References

1. Cohen, H.; Cooley, J. The numerical solution of the time-dependent Nernst-Planck equations. Biophys. J. 1965, 5, 145–162.
2. Van Roosbroeck, W. Theory of flows of electrons and holes in germanium and other semiconductors. Bell Sys. Tech. J. 1950, 29, 560–607.
3. Selberherr, S. Analysis and Simulation of Semiconductor Devices; Springer: New York, NY, USA, 1984; pp. 1–293.
4. Brumleve, T.R.; Buck, R.P. Numerical solution of the Nernst-Planck and Poisson equation system with applications to membrane electrochemistry and solid state physics. J. Electroanal. Chem. 1978, 90, 1–31.
5. Ivaska, A.; Bobacka, J.; Lewenstam, A. Potentiometric Ion Sensors. Chem. Rev. 2008, 108, 329–351.
6. Eisenberg, B. Interacting Ions in Biophysics: Real is not Ideal. Biophys. J. 2013, 104, 1849–1866.
7. Planck, M. Über die Potenzialdifferenz zwischen zwei werdünnten Lösungen binärer Electrolyte. Ann. Phys. Chem. 1890, 40, 561–576.
8. Schlögl, R. Elektrodiffusion i freier Lösung und geladenen membranen. Z. Phys. Chem. 1954, 1, 305–339.
9. Helfferich, F.G. Ion. Exchange; McGraw-Hill: New York, NY, USA, 1962; pp. 1–624.
10. Teorell, T. Transport process and electrical phenomena in ionic membranes. In Progress in Biophysics and Biophysical Chemistry; Butler, J.A.V., Randall, R.T., Eds.; Academic Press: New York, NY, USA, 2016; Volume 3, pp. 305–369.
11. Conti, F.; Eisenman, G. The non-steady state membrane potential of ion exchangers with fixed sites. Biophys. J. 1965, 5, 247–256.
12. Mafé, S.; Pellicer, J.; Aguilella, V.M. The Goldman constant field assumption: significance and applicability conditions. Ber. Bunsenges. Phys. Chem. 1986, 90, 476–479.
13. MacGillivray, A.D. Nernst-Planck equations and the electroneutrality and Donnan equilibrium assumptions. J. Chem. Phys. 1968, 48, 2903–2907.
14. MacGillivray, A.D.; Hare, D. Applicability of Goldman’s constant field assumption to biological systems. J. Theor. Biol. 1969, 25, 113–126.
15. Kato, M. Numerical analysis of the Nernst-Planck-Poisson system. J. Theor. Biol. 1995, 177, 299–304.
16. Savtchenko, L.P.; Poo, M.M.; Rusakov, D.A. Electrodiffusion phenomena in neuroscience: A neglected companion. Nature 2017, 18, 598–612.
17. Dickinson, E.J.F.; Limon-Petersen, J.G.; Compton, R.G. The electroneutrality approximation in electrochemistry. J. Solid State Electrochem. 2011, 15, 1335–1345.
18. Perram, J.W.; Stiles, P.J. On the nature of liquid junction and membrane potentials. Phys. Chem. Chem. Phys. 2006, 8, 4200–4213.
19. Mafé, S.; Pellicer, J.; Aguilella, V.M. Ionic transport and space charge density in electrolytic solutions as described by Nernst-Planck and Poisson equations. J. Phys. Chem. 1986, 90, 6045–6050.
20. Manzanares, J.A.; Mafé, S.; Pellicer, J. Transport phenomena and asymmetry effects in membranes with asymmetric fixed charge distributions. J. Phys. Chem. 1991, 95, 5620–5624.
21. Kontturi, A.K.; Kontturi, K.; Mafé, S.; Manzanares, J.A.; Niinikoski, P.; Vouristo, M. Convective diffusion in porous membranes with adsorbed charges. Langmuir 1994, 10, 949–954.
22. Kontturi, K.; Mafé, S.; Manzanares, J.A.; Pellicer, J.A. New Method for Determining Transport Numbers of Charged Membranes from Convective Diffusion Experiments. J. Electroanal. Chem. Interfacial Electrochem. 1994, 378, 111–116.
23. Sokalski, T.; Lewenstam, A. Application of Nernst-Planck and Poisson equations for interpretation of liquid junction and membrane potentials in real-time and space domains. Electrochem. Comm. 2001, 3, 107–112.
