Skip to main content
SpringerLink
Log in
Book cover

Birth, Life and Death of Dopaminergic Neurons in the Substantia Nigra pp 121–128Cite as

Chaotic Versus Stochastic Dynamics: A Critical Look at the Evidence for Nonlinear Sequence Dependent Structure in Dopamine Neurons

  • Chapter
  • First Online:

  • 1330 Accesses

Part of the book series: Journal of Neural Transmission. Supplementa ((NEURALTRANS,volume 73))

Abstract

The firing pattern of midbrain dopamine neurons is thought to have important behavioral consequences. Although these neurons fire regularly in vitro when deprived of their afferent inputs, they usually fire irregularly in vivo. It is not known whether the irregularity is functionally important and whether it derives from the intrinsic properties of dopamine neurons or network interactions. It is also not known whether the irregular firing pattern is fundamentally stochastic or deterministic in nature. Distinguishing between the deterministic nonlinear structure associated with chaos and other sources of structure including correlated noise is an inherently nontrivial problem. Here we explain the geometric tools provided by the field of nonlinear dynamics and their application to the analysis of interspike interval (ISI) data from midbrain dopamine neurons. One study failed to find strong evidence of nonlinear determinism, but others have identified such a structure and correlated it with network interactions.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Bertschinger N, Natschlager T (2004) Real-time computation at the edge of chaos in recurrent neural networks. Neural Comput 16:1413–1436

    Article  PubMed  Google Scholar 

  • Canavier CC, Clark JW, Byrne JH (1990) Routes to chaos in a model of a bursting neuron. Biophys J 57:1245–1251

    Article  CAS  PubMed  Google Scholar 

  • Canavier CC, Clark JW, Baxter DA, Byrne JH (1993) Nonlinear dynamics in a model neuron provide a novel mechanism for transient synaptic inputs to produce long-term alterations of postsynaptic activity. J Neurophysiol 69:2252–2257

    CAS  PubMed  Google Scholar 

  • Canavier CC, Perla SR, Shepard PD (2004) Scaling of prediction error does not confirm chaotic dynamics underlying irregular firing using interspike intervals from midbrain dopamine neurons. Neuroscience 129:491–502

    Article  CAS  PubMed  Google Scholar 

  • Castro R, Sauer T (1997) Correlation dimension of attractors through interspike intervals. Phys Rev E 55:287–290

    Article  CAS  Google Scholar 

  • Di Mascio M, Di Giovanni G, Di Matteo V, Esposito E (1999a) Reduced chaos of interspike interval of midbrain dopaminergic neurons in aged rats. Neuroscience 89:1003–1008

    Article  PubMed  Google Scholar 

  • Di Mascio M, Di Giovanni G, Di Matteo V, Esposito E (1999b) Decreased chaos of midbrain dopaminergic neurons after serotonin denervation. Neuroscience 92:237–243

    Article  PubMed  Google Scholar 

  • Farmer JD, Sidorowich JJ (1979) Predicting chaotic time series. Phys Rev Let 59:845–848

    Article  Google Scholar 

  • Freeman AS, Meltzer LT, Bunney BS (1985) Firing properties of substantia nigra dopaminergic neurons in freely moving rats. Life Sci 36:1983–1994

    Article  CAS  PubMed  Google Scholar 

  • Fujimura K, Matsuda Y (1989) Autogenous oscillatory potentials in neurons of the guinea pig substantia nigra pars compacta in vitro. Neurosci Lett 104:53–57

    Article  CAS  PubMed  Google Scholar 

  • Grace AA, Bunney BS (1984a) The control of firing pattern in the nigral dopamine neurons: single spike firing. J Neurosci 4:2866–2876

    CAS  PubMed  Google Scholar 

  • Grace AA, Bunney BS (1984b) The control of firing pattern in the nigral dopamine neurons: burst firing. J Neurosci 4:2877–2890

