A mathematical model towards understanding the mechanism of neuronal regulation of wake-NREMS-REMS states

PLoS One. 2012;7(8):e42059. doi: 10.1371/journal.pone.0042059. Epub 2012 Aug 8.


In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s) that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Circadian Rhythm
  • Computer Simulation
  • Homeostasis
  • Humans
  • Hypothalamus / metabolism
  • Intracellular Signaling Peptides and Proteins / physiology
  • Models, Neurological
  • Models, Theoretical
  • Neurons / metabolism*
  • Neuropeptides / physiology
  • Orexins
  • Sleep / physiology*
  • Sleep, REM / physiology*
  • Substantia Nigra / physiology
  • Wakefulness / physiology*


  • Intracellular Signaling Peptides and Proteins
  • Neuropeptides
  • Orexins

Grants and funding

Financial supports from the Council of Scientific and Industrial Research; Department of Biotechnology; Department of Science and Technology; UGC Capacity build-up funds and JC Bose Fellowship to BNM are acknowledged. Financial support from the Fulbright-Nehru Program and from the National Science Foundation DMS-1122291, USA to AB is also acknowledged. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.