24. Sokalski, T.; Lingenfelter, P.; Lewenstam, A. Numerical solution of coupled Nernst-Planck and Poisson equations for liquid junction and ion selective membrane potentials. J. Phys. Chem. B 2003, 107, 2443–2452.
25. Lingenfelter, P.; Bedlechowicz-Śliwakowska, I.; Sokalski, T.; Maj-Żurawska, M.; Lewenstam, A. Time-dependent phenomena in the potential response of ion-selective electrodes treated by the Nernst-Planck-Poisson model. 1: Intramembrane processes and selectivity. Anal. Chem. 2006, 78, 6783–6791.
26. Lewenstam, A.; Sokalski, T.; Jasielec, J.; Kucza, W.; Filipek, R.; Wierzba, B.; Danielewski, M. Modelling Non Equilibrium Potentiometry to Understand and Control Selectivity and Detection Limit. ECS Trans. 2009, 19, 219–224.
27. Jasielec, J.J.; Sokalski, T.; Filipek, R.; Lewenstam, A. Comparison of different approaches to the description of the detection limit of ion-selective electrodes. Electrochim. Acta 2010, 55, 6836–6848.
28. Szyszkiewicz, K.; Danielewski, M.; Fausek, J.; Jasielec, J.J.; Kucza, W.; Lewenstam, A.; Sokalski, T.; Filipek, R. Breakthrough in modeling of electrodiffusion processes: Continuation and extensions of the classical work of Richard Buck. ECS Trans. 2014, 61, 21–30.
29. Jasielec, J.J.; Mousavi, Z.; Granholm, K.; Sokalski, T.; Lewenstam, A. Sensitivity and Selectivity of Ion-Selective Electrodes interpreted using the Nernst-Planck-Poisson model (NPP). Anal. Chem. 2018, 90, 9644–9649.
30. Rudolph, M.J. Digital simulations with the fast implicit finite-difference (FIFD) algorithm. Part 4. Simulation of electrical migration and diffuse double-layer effects. Electroanal. Chem. 1994, 375, 89–99.
31. Samson, E.; Marchand, J. Numerical solution of the extended Nernst-Planck model. J. Colloid Interface Sci. 1999, 215, 1–8.
32. Samson, E.; Marchand, J.; Robert, J.-L.; Bournazel, J.-P. Modelling ion diffusion mechanisms in porous media. Int. J. Numer. Meth. Engng. 1999, 46, 2043–2060.
33. Zhou, Y.C.; Lu, B.Z.; Huber, G.A.; Holst, M.J.; McCammon, J.A. Continuum simulations of acetylcholine consumption by acetylcholinesterase—A Poisson-Nernst-Planck approach. J. Phys. Chem. B 2008, 112, 270–275.
34. Lu, B.; Holst, M.J.; McCammon, J.A.; Zhou, Y.C. Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions. J. Comput. Phys. 2010, 229, 6979–6994.
35. Moya, A.A.; Horno, J. Application of the network simulation method to ionic transport in ion-exchange membranes including diffuse double-layer effects. J. Phys. Chem. B 1999, 103, 10791.
36. Moleón, J.A.; Moya, A.A. Network simulation of the electrical response of ion-exchange membranes with fixed charge varying linearly with position. J. Electroanal. Chem. 2008, 613, 23–34.
37. Moleón, J.A.; Moya, A.A. Transient electrical response of ion-exchange membranes with fixed-charge due to ion adsorption. A network simulation approach. J. Electroanal. Chem. 2009, 633, 306–313.
38. MacGillivray, A.D. Asymptotic Solutions of the Time-Dependent Nernst-Planck Equations. J. Chem. Phys. 1970, 52, 3126–3132.
39. Jasielec, J.J.; Filipek, R.; Szyszkiewicz, K.; Fausek, J.; Danielewski, M.; Lewenstam, A. Computer simulations of electrodiffusion problems based on Nernst-Planck and Poisson equations. Comp. Mat. Sci. 2012, 63, 75–90.
40. Grysakowski, B.; Bożek, B.; Danielewski, M. Electro-Diffusion in Multicomponent Ion-Selective Membranes; Numerical Solution of the Coupled Nernst–Planck–Poisson Equations. Defect Diffus. Forum 2008, 273–276, 113–118.
