Calcium is an abundant element with a wide variety of important roles within cells. Calcium ions are inter- and intra-cellular messengers that are involved in numerous signalling pathways. Fluctuating compartment-specific calcium ion concentrations can lead to localised and even plant-wide oscillations that can regulate downstream events. Understanding the mechanisms that give rise to these complex patterns that vary both in space and time can be challenging, even in cases for which individual components have been identified. Taking a systems biology approach, mathematical and computational techniques can be employed to produce models that recapitulate experimental observations and capture our current understanding of the system. Useful models make novel predictions that can be investigated and falsified experimentally. This review brings together recent work on the modelling of calcium signalling in plants, from the scale of ion channels through to plant-wide responses to external stimuli. Some in silico results that have informed later experiments are highlighted.
References
[1]
Morr, S.; Cuartas, E.; Alwattar, B.; Lane, J.M. How much calcium is in your drinking water? A survey of calcium concentrations in bottled and tap water and their significance for medical treatment and drug administration. HSS J. 2006, 2, 130–135, doi:10.1007/s11420-006-9000-9.
[2]
Katz, A.K.; Glusker, J.P.; Beebe, S.A.; Bock, C.W. Calcium ion coordination: A comparison with that of beryllium, magnesium, and zinc. J. Am. Chem. Soc. 1996, 118, 5752–5763, doi:10.1021/ja953943i.
[3]
Williamson, R.E. Cytoplasmic streaming in Chara: A cell model activated by ATP and inhibited by cytochalasin B. J. Cell Sci. 1975, 17, 655–668.
[4]
Tazawa, M.; Kikuyama, M.; Shimmen, T. Electrical characteristics and cytoplasmic streaming of Characeae cells lacking tonoplast. Cell Struct. Funct. 1976, 1, 165–176, doi:10.1247/csf.1.165.
Huala, E.; Dickerman, A.W.; Garcia-Hernandez, M.; Weems, D.; Reiser, L.; LaFond, F.; Hanley, D.; Kiphart, D.; Zhuang, M.; Huang, W.; et al. The Arabidopsis Information Resource (TAIR): A comprehensive database and web-based information retrieval, analysis, and visualization system for a model plant. Nucleic Acids Res. 2001, 29, 102–105, doi:10.1093/nar/29.1.102.
[7]
Webb, A.A.R.; McAinsh, M.R.; Taylor, J.E.; Hetherington, A.M. Calcium ions as intracellular second messengers in higher plants. Adv. Bot. Res. 1996, 22, 45–96, doi:10.1016/S0065-2296(08)60056-7.
[8]
Dodd, A.N.; Kudla, J.; Sanders, D. The language of calcium signaling. Annu. Rev. Plant Biol. 2010, 61, 593–620, doi:10.1146/annurev-arplant-070109-104628.
[9]
Sanders, D.; Pelloux, J.; Brownlee, C.; Harper, J.F. Calcium at the crossroads of signaling. Plant Cell 2002, 14, S401–S417.
[10]
Berridge, M.J.; Lipp, P.; Bootman, M.D. The versatility and universality of calcium signalling. Nat. Rev. Mol. Cell Biol. 2000, 1, 11–21, doi:10.1038/35036035.
Kummer, U.; Krajnc, B.; Pahle, J.; Green, A.K.; Dixon, C.J.; Marhl, M. Transition from stochastic to deterministic behavior in calcium oscillations. Biophys. J. 2005, 89, 1603–1611, doi:10.1529/biophysj.104.057216.
[13]
Schuster, S.; Marhl, M.; Hofer, T. Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling. Eur. J. Biochem. 2002, 269, 1333–1355, doi:10.1046/j.0014-2956.2001.02720.x.
[14]
Gillespie, D.T. Exact stochastic simulation of coupled chemical-reactions. J. Phys. Chem. Us 1977, 81, 2340–2361, doi:10.1021/j100540a008.
[15]
Hodgkin, A.L.; Huxley, A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 1952, 117, 500–544.
[16]
Hill, A.V. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J. Physiol. 1910, 40, iv–vii.
[17]
Carafoli, E. The unusual history and unique properties of the calcium signal. New Comp. Biochem. 2007, 41, 3–22, doi:10.1016/S0167-7306(06)41001-2.
[18]
Bauer, C.S.; Plieth, C.; Bethmann, B.; Popescu, O.; Hansen, U.P.; Simonis, W.; Schonknecht, G. Strontium-induced repetitive calcium spikes in a unicellular green alga. Plant Physiol. 1998, 117, 545–557, doi:10.1104/pp.117.2.545.
[19]
Sch？nknecht, G.; Bauer, C. Modelling Ca2+ Oscillations in Plants. In Rhythms in Plants: Phenomenology, Mechanisms, and Adaptive Significance; Mancuso, S., Shabala, S., Eds.; Springer: Wien, Austria, New York, NY, USA, 2007; pp. 295–311.
[20]
Tidow, H.; Poulsen, L.R.; Andreeva, A.; Knudsen, M.; Hein, K.L.; Wiuf, C.; Palmgren, M.G.; Nissen, P. A bimodular mechanism of calcium control in eukaryotes. Nature 2012, 491, 468–472, doi:10.1038/nature11539.
[21]
Charpentier, M.; Vaz Martins, T.; Granqvist, E.; Oldroyd, G.E.; Morris, R.J. The role of DMI1 in establishing Ca2+ oscillations in legume symbioses. Plant Signal. Behav. 2013, 8.
[22]
Granqvist, E.; Wysham, D.; Hazledine, S.; Kozlowski, W.; Sun, J.; Charpentier, M.; Martins, T.V.; Haleux, P.; Tsaneva-Atanasova, K.; Downie, J.A.; et al. Buffering capacity explains signal variation in symbiotic calcium oscillations. Plant Physiol. 2012, 160, 2300–2310, doi:10.1104/pp.112.205682.
[23]
Stucki, J.W.; Somogyi, R. A dialog on Ca2+ oscillations—An attempt to understand the essentials of mechanisms leading to hormone-induced intracellular Ca2+ oscillations in various kinds of cell on a theoretical level. Bba Bioenerg. 1994, 1183, 453–472, doi:10.1016/0005-2728(94)90073-6.
[24]
Ane, J.M.; Kiss, G.B.; Riely, B.K.; Penmetsa, R.V.; Oldroyd, G.E.D.; Ayax, C.; Levy, J.; Debelle, F.; Baek, J.M.; Kalo, P.; et al. Medicago truncatula DMI1 required for bacterial and fungal symbioses in legumes. Science 2004, 303, 1364–1367, doi:10.1126/science.1092986.
[25]
Buschmann, P.; Gradmann, D. Minimal model for oscillations of membrane voltage in plant cells. J. Theor. Biol. 1997, 188, 323–332, doi:10.1006/jtbi.1997.0483.
