Whole cell stochastic model reproduces the irregularities found in the membrane potential of bursting neurons

Journal of Neurophysiology

Volumn 94, Issue 2, 2005, Pages 1169-1179

  Carelli, Pedro V ^a   Reyes, Marcelo B ^a   Sartorelli, José C ^a   Pinto, Reynaldo D ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

CALCIUM; ION CHANNEL;

ADAPTATION; ARTICLE; CHAOTIC DYNAMICS; COMPARTMENT MODEL; CONDUCTANCE; CRUSTACEA; CYTOSOL; GANGLION; HODGKIN HUXLEY EQUATION; MOTONEURON; NERVE CELL MEMBRANE POTENTIAL; NERVE CELL NETWORK; NERVOUS SYSTEM; OSCILLATION; PRIORITY JOURNAL; PROBABILITY; RELIABILITY; REPRODUCIBILITY; STOCHASTIC MODEL; STOMATOGASTRIC GANGLION; SYNAPSE; WHOLE CELL;

ACTION POTENTIALS; ANIMALS; ELECTRIC STIMULATION; GANGLIA, INVERTEBRATE; ION CHANNELS; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NEURAL CONDUCTION; NEURONS; NONLINEAR DYNAMICS; PALINURIDAE; REACTION TIME; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 23044473361     PISSN: 00223077     EISSN: None     Source Type: Journal    
DOI: 10.1152/jn.00070.2005     Document Type: Article

References (51)