41. Grysakowski, B.; Jasielec, J.J.; Wierzba, B.; Sokalski, T.; Lewenstam, A.; Danielewski, M. Electrochemical Impedance Spectroscopy (EIS) of Ion Sensors. Direct modelling and inverse problem solving using the Nernst-Planck-Poisson (NPP) model and the HGS(FP) optimization strategy. J. Electroanal. Chem. 2011, 662, 143–149.
42. Jasielec, J.J.; Sokalski, T.; Filipek, R.; Lewenstam, A. Neutral-Carrier Ion-Selective Electrodes Assessed by Nernst-Planck-Poisson Model. Anal. Chem. 2015, 87, 8665–8672.
43. Jasielec, J.J.; Lisak, G.; Wagner, M.; Sokalski, T.; Lewenstam, A. Nernst-Planck-Poisson Model for the Qualitative Description of the Behaviour of Solid-Contact Ion-Selective-Electrodes at Low Analyte Concentration. Electroanalysis 2013, 25, 133–140.
44. Sanders, T.M.; Myers, M.; Asadnia, M.; Umana-Membreno, G.A.; Baker, M.; Fowkes, N.; Parish, G.; Nener, B. Description of ionophore-doped membranes with a blocked interface. Sens. Actuators B 2017, 250, 499–508.
45. Paczosa-Bator, B.; Stępień, M.; Maj-Żurawska, M.; Lewenstam, A. Biomimetic study of the Ca2+-Mg2+ and K+-Li+ antagonism on biologically active sites: New methodology to study potential dependent ion exchange. Magnes. Res. 2009, 22, 10–20.
46. Nowak, L.; Bregestovski, P.; Ascher, P.; Herbet, A.; Prochiantz, A. Magnesium gates glutamate-activated channels in mouse central neurons. Nature 1984, 307, 462–465.
47. Vargas-Caballero, M.; Robinson, H.P.C. Fast and slow voltage-dependent dynamics of magnesium block inthe NMDA receptor: The asymmetric trapping block model. J. Neurosci. 2004, 24, 6171–6180.
48. Chen, D.P.; Eisenberg, R.S. Poisson-Nernst-Planck (PNP) theory of open ionic channels. Biophys. J. 1993, 64, A22.
49. Harden, J.L.; Viovy, J.L. Numerical studies of pulsed iontophoresis through model membranes. J. Control. Released 1996, 38, 129–139.
50. Kurnikova, M.G.; Coalson, R.D.; Graf, P.; Nitzan, A. A lattice relaxation algorithm for 3D Poisson-Nernst-Planck with application to ion transport through the gramicidin A channel. Biophys. J. 1999, 76, 642–656.
51. McKelvey, J.P. Solid State and Semiconductor Physics; Krieger: Malabar, FL, USA, 1982; pp. 1–504.
52. Marchand, J.; Gérard, B.; Delagrave, A. Ion transport mechanism in cement-based materials. In Materials Science of Concrete; Skalny, J.P., Ed.; American Ceramic Society: Westerville, OH, USA, 1998; Volume V, pp. 307–400.
53. Krabbenhøft, K.; Krabbenhøft, J. Application of the Poisson–Nernst–Planck equations to the migration test. Cem. Concr. Res. 2008, 38, 77–88.
54. Szyszkiewicz, K.; Jasielec, J.J.; Danielewski, M.; Lewenstam, A.; Filipek, R. Modeling of electrodiffusion processes from nano to macro scale. J. Electrochem. Soc. 2017, 164, E3559–E3568.
55. Lakshminarayanaiah, N. Equations of Membrane Biophysics; Academic Press: New York, NY, USA, 1984.
56. Probstein, R.F. Physicochemical Hydrodynamics; Butterworth: Stoneham, NA, USA, 1989.
57. Critchlow, D.L. MOSFET scaling—The driver of VLSI technology. Proc. IEEE 1999, 87, 659–667.
58. Dennard, R.H.; Gaensslen, F.H.; LeBlanc, A.R. Design of non-implanted MOSFET’s with very small physical dimensions. Proc. IEEE 1999, 87, 668–678.