[26]
Glansdorff, P.; Prigogine, I. Thermodynamic Theory of Structure, Stability and Fluctuations; Wiley-Interscience: London, UK, New York, NY, USA, 1971.
[27]
Venkateshwaran, M.; Cosme, A.; Han, L.; Banba, M.; Satyshur, K.A.; Schleiff, E.; Parniske, M.; Imaizumi-Anraku, H.; Ane, J.M. The recent evolution of a symbiotic ion channel in the legume family altered ion conductance and improved functionality in calcium signaling. Plant Cell 2012, 24, 2528–2545, doi:10.1105/tpc.112.098475.
[28]
Rea, P.A.; Britten, C.J.; Jennings, I.R.; Calvert, C.M.; Skiera, L.A.; Leigh, R.A.; Sanders, D. Regulation of vacuolar H+-pyrophosphatase by free calcium—A reaction kinetic-analysis. Plant Physiol. 1992, 100, 1706–1715, doi:10.1104/pp.100.4.1706.
[29]
Gradmann, D.; Johannes, E.; Hansen, U. Kinetic analysis of Ca2+/K+ selectivity of an ion channel by single-binding-site models. J. Membr. Biol. 1997, 159, 169–178, doi:10.1007/s002329900280.
[30]
Allen, G.J.; Sanders, D.; Gradmann, D. Calcium-potassium selectivity: Kinetic analysis of current-voltage relationships of the open, slowly activating channel in the vacuolar membrane of Vicia faba guard-cells. Planta 1998, 204, 528–541, doi:10.1007/s004250050288.
[31]
Hansen, U.P.; Keunecke, M.; Blunck, R. Gating and permeation models of plant channels. J. Exp. Bot. 1997, 48, 365–382, doi:10.1093/jxb/48.Special_Issue.365.
[32]
Plieth, C.; Hansen, U.P. Cytosolic Ca2+ and H+ buffers in green algae: A reply. Protoplasma 1998, 203, 210–213, doi:10.1007/BF01279478.
[33]
Pottosin, I.I.; Martinez-Estevez, M.; Dobrovinskaya, O.R.; Muniz, J.; Sch？nknecht, G. Mechanism of luminal Ca2+ and Mg2+ action on the vacuolar slowly activating channels. Planta 2004, 219, 1057–1070, doi:10.1007/s00425-004-1293-7.
[34]
Perez, V.; Wherrett, T.; Shabala, S.; Muniz, J.; Dobrovinskaya, O.; Pottosin, I. Homeostatic control of slow vacuolar channels by luminal cations and evaluation of the channel-mediated tonoplast Ca2+ fluxes in situ. J. Exp. Bot. 2008, 59, 3845–3855, doi:10.1093/jxb/ern225.
[35]
Peiter, E. The plant vacuole: Emitter and receiver of calcium signals. Cell Calcium. 2011, 50, 120–128, doi:10.1016/j.ceca.2011.02.002.
[36]
Isayenkov, S.; Isner, J.C.; Maathuis, F.J. Vacuolar ion channels: Roles in plant nutrition and signalling. FEBS Lett. 2010, 584, 1982–1988, doi:10.1016/j.febslet.2010.02.050.
[37]
Pottosin, I.I.; Sch？nknecht, G. Vacuolar calcium channels. J. Exp. Bot. 2007, 58, 1559–1569, doi:10.1093/jxb/erm035.
[38]
Dobrovinskaya, O.R.; Muniz, J.; Pottosin, I.I. Asymmetric block of the plant vacuolar Ca(2+)-permeable channel by organic cations. Eur. Biophys. J. 1999, 28, 552–563, doi:10.1007/s002490050237.
[39]
Kaplan, B.; Sherman, T.; Fromm, H. Cyclic nucleotide-gated channels in plants. FEBS Lett. 2007, 581, 2237–2246, doi:10.1016/j.febslet.2007.02.017.
[40]
Zelman, A.K.; Dawe, A.; Gehring, C.; Berkowitz, G.A. Evolutionary and structural perspectives of plant cyclic nucleotide-gated cation channels. Front. Plant Sci. 2012, doi:10.3389/fpls.2012.00095.
[41]
Craven, K.B.; Zagotta, W.N. CNG and HCN channels: Two peas, one pod. Annu. Rev. Physiol. 2006, 68, 375–401, doi:10.1146/annurev.physiol.68.040104.134728.
[42]
Oldroyd, G.E. Speak, friend, and enter: Signalling systems that promote beneficial symbiotic associations in plants. Nat. Rev. Microbiol. 2013, 11, 252–263, doi:10.1038/nrmicro2990.
[43]
Sieberer, B.J.; Chabaud, M.; Fournier, J.; Timmers, A.C.; Barker, D.G. A switch in Ca2+ spiking signature is concomitant with endosymbiotic microbe entry into cortical root cells of Medicago truncatula. Plant J. 2012, 69, 822–830, doi:10.1111/j.1365-313X.2011.04834.x.
[44]
Bootman, M.D.; Fearnley, C.; Smyrnias, I.; MacDonald, F.; Roderick, H.L. An update on nuclear calcium signalling. J. Cell Sci. 2009, 122, 2337–2350.
[45]
Gerasimenko, O.; Gerasimenko, J. New aspects of nuclear calcium signalling. J. Cell Sci. 2004, 117, 3087–3094, doi:10.1242/jcs.01295.
[46]
Mazars, C.; Bourque, S.; Mithofer, A.; Pugin, A.; Ranjeva, R. Calcium homeostasis in plant cell nuclei. New Phytol. 2009, 181, 261–274, doi:10.1111/j.1469-8137.2008.02680.x.
[47]
Charpentier, M.; Oldroyd, G.E. Nuclear calcium signaling in plants. Plant Physiol. 2013, doi:10.1104/pp.113.220863.
[48]
Xiong, T.C.; Jauneau, A.; Ranjeva, R.; Mazars, C. Isolated plant nuclei as mechanical and thermal sensors involved in calcium signalling. Plant J. 2004, 40, 12–21, doi:10.1111/j.1365-313X.2004.02184.x.
[49]
Briere, C.; Xiong, T.C.; Mazars, C.; Ranjeva, R. Autonomous regulation of free Ca2+ concentrations in isolated plant cell nuclei: A mathematical analysis. Cell Calcium. 2006, 39, 293–303, doi:10.1016/j.ceca.2005.11.005.
[50]
Boruc, J.; Zhou, X.; Meier, I. Dynamics of the plant nuclear envelope and nuclear pore. Plant Physiol. 2012, 158, 78–86, doi:10.1104/pp.111.185256.
