Membranes with the same ion channel populations but different excitabilities

PLoS ONE

Volumn 7, Issue 4, 2012, Pages

  Herrera Valdez, Marco Arieli ^a,b,c  

^a The University of Arizona   (United States)

^b UNIVERSITY OF ARIZONA   (United States)

^c UNIVERSITY OF PUERTO RICO AT CAYEY   (Puerto Rico)

Author keywords

[No Author keywords available]

Indexed keywords

ION CHANNEL;

ARTICLE; DYNAMICS; ELECTRIC CURRENT; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MEMBRANE CONDUCTANCE; MEMBRANE ELECTROPHYSIOLOGY; MEMBRANE POTENTIAL; NERVE CELL MEMBRANE; NERVE CELL STIMULATION; OSCILLATION; QUALITATIVE ANALYSIS; QUANTITATIVE ANALYSIS; SYNAPTIC POTENTIAL; ANIMAL; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; DIFFUSION; DROSOPHILA; PHYSIOLOGY; SYNAPSE;

ANIMALS; DIFFUSION; DROSOPHILA; ION CHANNELS; MEMBRANE POTENTIALS; MODELS, BIOLOGICAL; SYNAPSES;

EID: 84859810078     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0034636     Document Type: Article

References (84)

1. Hille B, (1992) Ionic Channels of Excitable Membranes. Sinauer Associates, Inc. Sunderland, Mass. 01375: Sinauer Associates.
2. Hodgkin AL, Huxley AF, (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117: 500-544.
3. DiFrancesco D, Noble D, (1985) A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philosophical Transactions of the Royal Society of London Series B, Biological Sciences 307: 353-398.
4. Johnston D, Wu SMS, Gray R, (1995) Foundations of cellular neurophysiology. MIT press Cambridge, MA.
5. Koch C, Segev I, (1998) Methods in neuronal modeling: from ions to networks. MIT press Cambridge, MA.
6. Izhikevich E, (2007) Dynamical Systems in Neuroscience. MIT Press, 55 Hayward Street, Cambridge MA 02142: MIT.
7. Ermentrout GB, Terman D, (2010) Foundations of mathematical neuroscience (Interdisciplinary applied mathematics series, Vol. 35) Springer Verlag.
8. Stevens CF, Tsien RW, (1979) Ion permeation through membrane channels, volume 3 Raven Press.
9. Weiss TF, (1996) Cellular biophysics, volume 2: electrical properties MIT Press.
10. Weiss TF, (1996) Cellular Biophysics, Volume 1: Transport MIT Press.
11. Goldman DE, (1943) Potential, impedance, and rectification in membranes. Journal of general Physiology 27: 37.
12. Eisenberg B, (1998) Ionic channels in biological membranes: natural nanotubes. Accounts of chemical research 31: 117-123.
13. Endresen LP, Hall K, Hoye JS, Myrheim J, (2000) A theory for the membrane potential of living cells. European Journal of Biophysics 29: 90-103.
14. Clay JR, Paydarfar D, Forger DB, (2008) A simple modification of the hodgkin and huxley equations explains type 3 excitability in squid giant axons. Journal of The Royal Society Interface 5: 1421-1428.
15. Clay JR, (2009) Determining k+ channel activation curves from k+ channel currents often requires the goldman-hodgkin-katz equation. Frontiers in Cellular Neuroscience 3.
16. Krinskiä VI, Kokoz IM, (1973) Analysis of the equations of excitable membranes. i. reduction of the hodgkins-huxley equations to a 2d order system]. Biofizika 18: 506.
17. Morris C, Lecar H, (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal 35: 193-213.
18. Rinzel J, (1985) Excitation dynamics: insights from simplified membrane models. In: Fed. Proc. 44. volume 2944.
19. Av-Ron E, Parnas H, Segel LA, (1991) A minimal biophysical model for an excitable and oscillatory neuron. Biological Cybernetics 65: 487-500.
20. Kepler TB, Abbott LF, Marder E, (1992) Reduction of conductance-based neuron models. Biological Cybernetics 66: 381-387.