59. Hof, P.R.; de Vellis, J.; Nimchinsky, E.A.; Kidd, G.; Claudio, L.; Trapp, B.D. Cellular Components of Nervous Tissue. In Fundamental Neuroscience, 3rd ed.; Squire, L., Berg, D., Bloom, F., du Lac, S., Gosh, A., Spitzer, N., Eds.; Elsevier Science Publishing Co. Inc.: San Diego, CA, USA, 2012; pp. 41–58.
60. Savtchenko, L.P.; Kulahin, N.; Korogod, S.M.; Rusakov, D.A. Electric fields of synaptic currents could influence diffusion of charged neurotransmitter molecules. Synapse 2004, 51, 270–278.
61. Sylantyev, S.; Savtchenko, L.P.; Niu, Y.-P.; Ivanov, A.I.; Jensen, T.P.; Kullmann, D.M.; Xiao, M.-Y.; Rusakov, D.A. Electric Fields Due to Synaptic Currents Sharpen Excitatory Transmission. Science 2008, 319, 1845–1849.
62. Ercius, P.; Alaidi, O.; Rames, M.J.; Ren, G. Electron Tomography: A Three-Dimensional Analytic Tool for Hard and Soft Materials Research. Adv. Mater. 2015, 27, 5638–5663.
63. Leopre, C.L.; Bartol, T.M.; Coggan, J.S.; Keller, D.X.; Sosinsky, G.E.; Ellisman, M.H.; Sejnowski, T.J. Computational modelling of three dimensional electrodiffusion in biological systems: Application to the node of Ranvier. Biophys. J. 2008, 95, 2624–2635.
64. Cartailler, J.; Kwon, T.; Yuste, R.; Holcman, D. Deconvolution of voltage sensor time series and electro-diffusion modeling reveal the role of spine geometry in controlling synaptic strength. Neuron 2018, 97, 1–11.
65. Araya, R.; Jiang, J.; Eisenthal, K.B.; Yuste, R. The spine neck filters membrane potentials. Proc. Natl. Acad. Sci. USA 2006, 103, 17961–17966.
66. Araya, R.; Vogels, T.P.; Yuste, R. Activity-dependent dendritic spine neck changes are correlated with synaptic strength. Proc. Natl. Acad. Sci. USA 2014, 111, E2895–E2904.
67. Goldman, D.E. Potential, impedance, and rectification in membranes. J. Gen. Physiol. 1943, 27, 37–60.
68. 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.
69. Qian, N.; Sejnowski, T.J. An electro-diffusion model for computing membrane-potentials and ionic concentrations in branching dendrites, spines and axons. Biol. Cybern. 1989, 62, 1–15.
70. Holcman, D.; Yuste, R. The new nanophysiology: Regulation of ionic flow in neuronal subcompartments. Nat. Rev. Neurosci. 2015, 16, 685–692.
71. Gardner, C.L.; Jones, J.R.; Baer, S.M.; Chang, S. Simulation of the ephaptic effect in the cone-horizontal cell synapse of the retina. SIAM J. Appl. Math. 2013, 73, 636–648.
72. Gardner, C.L.; Jones, J.R.; Baer, S.M.; Crook, S.M. Drift-diffusion simulation of the ephaptic effect in the triad synapse of the retina. J. Comput. Neurosci. 2015, 38, 129–142.
73. Nanninga, P. A computational neuron model based on Poisson-Nernst-Planck theory. ANZIAM J. 2008, 50, 46–59.
74. Halnes, G.; Mäki-Marttunen, T.; Keller, D.; Pettersen, K.H.; Andreassen, O.A.; Einevoll, G.T. Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue. PLoS Comput. Biol. 2016, 12, e1005193.
75. Neher, E. Correction for liquid junction potentials in patch clamp experiments. Method Enzymol. 1992, 207, 123–131.
76. Lewenstam, A. Design and pitfalls of ion selective electrodes. Scand. J. Clin. Lab. Investig. Suppl. 1994, 54, 11–19.
77. Lewenstam, A. Ion-selective electrodes in clinical chemistry: State of the art. Anal. Proc. 1991, 28, 106–109.
78. Lewenstam, A.; Maj-Żurawska, M.; Hulanicki, A. Application of ion-selective electrodes in clinical analysis. Electroanalysis 1991, 3, 727–734.