[51]
Capoen, W.; Sun, J.; Wysham, D.; Otegui, M.S.; Venkateshwaran, M.; Hirsch, S.; Miwa, H.; Downie, J.A.; Morris, R.J.; Ane, J.M.; et al. Nuclear membranes control symbiotic calcium signaling of legumes. Proc. Natl. Acad. Sci. USA 2011, 108, 14348–14353, doi:10.1073/pnas.1107912108.
[52]
Danker, T.; Schillers, H.; Storck, J.; Shahin, V.; Kramer, B.; Wilhelmi, M.; Oberleithner, H. Nuclear hourglass technique: An approach that detects electrically open nuclear pores in Xenopus laevis oocyte. Proc. Natl. Acad. Sci. USA 1999, 96, 13530–13535, doi:10.1073/pnas.96.23.13530.
[53]
Al-Mohanna, F.A.; Caddy, K.W.; Bolsover, S.R. The nucleus is insulated from large cytosolic calcium ion changes. Nature 1994, 367, 745–750, doi:10.1038/367745a0.
[54]
Erickson, E.S.; Mooren, O.L.; Moore, D.; Krogmeier, J.R.; Dunn, R.C. The role of nuclear envelope calcium in modifying nuclear pore complex structure. Can. J. Physiol. Pharmacol. 2006, 84, 309–318, doi:10.1139/y05-109.
[55]
Perez-Terzic, C.; Pyle, J.; Jaconi, M.; Stehno-Bittel, L.; Clapham, D.E. Conformational states of the nuclear pore complex induced by depletion of nuclear Ca2+ stores. Science 1996, 273, 1875–1877, doi:10.1126/science.273.5283.1875.
[56]
Eder, A.; Bading, H. Calcium signals can freely cross the nuclear envelope in hippocampal neurons: Somatic calcium increases generate nuclear calcium transients. BMC Neurosci. 2007, doi:10.1186/1471-2202-8-57.
[57]
Keizer, J.; Smith, G.D.; Ponce-Dawson, S.; Pearson, J.E. Saltatory propagation of Ca2+ waves by Ca2+ sparks. Biophys. J. 1998, 75, 595–600, doi:10.1016/S0006-3495(98)77550-2.
[58]
Dawson, S.P.; Keizer, J.; Pearson, J.E. Fire-diffuse-fire model of dynamics of intracellular calcium waves. Proc. Natl. Acad. Sci. USA 1999, 96, 6060–6063, doi:10.1073/pnas.96.11.6060.
[59]
Coombes, S. The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of Ca2+ release. Bull. Math. Biol. 2001, 63, 1–20, doi:10.1006/bulm.2000.0193.
[60]
Sieberer, B.J.; Chabaud, M.; Timmers, A.C.; Monin, A.; Fournier, J.; Barker, D.G. A nuclear-targeted cameleon demonstrates intranuclear Ca2+ spiking in Medicago truncatula root hairs in response to rhizobial nodulation factors. Plant Physiol. 2009, 151, 1197–1206, doi:10.1104/pp.109.142851.
[61]
Mazel, T.; Raymond, R.; Raymond-Stintz, M.; Jett, S.; Wilson, B.S. Stochastic modeling of calcium in 3D geometry. Biophys. J. 2009, 96, 1691–1706.
[62]
Means, S.; Smith, A.J.; Shepherd, J.; Shadid, J.; Fowler, J.; Wojcikiewicz, R.J.; Mazel, T.; Smith, G.D.; Wilson, B.S. Reaction diffusion modeling of calcium dynamics with realistic ER geometry. Biophys. J. 2006, 91, 537–557, doi:10.1529/biophysj.105.075036.
[63]
Queisser, G.; Wiegert, S.; Bading, H. Structural dynamics of the cell nucleus: Basis for morphology modulation of nuclear calcium signaling and gene transcription. Nucleus 2011, 2, 98–104, doi:10.4161/nucl.2.2.15116.
[64]
Klann, M.; Koeppl, H. Spatial simulations in systems biology: From molecules to cells. Int. J. Mol. Sci. 2012, 13, 7798–7827, doi:10.3390/ijms13067798.
[65]
Lenton, T.M.; Crouch, M.; Johnson, M.; Pires, N.; Dolan, L. First plants cooled the Ordovician. Nat. Geosci. 2012, 5, 86–89, doi:10.1038/ngeo1390.
[66]
Thuiller, W.; Lavorel, S.; Araujo, M.B.; Sykes, M.T.; Prentice, I.C. Climate change threats to plant diversity in Europe. Proc. Natl. Acad. Sci. USA 2005, 102, 8245–8250.
[67]
Walbot, V. How plants cope with temperature stress. Bmc. Biol. 2011, doi:10.1186/1741-7007-9-79.
[68]
Knight, M.R.; Campbell, A.K.; Smith, S.M.; Trewavas, A.J. Transgenic plant aequorin reports the effects of touch and cold-shock and elicitors on cytoplasmic calcium. Nature 1991, 352, 524–526, doi:10.1038/352524a0.
[69]
Minorsky, P.V. Temperature sensing by plants—A review and hypothesis. Plant Cell Environ. 1989, 12, 119–135, doi:10.1111/j.1365-3040.1989.tb01924.x.
[70]
Minorsky, P.V.; Spanswick, R.M. Electrophysiological evidence for a role for calcium in temperature sensing by roots of cucumber seedlings. Plant Cell Environ. 1989, 12, 137–143, doi:10.1111/j.1365-3040.1989.tb01925.x.
[71]
Ruelland, E.; Zachowski, A. How plants sense temperature. Environ. Exp. Bot. 2010, 69, 225–232, doi:10.1016/j.envexpbot.2010.05.011.
[72]
McClung, C.R.; Davis, S.J. Ambient thermometers in plants: From physiological outputs towards mechanisms of thermal sensing. Curr. Biol. 2010, 20, R1086–R1092, doi:10.1016/j.cub.2010.10.035.
[73]
Browse, J.; Xin, Z. Temperature sensing and cold acclimation. Curr. Opin. Plant. Biol. 2001, 4, 241–246, doi:10.1016/S1369-5266(00)00167-9.
[74]
Plieth, C.; Hansen, U.P.; Knight, H.; Knight, M.R. Temperature sensing by plants: The primary characteristics of signal perception and calcium response. Plant J. 1999, 18, 491–497, doi:10.1046/j.1365-313X.1999.00471.x.
[75]
Plieth, C. Temperature sensing by plants: Calcium-permeable channels as primary sensors—A model. J. Membr. Biol. 1999, 172, 121–127, doi:10.1007/s002329900590.
[76]
Caldwell, C.R.; Haug, A. Temperature-dependence of the barley root plasma membrane-bound Ca2+-dependent and Mg2+-dependent atpase. Physiol. Plant. 1981, 53, 117–124, doi:10.1111/j.1399-3054.1981.tb04120.x.
