Fractal Stochastic Modeling of Spiking Activity in Suprachiasmatic Nucleus Neurons

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.

[1]  K. Kitahama,et al.  Demonstration of GABAergic cell bodies in the suprachiasmatic nucleus: In situ hybridization of glutamic acid decarboxylase (GAD) mRNA and immunocytochemistry of GAD and GABA , 1989, Neuroscience Letters.

[2]  Ganapati P. Patil,et al.  Statistical Distributions in Scientific Work , 1981 .

[3]  K. Linkenkaer-Hansen,et al.  Stimulus‐induced change in long‐range temporal correlations and scaling behaviour of sensorimotor oscillations , 2004, The European journal of neuroscience.

[4]  A. Winfree.  On Emerging Coherence , 2002, Science.

[5]  S. Honma,et al.  MULTIPLE OSCILLATORS IN THE SUPRACHIASMATIC NUCLEUS , 2001, Chronobiology international.

[6]  Steven H. Strogatz,et al.  Cellular Construction of a Circadian Clock: Period Determination in the Suprachiasmatic Nuclei , 1997, Cell.

[7]  Statistical analysis of ongoing activity of neurones in the substantia gelatinosa and in lamina III of cat spinal cord. , 1983, Quarterly journal of experimental physiology.

[8]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.

[9]  Cyriel M A Pennartz,et al.  Electrophysiology of the Circadian Pacemaker in Mammals , 2003, Chronobiology international.

[10]  P Achermann,et al.  Modeling Circadian Rhythm Generation in the Suprachiasmatic Nucleus with Locally Coupled Self-Sustained Oscillators: Phase Shifts and Phase Response Curves , 1999, Journal of biological rhythms.

[11]  R. Kronauer,et al.  Refinement of a limit cycle oscillator model of the effects of light on the human circadian pacemaker. , 1998, Journal of theoretical biology.

[12]  Larry S. Liebovitch,et al.  Using fractals to understand the opening and closing of ion channels , 2006, Annals of Biomedical Engineering.

[13]  S. Zachary,et al.  Characteristics of background and evoked discharges of multireceptive neurons in lumbar spinal cord of cat. , 1990, Journal of neurophysiology.

[14]  F. Dudek,et al.  Cellular communication in the circadian clock, the suprachiasmatic nucleus , 1993, Neuroscience.

[15]  M. Teich,et al.  The periodogram and Allan variance reveal fractal exponents greater than unity in auditory-nerve spike trains. , 1996, The Journal of the Acoustical Society of America.

[16]  E. Salpeter,et al.  Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Shimon Marom,et al.  Interaction between Duration of Activity and Time Course of Recovery from Slow Inactivation in Mammalian Brain Na+Channels , 1998, The Journal of Neuroscience.

[18]  Henry C. Tuckwell,et al.  Stochastic processes in the neurosciences , 1989 .

[19]  M. Teich,et al.  Fractal character of the auditory neural spike train , 1988, IEEE Transactions on Biomedical Engineering.

[20]  L. P. Morin.  The circadian visual system , 1994, Brain Research Reviews.

[21]  T Pavlidis,et al.  A model for circadian clocks. , 1967, The Bulletin of mathematical biophysics.

[22]  S. Yamaguchi,et al.  Synchronization of Cellular Clocks in the Suprachiasmatic Nucleus , 2003, Science.

[23]  D H Johnson,et al.  Fractal noise strength in auditory-nerve fiber recordings. , 1996, The Journal of the Acoustical Society of America.

[24]  R. Wever,et al.  Virtual synchronization towards the limits of the range of entrainment. , 1972, Journal of theoretical biology.

[25]  J. Meijer,et al.  Neurophysiology of the suprachiasmatic circadian pacemaker in rodents. , 1989, Physiological reviews.

[26]  C. Pennartz,et al.  Cellular mechanisms underlying spontaneous firing in rat suprachiasmatic nucleus: involvement of a slowly inactivating component of sodium current. , 1997, Journal of neurophysiology.

[27]  A. N. van den Pol,et al.  Calcium excitability and oscillations in suprachiasmatic nucleus neurons and glia in vitro , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[28]  L S Liebovitch,et al.  A model of ion channel kinetics using deterministic chaotic rather than stochastic processes. , 1991, Journal of theoretical biology.

[29]  M. Teich,et al.  Fractal features of dark, maintained, and driven neural discharges in the cat visual system. , 1999, Methods.

[30]  K. Linkenkaer-Hansen,et al.  Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations , 2001, The Journal of Neuroscience.