79. Henderson, P. Zur thermodynamik der flüssigkeitsketten. Z. Phys. Chem. 1907, 59, 118–127.
80. Henderson, P. Zur thermodynamik der flüssigkeitsketten. Z. Phys. Chem. 1908, 63, 325–345.
81. Jerzy, J. Jasielec Website. Available online: (accessed on 9 December 2020).
82. Hickman, H.J. The liquid junction potential—The free diffusion junction. Chem. Eng. Sci. 1970, 25, 381–398.
83. Lingane, J.J. Electroanalytical Chemistry, 2nd ed.; Wiley: New York, NY, USA, 1998.
84. MacInnes, D.A. The Principles of Electrochemistry, 2nd ed.; Dover Publications: New York, NY, USA, 1961.
85. Nernst, W.H. Die elektromotorische wirksamkeit der jonen. Z. Phys. Chem. 1889, 4, 129–181.
86. Guggenheim, E.A. A study of cells with liquid-liquid junctions. J. Am. Chem. Soc. 1930, 52, 1315–1337.
87. Hafemann, D.R. Charge Separation in Liquid Junctions. J. Phys. Chem. 1965, 69, 4226–4231.
88. Dickinson, E.J.F.; Freitag, L.; Compton, R.G. Dynamic theory of liquid junction potentials. J. Phys. Chem. B 2010, 114, 187–197.
89. Ward, K.R.; Dickinson, E.J.F.; Compton, R.G. Dynamic theory of type 3 liquid junctions potentials: Formation of multilayer liquid junctions. J. Phys. Chem. B 2010, 114, 4521–4528.
90. Nelson, D.L.; Cox, M.M. Lehninger Principles of Biochemistry, 6th ed.; Freeman/Worth: New York, NY, USA, 2012; pp. 690–748.
91. Chung, S.-H.; Tieleman, D.P. Computational and theoretical approaches to Unraveling the Permeation Dynamics in Biological Nanotubes. In Handbook of Theoretical and Computational Nanotechnology; Rieth, M., Schommers, W., Eds.; American Scientific Publishers: Stevenson Ranch, CA, USA, 2006; Volume 10, pp. 1–54.
92. Århem, P.; Klement, G.; Blomberg, C. Channel Density Regulation of Firing Patterns in a Cortical Neuron Model. Biophys. J. 2006, 90, 4392–4404.
93. Zeberg, H.; Blomberg, C.; Århem, P. Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons. PLoS Comput. Biol. 2010, 6, e1000753.
94. Migliore, R.; Lupascu, C.A.; Bologna, L.L.; Romani, A.; Courcol, J.-D.; Antonel, S.; Van Geit, W.A.H.; Thomson, A.M.; Mercer, A.; Lange, S.; et al. The physiological variability of channel density in hippocampal CA1 pyramidal cells and interneurons explored using a unified data-driven modeling workflow. PLoS Comput. Biol. 2018, 14, e1006423.
95. Motipally, S.I.; Allen, K.M.; Williamson, D.K.; Marsat, G. Differences in Sodium Channel Densities in the Apical Dendrites of Pyramidal Cells of the Electrosensory Lateral Line Lobe. Front. Neural Circuits 2019, 13, 41.
96. Mori, Y.; Peskin, C.S.A. A numerical method for cellular electrophysiology based on the electrodiffusion equations with internal boundary conditions at membranes. Commun. Appl. Math. Comput. Sci. 2009, 4, 85–134.
97. Pods, J.; Schönke, J.; Bastian, P. Electrodiffusion model of neurons and extracellular space using the Poisson-Nernst-Planck equations—Numerical simnulation of intra- and extracellular potential for an axon model. Biophys. J. 2013, 105, 242–254.
98. Eisenberg, R.S. Channels are enzymes. J. Memb. Biol. 1990, 115, 1–12.
99. Schuss, Z.; Nadler, B.; Eisenberg, R.S. Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model. Phys. Rev. E 2001, 64, 036116.
100. Chen, D.; Lear, J.; Eisenberg, B. Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel. Biophys. J. 1997, 72, 97–116.
101. Woolley, G.A.; Biggin, P.C.; Schultz, A.; Lien, L.; Jaikaran, D.; Breed, J.; Crowhurst, K.; Sansom, M.S. Intrinsic rectifiction of ion flux in alamethicin channels: Studies with an alamethicin dimer. Biophys. J. 1997, 73, 770–778.
