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Journal of Computational Neuroscience

, Volume 19, Issue 1, pp 39–51 | Cite as

Fractal Stochastic Modeling of Spiking Activity in Suprachiasmatic Nucleus Neurons

  • Sung-IL Kim
  • Jaeseung Jeong
  • Yongho Kwak
  • Yang In Kim
  • Seung Hun Jung
  • Kyoung J. Lee
Article

Abstract

Individual neurons in the suprachiasmatic nucleus (SCN), the master biological clock in mammals, autonomously produce highly complex patterns of spikes. We have shown that most (~90%) SCN neurons exhibit truly stochastic interspike interval (ISI) patterns. The aim of this study was to understand the stochastic nature of the firing patterns in SCN neurons by analyzing the ISI sequences of 150 SCN neurons in hypothalamic slices. Fractal analysis, using the periodogram, Fano factor, and Allan factor, revealed the presence of a 1/f-type power-law (fractal) behavior in the ISI sequences. This fractal nature was persistent after the application of the GABAA receptor antagonist bicuculline, suggesting that the fractal stochastic activity is an intrinsic property of individual SCN neurons. Based on these physiological findings, we developed a computational model for the stochastic SCN neurons to find that their stochastic spiking activity was best described by a gamma point process whose mean firing rate was modulated by a fractal binomial noise. Taken together, we suggest that SCN neurons generate temporal spiking patterns using the fractal stochastic point process.

Keywords

suprachiasmatic nucleus interspike intervals fractal stochastic gamma point processes long-term correlations 