[77]
White, P.J.; Ridout, M.S. An energy-barrier model for the permeation of monovalent and divalent cations through the maxi cation channel in the plasma membrane of rye roots. J. Membr. Biol. 1999, 168, 63–75, doi:10.1007/s002329900498.
[78]
Eyring, H. The activated complex in chemical reactions. J. Chem. Phys. 1953, 3, 107:1–107:9.
[79]
Hanggi, P.; Talkner, P.; Borkovec, M. Reaction-rate theory—50 years after kramers. Rev. Mod. Phys. 1990, 62, 251–341, doi:10.1103/RevModPhys.62.251.
[80]
White, P.J.; Pineros, M.; Tester, M.; Ridout, M.S. Cation permeability and selectivity of a root plasma membrane calcium channel. J. Membr. Biol. 2000, 174, 71–83, doi:10.1007/s002320001033.
[81]
White, P.J. Calcium signals in root cells: The roles of plasma membrane calcium channels. Biologia 2004, 59, 77–83.
[82]
White, P.J. Depolarization-activated calcium channels shape the calcium signatures induced by low-temperature stress. New Phytol. 2009, 183, 6–8, doi:10.1111/j.1469-8137.2009.02857.x.
[83]
Bose, J.; Pottosin, I.I.; Shabala, S.S.; Palmgren, M.G.; Shabala, S. Calcium efflux systems in stress signaling and adaptation in plants. Front. Plant Sci. 2011, doi:10.3389/fpls.2011.00085.
[84]
Clapham, D.E.; Miller, C. A thermodynamic framework for understanding temperature sensing by transient receptor potential (TRP) channels. Proc. Natl. Acad. Sci. USA 2011, 108, 19492–19497, doi:10.1073/pnas.1117485108.
[85]
Voets, T.; Droogmans, G.; Wissenbach, U.; Janssens, A.; Flockerzi, V.; Nilius, B. The principle of temperature-dependent gating in cold- and heat-sensitive TRP channels. Nature 2004, 430, 748–754, doi:10.1038/nature02732.
[86]
Finka, A.; Cuendet, A.F.; Maathuis, F.J.; Saidi, Y.; Goloubinoff, P. Plasma membrane cyclic nucleotide gated calcium channels control land plant thermal sensing and acquired thermotolerance. Plant Cell 2012, 24, 3333–3348, doi:10.1105/tpc.112.095844.
[87]
Gao, F.; Han, X.W.; Wu, J.H.; Zheng, S.Z.; Shang, Z.L.; Sun, D.Y.; Zhou, R.G.; Li, B. A heat-activated calcium-permeable channel—Arabidopsis cyclic nucleotide-gated ion channel 6—is involved in heat shock responses. Plant J. 2012, 70, 1056–1069, doi:10.1111/j.1365-313X.2012.04969.x.
[88]
Tunc-Ozdemir, M.; Tang, C.; Ishka, M.R.; Brown, E.; Groves, N.R.; Myers, C.T.; Rato, C.; Poulsen, L.R.; McDowell, S.; Miller, G.; et al. A cyclic nucleotide-gated channel (CNGC16) in pollen is critical for stress tolerance in pollen reproductive development. Plant Physiol. 2013, 161, 1010–1020.
[89]
Liu, J.; Knight, H.; Hurst, C.H.; Knight, M.R. Modelling and experimental analysis of the role of interacting cytosolic and vacuolar pools in shaping low temperature calcium signatures in plant cells. Mol. Biosyst. 2012, 8, 2205–2220, doi:10.1039/c2mb25072a.
[90]
Jones, C.T.; Banks, P. The influence of the intracellular concentration of sodium on the uptake of L-( 14 C)valine by chopped tissue from cerebral cortex. Biochem. J. 1971, 123, 341–345.
[91]
Parent, B.; Turc, O.; Gibon, Y.; Stitt, M.; Tardieu, F. Modelling temperature-compensated physiological rates, based on the co-ordination of responses to temperature of developmental processes. J. Exp. Bot. 2010, 61, 2057–2069, doi:10.1093/jxb/erq003.
[92]
Murata, N.; Los, D.A. Membrane fluidity and temperature perception. Plant Physiol. 1997, 115, 875–879.
[93]
Finka, A.; Goloubinoff, P. The CNGCb and CNGCd genes from Physcomitrella patens moss encode for thermosensory calcium channels responding to fluidity changes in the plasma membrane. Cell Stress Chaperones 2013, doi:10.1007/s12192-013-0436-9.
[94]
Oldroyd, G.E.; Murray, J.D.; Poole, P.S.; Downie, J.A. The rules of engagement in the legume-rhizobial symbiosis. Annu. Rev. Genet. 2011, 45, 119–144, doi:10.1146/annurev-genet-110410-132549.
Miyawaki, A.; Griesbeck, O.; Heim, R.; Tsien, R.Y. Dynamic and quantitative Ca2+ measurements using improved cameleons. Proc. Natl. Acad. Sci. USA 1999, 96, 2135–2140, doi:10.1073/pnas.96.5.2135.
[103]
Deisseroth, K.; Heist, E.K.; Tsien, R.W. Translocation of calmodulin to the nucleus supports CREB phosphorylation in hippocampal neurons. Nature 1998, 392, 198–202, doi:10.1038/32448.
[104]
Sciacca, E.; Spinella, S.; Genre, A.; Calcagno, C. Analysis of calcium spiking in plant root epidermis through CWC modeling. Electron. Notes Theor. Comput. Sci. 2011, 277, 65–76, doi:10.1016/j.entcs.2011.09.036.
[105]
Coppo, M.; Damiani, F.; Drocco, M.; Grassi, E.; Troina, A. Stochastic calculus of wrapped compartments. In Proceeding of Eighth Workshop on Quantitative Aspects of Programming Languages (QAPL 2010), Paphos, Cyprus, 27–28 March 2010; pp. 82–98.
[106]
Terese Term Rewriting Systems. Cambridge University Press: Cambridge, UK, 2003.
[107]
Jaynes, E.T. Information theory and statistical mechanics. Phys. Rev. 1957, 106, 620–630, doi:10.1103/PhysRev.106.620.
[108]
Jaynes, E.T. Information theory and statistical mechanics 2. Phys. Rev. 1957, 108, 171–190, doi:10.1103/PhysRev.108.171.
[109]
Calcagno, C.; Coppo, M.; Damiani, F.; Drocco, M.; Sciacca, E.; Spinella, S.; Troina, A. Modelling spatial interactions in the arbuscular mycorrhizal symbiosis using the calculus of wrapped compartments. In Proceeding of EPTCS 2011, Aachen, Germany, 10 September 2011; pp. 3–18.