102. Nonner, W.; Chen, D.; Eisenberg, B. Anomalous mole fraction effect, electrostatics and binding in ionic channels. Biophys. J. 1998, 74, 2327–2334.
103. Aquilella-Arzo, M.; Aguilella, V.M.; Eisenberg, R.S. Computing numerically the access resistance of a pore. Eur. Biophys. J. 2005, 34, 314–322.
104. Hall, J.E. Access resistance of a small circular pore. J. Gen. Phys. 1975, 66, 531–532.
105. Nonner, W.; Eisenberg, B. Ion Permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels. Biophys. J. 1998, 75, 1287–1305.
106. Nonner, W.; Catacuzzeno, L.; Eisenberg, B. Binding and selectivity in L-type Ca channels. Biophys. J. 2000, 79, 1976–1992.
107. Eisenberg, B. Crowded Charges in Ion Channels. In Advances in Chemical Physics; Rice, S., Ed.; John Wiley & Sons: New York, NY, USA, 2011; pp. 77–223.
108. Eisenberg, B. Ionic interactions are everywhere. Physiology 2013, 28, 28–38.
109. Maffeo, C.; Bhattacharya, S.; Yoo, J.; Wells, D.; Aksimentiev, A. Modelling and simulation of Ion Channels. Chem. Rev. 2012, 112, 6250–6284.
110. Hollerbach, U.; Chen, D.-P.; Eisenberg, R.S. Two- and three- dimensional Poisson-Nernst-Planck simulations of current flow through Gramicidin A channel. J. Sci. Comp. 2001, 16, 373–409.
111. Valent, I.; Petrovič, P.; Neogrády, P.; Schreiber, I.; Marek, M. Electrodiffusion kinetics of ionic transport in a siple membrane channel. J. Phys. Chem. 2013, 117, 14283–14293.
112. Cárdenas, A.E.; Coalson, R.D.; Kurnikova, M.G. Three-dimensional Poisson-Nernst-Planck theory studies: Influence of membrane electrostatics on gramicidin A channel conductance. Biophys. J. 2000, 79, 80–93.
113. Koumanov, A.; Zachariae, U.; Engelhardt, H.; Karshikoff, A. Improved 3D continuum calculations of ion flux through membrane channels. Eur. Biophys. J. 2003, 32, 689–702.
114. Van der Straaten, T.A.; Tang, J.M.; Ravaioli, U.; Eisenberg, R.S.; Aluru, N.R. Simulating ion permeation through the ompF porin ion channel using three-dimensional drift-diffusion theory. J. Comput. Electron. 2003, 2, 29–47.
115. Roux, B. The membrane potential and its representation by a constant electric field in computer simulations. Biophys. J. 2008, 95, 4205–4216.
116. Kutzner, C.; Grubmuller, H.; de Groot, B.L.; Zachariae, U. Computational electrophysiology: The molecular dynamics of ion channel permeation and selectivity in atomistic detail. Biophys. J. 2011, 101, 809–817.
117. Jensen, M.; Borhani, W.; Lindorff-Larsen, K.; Maragakis, P.; Jogini, V.; Eastwood, M.P.; Dror, R.O.; Shaw, D.E. Principles of conduction and hydrophobic gating in K+ channels. Proc. Natl. Acad. Sci. USA 2010, 107, 5833–5838.
118. Bidon-Chanal, A.; Krammer, E.-M.; Blot, D.; Pebay-Peyroula, E.; Chipot, C.; Ravaud, S.; Dehez, F. How do membrane transporters sense pH? The case of mitochondrial ADP-ATP carrier. J. Phys. Chem. Lett. 2013, 4, 3787–3791.
119. Roux, B.; Allen, T.; Berneche, S.; Im, W. Theoretical and computational models of biological ion channels. Q. Rev. Biophys. 2004, 37, 15–103.
120. Krammer, E.-M.; Homblé, F.; Prévost, M. Molecular origin of VDAC selectivity towards inorganic ions: A combined molecular and Brownian dynamics study. Biochem. Biophys. Acta 2013, 1828, 1284–1292.