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References

  1. Achermann P, Kunz H (1999) Modeling circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators: Phase shifts and phase response curves. Journal of Biological Rhythms 14: 460–468.CrossRefPubMedGoogle Scholar
  2. Allan DW (1966) Statistics of atomic frequency standards. Proceedings of the IEEE 54: 221–230.Google Scholar
  3. Antle MC, Foley DK, Foley NC, Silver R (2003) Gates and oscillators: A network model of the brain clock. Journal of Biological Rhythms 18: 339–350.CrossRefPubMedGoogle Scholar
  4. Colwell CS (2000) Rhythmic coupling among cells in the suprachiasmatic nucleus. Journal of Neurobiology 43: 379–388.CrossRefPubMedGoogle Scholar
  5. Cox DR, Lewis PAW (1966) The Statistical Analysis of Series of Events. Wiley, New York, pp. 17–36.Google Scholar
  6. Forger DB, Dean DA 2nd, Gurdziel K, Leloup JC, Lee C, Von Gall C, Etchegaray JP, Kronauer RE, Goldbeter A, Peskin CS, Jewett ME, Weaver DR (2003) Development and validation of computational models for mammalian circadian oscillators. OMICS A Journal of Integrative Biology 7: 387–400.CrossRefPubMedGoogle Scholar
  7. Gillette MU (1991) SCN electrophysiology in vitro: Rhythmic activity and endogenous clock properties. In: DC Klein, RY Moore, SM Reppert, eds. Suprachiasmatic Nucleus: The Mind’s Clock, Oxford University Press, New York, NY, pp. 125–143.Google Scholar
  8. Goldbeter A (1995) A model for circadian oscillations in the Drosophila period protein (PER). Proceeding of Rotal Society in Lond B Biological Science 261: 319–324.Google Scholar
  9. Gruneis F, Nakao M, Mizutani Y, Yamamoto M, Meesmann M, Musha T (1993) Further study on 1/f fluctuations observed in central single neurons during REM sleep. Biological Cybernetics 68: 193–198.PubMedGoogle Scholar
  10. Inouye ST, Kawamura H (1979) Persistence of circadian rhythmicity in a mammalian hypothalamic “island” containing the suprachiasmatic nucleus. Proceedings of National Academy of Sciences USA 76: 5962–5966.Google Scholar
  11. Jagota A, de la Iglesia HO, Schwartz WJ (2000) Morning and evening circadian oscillations in the suprachiasmatic nucleus in vitro. Nature Neuroscience 3: 372–376.CrossRefPubMedGoogle Scholar
  12. Jeong J, Kwak Y, Kim YI, Lee KJ (submitted) Temporal dynamics underlying spiking patterns of the rat suprachiasmatic nucleus in vitro.Google Scholar
  13. Jewett ME, Kronauer RE (1998) Refinement of a limit cycle oscillator model of the effects of light on the human circadian pacemaker. Journal of Theoretical Biology 192: 455–465. Erratum in: J Theor Biol 1998, 194: 605.CrossRefPubMedGoogle Scholar
  14. Kelly OE, Johnson DH, Delgutte B, Cariani P (1996) Fractal noise strength in auditory-nerve fiber recordings. Journal of the Acoustical Society of America 99: 2210–2220.PubMedGoogle Scholar
  15. Kronauer RE (1990) A quantitative model for the effects of light on the amplitude and phase of the deep circadian pacemaker, based on human data. In JA Horne, ed. Sleep’90. Ponrenagel, Bocunm, Germany, pp. 306–309.Google Scholar
  16. Kumar AR, Johnson DH (1993) Analyzing and modeling fractal intensity point processes. Journal of the Acoustical Society of America 93: 3365–3373.PubMedGoogle Scholar
  17. Läuger P (1988) Internal motions in proteins and gating kinetics of ionic channels. Biophysical Journal 53: 877–884.PubMedGoogle Scholar
  18. Leloup JC, Goldbeter A (2003) Toward a detailed computational model for the mammalian circadian clock. Proceedings of National Academy of Science in USA 100: 7051–7056.CrossRefGoogle Scholar
  19. Leloup JC, Gonze D, Goldbeter A (1999) Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora. Journal of Biological Rhythms 14: 433–448.CrossRefPubMedGoogle Scholar
  20. Levine MW (1980) Firing rate of a retinal neuron is not predictable from interspike interval statistics. Biophysical Journal 30: 9–25.PubMedGoogle Scholar
  21. Lewis CD, Gerard LG, Peter DL, Susan MB (2001) Long-term correlations in the spike trains of medullary sympathetic neurons. Journal of Neurophysiology 85: 1614–1622.PubMedGoogle Scholar
  22. Liebovitch LS, Koniarek JP (1992) Ion channel kinetics. Protein switching between conformational states is fractal in time. IEEE Engineering in Medicine and Biology 11: 53–56.CrossRefGoogle Scholar
