Skip to main content
SpringerLink
Log in

A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep

  • Chapter
  • First Online:
Modeling Phase Transitions in the Brain

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 4))

Abstract

Previous studies have shown that activated cortical states (awake and rapid eye-movement (REM) sleep), are associated with increased cholinergic input into the cerebral cortex. However, the mechanisms that underlie the detailed dynamics of the cortical transition from slow-wave to REM sleep have not been quantitatively modeled. How does the sequence of abrupt changes in the cortical dynamics (as detected in the electrocorticogram) result from the more gradual change in subcortical cholinergic input? We compare the output from a continuum model of cortical neuronal dynamics with experimentally-derived rat electrocorticogram data. The output from the computer model was consistent with experimental observations. In slow-wave sleep, 0.5–2-Hz oscillations arise from the cortex jumping between “up” and “down” states on the stationary-state manifold. As cholinergic input increases, the upper state undergoes a bifurcation to an 8-Hz oscillation. The coexistence of both oscillations is similar to that found in the intermediate stage of sleep of the rat. Further cholinergic input moves the trajectory to a point where the lower part of the manifold in not available, and thus the slow oscillation abruptly ceases (REM sleep). The model provides a natural basis to explain neuromodulator-induced changes in cortical activity, and indicates that a cortical phase change, rather than a brainstem “flip-flop”, may describe the transition from slow-wave sleep to REM.

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

Access this chapter

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

Institutional subscriptions

Notes

  1. 1.

    See Appendix (Sects 9.5.2 and 9.5.3) for details of data processing, and calculation of coherence estimates from the Morlet wavelet transform.

  2. 2.

    Note that we have not included a representation of the thalamus in the model, because the slow oscillation of sleep can be generated in the cortex alone—without thalamic input [33], [41], [45].

References

  1. Bazhenov, M., Timofeev, I., Steriade, M., Sejnowski, T.J.: Model of thalamocortical slow-wave sleep oscillations and transitions to activated states. J. Neurosci. 22(19), 8691–704 (2002)

    CAS  PubMed  Google Scholar 

  2. Benington, J.H., Kodali, S.K., Heller, H.C.: Scoring transitions to REM sleep in rats based on the EEG phenomena of pre-REM sleep: an improved analysis of sleep structure. Sleep 17(1), 28–36 (1994)

    CAS  PubMed  Google Scholar 

  3. Borst, J., Leung, L.W., MacFabe, D.: Electrical activity of the cingulate cortex. ii. cholinergic modulation. Brain Res 407, 81–93. (1987), doi:10.1016/0006-8993(87)91221-2

    Article  CAS  PubMed  Google Scholar 

  4. Cantero, J., Atienza, M., Stickgold, R., Kahana, M., Madsen, J., Kocsis, B.: Sleep-dependent theta oscillations in the human hippocampus and neocortex. J. Neurosci. 23(34), 10897–10903 (2003)

    CAS  PubMed  Google Scholar 

  5. Cape, E., Jones, B.: Effects of glutamate agonist versus procaine microinjections into the basal forebrain cholinergic cell area upon gamma and theta EEG activity and sleep-wake state. Eur. J. Neurosci. 12, 2166–2184 (2000), doi:10.1046/j.1460-9568.2000.00099.x

    CAS  Google Scholar 

  6. Compte, A., Sanchez-Vives, M.V., McCormick, D.A., Wang, X.J.: Cellular and network mechanisms of slow oscillatory activity (\(<\)1 Hz) and wave propagations in a cortical network model. J. Neurophys. 89(5), 2707–2725 (2003), doi:10.1152/jn.00845.2002

    Article  Google Scholar 

  7. Datta, S., Siwek, D.F.: Excitation of the brainstem pedunculopontine tegmentum cholinergic cells induces wakefulness and REM sleep. J. Neurophys. 77(6), 2975–2988 (1997)

    CAS  Google Scholar 

  8. El Mansari, M., Sakai, K., Jouvet, M.: Unitary characteristics of presumptive cholinergic tegmental neurons during the sleep-waking cycle in freely moving cats. Exp. Brain. Res. 76, 519–529 (1989), doi:10.1007/BF00248908

    Article  CAS  PubMed  Google Scholar 

  9. Farge, M.: Wavelet transforms and their applications to turbulence. Ann. Rev. Fluid. Mech. 24, 395–457 (1992), doi:10.1146/annurev.fl.24.010192.002143

