Abstract
The source and dynamics of calcium is the key factor that regulates dendritic integration. Apart from the voltage-gated and ligand-gated calcium influx, an important source of calcium is from inner store of endoplasmic reticulum with a regenerative process of calcium-induced calcium release (CICR). To trigger this process, inositol 1,4,5-trisphosphate (IP3) and calcium are needed to satisfy certain requirements. The aim of our paper is to investigate how the CICR depends on the dynamics of membrane potential. We utilize one dimensional dendritic model to calculate membrane potential by Nernst–Planck Equation (NPE) and cable model and Pure Diffusion (PD) model, computational simulations are carried out to inject the calcium influx by synaptic stimulation and to predict subsequent CICR and calcium wave propagation. Our results demonstrate that CICR initiation and calcium wave propagation have much difference between electro-diffusion process of NPE and cable model. We find that cable model has lower threshold of IP3 stimulation to trigger CICR but is more difficult for calcium propagation than NPE, PD model requires even higher threshold of IP3 to initiate CICR process and calcium duration is shorter than NPE; the regenerative calcium wave propagates with faster speed in NPE than that in cable model and in PD model. Our work addresses the important role of electro-diffusion dynamics of charged ions in regulating CICR process in dendritic structure; and provides theoretical predictions for neurological process which requires sustaining calcium for downstream signaling processes.
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References
Adeoye T, Shah SI, Demuro A, Rabson DA, Ullah G (2022) Upregulated Ca2+ release from the endoplasmic reticulum leads to impaired presynaptic function in familial Alzheimer’s disease. Cells 11(14):2167. https://doi.org/10.3390/cells11142167
Allbritton NL, Meyer T, Stryer L (1992) Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science 258(5089):1812–5. https://doi.org/10.1126/science.1465619
Atri A, Amundson J, Clapham D, Sneyd J (1993) A single-pool model for intracellular calcium oscillations and waves in the Xenopus Laevis Oocyte. Biophys J 65(4):1727–39. https://doi.org/10.1016/S0006-3495(93)81191-3
Bardo S, Cavazzini MG, Emptage N (2006) The role of the endoplasmic reticulum Ca2 + store in the plasticity of central neurons. Trends Pharmacol Sci 27(2):78–84. https://doi.org/10.1016/j.tips.2005.12.008
Berridge MJ (1998) Neuronal calcium signaling. Neuron 21:13–26. https://doi.org/10.1016/s0896-6273(00)80510-3
Berridge MJ (2002) The endoplasmic reticulum: a multifunctional signaling organelle. Cell Calcium 32(5–6):235–49. https://doi.org/10.1016/s0143416002001823
Bianchi R, Young SR, Wong RK (1999) Group I mGluR activation causes voltage-dependent and -independent Ca2 + rises in hippocampal pyramidal cells. J Neurophysiol 81(6):2903–13. https://doi.org/10.1152/jn.1999.81.6.2903
Blackwell KT (2013) Approaches and tools for modeling signaling pathways and calcium dynamics in neurons. J Neurosci Methods 220(2):131–40. https://doi.org/10.1016/j.jneumeth.2013.05.008
Brini M, Calì T, Ottolini D, Carafoli E (2014) Neuronal calcium signaling: function and dysfunction. Cell Mol Life Sci 71(15):2787–2814. https://doi.org/10.1007/s00018-013-1550-7
Carter AG, Vogt KE, Foster KA, Regehr WG (2002) Assessing the role of calcium-induced calcium release in short-term presynaptic plasticity at excitatory central synapses. J Neurosci 22(1):21–8. https://doi.org/10.1523/JNEUROSCI.22-01-00021