  23. Liebovitch LS, Toth TI (1991) A model of ion channel kinetics using deterministic chaotic rather than stochastic processes. Journal of Theoretical Biology 148: 243–267.PubMedGoogle Scholar
  24. Liebovitch LS, Toth TI (1990) Using fractals to understand the opening and closing of ion channels. Annals of Biomedical Engineering 18: 177–194.PubMedGoogle Scholar
  25. Linkenkaer-Hansen K, Nikouline VV, Palva JM, Ilmoniemi RJ (2001) Long-range temporal correlations and scaling behavior in human brain oscillations. Journal of Neuroscience 21: 1370–1377.PubMedGoogle Scholar
  26. Linkenkaer-Hansen K, Nikulin VV, Palva JM, Kaila K, Ilmoniemi RJ (2004) Stimulus-induced change in long-range temporal correlations and scaling behaviour of sensorimotor oscillations. European Journal of Neuroscience 19: 203–211.CrossRefPubMedGoogle Scholar
  27. Liu C, Weaver DR, Strogatz SH, Reppert SM (1997) Cellular construction of a circadian clock: Period determination in the suprachiasmatic nuclei. Cell 91:855–860.CrossRefGoogle Scholar
  28. Longtin A (1993) Nonlinear forecasting of spike trains from sensory neurons. International Journal of Bifurcation and Chaos 3: 651–661.CrossRefGoogle Scholar
  29. Lowen SB, Teich MC (1993) Fractal renewal processes. IEEE Transactions in Information Theory 39: 1669–1671.CrossRefGoogle Scholar
  30. Lowen SB, Liebovitch LS, White JA (1999) Fractal ion-channel behavior generates fractal firing patterns in neuronal models. Physical Review E 59: 5970–80.CrossRefGoogle Scholar
  31. Lowen SB, Teich MC (1996) The periodogram and Allan variance reveal fractal exponents greater than unity in auditory-nerve spike trains. Journal of the Acoustical Society of America 99: 3585–3591.PubMedGoogle Scholar
  32. Lowen SB, Cash SS, Poo M, Teich MC (1997) Quantal neurotransmitter secretion rate exhibits fractal behavior. Journal of Neuroscience 17: 5666–5677.PubMedGoogle Scholar
  33. Lowen SB, Ozaki T, Kaplan E, Saleh BEA, Teich MC (2001) Fractal features of dark, maintained, and driven neural discharges in the cat visual system. Methods 24: 377–394.CrossRefPubMedGoogle Scholar
  34. Marom S (1998) Slow changes in the availability of voltage-gated ion channels: Effects on the dynamics of excitable membranes. Journal of Membrane Biology 161: 105–113.CrossRefPubMedGoogle Scholar
  35. Meijer JH, Rietveld WJ (1989) Neurophysiology of the suprachiasmatic circadian pacemaker in rodents. Physiological Reviews 69: 671–707.PubMedGoogle Scholar
  36. Millhauser GL, Salpeter EE, Oswald RE (1988) Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording. Proceedings of National Academy of Science 85: 1503–1507.Google Scholar
  37. Moore RY, Speh JC (1993) GABA is the principal neurotransmitter of the circadian system. Neuroscience Letters 150: 112–116.CrossRefPubMedGoogle Scholar
  38. Morin LP (1994) The circadian visual system. Brain Research Reviews 19: 102–127.CrossRefPubMedGoogle Scholar
  39. Newman GC, Hospod FE, Patlak CS, Moore RY (1992) Analysis of in vitro glucose utilization in a circadian pacemaker model. Journal of Neuroscience 12: 2015–2021.PubMedGoogle Scholar
  40. Okamura H, Berod A, Julien JF, Geffard M, Kitahama K, Mallet J, Bobillier P (1989) Demonstration of GABAergic cell bodies in the suprachiasmatic nucleus: in situ hybridization of glutamic acid decarboxylase (GAD) mRNA and immunocytochemistry of GAD and GABA. Neuroscience Letter 102: 131–136.CrossRefGoogle Scholar
  41. Pavlidis T (1967) A model for circadian clocks. Bulletin in Mathematical Biophysics 29: 781–791.Google Scholar
  42. Pennartz CM, Bierlaagh MA, Geurtsen AM (1997) Cellular mechanisms underlying spontaneous firing in rat suprachiasmatic nucleus: Involvement of a slowly inactivating component of sodium current. Journal of Neurophysiology 78: 1811–1825.PubMedGoogle Scholar
  43. Pennartz CM, De Jeu MT, Geurtsen AM, Sluiter AA, Hermes ML (1998) Electrophysiological and morphological heterogeneity of neurons in slices of rat suprachiasmatic nucleus. Journal of Physiology 506: 775–793.CrossRefPubMedGoogle Scholar
  44. Powers NL, Salvi RJ (1992) In: Abstracts of the XV Midwinter Reseach Meeting, Association for Research in Otolaryngology 292, p. 101.Google Scholar
  45. Reppert SM, Weaver DR (2001) Molecular analysis of mammalian circadian rhythms. Annual Review of Physiology 63: 647–676.CrossRefPubMedGoogle Scholar