    CAS  PubMed  Google Scholar 

  • Grace AA, Onn S-P (1989) Morphology and electrophysiological properties of immunocytochemically identified rat dopamine neurons recorded in vitro. J Neurosci 9:3463–3481

    CAS  PubMed  Google Scholar 

  • Harris NC, Webb C, Greenfield S (1989) A possible pacemaker mechanism in pars compacta neurons of the guinea-pig substantia nigra revealed by various ion channel blocking agents. Neuroscience 31:355–362

    Article  CAS  PubMed  Google Scholar 

  • Hegger R, Kantz H (1997) Embedding sequences of time intervals. Europhys Lett 38:267–272

    Article  CAS  Google Scholar 

  • Hoffman RE, Shi W-X, Bunney BS (1995) Nonlinear sequence-dependent structure of nigral dopamine neuron interspike interval firing patterns. Biophysical J 69:128–137

    Article  CAS  Google Scholar 

  • Hoffman RE, Shi W-X, Bunney BS (2001) Anatomic basis of sequence- dependent predictability exhibited by nigral dopamine neuron firing patterns. Synapse 39:133–138

    Article  CAS  PubMed  Google Scholar 

  • Johnson SW, Seutin V, North RA (1992) Burst-firing in dopamine neurons induced by N-methyl-D-aspartate: role of electrogenic sodium pump. Science 258:665–667

    Article  CAS  PubMed  Google Scholar 

  • Kang Y, Kitai ST (1993) Calcium spike underlying rhythmic firing in dopaminergic neurons of the rat substantia nigra. Neurosci Res 18:195–207

    Article  CAS  PubMed  Google Scholar 

  • Kantz H, Schreiber T (1999) Nonlinear time series analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Kaplan DT, Clay JR, Manning T, Glass L, Guevara MR, Shrier A (1996) Subthreshold dynamics in periodically stimulated squid giant axons. Phys Rev Lett 76:4074–4077

    Article  CAS  PubMed  Google Scholar 

  • King R, Barchas JD, Huberman BA (1984) Chaotic behavior in dopamine neurodynamics. Proc Natl Acad Sci USA 81:1244–1247

    Article  CAS  PubMed  Google Scholar 

  • Lovejoy LP, Shepard PD, Canavier CC (2001) Apamin-induced irregular firing in vitro and irregular single-spike firing observed in vivo in dopamine neurons is chaotic. Neuroscience 104:828–840

    Article  Google Scholar 

  • Osborne AR, Provenzale A (1989) Finite correlation dimension for stochastic systems with power-law spectra. Physica D 35:357–381

    Article  Google Scholar 

  • Packard N, Crutchfield J, Farmer JD, Shaw R (1980) Geometry from a time series. Phys Rev Lett 45:712–716

    Article  Google Scholar 

  • Ping HX, Shepard PD (1996) Apamin-sensitive Ca2+-activated K+ channels regulate pacemaker activity in nigral dopamine neurons. NeuroReport 7:809–814

    Article  CAS  PubMed  Google Scholar 

  • Plant RE, Kim M (1976) Mathematical description of a bursting pacemaker neuron by modification of the Hodgkin-Huxley equations. Biophys J 16:227–244

    Article  CAS  PubMed  Google Scholar 

  • Racicot DM, Longtin A (1997) Interspike interval attractors from chaotically driven model neurons. Physica D 104:184–204

    Article  Google Scholar 

  • Rapp PE (1993) Chaos in the neurosciences: cautionary tales from the frontier. Biologist 40:89–94

    Google Scholar 

  • Rapp PE, Albano AM, Scmah TI, Farwall LA (1993) Filtered noise can mimic low-dimensional chaotic attractors. Phys Rev E 46:2289–2297

    Article  Google Scholar 

  • Sauer T (1994) Reconstruction of dynamical systems from interspike intervals. Phys Rev Lett 72:3811–3814

    Article  CAS  PubMed  Google Scholar 

  • Sauer T (1997) Reconstruction of integrate and fire dynamics. Fields Inst Commun 11:63–75

