Theoretical Study of the Function of the IP3 Receptor / BK Channel Complex in a Single Neuron
Large conductance calcium-activated potassium (BK) channels carry out many functions in the central nervous system. The opening of BK channels requires a rise in the cytosolic calcium ([Ca2+]cyt) concentration, which can occur in two ways: calcium influx from voltage-gated calcium channels (VGCCs) located on the plasma membrane and calcium efflux through the endoplasmic reticulum (ER) membrane to the cytosol triggered by inositol 1,4,5-trisphosphate (IP3) receptors (IP3-Rs) and ryanodine receptors (RyRs). The BK channel/IP3-R/RyR interaction has been widely reported in smooth muscle but scarce information exist on neurons, where its presence is uncertain. The aim of this study was to develop a computational model of a neuron to replicate the interaction between the release of Ca2+ from the ER (through IP3-Rs and RyRs) and the opening of BK channels on the plasma membrane to regulate the level of [Ca2+]cyt, based on the Hodgkin-Huxley formalism and the Goldbeter model. The mathematical models were implemented on Visual Basic® and differential equations were solved numerically. Various conditions of BK conductance and the efflux of endoplasmic Ca2+ were explored. The results show that an abrupt increase in [Ca2+]cyt (≥ 5 mM) activates the BK channels and either pauses or stops the action potential train.
Sausbier U, Sausbier M, Sailer CA, Arntz C, Knaus HG, Neuhuber W, et al. Ca2+-activated K+ channels of the BK-type in the mouse brain. Histochem Cell Biol [Internet]. 2005;125(6):725–41. Available from: https://doi.org/10.1007/s00418-005-0124-7
Faber ESL, Sah P. Calcium-Activated Potassium Channels : Multiple Contributions to Neuronal Function. Neurosci [Internet]. 2003;9(3):181–94. Available from: https://doi.org/10.1177/1073858403009003011
Meech RW. Intracellular calcium injection causes increased potassium conductance in Aplysia nerve cells. Comp Biochem Physiol Part A Physiol [Internet]. 1972;42(2):493–9. Available from: https://doi.org/10.1016/0300-9629(72)90128-4
Latorre R, Castillo K, Carrasquel-Ursulaez W, Sepulveda RV, Gonzalez-Nilo F, Gonzalez C, et al. Molecular determinants of BK channel functional diversity and functioning. Physiol Rev [Internet]. 2017;97(1):39–87. Available from: https://doi.org/10.1152/physrev.00001.2016
Kshatri AS, Gonzalez-Hernandez A, Giraldez T. Physiological Roles and Therapeutic Potential of Ca2+ Activated Potassium Channels in the Nervous System. Front Mol Neurosci [Internet]. 2018;11:1–18. Available from: https://doi.org/10.3389/fnmol.2018.00258
Lee US, Cui J. BK channel activation : structural and functional insights. Trends Neurosci [Internet]. 2010;33(9):415–23. Available from: https://doi.org/10.1016/j.tins.2010.06.004
Horrigan FT, Aldrich RW. Coupling between voltage sensor activation , Ca2+ binding and channel opening in large conductance (BK) potassium channels. J Gen Physiol [Internet]. 2002;120:267–305. Available from: https://doi.org/10.1085/jgp.20028605
Ha GE, Cheong E. Spike frequency adaptation in neurons of the central nervous system. Exp Neurobiol [Internet]. 2017;26(4):179–85. Available from: https://doi.org/10.5607/en.2017.26.4.179
Bock T, Stuart GJ. The Impact of BK Channels on Cellular Excitability Depends on their Subcellular Location. Front Cell Neurosci [Internet]. 2016;10:1–8. Available from: https://doi.org/10.3389/fncel.2016.00206
Gu N, Vervaeke K, Storm JF. BK potassium channels facilitate high-frequency firing and cause early spike frequency adaptation in rat CA1 hippocampal pyramidal cells. J Physiol [Internet]. 2007;3:859–82. Available from: https://doi.org/10.1113/jphysiol.2006.126367