Cascella R, Cecchi C (2021) Calcium dyshomeostasis in Alzheimer’s disease pathogenesis. Int J Mol Sci 22(9):4914. https://doi.org/10.3390/ijms22094914
Chanaday NL, Kavalali ET (2022) Role of the endoplasmic reticulum in synaptic transmission. Curr Opin Neurobiol 73
Collin T, Marty A, Llano I (2005) Presynaptic calcium stores and synaptic transmission. Curr Opin Neurobiol 15(3):275–81. https://doi.org/10.1016/j.conb.2005.05.003
de Juan-Sanz J, Holt GT, Schreiter ER, de Juan F, Kim DS (2017) Ryan TA Axonal endoplasmic reticulum Ca2+ content controls release probability in CNS nerve terminals. Neuron 93(4):867-881.e6. https://doi.org/10.1016/j.neuron.2017.01.010
De Schutter E (2008) Why are computational neuroscience and systems biology so separate? PLoS Comput Biol 4(5)
De Schutter E, Smolen P (1998) Calcium dynamics in large neuronal models. In: Koch C, Segev I (eds) Methods in neuronal modeling: from ions to networks. MIT Press, Cambridge
Ermentrout B, Rinzel J (1996) Reflected waves in an inhomogeneous excitable medium. SIAM J Appl Math 56:1107–1128
Fitzpatrick JS, Hagenston AM, Hertle DN, Gipson KE, Bertetto-D’Angelo L, Yeckel MF (2009) Inositol-1,4,5-trisphosphate receptor-mediated Ca2 + waves in pyramidal neuron dendrites propagate through hot spots and cold spots. J Physiol 587(Pt 7):1439–59. https://doi.org/10.1113/jphysiol.2009.168930
Goto JI, Fujii S, Fujiwara H, Mikoshiba K, Yamazaki Y (2022) Synaptic plasticity in hippocampal CA1 neurons of mice lacking inositol-1,4,5-trisphosphate receptor-binding protein released with IP3 (IRBIT). Learn Mem 29:110–119. https://doi.org/10.1101/lm.053542.121
Hering H, Sheng M (2001) Dendritic spines: structure, dynamics and regulation. Nat Rev Neurosci 2:880–888. https://doi.org/10.1038/35104061
Hille B 1992 Ionic channels in excitable membranes. 2nd edn.; Sinauer
Hong M, Ross WN (2007) Priming of intracellular calcium stores in rat CA1 pyramidal neurons. J Physiol 584(Pt 1):75–87. https://doi.org/10.1113/jphysiol.2007.137661
Inoue T, Lin X, Kohlmeier KA, Orr HT, Zoghbi HY, Ross WN (2001) Calcium dynamics and electrophysiological properties of cerebellar Purkinje cells in SCA1 transgenic mice. J Neurophysiol 85(4):1750–60. https://doi.org/10.1152/jn.2001.85.4.1750
Jaffe DB, Brown TH (1994) Metabotropic glutamate receptor activation induces calcium waves within hippocampal dendrites. J Neurophysiol 72(1):471–4. https://doi.org/10.1152/jn.1994.72.1.471
Jiang M, Zhu J, Liu Y, Yang M, Tian C, Jiang S, Wang Y, Guo H, Wang K, Shu Y (2012) Enhancement of asynchronous release from fast-spiking interneuron in human and rat epileptic neocortex. PLoS Biol 10(5):e1001324. https://doi.org/10.1371/journal.pbio.1001324. (Epub 2012 May 8. PMID: 22589699; PMCID: PMC3348166)
Johnston D, Miao-Sin WuS (2001) Foundations of cellular neurophysiology. The MIT Press
Johnston D, Magee JC, Colbert CM, Cristie BR (1996) Active properties of neuronal dendrites. Annu Rev Neurosci 19:165–86. https://doi.org/10.1146/annurev.ne.19.030196.001121
Kaeser PS, Regehr WG (2014) Molecular mechanisms for synchronous, asynchronous, and spontaneous neurotransmitter release. Annu Rev Physiol 76:333–363. https://doi.org/10.1146/annurev-physiol-021113-170338. (Epub 2013 Nov 21. PMID: 24274737; PMCID: PMC4503208)
Karagas NE, Venkatachalam K (2019) Roles for the endoplasmic reticulum in regulation of neuronal calcium homeostasis. Cells. 10:1232. https://doi.org/10.3390/cells8101232
Kay AR, Wong RK (1987) Calcium current activation kinetics in isolated pyramidal neurones of the Ca1 region of the mature guinea-pig hippocampus. J Physiol 392:603–616. https://doi.org/10.1113/jphysiol.1987.sp016799
