A mathematical model of the sleep/wake cycle

Journal of Mathematical Biology

Volumn 60, Issue 5, 2010, Pages 615-644

  Rempe, Michael J ^a   Best, Janet ^a   Terman, David ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

Circadian pacemaker; NREM; REM; Sleep; Sleep homeostat

Indexed keywords

NEUROPEPTIDE; OREXINS; SIGNAL PEPTIDE;

ARTICLE; BIOLOGICAL MODEL; CIRCADIAN RHYTHM; ELECTROENCEPHALOGRAPHY; HUMAN; NERVE CELL; PHYSIOLOGY; SLEEP; WAKEFULNESS;

CIRCADIAN RHYTHM; ELECTROENCEPHALOGRAPHY; HUMANS; INTRACELLULAR SIGNALING PEPTIDES AND PROTEINS; MODELS, NEUROLOGICAL; NEURONS; NEUROPEPTIDES; SLEEP; WAKEFULNESS;

EID: 77951880479     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-009-0276-5     Document Type: Article

References (70)

1. Achermann P (2004) The two-process model of sleep regulation revisited. Aviat Space Environ Med 75(3): A37-A43.
2. Achermann P, Borbély AA (1990) Simulation of human sleep-ultradian dynamics of electroencephalographic slow-wave activity. J Biol Rhythms 5(2): 141-157.
3. Achermann P, Borbély AA (1994) Simulation of daytime vigilance by the additive interaction of a homeostatic and a circadian process. Biol Cybern 71(2): 115-121.
4. Achermann P, Borbély AA (2003) Mathematical models of sleep regulation. Front Biosci 8: S683-S693.
5. Bes FW, Jobert ML, Muller LC, Schulz H (1996) The diurnal distribution of sleep propensity: experimental data about the interaction of the propensities for slow-wave sleep and rem sleep. J Sleep Res 5: 90-98.
6. Boeve BF, Silber MH, Saper CB, Ferman TJ, Dickson DW, Parisi JE, Benarroch EE, Ahlskog JE, Smith GE, Caselli RC, Tippman-Peikert M, Olson EJ, Lin SC, Young T, Wszolek Z, Schenck CH, Mahowald MW, Castillo PR, Del Tredici K, Braak H (2007) Pathophysiology of REM sleep behaviour disorder and relevance to neurodegenerative disease. Brain 130: 2770-2788.
7. Boissard R, Gervasoni D, Schmidt MH, Barbagli B, Fort P, Luppi PH (2002) The rat ponto-medullary network responsible for paradoxical sleep onset and maintenance: a combined microinjection and functional neuroanatomical study. Eur J Neurosci 16(10): 1959-1973.
8. Borbély A (1982) A two process model of sleep regulation. Hum Neurobiol 1: 195-204.
9. Borbély A, Achermann P (1999) Sleep homeostasis and models of sleep regulation. J Biol Rhythms 14: 557-568.
10. Borbély AA, Achermann P (1992) Concepts and models of sleep regulation, an overview. J Sleep Res 1: 63-79.
11. Campbell S, Czeisler C, Dijk D, Kronauer R, Brown E, Duffy J, Allan J, Shanahan T, Rimmer D, Ronda J, Mitchell J, Silva E, Emens J (2000) Is there an intrinsic period of the circadian clock?. Science 288: 1174-1175.
12. Chemelli RM, Willie JT, Sinton CM, Elmquist JK, Scammell T, Lee C, Richardson JA, Williams SC, Xiong YM, Kisanuki Y, Fitch TE, Nakazato M, Hammer RE, Saper CB, Yanagisawa M (1999) Narcolepsy in orexin knockout mice: molecular genetics of sleep regulation. Cell 98(4): 437-451.
13. Chou T (2003) Regulation of wake-sleep timing: circadian rhythms and bistability of sleep-wake sates. Ph. D. thesis, Harvard University.
14. Chou TC, Bjorkum A, Gaus S, Lu J, Scammell T, Saper C (2002) Afferents to the ventrolateral preoptic nucleus. J Neurosci 22: 977-990.
15. Chou TC, Scammell TE, Gooley JJ, Gaus SE, Saper CB, Lu J (2003) Critical role of dorsomedial hypothalamic nucleus in a wide range of behavioral circadian rhythms. J Neurosci 23(33): 10691-10702.
16. Colwell CS, Michel S (2003) Sleep and circadian rhythms: do sleep centers talk back to the clock?. Nat Neurosci 6(10): 1005-1006.
17. Czeisler C, Duffy J, Shanahan T, Brown E, Mitchell J, Rimmer D, Ronda J, Silva E, Allan J, Emens J, Dijk D, Kronauer R (1999) Stability, precision, and near-24-hour period of the human circadian pacemaker. Science 284: 2177-2181.