[110]
Kroeger, J.; Geitmann, A. The pollen tube paradigm revisited. Curr. Opin. Plant. Biol. 2012, 15, 618–624, doi:10.1016/j.pbi.2012.09.007.
[111]
Kroeger, J.H.; Geitmann, A. Pollen tube growth: Getting a grip on cell biology through modeling. Mech. Res. Commun. 2012, 42, 32–39, doi:10.1016/j.mechrescom.2011.11.005.
[112]
Bibikova, T.N.; Zhigilei, A.; Gilroy, S. Root hair growth in Arabidopsis thaliana is directed by calcium and an endogenous polarity. Planta 1997, 203, 495–505, doi:10.1007/s004250050219.
[113]
Pierson, E.S.; Miller, D.D.; Callaham, D.A.; Shipley, A.M.; Rivers, B.A.; Cresti, M.; Hepler, P.K. Pollen tube growth is coupled to the extracellular calcium ion flux and the intracellular calcium gradient: Effect of BAPTA-type buffers and hypertonic media. Plant Cell 1994, 6, 1815–1828.
[114]
Weisenseel, M.H.; Nuccitelli, R.; Jaffe, L.F. Large electrical currents traverse growing pollen tubes. J. Cell Biol. 1975, 66, 556–567, doi:10.1083/jcb.66.3.556.
[115]
Geitmann, A.; Li, Y.Q.; Cresti, M. The role of the cytoskeleton and dictyosome activity in the pulsatory growth of Nicotiana tabacum and Petunia hybrida pollen tubes. Bot. Acta 1996, 109, 102–109.
[116]
Messerli, M.A.; Robinson, K.R. Ionic and osmotic disruptions of the lily pollen tube oscillator: Testing proposed models. Planta 2003, 217, 147–157.
[117]
Holdaway-Clarke, T.L.; Feijo, J.A.; Hackett, G.R.; Kunkel, J.G.; Hepler, P.K. Pollen tube growth and the intracellular cytosolic calcium gradient oscillate in phase while extracellular calcium influx is delayed. Plant Cell 1997, 9, 1999–2010.
[118]
Kroeger, J.H.; Geitmann, A.; Grant, M. Model for calcium dependent oscillatory growth in pollen tubes. J. Theor. Biol. 2008, 253, 363–374, doi:10.1016/j.jtbi.2008.02.042.
[119]
Skotheim, J.M.; Mahadevan, L. Dynamics of poroelastic filaments. Proc. R. Soc. Lond. A 2004, 460, 1995–2020, doi:10.1098/rspa.2003.1270.
[120]
Dumais, J.; Shaw, S.L.; Steele, C.R.; Long, S.R.; Ray, P.M. An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth. Int. J. Dev. Biol. 2006, 50, 209–222, doi:10.1387/ijdb.052066jd.
[121]
Holdaway-Clarke, T.L.; Hepler, P.K. Control of pollen tube growth: Role of ion gradients and fluxes. New Phytol. 2003, 159, 539–563, doi:10.1046/j.1469-8137.2003.00847.x.
[122]
Kroeger, J.H.; Zerzour, R.; Geitmann, A. Regulator or driving force? The role of turgor pressure in oscillatory plant cell growth. PLoS One 2011, 6, e18549, doi:10.1371/journal.pone.0018549.
[123]
Lockhart, J.A. An analysis of irreversible plant cell elongation. J. Theor. Biol. 1965, 8, 264–275.
[124]
Liu, J.; Piette, B.M.; Deeks, M.J.; Franklin-Tong, V.E.; Hussey, P.J. A compartmental model analysis of integrative and self-regulatory ion dynamics in pollen tube growth. PLoS One 2010, 5, e13157.
[125]
Yan, A.; Xu, G.; Yang, Z.B. Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes. Proc. Natl. Acad. Sci. USA 2009, 106, 22002–22007, doi:10.1073/pnas.0910811106.
[126]
Goodwin, B.C.; Trainor, L.E.H. Tip and whorl morphogenesis in acetabularia by calcium-regulated strain fields. J. Theor. Biol. 1985, 117, 79–106, doi:10.1016/S0022-5193(85)80165-X.
[127]
Briere, C. Dynamics of the goodwin-trainor mechanochemical model. Acta Biotheor. 1994, 42, 137–146, doi:10.1007/BF00709486.
[128]
Briere, C.; Goodwin, B. Geometry and dynamics of tip morphogenesis in acetabularia. J. Theor. Biol. 1988, 131, 461–475, doi:10.1016/S0022-5193(88)80041-9.
[129]
Briere, C.; Goodwin, B.C. Effects of calcium input output on the stability of a system for calcium-regulated viscoelastic strain fields. J. Math. Biol. 1990, 28, 585–593, doi:10.1007/BF00164164.
[130]
Kim, T.H.; Bohmer, M.; Hu, H.; Nishimura, N.; Schroeder, J.I. Guard cell signal transduction network: Advances in understanding abscisic acid, CO2, and Ca2+ signaling. Annu. Rev. Plant. Biol. 2010, 61, 561–591, doi:10.1146/annurev-arplant-042809-112226.
[131]
Albert, R. Network inference, analysis, and modeling in systems biology. Plant Cell 2007, 19, 3327–3338, doi:10.1105/tpc.107.054700.
[132]
Li, S.; Assmann, S.M.; Albert, R. Predicting essential components of signal transduction networks: A dynamic model of guard cell abscisic acid signaling. PLoS Biol. 2006, 4, e312, doi:10.1371/journal.pbio.0040312.
[133]
Albert, I.; Thakar, J.; Li, S.; Zhang, R.; Albert, R. Boolean network simulations for life scientists. Source Code Biol. Med. 2008, doi:10.1186/1751-0473-3-16.
[134]
Veresov, V.G.; Kabak, A.G.; Volotovsky, I.D. Modeling the calcium signaling in stomatal guard cells under the action of abscisic acid. Russ. J. Plant Physl. 2003, 50, 573–579, doi:10.1023/A:1025686603389.
[135]
Allen, G.J.; Muir, S.R.; Sanders, D. Release of Ca2+ from individual plant vacuoles by both insp(3) and cyclic adp-ribose. Science 1995, 268, 735–737, doi:10.1126/science.7732384.
[136]
Hills, A.; Chen, Z.H.; Amtmann, A.; Blatt, M.R.; Lew, V.L. OnGuard, a computational platform for quantitative kinetic modeling of guard cell physiology. Plant Physiol. 2012, 159, 1026–1042, doi:10.1104/pp.112.197244.
[137]
Chen, Z.H.; Hills, A.; Batz, U.; Amtmann, A.; Lew, V.L.; Blatt, M.R. Systems dynamic modeling of the stomatal guard cell predicts emergent behaviors in transport, signaling, and volume control. Plant Physiol. 2012, 159, 1235–1251, doi:10.1104/pp.112.197350.