121. Boda, D.; Valiskó, M.; Gillespie, D. Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models. Entropy 2020, 22, 1259.
122. Miękisz, J.; Gomułkiewicz, J.; Miękisz, S. Mathematical models of ion transport through cell membrane channels. Math. Appl. 2014, 42, 39–62.
123. Kuyucak, S.; Andersen, O.S.; Chung, S.-H. Models of permeation in ion channels. Rep. Prog. Phys. 2001, 64, 1427–1472.
124. Corry, B.; Chung, S.-H. Mechanism of valence selectivity in biological ion channels. Cell Mol. Life Sci. 2006, 63, 301–315.
125. Liu, J.-L.; Eisenberg, B. Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model. Entropy 2020, 22, 550.
126. Bezanilla, F. The voltage sensor in voltage-dependent ion channels. Physiol. Rev. 2000, 80, 555–592.
127. Catteral, W.A. Ion channel voltage sensors: Structure, function, and pathophysiology. Neuron 2010, 67, 915–928.
128. Tombola, F.; Pathak, M.M.; Isacoff, E.Y. How does voltage open an ion channel? Annu. Rev. Cell. Dev. Biol. 2006, 22, 23–52.
129. Clarke, D.D.; Sokoloff, L. Circulation and energy metabolism of the brain. In Basic Neurochemistry: Molecular, Cellular, and Medical Aspects, 6th ed.; Siegel, G.J., Agranoff, B.W., Albers, R.W., Fisher, S.K., Uhler, M.D., Eds.; Lippincott-Raven: New York, NY, USA, 1999; pp. 637–669.
130. Jasielec, J.J.; Filipek, R.; Dołowy, K.; Lewenstam, A. Precipitation of Inorganic Salts in Mitochondrial Matrix. Membranes 2020, 10, 81.
131. Griffiths, T.; Evans, M.C.; Meldrum, B.S. Intracellular sites of early calcium accumulation in the rat hippocampus during status epilepticus. Neurosci. Lett. 1982, 30, 329–334.
132. Erecińska, M.; Silver, I.A. Relationships between ions and energy metabolism: Celebral calcium movements during ischemia and subsequent recovery. Can. J. Physiol. Pharmacol. 1992, 70, S190–S193.
133. Zaidan, E.; Sims, N.R. The calcium content of mitochondria from brain subregions following short-term forebrain ischemia and recirculation in the rat. J. Neurochem. 1994, 63, 1812–1819.
134. Fineman, I.; Hovda, D.A.; Smith, M.; Yoshino, A.; Becker, D.P. Concussive brain injury is associated with a prolonged accumulation of calcium: A 45Ca autoradiographic study. Brain Res. 1993, 624, 94–102.
135. Sparagna, G.C.; Gunter, K.K.; Sheu, S.S.; Gunter, T.E. Mitochondrial calcium uptake from physiological-type pulses of calcium. A description of the rapid uptake mode. J. Biol. Chem. 1995, 270, 27510–27515.
136. Williams, G.S.; Boyman, L.; Chikando, A.C.; Khairallah, R.J.; Lederer, W.J. Mitochondrial calcium uptake. Proc. Natl. Acad. Sci. USA 2013, 110, 10479–10486.
137. McCormack, J.G.; Denton, R.M. The role of mitochondrial Ca2+ transport and matrix Ca2+ in signal transduction in mammalian tissues. Biochim. Biophys. Acta 1990, 1018, 287–291.
138. Kannurpatti, S.S.; Sanganahalli, B.G.; Herman, P.; Hyder, F. Role of mitochondrial calcium uptake homeostasis on resting-state fMRI brain networks. NMR Biomed. 2015, 28, 1579–1588.
139. Jasielec, J.J.; Filipek, R.; Szyszkiewicz, K.; Sokalski, T.; Lewenstam, A. Continuous Modeling of Calcium Transport through Biological Membranes. J. Mater. Eng. Perform. 2016, 25, 3285–3290.
140. Lehninger, A.L.; Rossi, C.S.; Greenawalt, J.W. Respiration-dependent accumulation of inorganic phosphate and Ca ions by rat liver mitochondria. Biochem. Biophys. Res. Commun. 1963, 10, 444–448.