18. Daan S, Beersma DGM, Borbely AA (1984) Timing of human sleep-recovery process gated by a circadian pacemaker. Am J Phys 246(2): R161-R178.
19. Dauvilliers Y, Amulf I, Mignot E (2007) Narcolepsy with cataplexy. Lancet 369(9560): 499-511.
20. Deurveilher S, Semba K (2006) Immediate early genes in sensory processing, cognitive performance and neurological disorders, chap. Mapping Sleep-wake control with the transcription factor c-Fos, pp 113-136. Springer, USA.
21. Dijk DJ, Czeisler CA (1994) Paradoxical timing of the circadian-rhythm of sleep propensity serves to consolidate sleep and wakefulness in humans. Neurosci Lett 166(1): 63-68.
22. Dijk DJ, Czeisler CA (1995) Contribution of the circadian pacemaker and the sleep homeostat to sleep propensity, sleep structure, electroencephalographic slow waves, and sleep spindle activity in humans. J Neurosci 15(5): 3526-3538.
23. Diniz Behn CG, Brown EN, Scammell TE, Kopell NJ (2007) Mathematical model of network dynamics governing mouse sleep-wake behavior. J Neurophysiol 97(6): 3828-3840.
24. Diniz Behn CG, Kopell N, Brown EN, Mochizuki T, Scammell TE (2008) Delayed orexin signaling consolidates wakefulness and sleep: physiology and modeling. J Neurophysiol 99(6): 3090-3103.
25. von Economo C (1930) Sleep as a problem of localization. J Nerv Ment Dis 71: 249-259.
26. Ferrillo F, Donadio S, De Carli F, Garbarino S (2007) A model-based approach to homeostatic and ultradian aspects of nocturnal sleep structure in narcolepsy. Sleep 30(2): 157-165.
27. FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1: 445-466.
28. Fuller PM, Saper CB, Lu J (2007) The pontine REM switch: past and present. J Phys Lond 584(3): 735-741.
29. Hill S, Tononi G (2005) Modeling sleep and wakefulness in the thelamocortical system. J Neurophysiol 93(3): 1671-1698.
30. Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117: 500-544.
31. Jewett ME, Kronauer RE (1999) Interactive mathematical models of subjective alertness and cognitive throughput in humans. J Biol Rhythm 14(6): 588-597.
32. John J, Wu M, Boehmer L, Siegel J (2004) Cataplexy-active neurons in the hypothalamus: implications for the role of histamine in sleep and waking behavior. Neuron 42(4): 619-634.
33. Kleitman N (1987) Sleep and wakefulness. University of Chicago Press, Chicago.
34. Krahn LE, Black JL, Silber MH (2001) Narcolepsy: new understanding of irresistible sleep. Mayo Clin Proc 76(2): 185-194.
35. Krueger JM, Obal F (1993) A neuronal group-theory of sleep function. J Sleep Res 2(3): 186-186.
36. Lavie P (1986) Ultrashort sleep-waking schedule. III. 'gates' and 'forbidden zones' for sleep. Elect Clin Neuro 63: 414-425.
37. Lu J, Bjorkum AA, Xu M, Gaus SE, Shiromani PJ, Saper CB (2002) Selective activation of the extended ventrolateral preoptic nucleus during rapid eye movement sleep. J Neurosci 22(11): 4568-4576.
38. Lu J, Sherman D, Devor M, Saper CB (2006) A putative flip-flop switch for control of rem sleep. Nature 441(7093): 589-594.
39. Massaquoi S, McCarley R (1992) Extension of the limit cycle reciprocal interaction model of REM cycle control. an integrated sleep control model. J Sleep Res 1: 138-143.
40. McCarley R, Massaquoi S (1992) Neurobiological structure of the revised limit cycle reciprocal interaction model of REM cycle control. J Sleep Res 1: 132-137.
41. McCarley RW (2007) Neurobiology of REM and NREM sleep. Sleep Med 8(4): 302-330.
42. McCarley RW, Hobson JA (1975) Neuronal excitability modulation over sleep cycle-structural and mathematical-model. Science 189(4196): 58-60.
43. McCarley RW, Massaquoi SG (1986) A limit-cycle mathematical-model of the rem-sleep oscillator system. Am J Physiol 251(6): R1011-R1029.