21. Adrian RH, Chandler WK, Hodgkin AL, (1970) Voltage clamp experiments in striated muscle fibres. The Journal of Physiology 208: 607.
22. Fohlmeister JF, Coleman PA, Miller RF, (1990) Modeling the repetitive firing of retinal ganglion cells. Brain research 510: 343-345.
23. Buchholtz F, Golowasch J, Epstein IR, Marder E, (1992) Mathematical model of an identified stomatogastric ganglion neuron. Journal of neurophysiology 67: 332.
24. Traub RD, Wong RK, Miles R, Michelson H, (1991) A model of a ca3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. Journal of Neurophysiology 66: 635-650.
25. Ikeno H, Usui S, (1999) Mathematical description of ionic currents of the kenyon cell in the mushroom body of honeybee. Neurocomputing 26: 177-184.
26. Clay JR, (1984) Potassium channel kinetics in squid axons with elevated levels of external potassium concentration. Biophysical journal 45: 481-485.
27. Herrera-Valdez MA, Lega J, (2011) Reduced models for the pacemaker dynamics of cardiac cells. Journal of Theoretical Biology 270: 164-176.
28. Mitchell C, Schaeffer D, (2003) A two-current model for the dynamics of cardiac membrane. Bulletin of mathematical biology 65: 767-793.
29. Herrera-Valdez MA, (2011) Geometry and dynamics of minimal biophysical models of membrane excitability. Dissertation PhD in Mathematics University of Arizona.
30. Nonner W, Eisenberg R, (1998) Ion permeation and glutamate residues linked by poisson-nernstplanck theory in l-type calcium channels. Biophysical Journal 75: 1287-1305.
31. Aldrich RW, DPC, Stevens CF, (1983) A reinterpretation of mammalian sodium channel gating based on single channel recording. Nature 306: 436-441.
32. Destexhe A, Mainen ZF, Sejnowski TJ, (1994) An Efficient Method for Computing Synaptic Conductances Based on a Kinetic Model of Receptor Binding. Neural Computation 6: 14-18.
33. Willms AR, Baro DJ, Harris-Warrick RM, Guckenheimer J, (1999) An improved parameter estimation method for hodgkin-huxley models. Journal of Computational Neuroscience 6: 145-168.
34. Gerstner W, Kistler W, (2002) Spiking neuron models Cambridge University Press.
35. Herrera-Valdez MA, (2009) Relationship between nearly coincident spiking and common excitatory synaptic input in motor neurons. Ph.D. thesis, The University of Arizona.
36. Jack JJ, Redman SJ, Wong K, (1981) The components of synaptic potentials evoked in cat spinal motoneurones by impulses in single group ia afferents. Journal of Physiology 321: 65-96.
37. Wei A, Covarrubias M, Butler A, Baker K, Pak M, et al. (1990) K+ current diversity is produced by an extended gene family conserved in Drosophila and mouse. Science 248: 599.
38. Tsunoda S, Salkoff L, (1995) Genetic Analysis of Drosophila Neurons: Shal, Shaw, and Shab Encode Most Embryonic Potassium Currents. Journal of Neuroscience 15: 1741-1754.
39. Tsunoda S, Salkoff L, (1995) The major delayed rectifier in both Drosophila neurons and muscle is encoded by Shab. Journal of Neuroscience 15: 5209-5221.
40. Islas LD, Sigworth FJ, (1999) Voltage sensitivity and gating charge in Shaker and Shab family potassium channels. Journal of General Physiology 114: 723.
41. O'Dowd DK, Aldrich RW, (1988) Voltage-clamp analysis of sodium channels in wild-type and mutant Drosophila neurons. Journal of Neuroscience 8: 3633-3643.
42. Lin WH, Wright DE, Muraro NI, Baines RA, (2009) Alternative Splicing in the Voltage-Gated Sodium Channel DmNav Regulates Activation, Inactivation, and Persistent Current. Journal of Neurophysiology 102: 1994.