Berkefeld H, Fakler B, Schulte U. Ca2+-Activated K+ Channels: From Protein Complexes to Function. Physiol Rev [Internet]. 2010;90(4):1437–59. Available from: https://doi.org/10.1152/physrev.00049.2009
Misonou H, Menegola M, Buchwalder L, Park E, Meredith A, Rhodes K, et al. Immunolocalization of the Ca2+ -activated K+ channel Slo1 in axons and nerve terminals of mammalian brain and cultured neurons. J Comp Neurol [Internet]. 2006;496(3):289–302. Available from: https://doi.org/10.1002/cne.20931
Wang Z-W. Regulation of Synaptic Transmission by Presynaptic CaMKII and BK Channels. Mol Neurobiol [Internet]. 2008;38(2):153–66. Available from: https://doi.org/10.1007/s12035-008-8039-7
Griguoli M, Sgritta M, Cherubini E. Presynaptic BK channels control transmitter release: physiological relevance and potential therapeutic implications. J Physiol [Internet]. 2016;13:3489–500. Available from: https://doi.org/10.1113/JP271841
Bygrave FL, Benedetti A. What is the concentration of calcium ions in the endoplasmic reticulum? Cell Calcium [Internet]. 1996;19(6):547–51. Available from: https://doi.org/10.1016/s0143-4160(96)90064-0
Berridge MJ. Calcium microdomains: Organization and function. Cell Calcium [Internet]. 2006;40(5–6):405–12. Available from: https://doi.org/10.1016/j.ceca.2006.09.002
Dopico AM, Bukiya AN, Jaggar JH. Calcium- and voltage-gated BK channels in vascular smooth muscle. Pflügers Archiv [Internet]. 2018;470(9):1271–89. Available from: https://doi.org/10.1007/s00424-018-2151-y
Fakler B, Adelman JP. Control of KCa Channels by Calcium Nano/Microdomains. Neuron [Internet]. 2008;59(6):873–81. Available from: https://doi.org/10.1016/j.neuron.2008.09.001
Samtleben S, Jaepel J, Fecher C, Andreska T, Rehberg M, Blum R. Direct imaging of ER calcium with targeted-esterase induced dye loading (TED). J Vis Exp [Internet]. 2013;(75):1–17. Available from: https://doi.org/10.3791/50317
Verkhratsky A. Physiology and Pathophysiology of the Calcium Store in the Endoplasmic Reticulum of Neurons. Physiol Rev [Internet]. 2005;85(1):201–79. Available from: https://doi.org/10.1152/physrev.00004.2004
Karagas NE, Venkatachalam K. Roles for the Endoplasmic Reticulum in Regulation of Neuronal Calcium Homeostasis. Cells [Internet]. 2019;8(10):1232. Available from: https://doi.org/10.3390/cells8101232
Foskett JK, White C, Cheung K-H, Mak D-OD. Inositol Trisphosphate Receptor Ca2+ Release Channels. Physiol Rev [Internet]. 2007;87(2):593–658. Available from: https://doi.org/10.1152/physrev.00035.2006
Irie T, Trussell LO. Double-Nanodomain Coupling of Calcium Channels, Ryanodine Receptors, and BK Channels Controls the Generation of Burst Firing. Neuron [Internet]. 2017;96(4):856-870.e4. Available from: https://doi.org/10.1016/j.neuron.2017.10.014
Wu Y, Whiteus C, Xu CS, Hayworth KJ, Weinberg RJ, Hess HF, et al. Contacts between the endoplasmic reticulum and other membranes in neurons. Proc Natl Acad Sci U S A [Internet]. 2017;114(24):E4859–67. Available from: https://doi.org/10.1073/pnas.1701078114
Terasaki M, Shemesh T, Kasthuri N, Klemm RW, Hayworth KJ, Hand AR, et al. Stacked endoplasmic reticulum sheets are connected by helicoidal membrane motifs. Cell [Internet]. 2013;154(2):285–96. Available from: https://doi.org/10.1016/j.cell.2013.06.031
Takahashi K, Wood RL. Subsurface cisterns in the Purkinje cells of cerebellum of Syrian hamster. Zeitschrift für Zellforsch und Mikroskopische Anat [Internet]. 1970;110(3):311–20. Available from: https://doi.org/10.1007/BF00321144
