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Narcolepsy pp 175–187Cite as

Mathematical Models of Narcolepsy

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Abstract

Mathematical modeling offers a way to critically test experimentally derived theories, integrate experimental results across spatial and temporal scales, and generate predictions to drive bench science and influence clinical practice. Although, in general, mathematical modeling approaches have been applied to narcolepsy only recently, developments in modeling normal sleep/wake behavior have laid an excellent foundation for linking the experimental insights about the orexin (also known as hypocretin) system to the observed features of the narcolepsy phenotype. Thus, many recent models have addressed aspects of narcolepsy including fragmentation of sleep and wake behavior, altered cycling between rapid eye movement (REM) and non-REM (NREM) sleep, sleep onset REM periods (SOREMPs), and cataplexy.

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References

  1. Borbely AA. A two process model of sleep regulation. Hum Neurobiol. 1982;1(3):195–204.

    PubMed  CAS  Google Scholar 

  2. Jenni OG, Achermann P, Carskadon MA. Homeostatic sleep regulation in adolescents. Sleep. 2005;28(11):1446–54.

    PubMed  Google Scholar 

  3. Tobler II, Franken P, Trachsel L, Borbely AA. Models of sleep regulation in mammals. J Sleep Res. 1992;1(2):125–7.

    Article  PubMed  Google Scholar 

  4. Dantz B, Edgar DM, Dement WC. Circadian rhythms in narcolepsy: studies on a 90 minute day. Electroen­cephalogr Clin Neurophysiol. 1994;90(1):24–35.

    Article  PubMed  CAS  Google Scholar 

  5. Nobili L, Besset A, Ferrillo F, Rosadini G, Schiavi G, Billiard M. Dynamics of slow wave activity in narcoleptic patients under bed rest conditions. Electroencephalogr Clin Neurophysiol. 1995;95(6):414–25.

    Article  PubMed  CAS  Google Scholar 

  6. Tafti M, Rondouin G, Besset A, Billiard M. Sleep deprivation in narcoleptic subjects: effect on sleep stages and EEG power density. Electroencephalogr Clin Neurophysiol. 1992;83(6):339–49.

    Article  PubMed  CAS  Google Scholar 

  7. Khatami R, Landolt HP, Achermann P, et al. Insufficient non-REM sleep intensity in narcolepsy-cataplexy. Sleep. 2007;30(8):980–9.

    PubMed  Google Scholar 

  8. Khatami R, Landolt HP, Achermann P, et al. Challenging sleep homeostasis in narcolepsy-cataplexy: implications for non-REM and REM sleep regulation. Sleep. 2008;31(6):859–67.

    PubMed  Google Scholar 

  9. Lawder RE. A proposed mathematical model for sleep patterning. J Biomed Eng. 1984;6(1):63–9.

    Article  PubMed  CAS  Google Scholar 

  10. McCarley RW, Hobson JA. Neuronal excitability modulation over the sleep cycle: a structural and mathematical model. Science. 1975;189(4196):58–60.

    Article  PubMed  CAS  Google Scholar 

  11. Lo CC, Chou T, Penzel T, et al. Common scale-invariant patterns of sleep-wake transitions across mammalian species. Proc Natl Acad Sci USA. 2004;101(50):17545–8.

    Article  PubMed  CAS  Google Scholar 

  12. Gall AJ, Joshi B, Best J, Florang VR, Doorn JA, Blumberg MS. Developmental emergence of power-law wake behavior depends upon the functional integrity of the locus coeruleus. Sleep. 2009;32(7): 920–6.

    PubMed  Google Scholar 

  13. Albert R, Jeong H, Barabasi AL. Error and attack tolerance of complex networks. Nature. 2000;406(6794):378–82.

    Article  PubMed  CAS  Google Scholar 

  14. Blumberg MS, Coleman CM, Johnson ED, Shaw C. Developmental divergence of sleep-wake patterns in orexin knockout and wild-type mice. Eur J Neurosci. 2006;25(2):512–8.

    Article  Google Scholar 

  15. Diniz Behn CG, Kopell N, Brown EN, Mochizuki T, Scammell TE. Delayed orexin signaling consolidates wakefulness and sleep: physiology and modeling. J Neurophysiol. 2008;99(6):3090–103.

    Article  PubMed  CAS  Google Scholar 

  16. Blumberg MS, Seelke AM, Lowen SB, Karlsson KA. Dynamics of sleep-wake cyclicity in developing rats. Proc Natl Acad Sci USA. 2005;102(41):14860–4.