43. King GF, Escoubas P, Nicholson GM, (2008) Peptide toxins that selectively target insect na and ca channels. Channels 2: 100-116.
44. Lee D, O'Dowd DK, (1999) Fast Excitatory Synaptic Transmission Mediated by Nicotinic Acetylcholine Receptors in Drosophila Neurons. Journal of Neuroscience 19: 5311-5321.
45. Katz B, Miledi R, (1973) The binding of acetylcholine to receptors and its removal from the synaptic cleft. The Journal of physiology 231: 549.
46. Roerig B, Nelson DA, Katz LC, (1997) Fast synaptic signaling by nicotinic acetylcholine and serotonin 5-ht3 receptors in developing visual cortex. The Journal of neuroscience 17: 8353.
47. Galligan JJ, LePard KJ, Schneider DA, Zhou X, (2000) Multiple mechanisms of fast excitatory synaptic transmission in the enteric nervous system. Journal of the autonomic nervous system 81: 97-103.
48. Rasmusson RL, Clark JW, Giles WR, Shibata EF, Campbell DL, (1990) A mathematical model of bullfrog cardiac pacemaker cell. Am J Physiol 259: H352-H369.
49. Rasmusson RL, Clark JW, Giles WR, Robinson K, Clark RB, et al. (1990) A mathematical model of electrophysiological activity in the bullfrog atrial cell. Am J Physiol 259: H370-H389.
50. Wilders R, (2007) Computer modelling of the sinoatrial node. Medical and Biological Engineering and Computing 45: 189-207.
51. Ribalet B, PMB, (1982) Effects of sodium on beta-cell electrical activity. American Journal of Physiology-Cell Physiology 242: C296.
52. Fohlmeister JF, Miller RF, (1997) Impulse Encoding Mechanisms of Ganglion Cells in the Tiger Salamander Retina. Journal of Neurophysiology 78: 1935-1947.
53. Rinzel J, Ermentrout GB, (1989) Analysis of neural excitability and oscillations, Methods in neuronal modeling: From synapses to networks.
54. Strogatz SH, (1994) Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering. Westview Pr.
55. Rall W, (1959) Branching dendritic trees and motoneuron membrane resistivity. Experimental Neurology 1: 491-527.
56. Rall W, (1962) Theory of physiological properties of dendrites. Annals of the New York Academy of Sciences 96: 1071-1092.
57. Rall W, Rinzel J, (1973) Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. Biophysical journal 13: 648-688.
58. Kuhn A, Aertsen A, Rotter S, (2004) Neuronal integration of synaptic input in the uctuationdriven regime. Journal of Neuroscience 24: 2345.
59. Peng IF, Wu CF, (2007) Differential contributions of Shaker and Shab K+ currents to neuronal firing patterns in Drosophila. Journal of Neurophysiology 97: 780.
60. Yang J, Xing JL, Wu NP, Liu YH, Zhang CZ, et al. (2009) Membrane current-based mechanisms for excitability transitions in neurons of the rat mesencephalic trigeminal nuclei. Neuroscience 163: 799-810.
61. Vandenberg CA, Bezanilla F, (1991) Single-channel, macroscopic, and gating currents from sodium channels in the squid giant axon. Biophysical journal 60: 1499-1510.
62. Rinzel J, Baer SM, (1988) Threshold for repetitive activity for a slow stimulus ramp: a memory effect and its dependence on uctuations. Biophysical journal 54: 551-555.
63. Demir SS, Clark JW, Murphey CR, Giles WR, (1994) A mathematical model of a rabbit sinoatrial node cell. American Journal of Physiology-Cell Physiology 266: C832-C852.
64. Clay JR, (1991) A paradox concerning ion permeation of the delayed rectifier potassium ion channel in squid giant axons. The Journal of Physiology 444: 499.
