×

zbMATH — the first resource for mathematics

What is required for neuronal calcium waves? A numerical parameter study. (English) Zbl 1395.92034
Summary: Neuronal calcium signals propagating by simple diffusion and reaction with mobile and stationary buffers are limited to cellular microdomains. The distance intracellular calcium signals can travel may be significantly increased by means of calcium-induced calcium release from internal calcium stores, notably the endoplasmic reticulum. The organelle, which can be thought of as a cell-within-a-cell, is able to sequester large amounts of cytosolic calcium ions via SERCA pumps and selectively release them into the cytosol through ryanodine receptor channels leading to the formation of calcium waves. In this study, we set out to investigate the basic properties of such dendritic calcium waves and how they depend on the three parameters dendrite radius, ER radius and ryanodine receptor density in the endoplasmic membrane. We demonstrate that there are stable and abortive regimes for calcium waves, depending on the above morphological and physiological parameters. In stable regimes, calcium waves can travel across long dendritic distances, similar to electrical action potentials. We further observe that abortive regimes exist, which could be relevant for spike-timing dependent plasticity, as travel distances and wave velocities vary with changing intracellular architecture. For some of these regimes, analytic functions could be derived that fit the simulation data. In parameter spaces, that are non-trivially influenced by the three-dimensional calcium concentration profile, we were not able to derive such a functional description, demonstrating the mathematical requirement to model and simulate biochemical signaling in three-dimensional space.

MSC:
92C20 Neural biology
92C37 Cell biology
35K57 Reaction-diffusion equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Sheng, M; McFadden, G; Greenberg, ME, Membrane depolarization and calcium induce c-fos transcription via phosphorylation of transcription factor CREB, Neuron, 4, 571-582, (1990)
[2] Sun, P; Enslen, H; Myung, PS; Maurer, RA, Differential activation of CREB by ca\^{}{2+}/calmodulin-dependent protein kinases type II and type IV involves phosphorylation of a site that negatively regulates activity, Genes Dev, 8, 2527-2539, (1994)
[3] Tao, X; Finkbeiner, S; Arnold, DB; Shaywitz, AJ; Greenberg, ME, Ca\^{}{2+} influx regulates BDNF transcription by a CREB family transcription factor-dependent mechanism, Neuron, 20, 709-726, (1998)
[4] Shieh, PB; Hu, SC; Bobb, K; Timmusk, T; Ghosh, A, Identification of a signaling pathway involved in calcium regulation of BDNF expression, Neuron, 20, 727-740, (1998)
[5] Limbäck-Stokin, K; Korzus, E; Nagaoka-Yasuda, R; Mayford, M, Nuclear calcium/calmodulin regulates memory consolidation, J Neurosci, 24, 10858-10867, (2004)
[6] Papadia, S; Stevenson, P; Hardingham, NR; Bading, H; Hardingham, GE, Nuclear ca\^{}{2+} and the camp response element-binding protein family mediate a late phase of activity-dependent neuroprotection, J Neurosci, 25, 4279-4287, (2005)
[7] Zhang, SJ; Zou, LL; Lau, D; Ditzel, DA; Delucinge-Vivier, C; Aso, Y; Descombes, P; Bading, H, Nuclear calcium signaling controls expression of a large gene pool: identification of a gene program for acquired neuroprotection induced by synaptic activity, PLoS Genet, 5, (2009)