    Article  Google Scholar 

  10. Gervasoni, D., Lin, S.C., Ribeiro, S., Soares, E.S., Pantoja, J., Nicolelis, M.A.: Global forebrain dynamics predict rat behavioral states and their transitions. J. Neurosci. 24(49), 11137–11147 (2004), doi:10.1523/jneurosci.3524-04.2004

    Article  CAS  PubMed  Google Scholar 

  11. Gottesmann, C.: The transition from slow-wave sleep to paradoxical sleep: Evolving facts and concepts of the neurophysiological processes underlying the intermediate stage of sleep. Neurosci. Biobehav. Rev. 20(3), 367–387 (1996), doi:10.1016/0149-7634(95)00055-0

    Article  CAS  Google Scholar 

  12. Gottesmann, C., Gandolfo, G., Arnaud, C., Gauthier, P.: The intermediate stage and paradoxical sleep in the rat: Influence of three generations of hypnotics. Eur. J. Neurosci. 10(2), 409–14 (1998), doi:10.1046/j.1460-9568.1998.00069.x

    CAS  Google Scholar 

  13. Hasselmo, M., McGaughy, J.: High acetylcholine levels set circuit dynamics for attention and encoding and low acetylcholine levels set dynamics for consolidation. Prog. Brain Res. 145, 207–231 (2004), doi:10.1016/S0079-6123(03)45015-2

    Article  CAS  PubMed  Google Scholar 

  14. Hill, S., Tononi, G.: Modeling sleep and wakefulness in the thalamocortical system. J. Neurophysiol. 93, 1671–1698 (2005), doi:10.1152/jn.00915.2004

    Article  PubMed  Google Scholar 

  15. Hobson, J.A., McCarley, R.W., Wyzinski, P.W.: Sleep cycle oscillation: Reciprocal discharge by two brainstem neuronal groups. Science 189(4196), 55–58 (1975), doi:10.1126/science.1094539

    Article  CAS  PubMed  Google Scholar 

  16. Hobson, J.A., Pace-Schott, E.F.: The cognitive neuroscience of sleep: Neuronal systems, consciousness and learning. Nat. Rev. Neurosci. 3(9), 679–693 (2002), doi:10.1038/nrn915

    Article  CAS  PubMed  Google Scholar 

  17. Holcman, C., Tsodyks, M.: The emergence of up and down states in cortical networks. PLoS. Comput. Biol. 2(3), 174–181 (2006), doi:10.1371/journal.pcbi.0020023

    Article  Google Scholar 

  18. Jones, B.: Activity, modulation and role of basal forebrain cholinergic neurons innervating the cerebral cortex. Prog. Brain Res. 145, 157–169 (2004), doi:10.1016/S0079-6123(03)45011-5

    Article  CAS  Google Scholar 

  19. Lachaux, J.P., Rudrauf Lutz, A., Cosmelli, D., Le Van Quyen, M., Martinerie, J., Varela, F.: Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence. Clin. Neurophysiol. 32(3), 157–174 (2002), doi:10.1016/S0987-7053(02)00301-5

    Article  Google Scholar 

  20. Lee, M., Hassani, O., Alonso, A., Jones, B.: Cholinergic basal forebrain neurons burst with theta during waking and paradoxical sleep. J. Neurosci. 25(17), 4365–4369. (2005), doi:10.1523/jneurosci.0178-05.2005

    Article  CAS  PubMed  Google Scholar 

  21. Leinekugel, X., Khazipov, R., Cannon, R., Hirase, H., Ben-Ari, Y., Buzsáki, G.: Correlated bursts of activity in the neonatal hippocampus in vivo. Science 296, 2049–2052 (2002), doi:10.1126/science.1071111

    Article  CAS  PubMed  Google Scholar 

  22. Liley, D., Cadusch, P., Wright, J.: A continuum theory of electro-cortical activity. Neurocomp. 26-27, 795–800 (1999), doi:10.1016/S0925-2312(98)00149-0

    Article  Google Scholar 

  23. Linster, C., Hasselmo, M.E.: Neuromodulation and the functional dynamics of piriform cortex. Chem. Senses 26(5), 585–594 (2001), doi:10.1093/chemse/26.5.585

    Article  CAS  PubMed  Google Scholar 

  24. Lu, J., Sherman, D., Devor, M., Saper, C.: A putative flip-flop switch for control of REM sleep. Nature 441, 583–591. (2006), doi:10.1038/nature04767