Khan S (2022) Endoplasmic reticulum in metaplasticity: from information processing to synaptic proteostasis. Mol Neurobiol 59(9):5630–5655. https://doi.org/10.1007/s12035-022-02916-1
Kim TH (2022) Schnitzer MJ Fluorescence imaging of large-scale neural ensemble dynamics. Cell. 185(1):9–41. https://doi.org/10.1016/j.cell.2021.12.007
Kirk LM, Harris KM, (2016) Dendritic spines In: eLS J, Wiley, Sons, Ltd (eds). https://doi.org/10.1002/9780470015902.a0000093.pub3
Koch C, Poggio T, Torre V (1983) Nonlinear interactions in a dendritic tree: localization, timing, and role in information processing. Proc Natl Acad Sci U S A 80(9):2799–2802. https://doi.org/10.1073/pnas.80.9.2799
LaFerla FM (2002) Calcium dyshomeostasis and intracellular signalling in Alzheimer’s disease. Nat Rev Neurosci 3(11):862–72. https://doi.org/10.1038/nrn960
Lagache T, Jayant K, Yuste R (2019) Electrodiffusion models of synaptic potentials in dendritic spines. J Comput Neurosci 47(1):77–89. https://doi.org/10.1007/s10827-019-00725-5
Larkum ME, Watanabe S, Nakamura T, Lasser-Ross N, Ross WN (2003) Synaptically activated Ca2 + waves in layer 2/3 and layer 5 rat neocortical pyramidal neurons. J Physiol 549(Pt 2):471–88. https://doi.org/10.1113/jphysiol.2002.037614
Lee KF, Soares C, Thivierge JP (2016) Béïque JC correlated synaptic inputs drive dendritic calcium amplification and cooperative plasticity during clustered synapse development. Neuron 89(4):784–99. https://doi.org/10.1016/j.neuron.2016.01.012
Li YX, Rinzel J (1994) Equations for InsP3 receptor-mediated [Ca2+] oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol 166(4):461–73. https://doi.org/10.1006/jtbi.1994.1041
Lopreore CL, Bartol TM, Coggan JS, Keller DX, Sosinsky GE, Ellisman MH, Sejnowski TJ (2008) Computational modeling of three-dimensional electrodiffusion in biological systems: application to the node of Ranvier. Biophys J 95(6):2624–35. https://doi.org/10.1529/biophysj.108.132167
Lu T, Trussell LO (2000) Inhibitory transmission mediated by asynchronous transmitter release. Neuron 26(3):683–94. https://doi.org/10.1016/s0896-6273(00)81204-0
Lu B, Zhou YC, Huber GA, Bond SD, Holst MJ, McCammon JA (2007) Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution. J Chem Phys. 127(13)
Mahajan G, Nadkarni S (2019) Intracellular calcium stores mediate metaplasticity at hippocampal dendritic spines. J Physiol. 597(13):3473–3502. https://doi.org/10.1113/JP277726
Martone ME, Zhang Y, Simpliciano VM, Carragher BO, Ellisman MH (1993) Three-dimensional visualization of the smooth endoplasmic reticulum in Purkinje cell dendrites. J Neurosci 13(11):4636–4646. https://doi.org/10.1523/JNEUROSCI.13-11-04636.1993
McCormick DA, Huguenard JR (1992) Oct;68(4):1384 – 400 A model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol. doi: https://doi.org/10.1152/jn.1992.68.4.1384. PMID: 1331356
Mori Y, Liu C, Eisenberg RS (2011) A model of electrodiffusion and osmotic water flow and its energetic structure. Physica D 240:1835–1852. https://doi.org/10.1016/j.physd.2011.08.010. (ISSN 0167–2789)
Nadkarni S, Sejnowski T, Bartol T, Thomas B, Charles S, Herbert L, Kristen H, Edward E (2013) Effects of presynaptic calcium store on short-term plasticity. Biophys J 102(3):670a
Nakamura T, Barbara JG, Nakamura K, Ross WN (1999) Synergistic release of Ca2 + from IP3-sensitive stores evoked by synaptic activation of mGluRs paired with backpropagating action potentials. Neuron 24(3):727–37. https://doi.org/10.1016/s0896-6273(00)81125-3