[8] Zhang, SJ; Buchthal, B; Lau, D; Hayer, S; Dick, O; Schwaninger, M; Veltkamp, R; Zou, M; Weiss, U; Bading, H, A signaling cascade of nuclear calcium-CREB-ATF3 activated by synaptic NMDA receptors defines a gene repression module that protects against extrasynaptic NMDA receptor-induced neuronal cell death and ischemic brain damage, J Neurosci, 31, 4978-4990, (2011)
[9] Brini, M; Carafoli, E, The plasma membrane ca\^{}{2+} atpase and the plasma membrane sodium calcium exchanger cooperate in the regulation of cell calcium, Cold Spring Harb Perspect Biol, 3, (2011)
[10] Görlach, A; Klappa, P; Kietzmann, T, The endoplasmic reticulum: folding, calcium homeostasis, signaling, and redox control, Antioxid Redox Signal, 8, 1391-1418, (2006)
[11] Berridge, MJ, Calcium microdomains: organization and function, Cell Calcium, 40, 405-412, (2006)
[12] Foskett, JK; White, C; Cheung, KH; Mak, DO, Inositol trisphosphate receptor ca\^{}{2+} release channels, Physiol Rev, 87, 593-658, (2007)
[13] Sutko, JL; Airey, JA, Ryanodine receptor ca\^{}{2+} release channels: does diversity in form equal diversity in function?, Physiol Rev, 76, 1027-1071, (1996)
[14] Rizzuto, R; Brini, M; Murgia, M; Pozzan, T, Microdomains with high ca\^{}{2+} close to IP_{3}-sensitive channels that are sensed by neighboring mitochondria, Science, 262, 744-747, (1993)
[15] Walsh, C; Barrow, S; Voronina, S; Chvanov, M; Petersen, OH; Tepikin, A, Modulation of calcium signalling by mitochondria, Biochim Biophys Acta, 1787, 1374-1382, (2009)
[16] Goetz, JG; Genty, H; St-Pierre, P; Dang, T; Joshi, B; Sauvé, R; Vogl, W; Nabi, IR, Reversible interactions between smooth domains of the endoplasmic reticulum and mitochondria are regulated by physiological cytosolic ca\^{}{2+} levels, J Cell Sci, 120, 3553-3564, (2007)
[17] Bezprozvanny, I; Hayden, MR, Deranged neuronal calcium signaling and huntington’s disease, Biochem Biophys Res Commun, 322, 1310-1317, (2004)
[18] Nimmrich, V; Grimm, C; Draguhn, A; Barghorn, S; Lehmann, A; Schoemaker, H; Hillen, H; Gross, G; Ebert, U; Bruehl, C, Amyloid \(β\) oligomers (A \(β_{1{-}42}\) globulomer) suppress spontaneous synaptic activity by inhibition of P/Q-type calcium currents, J Neurosci, 28, 788-797, (2008)
[19] Ito, E; Oka, K; Etcheberrigaray, R; Nelson, TJ; McPhie, DL; Tofel-Grehl, B; Gibson, GE; Alkon, DL, Internal ca\^{}{2+} mobilization is altered in fibroblasts from patients with alzheimer disease, Proc Natl Acad Sci USA, 91, 534-538, (1994)
[20] Yoo, AS; Cheng, I; Chung, S; Grenfell, TZ; Lee, H; Pack-Chung, E; Handler, M; Shen, J; Xia, W; Tesco, G; Saunders, AJ; Ding, K; Frosch, MP; Tanzi, RE; Kim, TW, Presenilin-mediated modulation of capacitative calcium entry, Neuron, 27, 561-572, (2000)
[21] Stutzmann, GE; Smith, I; Caccamo, A; Oddo, S; Laferla, FM; Parker, I, Enhanced ryanodine receptor recruitment contributes to ca\^{}{2+} disruptions in Young, adult, and aged alzheimer’s disease mice, J Neurosci, 26, 5180-5189, (2006)
[22] Cheung, K-H; Shineman, D; Müller, M; Cárdenas, C; Mei, L; Yang, J; Tomita, T; Iwatsubo, T; Lee, VM-Y; Foskett, JK, Mechanism of ca\^{}{2+} disruption in alzheimer’s disease by presenilin regulation of insp_{3} receptor channel gating, Neuron, 58, 871-883, (2008)
[23] Green, KN; Demuro, A; Akbari, Y; Hitt, BD; Smith, IF; Parker, I; LaFerla, FM, SERCA pump activity is physiologically regulated by presenilin and regulates amyloid \(β\) production, J Cell Biol, 181, 1107-1116, (2008)
[24] Sneyd, J; Tsaneva-Atanasova, K; Bruce, JIE; Straub, SV; Giovannucci, DR; Yule, DI, A model of calcium waves in pancreatic and parotid acinar cells, Biophys J, 85, 1392-1405, (2003)