    Article  PubMed  CAS  Google Scholar 

  17. Saper CB, Chou TC, Scammell TE. The sleep switch: hypothalamic control of sleep and wakefulness. Trends Neurosci. 2001;24(12):726–31.

    Article  PubMed  CAS  Google Scholar 

  18. Chemelli RM, Willie JT, Sinton CM, et al. Narcolepsy in orexin knockout mice: molecular genetics of sleep regulation. Cell. 1999;98(4):437–51.

    Article  PubMed  CAS  Google Scholar 

  19. Hungs M, Mignot E. Hypocretin/orexin, sleep and narcolepsy. Bioessays. 2001;23(5):397–408.

    Article  PubMed  CAS  Google Scholar 

  20. Beuckmann CT, Sinton CM, Williams SC, et al. Expression of a poly-glutamine-ataxin-3 transgene in orexin neurons induces narcolepsy-cataplexy in the rat. J Neurosci. 2004;24(18):4469–77.

    Article  PubMed  CAS  Google Scholar 

  21. Tamakawa Y, Karashima A, Koyama Y, Katayama N, Nakao M. A quartet neural system model orchestrating sleep and wakefulness mechanisms. J Neurophysiol. 2006;95(4):2055–69.

    Article  PubMed  Google Scholar 

  22. Lee MG, Hassani OK, Jones BE. Discharge of identified orexin/hypocretin neurons across the sleep-waking cycle. J Neurosci. 2005;25(28):6716–20.

    Article  PubMed  CAS  Google Scholar 

  23. Hara J, Beuckmann CT, Nambu T, et al. Genetic ablation of orexin neurons in mice results in narcolepsy, hypophagia, and obesity. Neuron. 2001;30(2):345–54.

    Article  PubMed  CAS  Google Scholar 

  24. Willie JT, Chemelli RM, Sinton CM, et al. Distinct narcolepsy syndromes in Orexin receptor-2 and Orexin null mice: molecular genetic dissection of Non-REM and REM sleep regulatory processes. Neuron. 2003;38(5):715–30.

    Article  PubMed  CAS  Google Scholar 

  25. Mochizuki T, Crocker A, McCormack S, Yanagisawa M, Sakurai T, Scammell TE. Behavioral state instability in orexin knock-out mice. J Neurosci. 2004;24(28):6291–300.

    Article  PubMed  CAS  Google Scholar 

  26. Fujiki N, Cheng T, Yoshino F, Nishino S. Specificity of direct transitions from wake to REM sleep in orexin/ataxin-3 narcoleptic mice. Sleep. 2006;29:A225.

    Google Scholar 

  27. Scammell TE, Willie JT, Guilleminault C, Siegel JM. A consensus definition of cataplexy in mouse models of narcolepsy. Sleep. 2009;32(1):111–6.

    PubMed  Google Scholar 

  28. Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys J. 1981;35(1):193–213.

    Article  PubMed  CAS  Google Scholar 

  29. Diniz Behn CG, Brown EN, Scammell TE, Kopell NJ. A mathematical model of network dynamics governing mouse sleep-wake behavior. J Neurophysiol. 2007;97(6):3828–40.

    Article  Google Scholar 

  30. Chou TC, Lee CE, Lu J, et al. Orexin (hypocretin) neurons contain dynorphin. J Neurosci. 2001;21(19):RC168.

    PubMed  CAS  Google Scholar 

  31. Eriksson KS, Sergeeva OA, Selbach O, Haas HL. Orexin (hypocretin)/dynorphin neurons control GABAergic inputs to tuberomammillary neurons. Eur J Neurosci. 2004;19(5):1278–84.

    Article  PubMed  Google Scholar 

  32. Li Y, van den Pol AN. Differential target-dependent actions of coexpressed inhibitory dynorphin and excitatory hypocretin/orexin neuropeptides. J Neurosci. 2006;26(50):13037–47.

    Article  PubMed  CAS  Google Scholar 

  33. Williams K, Diniz Behn CG. A Hodgkin-Huxley-type model orexin neuron. Sleep. 2009;32:A25.

    Google Scholar 

  34. McCarley RW, Massaquoi SG. A limit cycle mathematical model of the REM sleep oscillator system. Am J Physiol. 1986;251(6 Pt 2):R1011–29.