Nakamura T, Lasser-Ross N, Nakamura K, Ross WN (2002) Spatial segregation and interaction of calcium signalling mechanisms in rat hippocampal CA1 pyramidal neurons. J Physiol. 543(Pt 2):465–80. https://doi.org/10.1113/jphysiol.2002.020362
Narita K, Akita T, Osanai M, Shirasaki T, Kijima H, Kuba K (1998) A Ca2+-induced Ca2 + release mechanism involved in asynchronous exocytosis at frog motor nerve terminals. J Gen Physiol 112(5):593–609
Neymotin SA, Hilscher MM, Moulin TC, Skolnick Y, Lazarewicz MT, Lytton WW (2013) Ih tunes theta/gamma oscillations and cross-frequency coupling in an in silico CA3 model. PLoS One 8(10)
Neymotin SA, McDougal RA, Sherif MA, Fall CP, Hines ML, Lytton WW (2015) Neuronal calcium wave propagation varies with changes in endoplasmic reticulum parameters: a computer model. Neural Comput 27(4):898–924. https://doi.org/10.1162/NECO_a_00712
Padamsey Z, Foster WJ, Emptage NJ (2019) Intracellular Ca2+ release and synaptic plasticity: a tale of many stores. Neuroscientist 25(3):208–226. https://doi.org/10.1177/1073858418785334
Pawar A, Pardasani KR (2022) Effect of disturbances in neuronal calcium and IP3 dynamics on β-amyloid production and degradation. Cogn Neurodyn. https://doi.org/10.1007/s11571-022-09815-0
Pawar A, Pardasani KR (2022) Study of disorders in regulatory spatiotemporal neurodynamics of calcium and nitric oxide. Cogn Neurodyn. https://doi.org/10.1007/s11571-022-09902-2
Pawar A, Pardasani KR (2022) Effects of disorders in interdependent calcium and IP3 dynamics on nitric oxide production in a neuron cell. Eur Phys J Plus 137:543. https://doi.org/10.1140/epjp/s13360-022-02743-2
Pawar A, Pardasani KR (2022) Simulation of disturbances in interdependent calcium and β-amyloid dynamics in the nerve cell. Eur Phys J Plus 137:960. https://doi.org/10.1140/epjp/s13360-022-03164-x
Peercy BE (2008) Initiation and propagation of a neuronal intracellular calcium wave. J Comput Neurosci 25(2):334–48. https://doi.org/10.1007/s10827-008-0082-x
Pozzo Miller LD, Petrozzino JJ, Golarai G, Connor JA (1996) Ca2 + release from intracellular stores induced by afferent stimulation of CA3 pyramidal neurons in hippocampal slices. J Neurophysiol 76(1):554–62. https://doi.org/10.1152/jn.1996.76.1.554
Pozzo-Miller LD, Pivovarova NB, Leapman RD, Buchanan RA, Reese TS, Andrews SB (1997) Activity-dependent calcium sequestration in dendrites of hippocampal neurons in brain slices. J Neurosci. 17(22):8729–38. https://doi.org/10.1523/JNEUROSCI.17-22-08729.1997
Qian N, Sejnowski TJ (1989) An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons. Biol Cybern 62:1–15. https://doi.org/10.1007/BF00217656
Ross WN (2012) Understanding calcium waves and sparks in central neurons. Nat Rev Neurosci 13(3):157–68. https://doi.org/10.1038/nrn3168
Ross WN, Nakamura T, Watanabe S, Larkum M, Lasser-Ross N (2005) Synaptically activated ca2 + release from internal stores in CNS neurons. Cell Mol Neurobiol 25(2):283–95. https://doi.org/10.1007/s10571-005-3060-0
Sætra MJ, Einevoll GT, Halnes G (2020) An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms. PLoS Comput Biol 16(4)
Savić N, Sciancalepore M (1998) Intracellular calcium stores modulate miniature GABA-mediated synaptic currents in neonatal rat hippocampal neurons. Eur J Neurosci 10(11):3379–86. https://doi.org/10.1046/j.1460-9568.1998.00342.x
Schulte A, Blum R (2022) Shaped by leaky ER: homeostatic Ca2+ fluxes. Front Physiol 13
Singer A, Norbury J (2009) A Poisson-Nernst-Planck model for biological ion channels - an asymptotic analysis in a three-dimensional narrow funnel. SIAM J Appl Math 70(3):949–968. https://doi.org/10.1137/070687037