141. Lehninger, A.L. Mitochondria and calcium ion transport. Biochem. J. 1970, 119, 129–138.
142. Rossi, C.S.; Lehninger, A.L. Stoichiometric relationships between accumulation of ions by mitochondria and the energy-coupling sites in the respiratory chain. Biochem. Z. 1963, 338, 698–713.
143. Rossi, C.S.; Lehninger, A.L. Stoichiometry of respiratory stimulation, accumulation of Ca2+ and phosphate and oxidative phosphorylation in rat liver mitochondria. J. Biol. Chem. 1964, 239, 3971–3980.
144. Lehninger, A.L.; Carafoli, E.; Rossi, C.S. Energy-linked ion movements in mitochondrial systems. Adv. Enzymol. Relat. Areas Mol. Biol. 1967, 29, 259–320.
145. Arnaudeau, S.; Kelley, W.L.; Walsh, J.V.; Demaurex, N. Mitochondria recycle Ca2+ to the endoplasmic reticulum and prevent the depletion of neighboring endoplasmic reticulum regions. J. Biol. Chem. 2001, 276, 29430–29439.
146. Brandenburger, Y.; Kennedy, E.D.; Python, C.P.; Rossier, M.F.; Vallotton, M.B.; Wollheim, C.B.; Capponi, A.M. Possible role for mitochondrial calcium in angiotensin II- and potassium-stimulated steroidogenesis in bovine adrenal glomerulosa cells. Endocrinology 1996, 137, 5544–5551.
147. Schreur, J.H.; Figueredo, V.M.; Miyamae, M.; Shames, D.M.; Baker, A.J.; Camacho, S.A. Cytosolic and mitochondrial [Ca2+] in whole hearts using indo-1 acetoxymethyl ester: Effects of high extracellular Ca2+. Biophys. J. 1996, 70, 2571–2580.
148. Miyata, H.; Silverman, H.S.; Sollott, S.J.; Lakatta, E.G.; Stern, M.D.; Hansford, R.G. Measurement of mitochondrial free Ca2+ concentration in living single rat cardiac myocytes. Am. J. Physiol. 1991, 261, H1123–H1134.
149. Moreno-Sanchez, R.; Hansford, R.G. Dependence of cardiac mitochondrial pyruvate dehydrogenase activity on intramitochondrial free Ca2+ concentration. Biochem. J. 1988, 256, 403–412.
150. Allen, S.P.; Stone, D.; McCormack, J.G. The loading of fura-2 into mitochondria in the intact perfused rat heart and its use to estimate matrix Ca2+ under various conditions. J. Mol. Cell. Cardiol. 1992, 24, 765–773.
151. Lukács, G.L.; Kapus, A. Measurement of the matrix free Ca2+ concentration in heart mitochondria by entrapped fura-2 and quin2. Biochem. J. 1987, 248, 609–613.
152. Davis, M.H.; Altschuld, R.A.; Jung, D.W.; Brierley, G.P. Estimation of intramitochondrial pCa and pH by fura-2 and 2,7 biscarboxyethyl-5(6)-carboxyfluorescein (BCECF) fluorescence. Biochem. Biophys. Res. Commun. 1987, 149, 40–45.
153. Ivannikov, M.V.; Macleod, G.T. Mitochondrial free Ca2+ levels and their effects on energy metabolism in Drosophila motor nerve terminals. Biophys. J. 2013, 104, 2353–2361.
154. Dołowy, K. Calcium phosphate buffer formed in the mitochondrial matrix during preconditioning supports ∆pH formation and ischemic ATP production and prolongs cell survival—A hypothesis. Mitochondrion 2019, 47, 210–217.
155. Liou, G.Y.; Storz, P. Reactive oxygen species in cancer. Free Radic. Res. 2010, 44, 479–496.
156. Simonian, N.A.; Coyle, J.T. Oxidative Stress in Neurodegenerative Diseases. Ann. Rev. Pharmacol. Toxicol. 1996, 36, 83–106.
157. Barnham, K.J.; Masters, C.L.; Bush, A.I. Neurodegenerative diseases and oxidatives stress. Nat. Rev. Drug Discov. 2004, 3, 205–214.
158. Rao, A.V.; Balachandran, B. Role of oxidative stress and antioxidants in neurodegenerative diseases. Nutr. Neurosci. 2002, 5, 291–309.