65. Hardie RC, Minke B, (1994) Spontaneous activation of light-sensitive channels in drosophila photoreceptors. The Journal of general physiology 103: 389-407.
66. Smith LA, Wang XJ, Peixoto AA, Neumann EK, Hall LM, et al. (1996) A drosophila calcium channel α1 subunit gene maps to a genetic locus associated with behavioral and visual defects. The Journal of neuroscience 16: 7868-7879.
67. Warmke JW, Reenan RAG, Wang P, Qian S, Arena JP, et al. (1997) Functional expression of drosophila para sodium channels. The Journal of general physiology 110: 119.
68. Neher E, (1971) Two fast transient current components during voltage clamp on snail neurons. Journal of General Physiology 58: 36.
69. Baranauskas G, Martina M, (2006) Sodium currents activate without a hodgkin and huxley-type delay in central mammalian neurons. The Journal of Neuroscience 26: 671-684.
70. Tang X, Schmidt TM, Perez-Leighton CE, Kofuji P, (2010) Inwardly rectifying potassium channel kir4. 1 is responsible for the native inward potassium conductance of satellite glial cells in sensory ganglia. Neuroscience 166: 397-407.
71. Baer SM, Erneux T, Rinzel J, (1989) The slow passage through a Hopf bifurcation: delay, memory effects, and resonance. SIAM Journal on Applied mathematics 49: 55-71.
72. Hounsgaard J, Hultborn H, Jespersen B, Kiehn O, (1984) Intrinsic membrane properties causing a bistable behaviour of α-motoneurones. Experimental brain research 55: 391-394.
73. Lee RH, Heckman CJ, (1998) Bistability in spinal motoneurons in vivo: systematic variations in persistent inward currents. Journal of neurophysiology 80: 583.
74. Caldwell JH, Schaller KL, Lasher RS, Peles E, Levinson SR, (2000) Sodium channel Nav1. 6 is localized at nodes of Ranvier, dendrites, and synapses. Proceedings of the National Academy of Sciences of the United States of America 97: 5616.
75. Pak MD, Covarrubias M, Ratcliffe A, Salkoff L, (1991) A mouse brain homolog of the Drosophila Shab K+ channel with conserved delayed-rectifier properties. Journal of Neuroscience 11: 869.
76. Salkoff L, Baker K, Butler A, Covarrubias M, Pak MD, et al. (1992) An essential set of K+ channels conserved in ies, mice and humans. Trends in Neurosciences 15: 161-166.
77. Chu ZG, Zhou F, Hablitz JJ, (2000) Nicotinic acetylcholine receptor-mediated synaptic potentials in rat neocortex. Brain research 887: 399-405.
78. Walmsley B, Edwards FR, Tracey DJ, (1987) The probabilistic nature of synaptic transmission at a mammalian excitatory central synapse. The Journal of neuroscience 7: 1037.
79. Destexhe A, Mainen ZF, Sejnowski TJ, (1994) Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. Journal of Computational Neuroscience 1: 195-230.
80. Prinz A, Billimoria C, Marder E, (2003) Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. Journal of Neurophysiology 90: 3998.
81. Nowotny T, Szücs A, Levi R, Selverston AI, (2007) Models wagging the dog: are circuits constructed with disparate parameters? Neural Computation 19: 1985-2003.
82. Schulz DJ, Goaillard JM, Marder EE, (2007) Quantitative expression profiling of identified neurons reveals cell-specific constraints on highly variable levels of gene expression. Proceedings of the National Academy of Sciences 104: 13187.
83. Pedersen MG, (2010) A Biophysical Model of Electrical Activity in Human β-Cells. Biophysical journal 99: 3200-3207.
84. Duch C, Vonhoff F, Ryglewski S, (2008) Dendrite elongation and dendritic branching are affected separately by different forms of intrinsic motoneuron excitability. Journal of Neurophysiology 100: 2525.