[25] Ross, WN, Understanding calcium waves and sparks in central neurons, Nat Rev Neurosci, 13, 157-168, (2012)
[26] Thul, R; Rietdorf, K; Bootman, MD; Coombes, S, Unifying principles of calcium wave propagation—insights from a three-dimensional model for atrial myocytes, Biochim Biophys Acta, Mol Cell Res, 1853, 2131-2143, (2015)
[27] Falcke, M, Deterministic and stochastic models of intracellular ca\^{}{2+} waves, New J Phys, 5, 96.1-96.28, (2003)
[28] Kaźmierczak, B; Peradzyński, Z, Calcium waves with fast buffers and mechanical effects, J Math Biol, 62, 1-38, (2011) · Zbl 1232.92044
[29] Dani, JW; Chernjavsky, A; Smith, SJ, Neuronal activity triggers calcium waves in hippocampal astrocyte networks, Neuron, 8, 429-440, (1992)
[30] Smith, N, Generation of calcium waves in living cells by pulsed-laser-induced photodisruption, Appl Phys Lett, 79, 1208-1210, (2001)
[31] Yang, X, Computational modelling of nonlinear calcium waves, Appl Math Model, 30, 200-208, (2006) · Zbl 1163.76456
[32] Thul, R; Smith, GD; Coombes, S, A bidomain threshold model of propagating calcium waves, J Math Biol, 56, 435-463, (2008) · Zbl 1143.92007
[33] Timofeeva, Y; Coombes, S, Wave bifurcation and propagation failure in a model of ca\^{}{2+} release, J Math Biol, 47, 249-269, (2003) · Zbl 1037.92014
[34] Petrovic, P; Valent, I; Cocherova, E; Pavelkova, J; Zahradnikova, A, Ryanodine receptor gating controls generation of diastolic calcium waves in cardiac myocytes, J Gen Physiol, 145, 489-511, (2015)
[35] Thurley, K; Skupin, A; Thul, R; Falcke, M, Fundamental properties of ca\^{}{2+} signals, Biochem Biophys Acta, 1820, 1185-1194, (2012)
[36] Falcke, M; Li, Y; Lechleiter, JD; Camacho, P, Modeling the dependence of the period of intracellular ca\^{}{2+} waves on SERCA expression, Biophys J, 85, 1474-1481, (2003)
[37] Guisoni, N; Ferrero, P; Layana, C; Diambra, L, Abortive and propagating intracellular calcium waves: analysis from a hybrid model, PLoS ONE, 10, 1-15, (2015)
[38] Thul, R; Falcke, M, Stability of membrane bound reactions, Phys Rev Lett, 93, (2004)
[39] Wittmann, M; Queisser, G; Eder, A; Wiegert, JS; Bengtson, CP; Hellwig, A; Wittum, G; Bading, H, Synaptic activity induces dramatic changes in the geometry of the cell nucleus: interplay between nuclear structure, histone H3 phosphorylation, and nuclear calcium signaling, J Neurosci, 29, 14687-14700, (2009)
[40] Queisser, G; Wiegert, JS; Bading, H, Structural dynamics of the cell nucleus: basis for morphology modulation of nuclear calcium signaling and gene transcription, Nucleus, 2, 98-104, (2011)
[41] Wu, Y; Whiteus, C; Xu, CS; Hayworth, KJ; Weinberg, RJ; Hess, HF; Camilli, P, Contacts between the endoplasmic reticulum and other membranes in neurons, Proc Natl Acad Sci, 114, 4859-4867, (2017)
[42] Popov, V; Medvedev, NI; Davies, HA; Stewart, MG, Mitochondria form a filamentous reticular network in hippocampal dendrites but are present as discrete bodies in axons: a three-dimensional ultrastructural study, J Comp Neurol, 492, 50-65, (2005)
[43] Terasaki, M; Slater, NT; Fein, A; Schmidek, A; Reese, TS, Continuous network of endoplasmic reticulum in cerebellar purkinje neurons, Proc Natl Acad Sci, 91, 7510-7514, (1994)
[44] Berridge, MJ, Neuronal calcium signaling, Neuron, 21, 13-26, (1998)
[45] Shemer, I; Brinne, B; Tegnér, J; Grillner, S, Electrotonic signals along intracellular membranes may interconnect dendritic spines and nucleus, PLoS Comput Biol, 4, 1-19, (2008)