McAinsh, M.R.; Pittman, J.K. Shaping the calcium signature. New Phytol. 2009, 181, 275–294, doi:10.1111/j.1469-8137.2008.02682.x.
[140]
Dodd, A.N.; Jakobsen, M.K.; Baker, A.J.; Telzerow, A.; Hou, S.W.; Laplaze, L.; Barrot, L.; Poethig, R.S.; Haseloff, J.; Webb, A.A. Time of day modulates low-temperature Ca signals in Arabidopsis. Plant J. 2006, 48, 962–973, doi:10.1111/j.1365-313X.2006.02933.x.
[141]
Locke, J.C.; Kozma-Bognar, L.; Gould, P.D.; Feher, B.; Kevei, E.; Nagy, F.; Turner, M.S.; Hall, A.; Millar, A.J. Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana. Mol. Syst. Biol. 2006.
[142]
Locke, J.C.; Millar, A.J.; Turner, M.S. Modelling genetic networks with noisy and varied experimental data: The circadian clock in Arabidopsis thaliana. J. Theor. Biol. 2005, 234, 383–393, doi:10.1016/j.jtbi.2004.11.038.
[143]
Locke, J.C.; Southern, M.M.; Kozma-Bognar, L.; Hibberd, V.; Brown, P.E.; Turner, M.S.; Millar, A.J. Extension of a genetic network model by iterative experimentation and mathematical analysis. Mol. Syst. Biol. 2005, 1, 2005.0013.
Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control 1974, 19, 716–723, doi:10.1109/TAC.1974.1100705.
[146]
Burnham, K.P.; Anderson, D.R. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. ed.; Springer-Verlag: New York, NY, USA, 2002.
[147]
Dalchau, N. Understanding biological timing using mechanistic and black-box models. New Phytol. 2012, 193, 852–858, doi:10.1111/j.1469-8137.2011.04004.x.
Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning; The MIT Press: Cambridge, MA, USA, 2006.
[150]
Fromm, J.; Lautner, S. Electrical signals and their physiological significance in plants. Plant Cell Environ. 2007, 30, 249–257, doi:10.1111/j.1365-3040.2006.01614.x.
[151]
Felle, H.H.; Zimmermann, M.R. Systemic signalling in barley through action potentials. Planta 2007, 226, 203–214, doi:10.1007/s00425-006-0458-y.
[152]
Cosgrove, D.J.; Hedrich, R. Stretch-activated chloride, potassium, and calcium channels coexisting in plasma membranes of guard cells of Vicia faba L. Planta 1991, 186, 143–153.
[153]
Malone, M. Rapid, long-distance signal transmission in higher plants. Adv. Bot. Res. 1996, 22, 163–228, doi:10.1016/S0065-2296(08)60058-0.
[154]
Sukhov, V.S.; Vodeneev, V.A. Mathematical Model of Action Potential in Higher Plants. In Proceedings of the XII International Conference “Mathematics. Computer. Education”Section 8: Mathematical methods in biology, ecology and chemistry, Pushchino, Russia, 17–22 January 2005; Riznichenko, G.J., Ed.; Scientific Publishing Centre “Regular and Chaotic Dynamics”: Izhevsk, Russia, 2005; Volume 3, pp. 967–978. (in Russian).
[155]
Gradmann, D. Impact of apoplast volume on ionic relations in plant cells. J. Membr. Biol. 2001, 184, 61–69, doi:10.1007/s00232-001-0074-5.
[156]
Gradmann, D.; Hoffstadt, J. Electrocoupling of ion transporters in plants: Interaction with internal ion concentrations. J. Membr. Biol. 1998, 166, 51–59, doi:10.1007/s002329900446.
[157]
Sukhov, V.; Nerush, V.; Orlova, L.; Vodeneev, V. Simulation of action potential propagation in plants. J. Theor. Biol. 2011, 291, 47–55, doi:10.1016/j.jtbi.2011.09.019.
[158]
Sibaoka, T. Rapid plant movements triggered by action-potentials. Bot. Mag. Tokyo 1991, 104, 73–95, doi:10.1007/BF02493405.
[159]
Trebacz, K.; Dziubinska, H.; Krol, E. Electrical signals in long-distance communication in plants. Commun. Plants Neuronal Asp. Plant Life 2006, 2006, 277–290.
[160]
Sukhov, V.; Akinchits, E.; Katicheva, L.; Vodeneev, V. Simulation of variation potential in higher plant cells. J. Membr. Biol. 2013, 246, 287–296, doi:10.1007/s00232-013-9529-8.
[161]
Stahlberg, R.; Cleland, R.E.; van Volkenburgh, E. Decrement and amplification of slow wave potentials during their propagation in Helianthus annuus L. shoots. Planta 2005, 220, 550–558, doi:10.1007/s00425-004-1363-x.
[162]
Sukhov, V.; Vodeneev, V. A mathematical model of action potential in cells of vascular plants. J. Membr. Biol. 2009, 232, 59–67, doi:10.1007/s00232-009-9218-9.
[163]
Plieth, C.; Sattelmacher, B.; Hansen, U.P.; Thiel, G. The action potential in Chara: Ca2+ release from internal stores visualized by Mn2+-induced quenching of fura-dextran. Plant J. 1998, 13, 167–175, doi:10.1046/j.1365-313X.1998.00019.x.
[164]
Dolmetsch, R.E.; Xu, K.; Lewis, R.S. Calcium oscillations increase the efficiency and specificity of gene expression. Nature 1998, 392, 933–936, doi:10.1038/31960.
[165]
Scrase-Field, S.A.; Knight, M.R. Calcium: Just a chemical switch? Curr. Opin. Plant Biol. 2003, 6, 500–506, doi:10.1016/S1369-5266(03)00091-8.
[166]
Plieth, C. Calcium: Just another regulator in the machinery of life? Ann. Bot. 2005, 96, 1–8, doi:10.1093/aob/mci144.
[167]
Granqvist, E.; Oldroyd, G.E.; Morris, R.J. Automated Bayesian model development for frequency detection in biological time series. BMC Syst. Biol. 2011, doi:10.1186/1752-0509-5-97.
[168]
Granqvist, E.; Hartley, M.; Morris, R.J. BaSAR-A tool in R for frequency detection. Biosystems 2012, 110, 60–63, doi:10.1016/j.biosystems.2012.07.004.
[169]
Sivia, D.S.; Skilling, J. Data Analysis: A Bayesian Tutorial, 2nd ed. ed.; Oxford University Press: Oxford, UK, New York, NY, USA, 2006; pp. xii, 246.