1. Abarbanel HDI. Analysis of Observed Chaotic Data. New York: Springer-Verlag, 1996.
2. Abraham RH and Shaw CD. Dynamics: The Geometry of Behavior. Redwood City, CA: Addison-Wesley, 1992.
3. Ayers J, Underwater walking. Arthropod Struct Dev 33: 347-360, 2004.
4. Bal T, Nagy F, and Moulins M. The pyloric central pattern generator in crustacea: a set of conditional neural oscillators. J Comp Physiol [A] 163: 715-727, 1988.
5. Carelli PV and Pinto RD. Chaos versus stochasticity in neural activity. First Neuroscience Symposium of the International Institute for Neuroscience of Natal, March 3-7. Natal, RN, Brazil, 2004.
6. Carelli PV, Reyes MB, Selverston AI, Sartorelli JC, and Pinto RD. A whole cell microscopic stochastic modeling of ion channels reproduces the low dimensional dynamics and sensitivity to initial conditions found in the macroscopic membrane potential of living neurons. Soc Neurosci Abstr 921.4, 2004.
7. Dayan P and Abbott LF. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, MIT Press 2001.
8. Desthexhe A, Mainen ZF, and Sejnowski TJ. Syntesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J Comput Neurosci 1: 195-231, 1994.
9. Elson RC, Huerta R, Abarbanel HDI, Rabinovich MI, and Selverston AI. Dynamic control of irregular bursting in an identified neuron of an oscillatory circuit. J Neurophysiol 82: 115-122, 1999.
10. Falcke M, Huerta R, Rabinovich MI, Abarbanel HDI, Elson RE, and Selverston AI. Modeling observed chaotic oscillations in bursting neurons: the role of calcium dynamics and IP3. Biol Cybern 82, 517-527, 2000.
11. Gillespie DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81: 2340-2361, 1977.
12. Guckenheimer J and Oliva R. Chaos in the Hodkin-Huxley model. SIAM J Appl Dyn Systems 1: 105-114, 2002.
13. Hegger, R, Kantz, H, and Schreiber, T. Practical implementation of nonlinear time series methods: the TISEAN package (TISEAN is freely down-loadable at http://www.mpipks-dresden.mpg.de/~tisean/). Chaos 9: 413-435, 1999.
14. Hille, B. Ionic Channels of Excitable Membranes (3rd ed.). Sunderland, MA: Sinauer, 2001.
15. Hodgkin AL and Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117: 500-544, 1952.
16. Holden AV. Nonlinear Science - The impact of biology. Int J Bif Chaos 7: 2075-2104, 1997.
17. Ikeda M. Calcium dynamics and circadian rhythms in suprachiasmatic nucleus neurons. Neuroscientist 10: 315-324, 2004.
18. Izhikevich EM. Neural excitability, spiking and bursting. Int J Bif and Chaos 10: 1171-1266, 2000.
19. Kandel ER, Schwartz JH, and Jessel TM. Principles of Neural Science (3rd ed.). Norwalk, CT: Appleton and Lange, 1991.
20. Kennel MB, Brown R, and Abarbanel HDI. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physiol Rev A 45: 3403, 1992.
21. Kepecs A and Wang X-J. Analysis of complex bursting in cortical pyramidal neuron models. Neurocomputing 32: 181-187, 2000.
22. Komendantov AO and Kononenko NI. Deterministic chaos in mathematical model of pacemaker activity in bursting neurons of snail Helix pomatia. J theor Biol 183: 219-230, 1996.
23. Levi R, Samoilova M, and Selverston AI. Calcium signaling components of oscillating invertebrate neurons in vitro. Neuroscience 118: 283-296, 2003.
24. Levitan IB and Kaczmarek LK. The Neuron: Cell and Molecular Biology (2nd ed.). Houston, TX: Oxford, 1997.
25. Meinen ZF and Sejnowski T. Reliability of spike timing in neocortical neurons. Science 268: 1503-1508, 1995.
26. Marder E. From biophysics to models of network function. Annu Rev Neurosci 21: 25-45, 1998.
27. Miller JP and Selverston AI. Rapid killing of single neurons by irradiation of intracellularly injected dye. Science 206: 702-704, 1979.
28. Mino H, Rubinstein JT, and White JA. Comparison of algorithms for the simulation of action potentials with stochastic sodium channels. Ann Biomed Eng 30: 578-587, 2002.
29. Mulloney B and Selverston AI. Organization of the stomatogastric ganglion of the spiny lobster. J Comp Physiol 91: 1-32, 1974.
30. Nicolelis MAL. Brain machine interfaces to restore motor function and probe neural circuits. Nat Rev Neurosci 4: 417-422, 2003.
31. Panchin YV, Arshavsky YI, Selverston AI, and Cleland TA. Lobster stomatogastric neurons in primary culture. I. Basic characteristics. J Neurophysiol 69: 1976-1992, 1993.
32. Parri HR and Crunelli V. Pacemaker calcium oscillations in thalamic astrocytes in situ. Neuroreport 12: 3897-3900, 2001.
33. Pinto RD, Varona P, Volkovskii AR, Szücs A, Abarbanel HDI, and Rabinovich MI. Synchronous behaviour of two coupled electronic neurons. Physiol Rev E 62: 2644-2656, 2000.
34. Prinz A. Neural networks: models and neurons show hybrid vigor in real time. Curr Biol 14: R661-R662, 2004.
35. Prinz A, Billimoria CP, and Marder E. Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. J Neurophysiol 90: 3998-4015, 2003a.
36. Prinz AA, Ramirez JM, Buzsaki G, and Stanley KJ. How dynamic interactions of intrinsic bursting and synaptic properties shape network functions. Soc Neurosci Abstr 813, 2004.
37. Prinz A, Thirumalai V, and Marder E. The functional consequences of changes in the strength and duration of synaptic inputs to oscillatory neurons. J Neurosci 23: 943-954, 2003b.
38. Rabinovich MI, Abarbanel HDI, Huerta R, Elson R, and Selverston AI. Self-regulation of chaos in neural systems: experimental and theoretical results. IEEE Trans Circ Syst I 44: 997-1005, 1997.
39. Rinzel J and Ermentrout GB. Analysis of neural excitability and oscillations. In: Methods in Neuronal Modelling, edited by Koch C and Segev I. Cambridge, MA: MIT Press, MA 1998.
40. Rowat PF and Elson RC. State-dependent effects of Na channel noise on neuronal burst generation. J Comput Neurosci 16: 87-112, 2004.
41. Sano M and Sawada Y. Measurement of the Lyapunov spectrum from a chaotic time series. Phys Rev Lett 55: 1082, 1985.
42. Schneidman E, Freedman B, and Segev I. Ion channel stochasticity may be critical in determining the reliability of spike timing. Neural Comput 10: 1679-1703, 1998.
43. Selverston AI and Moulins M (Editors). The Crustacean Stomatogastric System. Berlin: Springer-Verlag, 1986.
44. Selverston AI, Rabinovich MI, Abarbanel HDI, Elson R, Szucs A, Pinto RD, Huerta R, and Varona, P. Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators. J Physiol (Paris) 94: 357-374, 2000.
45. Skaugen E and Walløe L. Firing behavior in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta Physiol Scand 107: 343-363, 1979.
46. Szucs A, Pinto RD, Rabinovich MI, Abarbanel HDI, and Selverston AI. Synaptic modulation of the interspike interval signatures of bursting pyloric neurons. J Neurophysiol 89: 1363-1377, 2003.
47. Szücs A, Varona P, Volkovskii AR, Abarbanel HDI, Rabinovich MI, and Selverston AI. Interacting biological and electronic neurons generate realistic oscillatory rhythms. Neuroreport 11: 563-569, 2000.
48. Turrigiano G, LeMasson G, and Marder E. Selective regulation of current densities underlies spontaneous changes in the activity of cultured neurons. J Neurosci 15: 3640-3652, 1995.
49. White JA, Klink R, Alonso A, and Kay AR. Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J Neurophysiol 80: 262-269, 1998.
50. White JA, Rubinstein JT, and Kay AR. Channel noise in neurons. Trends Neurosci 23: 131-137, 2000.
51. +2 dynamics of isolated mouse β-cells and islets: implications for mathematical models. Biophys J 84: 2852-2870, 2003.