    Article  Google Scholar 

  25. Mandile, P., Vescia, S., Montagnese, P., Romano, F., Giuditta, A.: Characterization of transition sleep episodes in baseline EEG recordings of adult rats. Physiol. Behav. 60(6), 1435–9 (1996), doi:10.1016/S0031-9384(96)00301-0

    Article  CAS  PubMed  Google Scholar 

  26. Massimini, M., Huber, R., Ferrarelli, F., Hill, S., Tononi, G.: The sleep slow oscillation as a traveling wave. J. Neurosci. 24(31), 6862–6870 (2004), doi:10.1523/jneurosci.1318-04.2004

    Article  CAS  PubMed  Google Scholar 

  27. Metherate, R., Cox, C.L., Ashe, J.H.: Cellular bases of neocortical activation: modulation of neural oscillations by the nucleus basalis and endogenous acetylcholine. J. Neurosci. 12(12), 4701–4711 (1992)

    CAS  PubMed  Google Scholar 

  28. Morrissey, M.J., Anch, A.M., Duntley, S.P.: An evaluation of the use of seizure prone rats when investigating intermediate stage sleep. J. Neurosci. Meth. 143(2), 159–162 (2005), doi:10.1016/j.jneumeth.2004.09.026

    Article  Google Scholar 

  29. Nunez, A., Cervera-Ferri, A., Olucha-Bordonau, F., Ruiz-Torna, A., Teruel, V.: Nucleus incertus contribution to hippocampal theta rhythm generation. Eur. J. Neurosci. 23, 2731–2738 (2006), doi:10.1111/j.1460-9568.2006.04797.x

    CAS  Google Scholar 

  30. Pace-Schott, E.F., Hobson, J.A.: The neurobiology of sleep: genetics, cellular physiology and subcortical networks. Nat. Rev. Neurosci. 3(8), 591–605 (2002)

    CAS  PubMed  Google Scholar 

  31. Porkka-Heiskanen, T., Alanko, L., Kalinchuk, A., Stenberg, D.: Adenosine and sleep. Sleep Med. Rev. 6(4), 321–332 (2002), doi:10.1053/smrv.2001.0201

    Article  PubMed  Google Scholar 

  32. Saito, H., Sakai, K., Jouvet, M.: Discharge patterns of the nucleus parabrachialis lateralis neurons of the cat during sleep and waking. Brain Res. 134(1), 59–72 (1977), doi:10.1016/0006-8993(77)90925-8

    Article  CAS  PubMed  Google Scholar 

  33. Sanchez-Vives, M.V., McCormick, D.A.: Cellular and network mechanisms of rhythmic recurrent activity in neocortex. Nat. Neurosci. 3(10), 1027–1034 (2000), doi:10.1038/79848

    Article  CAS  PubMed  Google Scholar 

  34. Saper, C., Scammell, T., Lu, J.: Hypothalamic regulation of sleep and circadian rhythms. Nature 437, 1257–1263 (2005), doi:10.1038/nature04284

    Article  CAS  PubMed  Google Scholar 

  35. Shepherd, G., Stepanyants, A., Bureau, I., Chklovskii, D., Svoboda, K.: Geometric and functional organization of cortical circuits. Nat. Neurosci. 8(6), 782–791 (2005), doi:10.1038/nn1447

    CAS  Google Scholar 

  36. Shu, Y., Hasenstaub, A., McCormick, D.A.: Turning on and off recurrent balanced cortical activity. Nature 423(6937), 288–293 (2003), doi:10.1038/nature01616

    Article  CAS  PubMed  Google Scholar 

  37. Steriade, M., Datta, S., Pare, D., Oakson, G., Curro Dossi, R.C.: Neuronal activities in brain-stem cholinergic nuclei related to tonic activation processes in thalamocortical systems. J. Neurosci. 10(8), 2541–2559 (1990)

    CAS  PubMed  Google Scholar 

  38. Steriade, M., Timofeev, I., Grenier, F.: Natural waking and sleep states: A view from inside neocortical neurons. J. Neurophys. 85(5), 1969–1985 (2001)

    CAS  Google Scholar 

  39. Steyn-Ross, D.A., Steyn-Ross, M.L., Sleigh, J.W., Wilson, M.T., Gillies, I.P., Wright, J.J.: The sleep cycle modelled as a cortical phase transition. J. Biol. Phys. 31, 547–569 (2005), doi:10.1007/s10867-005-1285-2