Solbrå A, Bergersen AW, van den Brink J, Malthe-Sørenssen A, Einevoll GT, Halnes G (2018) A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons. PLoS Comput Biol 14(10)
Solovyova N, Veselovsky N, Toescu EC, Verkhratsky A (2002) Ca(2+) dynamics in the lumen of the endoplasmic reticulum in sensory neurons: direct visualization of Ca(2+)-induced Ca(2+) release triggered by physiological Ca(2+) entry. EMBO J 21(4):622–30. https://doi.org/10.1093/emboj/21.4.622
Spacek J, Harris KM (1997) Three-dimensional organization of smooth endoplasmic reticulum in hippocampal CA1 dendrites and dendritic spines of the immature and mature rat. J Neurosci 17(1):190–203. https://doi.org/10.1523/JNEUROSCI.17-01-00190.1997
Stuart GJ, Spruston N (2015 Dec) Dendritic integration: 60 years of progress. Nat Neurosci 18(12):1713–1721. https://doi.org/10.1038/nn.4157Epub 2015 Nov 25. PMID: 26605882
Stutzmann GE (2005) Apr;11(2):110-5 Calcium dysregulation, IP3 signaling, and Alzheimer’s disease. Neuroscientist. doi: https://doi.org/10.1177/1073858404270899. PMID: 15746379
Taylor CW, Tovey SC (2010 Dec) IP(3) receptors: toward understanding their activation. Cold Spring Harb Perspect Biol 2(12):a004010. https://doi.org/10.1101/cshperspect.a004010Epub 2010 Oct 27. PMID: 20980441; PMCID: PMC2982166
Terasaki M, Slater NT, Fein A, Schmidek A, Reese TS (1994) Continuous network of endoplasmic reticulum in cerebellar Purkinje neurons. Proc Natl Acad Sci U S A. Aug 2;91(16):7510-4. doi: https://doi.org/10.1073/pnas.91.16.7510. PMID: 7519781; PMCID: PMC44431
Timofeeva Y, Coombes S (2003 Sep) Wave bifurcation and propagation failure in a model of ca(2+) release. J Math Biol 47(3):249–269. https://doi.org/10.1007/s00285-003-0205-yEpub 2003 May 15. PMID: 12955459
Watanabe S, Hong M, Lasser-Ross N, Ross WN (2006) Modulation of calcium wave propagation in the dendrites and to the soma of rat hippocampal pyramidal neurons. J Physiol. Sep 1;575(Pt 2):455 – 68. doi: https://doi.org/10.1113/jphysiol.2006.114231. Epub 2006 Jun 29. PMID: 16809362; PMCID: PMC1819440
Wen H, Hubbard JM, Rakela B, Linhoff MW, Mandel G, Brehm P Synchronous and asynchronous modes of synaptic transmission utilize different calcium sources.Elife. 2013 Dec24;2:e01206. doi: https://doi.org/10.7554/eLife.01206. PMID: 24368731; PMCID: PMC3869123.
Winograd M, Destexhe A, Sanchez-Vives MV, S A (2008) Hyperpolarization-activated graded persistent activity in the prefrontal cortex. Proc Natl Acad Sci U. May 20;105(20):7298 – 303. doi: https://doi.org/10.1073/pnas.0800360105. Epub 2008 May 12. PMID: 18474856; PMCID: PMC2438244
Yuste R (2013) Electrical compartmentalization in dendritic spines. Annu Rev Neurosci. Jul 8;36:429 – 49. doi: https://doi.org/10.1146/annurev-neuro-062111-150455. Epub 2013 May 29. PMID: 23724997
Acknowledgements
The research is supported by Science and Technology Innovation 2030 major projects(No. 2021ZD0203803), National Key R&D Program of China (No. 2019 YFA0709503), and China Scholarship Council, Beijing high-level discipline construction project-cognitive neuroscience, and China National Science Foundation (No.31601145). The Author thanks Dr. Alexander Dimitrov very much for his deep discussions.
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Li, Y. Differential behaviors of calcium-induced calcium release in one dimensional dendrite by Nernst–Planck equation, cable model and pure diffusion model. Cogn Neurodyn (2023). https://doi.org/10.1007/s11571-023-09952-0
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DOI: https://doi.org/10.1007/s11571-023-09952-0