Pan NC, Bai YF, Yang Y, Hökfelt T, Xu ZQD. Activation of galanin receptor 2 stimulates large conductance Ca2+ -dependent K+ (BK) channels through the IP3 pathway in human embryonic kidney (HEK293) cells. Biochem Biophys Res Commun [Internet]. 2014;446(1):316–21. Available from: https://doi.org/10.1016/j.bbrc.2014.02.110
Mujica PE, González FG. Interaction between IP3 receptors and BK channels in arterial smooth muscle: Non-canonical IP3 signaling at work. J Gen Physiol [Internet]. 2011;137(5):473–7. Available from: https://doi.org/10.1085/jgp.201110607
Bootman MD, Collins TJ, Peppiatt CM, Prothero LS, MacKenzie L, De Smet P, et al. Calcium signalling - An overview. Semin Cell Dev Biol [Internet]. 2001;12(1):3–10. Available from: https://doi.org/10.1006/scdb.2000.0211
Larkum ME, Watanabe S, Nakamura T, Lasser-Ross N, Ross WN. Synaptically Activated Ca2+ Waves in Layer 2/3 and Layer 5 Rat Neocortically Pyramidal Neurons. J Physiol [Internet]. 2003;549(2):471–88. Available from: https://doi.org/10.1113/jphysiol.2002.037614
Ross WN. Understanding calcium waves and sparks in central neurons. Nat Rev Neuoscience [Internet]. 2015;13(3):157–68. Available from: https://doi.org/10.1038/nrn3168
Goldbeter A, Dupont G, Berridge MJ. Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci U S A [Internet]. 1990;87(4):1461–5. Available from: https://doi.org/10.1073/pnas.87.4.1461
De Young GW, Keizer J. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci U S A [Internet]. 1992;89(20):9895–9. Available from: https://doi.org/10.1073/pnas.89.20.9895
Li Y-X, Rinzel J. Equations for InsP3 Receptor-mediated [Ca2+]i Oscillations Derived from a Detailed Kinetic Model: A Hodgkin-Huxley Like Formalism. J Theor Biol [Internet]. 1994;166(4):461–73. Available from: https://doi.org/10.1006/jtbi.1994.1041
Bezprozvanny I, Ehrlich BE. Inositol (1,4,5)-trisphosphate (Insp3)-gated Ca channels from cerebellum: Conduction properties for divalent cations and regulation by intraluminal calcium. J Gen Physiol [Internet]. 1994;104(5):821–56. Available from: https://doi.org/10.1085/jgp.104.5.821
Keizer J, Li YX, Stojilkovic S, Rinzel J. Essay InsP3-induced Ca2+ excitability of the endoplasmic reticulum. Mol Biol Cell [Internet]. 1995;6:945–51. Available from: https://doi.org/10.1091/mbc.6.8.945
Tang Y, Stephenson JL, Othmer HG. Simplification and Analysis of Models of Calcium Dynamics Based on IP3-Sensitive Calcium Channel Kinetics. Biophys J [Internet]. 1996;70(1):246–63. Available from: https://doi.org/10.1016/S0006-3495(96)79567-X
Sneyd J, Falcke M. Models of the inositol trisphosphate receptor. Prog Biophys Mol [Internet]. 2005;89(3):207–45. Available from: https://doi.org/10.1016/j.pbiomolbio.2004.11.001
Kötter R. Neuroscience Databases: A Practical Guide. New York: Springer; 2003. 310 p.
Hituri K, Linne M-L. Comparison of Models for IP3 Receptor Kinetics Using Stochastic Simulations. PLoS One [Internet]. 2013;8(4): e59618. Available from: https://doi.org/10.1371/journal.pone.0059618
Edgerton JR, Reinhart PH. Distinct contributions of small and large conductance Ca2+- activated K+ channels to rat Purkinje neuron function. J Physiol [Internet]. 2003;548(1):53–69. Available from: https://doi.org/10.1113/jphysiol.2002.027854
Blaustein MP, Golovina VA. Structural complexity and functional diversity of endoplasmic reticulum Ca2+ stores. Trends Neurosci [Internet]. 2001;24(10):602–8. Available from: https://doi.org/10.1016/s0166-2236(00)01891-9
Sterratt D, Graham B, Gillies A, Willshaw D. Principles of Computational Modelling in Neuroscience. Cambridge: Cambridge University Press; 2011. 300p.
Traub RD, Miles R. Neuronal Networks Hippocampus. Cambridge: Cambridge University Press; 1991. 281p.
Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in Nerve. J Physiol [Internet]. 1952;117(4):500–44. Available from: https://doi.org/10.1113/jphysiol.1952.sp004764
McCarron JG, Chalmers S, Bradley KN, MacMillan D, Muir TC. Ca2+ microdomains in smooth muscle. Cell Calcium [Internet]. 2006;40(5–6):461–93. Available from: https://doi.org/10.1016/j.ceca.2006.08.010
Blackwell KT. Approaches and tools for modeling signaling pathways and calcium dynamics in neurons. J Neurosci Methods [Internet]. 2013;220(2):131-140. Available from: https://doi.org/10.1016/j.jneumeth.2013.05.008
Chen-Engerer HJ, Hartmann J, Karl RM, Yang J, Feske S, Konnerth A. Two types of functionally distinct Ca2+ stores in hippocampal neurons. Nat Commun [Internet]. 2019;10(1):1–8. Available from: https://doi.org/10.1038/s41467-019-11207-8
Dupont G, Goldbeter A. One-pool model for Ca2+ oscillations involving Ca2+ and inositol 1,4,5-triphosphate as co-agonists for Ca2+ release. Cell Calcium [Internet]. 1993;14(4):311–22. Available from: https://doi.org/10.1016/0143-4160(93)90052-8
Blackwell KT. Modeling calcium concentration and biochemical reactions. Brains, Minds, and Media [Internet]. 2005;1:1–27. Available from: https://www.brains-minds-media.org/archive/224
Zill DG. Ecuaciones diferenciales con aplicaciones. México: Grupo Editorial Iberoamérica; 1988. 516p. Spanish.
Constantinides A. Applied Numerical Methods with Personal Computers. New York, USA: McGraw-Hill International Editions; 1987. 626p.
Foskett JK, White C, Cheung K-H, Mak D-OD. Inositol Trisphosphate Receptor Ca2+ release channels. Physiol Rev [Internet]. 2007;87(2):593–658. Available from: https://doi.org/10.1152/physrev.00035.2006
Khodakhah K, Ogden D. Fast activation and inactivation of inositol trisphosphate‐evoked Ca2+ release in rat cerebellar Purkinje neurones. J Physiol [Internet]. 1995;487(2):343–58. Available from: https://doi.org/10.1113/jphysiol.1995.sp020884
Cheng H, Lederer WJ. Calcium Sparks. Physiol Rev [Internet]. 2008;88(4):1491–545. Available from: https://doi.org/10.1152/physrev.00030.2007
Naraghi M, Neher E. Linearized Buffered Ca2+ Diffusion in Microdomains and Its Implications for Calculation of [Ca2+] at the Mouth of a Calcium Channel. J Neurosci [Internet]. Available from: 1997;17(18):6961–73. Available from: https://doi.org/10.1523/JNEUROSCI.17-18-06961.1997
Rizzuto R, Pozzan T. Microdomains of Intracellular Ca2+: Molecular Determinants and Functional Consequences. Physiol Rev [Internet]. 2006;86(1):369–408. Available from: https://doi.org/10.1152/physrev.00004.2005
Weaver AK, Olsen ML, McFerrin MB, Sontheimer H. BK Channels Are Linked to Inositol 1,4,5-Triphosphate Receptors via Lipid Rafts: A novel mechanism for coupling [Ca2+]i to ion channel activation. J Biol Chem [Internet]. 2007;282(43):31558–68. Available from: https://doi.org/10.1074/jbc.M702866200
Koch C, Segev I. Methods in Neuronal Modeling. Cambridge: The MIT Press; 1999. 671p.
Berkefeld H, Fakler B. Repolarizing Responses of BKCa-Cav Complexes Are Distinctly Shaped by Their Cav Subunits. J Neurosci [Internet]. 2008;28(33):8238–45. Available from: https://doi.org/10.1523/JNEUROSCI.2274-08.2008
Hou P, Xiao F, Liu H, Yuchi M, Zhang G, Wu Y, et al. Extrapolating microdomain Ca2+ dynamics using BK channels as a Ca2+ sensor. Sci Rep [Internet]. 2016;6:17343. Available from: https://doi.org/10.1038/srep17343
Meyer T, Stryer L. Molecular model for receptor-stimulated calcium spiking. Proc Natl Acad Sci U S A [Internet]. 1988;85(14):5051–5. Available from: https://doi.org/10.1073/pnas.85.14.5051
Clements MA, Swapna I, Morikawa H. Inositol 1,4,5-Triphosphate Drives Glutamatergic and Cholinergic Inhibition Selectively in Spiny Projection Neurons in the Striatum. J Neurosci [Internet]. 2013;33(6):2697–708. Available from: https://doi.org/10.1523/JNEUROSCI.4759-12.2013
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