    Article  Google Scholar 

  40. Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W., Wilson, M.T., Wilcocks, L.C.: Proposed mechanism for learning and memory erasure in a white-noise-driven sleeping cortex. Phys. Rev. E 72, 061910 (2005), doi:10.1103/PhysRevE.72.061910

    Article  Google Scholar 

  41. Timofeev, I., Grenier, F., Steriade, M.: Impact of intrinsic properties and synaptic factors on the activity of neocortical networks in vivo. J. Physiology-Paris 94(5-6), 343–355 (2000), doi:10.1016/S0928-4257(00)01097-4

    Article  CAS  Google Scholar 

  42. Torrence, C., Webster, P.J.: Interdecadal changes in the ENSO-monsoon system. J. Climate 12(8), 2679–2690 (1999), doi:10.1175/1520-0442(1999)012<2679:icitem>2.0.CO;2

    Article  Google Scholar 

  43. Tsodyks, M.V., Markram, H.: The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. P. Natl. Acad. Sci. USA 94(2), 719–723 (1997), doi:10.1073/pnas.94.2.719

    Article  CAS  Google Scholar 

  44. van Betteray, J.N., Vossen, J.M., Coenen, A.M.: Behavioural characteristics of sleep in rats under different light/dark conditions. Physiol. Behav. 50(1), 79–82 (1991), doi:10.1016/0031-9384(91)90501-E

    Article  PubMed  Google Scholar 

  45. Volgushev, M., Chauvette, S., Mukovski, M., Timofeev, I.: Precise long-range synchronization of activity and silence in neocortical neurons during slow-wave sleep. J. Neurosci. 26(21), 5665–5672 (2006), doi:10.1523/jneurosci.0279-06.2006

    Article  CAS  PubMed  Google Scholar 

  46. Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12(1), 1–24 (1972)

    CAS  Google Scholar 

  47. Wilson, M.T., Sleigh, J.W., Steyn-Ross, D.A., Steyn-Ross, M.L.: General anaesthetic-induced seizures can be explained by a mean-field model of cortical dynamics. Anesthesiology 104(3), 588–593 (2006), doi:10.1097/00000542-200603000-00026

    Article  PubMed  Google Scholar 

  48. Wilson, M.T., Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W.: Predictions and simulations of cortical dynamics during natural sleep using a continuum approach. Phys. Rev. E 72(5), 051910 (2005), doi:10.1103/PhysRevE.72.051910

    Article  CAS  Google Scholar 

  49. Wilson, M., Steyn-Ross, D., Sleigh, J., Steyn-Ross, M., Wilcocks, L., Gillies, I.: The K-complex and slow oscillation in terms of a mean-field cortical model. J. Comput. Neurosci. 21, 243–257 (2006), doi:10.1007/s10827-006-7948-6

    Article  CAS  PubMed  Google Scholar 

  50. Wright, J.J., Liley, D.T.: Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behav. Brain Sci. 19, 285–320 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Anaesthesia, Waikato Clinical School, University of Auckland, Waikato Hospital, Hamilton, 3204, New Zealand

    J.W. Sleigh & L.J. Voss

  2. Department of Engineering, University of Waikato, P.B. 3105, Hamilton, 3240, New Zealand

    M.T. Wilson, D.A. Steyn-Ross & M.L. Steyn-Ross

  3. School of Computer Science, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    X. Li

Authors
  1. J.W. Sleigh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M.T. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L.J. Voss
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D.A. Steyn-Ross
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M.L. Steyn-Ross
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. X. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J.W. Sleigh .

Editor information

Editors and Affiliations

  1. Dept. Engineering, University of Waikato, Hillcrest Road, Hamilton, 3240, New Zealand

    D. Alistair Steyn-Ross

  2. Dept. Engineering, University of Waikato, Hillcrest Road, Hamilton, 3240, New Zealand

    Moira Steyn-Ross

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Sleigh, J., Wilson, M., Voss, L., Steyn-Ross, D., Steyn-Ross, M., Li, X. (2010). A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep. In: Steyn-Ross, D., Steyn-Ross, M. (eds) Modeling Phase Transitions in the Brain. Springer Series in Computational Neuroscience, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0796-7_9

Download citation

Publish with us

Policies and ethics

Search

Navigation