[46] Veenstra, TD; Johnson, KL; Tomlinson, AJ; Naylor, S; Kumar, R, Determination of calcium-binding sites in rat brain calbindin D_{28k} by electrospray ionization mass spectrometry, Biochemistry, 36, 3535-3542, (1997)
[47] Müller, A; Kukley, M; Stausberg, P; Beck, H; Müller, W; Dietrich, D, Endogenous ca\^{}{2+} buffer concentration and ca\^{}{2+} microdomains in hippocampal neurons, J Neurosci, 25, 558-565, (2005)
[48] Allbritton, NL; Meyer, T; Stryer, L, Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate, Science, 258, 1812-1815, (1992)
[49] Schmidt, H; Stiefel, KM; Racay, P; Schwaller, B; Eilers, J, Mutational analysis of dendritic ca\^{}{2+} kinetics in rodent purkinje cells: role of parvalbumin and calbindin D_{28k}, J Physiol, 551, 13-32, (2003)
[50] Keizer, J; Levine, L, Ryanodine receptor adaptation and ca\^{}{2+}-induced ca\^{}{2+} release-dependent ca\^{}{2+} oscillations, Biophys J, 71, 3477-3487, (1996)
[51] Tinker, A; Lindsay, ARG; Williams, AJ, Cation conduction in the calcium release channel of the cardiac sarcoplasmic reticulum under physiological and pathophysiological conditions, Cardiovasc Res, 27, 1820-1825, (1993)
[52] Chiu, VCK; Haynes, DH, Rapid kinetic studies of active ca\^{}{2+} transport in sarcoplasmic reticulum, J Membr Biol, 56, 219-239, (1980)
[53] Graupner M. A theory of plasma membrane calcium pump function and its consequences for presynaptic calcium dynamics. Diploma thesis. Technische Universität Dresden; 2003.
[54] Elwess, NL; Filoteo, AG; Enyedi, A; Penniston, JT, Plasma membrane ca\^{}{2+} pump isoforms 2a and 2b are unusually responsive to calmodulin and ca\^{}{2+}, J Biol Chem, 272, 17981-17986, (1997)
[55] Higgins, ER; Cannell, MB; Sneyd, J, A buffering SERCA pump in models of calcium dynamics, Biophys J, 91, 151-163, (2006)
[56] Deuflhard, P; Hairer, E; Zugck, J, One-step and extrapolation methods for differential-algebraic systems, Numer Math, 51, 501-516, (1987) · Zbl 0635.65083
[57] Deuflhard, P, Order and stepsize control in extrapolation methods, Numer Math, 41, 399-422, (1983) · Zbl 0543.65049
[58] Vorst, HA, Bi-CGSTAB: a fast and smoothly converging variant of bi-CG for the solution of nonsymmetric linear systems, SIAM J Sci Stat Comput, 13, 631-644, (1992) · Zbl 0761.65023
[59] Demmel, JW; Eisenstat, SC; Gilbert, JR; Li, XS; Liu, JWH, A supernodal approach to sparse partial pivoting, SIAM J Matrix Anal Appl, 20, 720-755, (1999) · Zbl 0931.65022
[60] Vogel, A; Reiter, S; Rupp, M; Nägel, A; Wittum, G, UG 4: a novel flexible software system for simulating PDE based models on high performance computers, Comput Vis Sci, 16, 165-179, (2013) · Zbl 1375.35003
[61] Jülich Supercomputing Centre, JURECA: general-purpose supercomputer at Jülich supercomputing centre, J Large-Scale Res Facil, 2, (2016)
[62] Breit, M; Stepniewski, M; Grein, S; Gottmann, P; Reinhardt, L; Queisser, G, Anatomically detailed and large-scale simulations studying synapse loss and synchrony using neurobox, Front Neuroanat, 10, (2016)
[63] Hoffer, M; Poliwoda, C; Wittum, G, Visual reflection library: a framework for declarative GUI programming on the Java platform, Comput Vis Sci, 16, 181-192, (2013)
[64] Hertle, DN; Yeckel, MF, Distribution of inositol-1,4,5-trisphosphate receptor isotypes and ryanodine receptor isotypes during maturation of the rat hippocampus, Neuroscience, 150, 625-638, (2007)
[65] Kirichok, Y; Krapivinsky, G; Clapham, DE, The mitochondrial calcium uniporter is a highly selective ion channel, Nature, 427, 360-364, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.