    Google Scholar 

  • Schreiber T, Schmitz A (2000) Surrogate time series. Physica D 142:346–382

    Article  Google Scholar 

  • Shaner A (1999) Delusions, superstitious conditioning and chaotic dopamine neurodynamics. Med Hypotheses 52:119–123

    Article  CAS  PubMed  Google Scholar 

  • Shepard PD, Bunney BS (1988) Effects of apamin on the discharge properties of putative dopamine-containing neurons in vitro. Brain Res 463:380–384

    Article  CAS  PubMed  Google Scholar 

  • Stam CJ, Pijn JPM, Pritchard WS (1998) Reliable detection of nonlinearity in experimental time series with strong periodic components. Physica D 112:361–380

    Article  Google Scholar 

  • Strogatz SH (2000) Nonlinear dynamics and chaos: with applications to Physics, Biology, Chemistry and Engineering. Westview Press, Cambridge

    Google Scholar 

  • Theiler J (1986) Spurious dimension from correlation algorithms applied to limited time series data. Phys Rev A 34:2427–2432

    Article  PubMed  Google Scholar 

  • Thieler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: the method of surrogate data. Physica D 58:77–94

    Article  Google Scholar 

  • Wales DJ (1991) Calculating the rate of loss of information from chaotic time series by forecasting. Nature 350:485–488

    Article  Google Scholar 

  • Yunfan G, Jianxue X, WEi R, Sanjue H, Fuzhou W (1998) Determining the degree of chaos from analysis of ISI time series in the nervous system: a comparison between correlation dimension and nonlinear forecasting methods. Biol Cybern 78:159–165

    Article  Google Scholar 

  • Yung WH, Hausser MA, Jack JJB (1991) Intrinsic memrane properties of dopaminergic and nondopaminergic neurones of the guinea-pig substantia nigra pars compacta in vitro. J Physiol (Lond) 426: 643–667

    Google Scholar 

Download references

Acknowledgments

The authors acknowledge the support from National Institute of Neurological Disorders and Stroke grant number NS061097

Author information

Authors and Affiliations

  1. Neuroscience Center of Excellence and Department of Ophthalmology, Louisiana State University Health Sciences Center, New Orleans, LA, 70112, USA

    C. C. Canavier

  2. Department of Psychiatry and the Maryland Psychiatric Research Center, University of Maryland School of Medicine, Baltimore, MD, 21228, USA

    P. D. Shepard

Authors
  1. C. C. Canavier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. D. Shepard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to C. C. Canavier or P. D. Shepard .

Editor information

Editors and Affiliations

  1. Fac. Medicina e Chirurgia, Università di Palermo, Corso Tukory 129, Palermo, 90134, Italy

    Giuseppe Giovanni

  2. Mario Negri, Istituto di Ricerche Farmacologiche, Via Nazionale 8, Santa Maria Imbaro, 66030, Italy

    Vincenzo Di Matteo

  3. Mario Negri, Istituto di Ricerche Farmacologiche, Via Nazionale 8, Santa Maria Imbaro, 66030, Italy

    Ennio Esposito

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag/Wien Printed in Germany

About this chapter

Cite this chapter

Canavier, C.C., Shepard, P.D. (2009). Chaotic Versus Stochastic Dynamics: A Critical Look at the Evidence for Nonlinear Sequence Dependent Structure in Dopamine Neurons. In: Giovanni, G., Di Matteo, V., Esposito, E. (eds) Birth, Life and Death of Dopaminergic Neurons in the Substantia Nigra. Journal of Neural Transmission. Supplementa, vol 73. Springer, Vienna. https://doi.org/10.1007/978-3-211-92660-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-211-92660-4_9

  • Published:

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-92659-8

  • Online ISBN: 978-3-211-92660-4

  • eBook Packages: MedicineMedicine (R0)

Publish with us

Policies and ethics

Search

Navigation