44. McGinty D, Szymusiak R (2003) Hypothalamic regulation of sleep and arousal. Front Biosci 8: S1074-S1083.
45. Merica H, Fortune RD (2004) State transitions between wake and sleep, and within the ultradian cycle, with focus on the link to neuronal activity. Sleep Med Rev 8(6): 473-485.
46. Mochizuki T, Crocker A, McCormack S, Yanagisawa M, Sakurai T, Scammell TE (2004) Behavioral state instability in orexin knock-out mice. J Neurosci 24(28): 6291-6300.
47. Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35: 193-213.
48. Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50: 2061-2070.
49. Nobili L, Beelke M, Besset A, Billiard M, Ferrillo F (2001) Nocturnal sleep features in narcolepsy: a model-based approach. Rev Neurol 157(11): S82-S86.
50. Phillips A, Robinson P (2008) Sleep deprivation in a quantitative physiologically based model of the ascending arousal system. J Theor Biol 255(4): 413-423.
51. Phillips AJK, Robinson PA (2007) A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system. J Biol Rhythms 22(2): 167-179.
52. Plazzi G, Serra L, Ferri R (2008) Nocturnal aspects of narcolepsy with cataplexy. Sleep Med Rev 12: 109-128.
53. Porkka-Heiskanen T, Strecker RE, Thakkar M, Bjorkum AA, Greene RW, McCarley RW (1997) Adenosine: a mediator of the sleep-inducing effects of prolonged wakefulness. Science 276(5316): 1265-1268.
54. Rubin JE, Shevtsova NA, Ermentrout GB, Smith JC, Rybak IA (2009) Multiple rhythmic states in a model of the respiratory central pattern generator. J Neurophysiol 101(4): 2146-2165.
55. Sakurai T (2007) The neural circuit of orexin (hypocretin): maintaining sleep and wakefulness. Nat Rev Neurosci 8(3): 171-181.
56. Saper CB, Chou TC, Scammell TE (2001) The sleep switch: hypothalamic control of sleep and wakefulness. Trends Neurosci 24(12): 726-731.
57. Saper CB, Scammell TE, Lu J (2005) Hypothalamic regulation of sleep and circadian rhythms. Nature 437(7063): 1257-1263.
58. Sasaki Y, Fukuda K, Takeuchi T, Inugami M, Miyasita A (2000) Sleep onset REM period appearance rate is affected by REM propensity in circadian rhythm in normal nocturnal sleep. Clin Neurophysiol 111(3): 428-433.
59. Siegel JM (2006) The stuff dreams are made of: anatomical substrates of rem sleep. Nat Neurosci 9(6): 721-722.
60. Siegel JM (2008) Do all animals sleep?. Trends Neurosci 31(4): 208-213.
61. Strogatz S (1986) The mathematical structure of the human sleep-wake cycle. Springer, Heidelberg.
62. Strogatz SH (1987) Human sleep and circadian-rhythms-a simple-model based on 2 coupled oscillators. J Math Biol 25(3): 327-347.
63. Swick TJ (2005) The neurology of sleep. Neurol Clin 23(4): 967-989.
64. Szymusiak R, Gvilia I, McGinty D (2007) Hypothalamic control of sleep. Sleep Med 8(4): 291-301.
65. Takeuchi T, Ogilvie R, Murphy T, Ferrelli A (2003) EEG activities during elicited sleep onset REM and NREM periods reflect different mechanisms of dream generation. Clin Neurophysiol 114: 210-220.
66. Tamakawa Y, Karashima A, Koyama Y, Katayama N, Nakao M (2006) A quartet neural system model orchestrating sleep and wakefulness mechanisms. J Neurophysiol 95(4): 2055-2069.
67. Wright K, Hughes R, Kronauer R, Dijk D, Czeisler C (2001) Intrinsic near-24-h pacemaker period determines limits of circadian entrainment to a weak synchronizer in humans. Proc Natl Acad Sci 98: 14027-14032.
68. Wu M, Gulyani S, Yau E, Mignot E, Phan B, Siegel J (1999) Locus coeruleus neurons: cessation of activity during cataplexy. Neuroscience 91(4): 1389-1399.
69. Wu M, John J, Boehmer L, Yau D, Nguyen G, Siegel J (2004) Activity of dorsal raphe cells across the sleep-waking cycle and during cataplexy in narcoleptic dogs. J Physiol 554(1): 202-215.
70. Yin W (2007) A mathematical model of the sleep-wake cycle. Master's thesis, Georgia Institute of Technology.