[31]  André Longtin,et al.  NONLINEAR FORECASTING OF SPIKE TRAINS FROM SENSORY NEURONS , 1993 .

[32]  Nicholas C. Foley,et al.  Gates and Oscillators: A Network Model of the Brain Clock , 2003, Journal of biological rhythms.

[33]  R. Gross,et al.  The suprachiasmatic nuclei contain a tetrodotoxin-resistant circadian pacemaker. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[34]  David R. Cox,et al.  The statistical analysis of series of events , 1966 .

[35]  Mu-ming Poo,et al.  Quantal Neurotransmitter Secretion Rate Exhibits Fractal Behavior , 1997, The Journal of Neuroscience.

[36]  R. Moore,et al.  GABA is the principal neurotransmitter of the circadian system , 1993, Neuroscience Letters.

[37]  C. Pennartz,et al.  Electrophysiological and morphological heterogeneity of neurons in slices of rat suprachiasmatic nucleus , 1998, The Journal of physiology.

[38]  M. E. Wise.  Spike Interval Distributions for Neurons and Random Walks with Drift to a Fluctuating Threshold , 1981 .

[39]  William J. Schwartz,et al.  Morning and evening circadian oscillations in the suprachiasmatic nucleus in vitro , 2000, Nature Neuroscience.

[40]  C. Colwell,et al.  Rhythmic coupling among cells in the suprachiasmatic nucleus. , 2000, Journal of neurobiology.

[41]  P. F. Meier,et al.  Dimensional complexity and spectral properties of the human sleep EEG , 2003, Clinical Neurophysiology.

[42]  A. Goldbeter,et al.  Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora , 1999, Journal of biological rhythms.

[43]  L. Liebovitch,et al.  Ion channel kinetics , 1992, IEEE Engineering in Medicine and Biology Magazine.

[44]  A. Winfree.  Oscillating systems. On emerging coherence. , 2002, Science.

[45]  S. Marom,et al.  Slow Changes in the Availability of Voltage-gated Ion Channels: Effects on the Dynamics of Excitable Membranes , 1998, The Journal of Membrane Biology.

[46]  Malte Meesmann,et al.  Further study on 1/f fluctuations observed in central single neurons during REM sleep , 2004, Biological Cybernetics.

[47]  P. Larsen,et al.  Long-term correlations in the spike trains of medullary sympathetic neurons. , 2001, Journal of neurophysiology.

[48]  A. Goldbeter,et al.  Toward a detailed computational model for the mammalian circadian clock , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[49]  Bruce J. West,et al.  FRACTAL PHYSIOLOGY AND CHAOS IN MEDICINE , 1990 .

[50]  D. W. Allan,et al.  Statistics of atomic frequency standards , 1966 .

[51]  Robert G. Turcott,et al.  Long-duration correlation in the sequence of action potentials in an insect visual interneuron , 1995 .

[52]  D H Johnson,et al.  Analyzing and modeling fractal intensity point processes. , 1993, The Journal of the Acoustical Society of America.

[53]  R. Moore,et al.  Analysis of in vitro glucose utilization in a circadian pacemaker model , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[54]  S. Reppert,et al.  Molecular analysis of mammalian circadian rhythms. , 2001, Annual review of physiology.

[55]  Albert Goldbeter,et al.  Development and validation of computational models for mammalian circadian oscillators. , 2003, Omics : a journal of integrative biology.

[56]  Malvin Carl Teich,et al.  Fractal renewal processes , 1993, IEEE Trans. Inf. Theory.

[57]  S. Reppert,et al.  Coordination of circadian timing in mammals , 2002, Nature.

[58]  A. Goldbeter.  A model for circadian oscillations in the Drosophila period protein (PER) , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[59]  Y Soen,et al.  Scale-invariant fluctuations at different levels of organization in developing heart cell networks. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[60]  M. Teich,et al.  Fractal character of the neural spike train in the visual system of the cat. , 1997, Journal of the Optical Society of America. A, Optics, image science, and vision.

[61]  P. Läuger.  Internal motions in proteins and gating kinetics of ionic channels. , 1988, Biophysical journal.

[62]  M W Levine,et al.  Firing rate of a retinal neuron are not predictable from interspike interval statistics. , 1980, Biophysical journal.

[63]  S. T. Inouye,et al.  Persistence of circadian rhythmicity in a mammalian hypothalamic "island" containing the suprachiasmatic nucleus. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[64]  L. Liebovitch,et al.  Fractal ion-channel behavior generates fractal firing patterns in neuronal models. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.