+ oscillations in HSY human parotid cell line with FRET-based IP3 biosensors. J Med Invest 56 Suppl:357–61, DOI: 10.​2152/​jmi.​56.​357 CrossRef
Zurück zum Zitat Winfree A (1980) The Geometry of Biological Time. Springer-Verlag, Berlin, Heidelberg, New YorkMATHCrossRef Winfree A (1980) The Geometry of Biological Time. Springer-Verlag, Berlin, Heidelberg, New YorkMATHCrossRef
Zurück zum Zitat Yao Y, Parker I (1994) Ca2+ influx modulation of temporal and spatial patterns of inositol trisphosphate-mediated Ca2+ liberation in Xenopus oocytes. J Physiol 476(1):17–28 Yao Y, Parker I (1994) Ca2+ influx modulation of temporal and spatial patterns of inositol trisphosphate-mediated Ca2+ liberation in Xenopus oocytes. J Physiol 476(1):17–28
Metadaten
Titel
Basic Modelling Principles: Deterministic Models
verfasst von
Geneviève Dupont
Martin Falcke
Vivien Kirk
James Sneyd
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-29647-0_3