  46. Reppert SM, Weaver DR (2002) Coordination of circadian timing in mammals. Nature 418: 935–941.CrossRefPubMedGoogle Scholar
  47. Schaap J, Pennartz CM, Meijer JH (2003) Electrophysiology of the circadian pacemaker in mammals. Chronobiology International 20:171–188.CrossRefPubMedGoogle Scholar
  48. Schreiber T, Schmitz A (2000) Surrogate data methods. Physica D 142: 346–382.MathSciNetGoogle Scholar
  49. Schwartz WJ, Gross RA, Morton MT (1987) The suprachiasmatic nuclei contain a tetrodotoxin-resistant circadian pacemaker. Proceedings of National Academy of Sciences USA 84: 1694–1698.Google Scholar
  50. Shen Y, Olbrich E, Achermann P, Meier PF (2003) Dimensional complexity and spectral properties of the human sleep EEG. Clinical Neurophysiology 114: 199–209.CrossRefPubMedGoogle Scholar
  51. Shirakawa T, Honma S, Honma K (2001) Multiple oscillators in the suprachiasmatic nucleus. Chronobiology International 18: 371–387.CrossRefPubMedGoogle Scholar
  52. Soen Y, Braun E (2000) Scale-invariant fluctuations at different levels of organization in developing heart cell networks. Physical Review E 61: R2216–R2219.CrossRefGoogle Scholar
  53. Steedman WM, Zachary S (1990) Characteristics of background and evoked discharges of multireceptive neurons in lumbar spinal cord of cat. Journal of Neurophysiology 63: 1–15.PubMedGoogle Scholar
  54. Steedman WM, Iggo A, Molony V, Korogod S, Zachary S (1983) Statistical analysis of ongoing activity of neurones in the substantia gelatinosa and in lamina III of cat spinal cord. Quarterly Journal of Experimental Physiology 68: 733–746.PubMedGoogle Scholar
  55. Teich MC, Heneghan C, Lowen SB, Ozaki T, Kaplan E (1997) Fractal character of the neural spike train in the visual system of the cat. Journal of Optical Society of America A 14: 529–546.Google Scholar
  56. Teich MC (1989) Fractal character of the auditory neural spike train. IEEE Transactions in Biomedical Engineering 36: 150–160.CrossRefGoogle Scholar
  57. Toib A, Lyakhov V, Marom S (1998) Interaction between duration of activity and time course of recovery from slow inactivation in mammalian brain Na+ channels. Journal of Neuroscience 18: 1893–1903.PubMedGoogle Scholar
  58. Tuckwell HC (1989) Stochastic processes in the neurosciences. Society for Industrial and Applied mathematics, Philadelphia, PA.Google Scholar
  59. Turcott RG, Barker PDR, Teich MC (1995) Long-duration correlation in the sequence of action potentials in an insect visual interneuron. Journal of Statistical Computation and Simulation 52: 253–271.Google Scholar
  60. Van Den Pol AN, Dudek FE (1993) Cellular communication in the circadian clock, the suprachiasmatic nucleus. Neuroscience 56: 793–811.CrossRefPubMedGoogle Scholar
  61. Van Den Pol AN, Finkbeiner SM, Cornell-Bell AH (1992) Calcium excitability and oscillations in suprachiasmatic nucleus neurons and glia in vitro. Journal of Neuroscience 12: 2648–2664.PubMedGoogle Scholar
  62. West BJ (1990) Fractal Physiology and Chaos in Medicine. World Scientific, Singapore, pp.67–78.Google Scholar
  63. Wever R (1972) Virtual synchronization towards the limits of the range of entrainment. Journal of Theoretical Biology 36: 119–132.CrossRefPubMedGoogle Scholar
  64. Winfree AT (2002) Oscillating systems. On emerging coherence. Science 298: 2336–2337.CrossRefPubMedGoogle Scholar
  65. Wise ME (1981) In: Statistical Distributions in Scientific Work. Reidel, Boston, pp. 211–231.Google Scholar
  66. Yamaguchi S, Isejima H, Matsuo T, Okura R, Yagita K, Kobayashi M, Okamura H (2003) Synchronization of cellular clocks in the suprachiasmatic nucleus. Science 302: 1408–1412.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Sung-IL Kim
    • 1
  • Jaeseung Jeong
    • 1
  • Yongho Kwak
    • 1
  • Yang In Kim
    • 2
  • Seung Hun Jung
    • 2
  • Kyoung J. Lee
    • 3
  1. 1.National Creative Research Initiative Center for Neurodynamics and Department of PhysicsKorea UniversitySeoulSouth Korea
  2. 2.Department of Physiology and Neuroscience Research InstituteKorea University College of MedicineSeoulSouth Korea
  3. 3.National Creative Research Initiative Center for Neurodynamics and Department of PhysicsKorea UniversitySeoulSouth Korea

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