[170]
Bretthorst, G.L. Bayesian Spectrum Analysis and Parameter Estimation; Springer-Verlag: New York, NY, USA, 1988; pp. xii, 209.
[171]
Skilling, J. Nested sampling for general bayesian computation. Bayesian Anal. 2006, 1, 833–859, doi:10.1214/06-BA127.
[172]
Casdagli, M. Chaos and deterministic versus stochastic nonlinear modeling. J. R. Stat. Soc. Ser. B Methodol. 1992, 54, 303–328.
[173]
Kosuta, S.; Hazledine, S.; Sun, J.; Miwa, H.; Morris, R.J.; Downie, J.A.; Oldroyd, G.E. Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes. Proc. Natl. Acad. Sci. USA 2008, 105, 9823–9828.
[174]
Aparicio, T.; Pozo, E.F.; Saura, D. Detecting determinism using recurrence quantification analysis: Three test procedures. J. Econ. Behav. Organ. 2008, 65, 768–787, doi:10.1016/j.jebo.2006.03.005.
[175]
Kantz, H.; Schreiber, T. Nonlinear Time Series Analysis; Cambridge University Press: Cambridge, UK, New York, NY, USA, 1997; pp. xvi, 304.
[176]
Hazledine, S.; Sun, J.; Wysham, D.; Downie, J.A.; Oldroyd, G.E.; Morris, R.J. Nonlinear time series analysis of nodulation factor induced calcium oscillations: Evidence for deterministic chaos? PLoS One 2009, 4, e6637.
[177]
Kiegle, E.; Moore, C.A.; Haseloff, J.; Tester, M.A.; Knight, M.R. Cell-type-specific calcium responses to drought, salt and cold in the Arabidopsis root. Plant J. 2000, 23, 267–278, doi:10.1046/j.1365-313x.2000.00786.x.
Marhl, M.; Perc, M.; Schuster, S. A minimal model for decoding of time-limited Ca2+ oscillations. Biophys. Chem. 2006, 120, 161–167, doi:10.1016/j.bpc.2005.11.005.
[183]
Miwa, H.; Sun, J.; Oldroyd, G.E.; Downie, J.A. Analysis of calcium spiking using a cameleon calcium sensor reveals that nodulation gene expression is regulated by calcium spike number and the developmental status of the cell. Plant J. 2006, 48, 883–894, doi:10.1111/j.1365-313X.2006.02926.x.
[184]
Li, Y.; Wang, G.X.; Xin, M.; Yang, H.M.; Wu, X.J.; Li, T. The parameters of guard cell calcium oscillation encodes stomatal oscillation and closure in Vicia faba. Plant Sci. 2004, 166, 415–421, doi:10.1016/j.plantsci.2003.10.008.
DeFalco, T.A.; Bender, K.W.; Snedden, W.A. Breaking the code: Ca2+ sensors in plant signalling. Biochem. J. 2010, 425, 27–40, doi:10.1042/BJ20091147.
[187]
Schwaller, B. The continuing disappearance of “pure” Ca2+ buffers. Cell. Mol. Life Sci. 2009, 66, 275–300, doi:10.1007/s00018-008-8564-6.
[188]
Gilroy, S.; Hughes, W.A.; Trewavas, A.J. The measurement of intracellular calcium levels in protoplasts from higher plant cells. FEBS Lett. 1986, 199, 217–221, doi:10.1016/0014-5793(86)80483-5.
[189]
Miller, A.J.; Sanders, D. Depletion of cytosolic free calcium induced by photosynthesis. Nature 1987, 326, 397–400, doi:10.1038/326397a0.
[190]
Felle, H. Auxin causes oscillations of cytosolic free calcium and Ph in zea-mays coleoptiles. Planta 1988, 174, 495–499, doi:10.1007/BF00634478.
Hepler, P.K. Calcium: A central regulator of plant growth and development. Plant Cell 2005, 17, 2142–2155, doi:10.1105/tpc.105.032508.
[193]
Swanson, S.J.; Choi, W.G.; Chanoca, A.; Gilroy, S. In vivo imaging of Ca2+, pH, and reactive oxygen species using fluorescent probes in plants. Annu. Rev. Plant Biol. 2011, 62, 273–297, doi:10.1146/annurev-arplant-042110-103832.
[194]
Fricker, M.; Runions, J.; Moore, I. Quantitative fluorescence microscopy: From art to science. Annu. Rev. Plant Biol. 2006, 57, 79–107, doi:10.1146/annurev.arplant.57.032905.105239.
[195]
McCombs, J.E.; Palmer, A.E. Measuring calcium dynamics in living cells with genetically encodable calcium indicators. Methods 2008, 46, 152–159, doi:10.1016/j.ymeth.2008.09.015.
[196]
Iwano, M.; Entani, T.; Shiba, H.; Kakita, M.; Nagai, T.; Mizuno, H.; Miyawaki, A.; Shoji, T.; Kubo, K.; Isogai, A.; et al. Fine-tuning of the cytoplasmic Ca2+ concentration is essential for pollen tube growth. Plant Physiol. 2009, 150, 1322–1334, doi:10.1104/pp.109.139329.
Tsien, R.Y. Very long-term memories may be stored in the pattern of holes in the perineuronal net. Proc. Natl. Acad. Sci. USA 2013, 110, 12157–12158, doi:10.1073/pnas.1310158110.
[199]
Magde, D.; Webb, W.W.; Elson, E. Thermodynamic fluctuations in a reacting system—Measurement by fluorescence correlation spectroscopy. Phys. Rev. Lett. 1972, 29, 705–709, doi:10.1103/PhysRevLett.29.705.
[200]
Eigen, M.; Rigler, R. Sorting single molecules: Application to diagnostics and evolutionary biotechnology. Proc. Natl. Acad. Sci. USA 1994, 91, 5740–5747, doi:10.1073/pnas.91.13.5740.
[201]
Digman, M.A.; Dalal, R.; Horwitz, A.F.; Gratton, E. Mapping the number of molecules and brightness in the laser scanning microscope. Biophys. J. 2008, 94, 2320–2332, doi:10.1529/biophysj.107.114645.
Sanabria, H.; Digman, M.A.; Gratton, E.; Waxham, M.N. Spatial diffusivity and availability of intracellular calmodulin. Biophys. J. 2008, 95, 6002–6015, doi:10.1529/biophysj.108.138974.
[205]
Hebert, B.; Costantino, S.; Wiseman, P.W. Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells. Biophys. J. 2005, 88, 3601–3614, doi:10.1529/biophysj.104.054874.
[206]
Brown, C.M.; Hebert, B.; Kolin, D.L.; Zareno, J.; Whitmore, L.; Horwitz, A.R.; Wiseman, P.W. Probing the integrin-actin linkage using high-resolution protein velocity mapping. J. Cell Sci. 2006, 119, 5204–5214, doi:10.1242/jcs.03321.