    PubMed  CAS  Google Scholar 

  35. Massaquoi SG, McCarley RW. Extension of the limit cycle reciprocal interaction model of REM cycle ­control. An integrated sleep control model. J Sleep Res. 1992;1(2):138–43.

    Article  PubMed  Google Scholar 

  36. McCarley RW. Neurobiology of REM and NREM sleep. Sleep Med. 2007;8(4):302–30.

    Article  PubMed  Google Scholar 

  37. Abrahamson EE, Leak RK, Moore RY. The suprachiasmatic nucleus projects to posterior hypothalamic arousal systems. Neuroreport. 2001;12(2):435–40.

    Article  PubMed  CAS  Google Scholar 

  38. Chou TC, Scammell TE, Gooley JJ, Gaus SE, Saper CB, Lu J. Critical role of dorsomedial hypothalamic nucleus in a wide range of behavioral circadian rhythms. J Neurosci. 2003;23(33):10691–702.

    PubMed  CAS  Google Scholar 

  39. Deurveilher S, Semba K. Indirect projections from the suprachiasmatic nucleus to major arousal-promoting cell groups in rat: implications for the circadian control of behavioural state. Neuroscience. 2005;130(1):165–83.

    Article  PubMed  CAS  Google Scholar 

  40. Nishino S. Clinical and neurobiological aspects of narcolepsy. Sleep Med. 2007;8(4):373–99.

    Article  PubMed  Google Scholar 

  41. Kantor S, Mochizuki T, Janisiewicz AM, Clark E, Nishino S, Scammell TE. Orexin neurons are necessary for the circadian control of REM sleep. Sleep. 2009;32(9):1127–34.

    PubMed  Google Scholar 

  42. Nobili L, Ferrillo F, Besset A, Rosadini G, Schiavi G, Billiard M. Ultradian aspects of sleep in narcolepsy. Neurophysiol Clin. 1996;26(1):51–9.

    Article  PubMed  CAS  Google Scholar 

  43. Ferrillo F, Donadio S, De Carli F, Garbarino S, Nobili L. A model-based approach to homeostatic and ultradian aspects of nocturnal sleep structure in narcolepsy. Sleep. 2007;30(2):157–65.

    PubMed  Google Scholar 

  44. Mileykovskiy BY, Kiyashchenko LI, Siegel JM. Behavioral correlates of activity in identified hypocretin/orexin neurons. Neuron. 2005;46(5):787–98.

    Article  PubMed  CAS  Google Scholar 

  45. Phillips AJ, Robinson PA. A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system. J Biol Rhythms. 2007;22(2):167–79.

    Article  PubMed  CAS  Google Scholar 

  46. Rempe MJ, Best J, Terman D. A mathematical model of the sleep/wake cycle. J Math Biol. 2009;60(5):615–44.

    Article  PubMed  Google Scholar 

  47. Lu J, Sherman D, Devor M, Saper CB. A putative flip-flop switch for control of REM sleep. Nature. 2006;441(7093):589–94.

    Article  PubMed  CAS  Google Scholar 

  48. John J, Wu MF, Boehmer LN, Siegel JM. Cataplexy-active neurons in the hypothalamus: implications for the role of histamine in sleep and waking behavior. Neuron. 2004;42(4):619–34.

    Article  PubMed  CAS  Google Scholar 

  49. Wu MF, John J, Boehmer LN, Yau D, Nguyen GB, Siegel JM. Activity of dorsal raphe cells across the sleep-waking cycle and during cataplexy in narcoleptic dogs. J Physiol. 2004;554(1):202–15.

    Article  PubMed  CAS  Google Scholar 

  50. Postnova S, Voigt K, Braun HA. A mathematical model of homeostatic regulation of sleep-wake cycles by hypocretin/orexin. J Biol Rhythms. 2009;24:523–35.

    Article  PubMed  Google Scholar 

  51. Williams K, Diniz Behn CG. Dynamic interactions between orexin and dynorphin may delay onset of functional orexin effects: a modeling study. J Bio Rhythms. 2011;26(2):171–81.

    Article  PubMed  Google Scholar 

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Correspondence to Cecilia Diniz Behn .

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Behn, C.D. (2011). Mathematical Models of Narcolepsy. In: Baumann, C., Bassetti, C., Scammell, T. (eds) Narcolepsy. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8390-9_16

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  • DOI: https://doi.org/10.1007/978-1-4419-8390-9_16

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