[207]
Cardarelli, F.; Gratton, E. In vivo imaging of single-molecule translocation through nuclear pore complexes by pair correlation functions. PLoS One 2010, 5, e10475, doi:10.1371/journal.pone.0010475.
[208]
Schermelleh, L.; Heintzmann, R.; Leonhardt, H. A guide to super-resolution fluorescence microscopy. J. Cell Biol. 2010, 190, 165–175, doi:10.1083/jcb.201002018.
[209]
Baker, S.; Kanade, T. Limits on super-resolution and how to break them. IEEE Trans. Pattern Anal. 2002, 24, 1167–1183, doi:10.1109/TPAMI.2002.1033210.
[210]
Cho, S.; Jang, J.; Song, C.; Lee, H.; Ganesan, P.; Yoon, T.Y.; Kim, M.W.; Choi, M.C.; Ihee, H.; Do Heo, W.; et al. Simple super-resolution live-cell imaging based on diffusion-assisted Forster resonance energy transfer. Sci. Rep. 2013, 3, 1208:1–1208:16.
[211]
Fernandez-Suarez, M.; Ting, A.Y. Fluorescent probes for super-resolution imaging in living cells. Nat. Rev. Mol. Cell Biol. 2008, 9, 929–943, doi:10.1038/nrm2531.
Huang, B.; Babcock, H.; Zhuang, X. Breaking the diffraction barrier: Super-resolution imaging of cells. Cell 2010, 143, 1047–1058, doi:10.1016/j.cell.2010.12.002.
[214]
Lippincott-Schwartz, J.; Manley, S. Putting super-resolution fluorescence microscopy to work. Nat. Methods 2009, 6, 21–23, doi:10.1038/nmeth.f.233.
[215]
Lu, D.; Liu, Z. Hyperlenses and metalenses for far-field super-resolution imaging. Nat. Commun. 2012, 3, 1205:1–1205:7.
[216]
Lubeck, E.; Cai, L. Single-cell systems biology by super-resolution imaging and combinatorial labeling. Nat. Methods 2012, 9, 743–748, doi:10.1038/nmeth.2069.
[217]
Tipping, M.E.; Bishop, C.M. Bayesian Image Super-Resolution. In Advances in Neural Information Processing Systems; Thrun, S., Becker, S., Obermayer, K., Eds.; MIT Press: Cambridge, MA, USA, 2003; Volume 15, pp. 1279–1286.
Fitzgibbon, J.; Bell, K.; King, E.; Oparka, K. Super-resolution imaging of plasmodesmata using three-dimensional structured illumination microscopy. Plant Physiol. 2010, 153, 1453–1463, doi:10.1104/pp.110.157941.
[220]
Sparkes, I.A.; Graumann, K.; Martiniere, A.; Schoberer, J.; Wang, P.; Osterrieder, A. Bleach it, switch it, bounce it, pull it: Using lasers to reveal plant cell dynamics. J. Exp. Bot. 2011, 62, 1–7, doi:10.1093/jxb/erq351.
[221]
Da Fonseca, P.C.A.; Morris, S.A.; Nerou, E.P.; Taylor, C.W.; Morris, E.P. Domain organization of the type 1 inositol 1,4,5-trisphosphate receptor as revealed by single-particle analysis. Proc. Natl. Acad. Sci. USA 2003, 100, 3936–3941.
[222]
Thuleau, P.; Briere, C.; Mazars, C. Recent advances in plant cell nuclear signaling. Mol. Plant 2012, 5, 968–970, doi:10.1093/mp/sss083.
[223]
Falcke, M. Reading the patterns in living cells—The physics of Ca2+ signaling. Adv. Phys. 2004, 53, 255–440, doi:10.1080/00018730410001703159.
[224]
Shuai, J.W.; Jung, P. Optimal ion channel clustering for intracellular calcium signaling. Proc. Natl. Acad. Sci. USA 2003, 100, 506–510, doi:10.1073/pnas.0236032100.
[225]
Skupin, A.; Falcke, M. From puffs to global Ca2+ signals: How molecular properties shape global signals. Chaos 2009, doi:10.1063/1.3184537.
[226]
Williams, G.S.; Molinelli, E.J.; Smith, G.D. Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors. J. Theor. Biol. 2008, 253, 170–188, doi:10.1016/j.jtbi.2008.02.040.
[227]
Moenke, G.; Falcke, M.; Thurley, K. Hierarchic stochastic modelling applied to intracellular Ca(2+) signals. PLoS One 2012, 7, e51178, doi:10.1371/journal.pone.0051178.
[228]
Dupont, G.; Croisier, H. Spatiotemporal organization of Ca dynamics: A modeling-based approach. HFSP J. 2010, 4, 43–51, doi:10.2976/1.3385660.
[229]
Solovey, G.; Dawson, S.P. Intra-cluster percolation of calcium signals. PLoS One 2010, 5, e8997, doi:10.1371/journal.pone.0008997.
Baddeley, D.; Jayasinghe, I.D.; Lam, L.; Rossberger, S.; Cannell, M.B.; Soeller, C. Optical single-channel resolution imaging of the ryanodine receptor distribution in rat cardiac myocytes. Proc. Natl. Acad. Sci. USA 2009, 106, 22275–22280.
[232]
Wiltgen, S.M.; Smith, I.F.; Parker, I. Superresolution localization of single functional IP3R channels utilizing Ca2+ flux as a readout. Biophys. J. 2010, 99, 437–446, doi:10.1016/j.bpj.2010.04.037.
[233]
Parker, I.; Smith, I.F. Recording single-channel activity of inositol trisphosphate receptors in intact cells with a microscope, not a patch clamp. J. Gen. Physiol. 2010, 136, 119–127, doi:10.1085/jgp.200910390.
[234]
Smith, I.F.; Parker, I. Imaging the quantal substructure of single IP3R channel activity during Ca2+ puffs in intact mammalian cells. Proc. Natl. Acad. Sci. USA 2009, 106, 6404–6409, doi:10.1073/pnas.0810799106.
[235]
Vogelstein, J.T.; Watson, B.O.; Packer, A.M.; Yuste, R.; Jedynak, B.; Paninski, L. Spike inference from calcium imaging using sequential monte carlo methods. Biophys. J. 2009, 97, 636–655, doi:10.1016/j.bpj.2008.08.005.
[236]
Bhargava, A.; Lin, X.; Novak, P.; Mehta, K.; Korchev, Y.; Delmar, M.; Gorelik, J. Super-resolution scanning patch clamp reveals clustering of functional ion channels in adult ventricular myocyte. Circ. Res. 2013, 112, 1112–1120, doi:10.1161/CIRCRESAHA.111.300445.
