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ISSN 2542-1905 (Print)

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Postnov D. D., Sosnovceva O. V., Postnov D. E. Autonomous and nonautonomous dynamics of functional model of serotonergic neuron. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 3, pp. 26-44. DOI:


Autonomous and nonautonomous dynamics of functional model of serotonergic neuron

Postnov Dmitrij Dmitrievich, Saratov State University
Sosnovceva Olga Vladimirovna, Danmarks Tekniske Universitet
Postnov Dmitrij Engelevich, Saratov State University

Serotonin is a key modulator of neuronal activity both at the system level and at the level of local (short­range) interactions. However, in contrast to the synaptically connected neuron ensembles, there are much less qualitative models that describe the serotonin­controlled neural circuits. In this paper, we propose a relatively simple model of serotonergic (serotonin­releasing and serotonin­sensitive) neuron. It is shown that specific features of both autonomous and nonautonomous dynamics of such model are considerably dependent on a weak depolarizing voltage­independent current of neuron and on the presence of serotonin auto­receptors. Our work is aimed on development of «computational image» for basic serotonin­controlled neural circuits, which role for basic neuronal features plays the famous FitzHugh–Nagumo model.

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1. Kravitz E.A. Serotonin and aggression: Ingsights gained from a lobster model system and speculations on the role of amine neurons in a coplex behavior // J. Comp. Physiol. A. 2000. Vol. 186. P. 221. 2. Lesch K.P. and Merschdorf U. Impulsivity, agression, and serotonin: A molecular psychobiological perspective // Behav. Sci. Law. 2000. Vol. 18. P. 581. 3. Sakurai A. and Katz P.S. Spike timing-dependent serotonergic neuromodulation of synaptic strength intrinsic to a central pattern generator circuit // J. Neurosci. 2003. Vol. 23. 10745. 4. Satterlie R.A. and Norekian T.P. Modulation of swimming speed in the pteropod mollusc, Clione limacina: Role of a compartmental serotonergic system // Invert. Neurosci. 1996. Vol. 2. P. 157. 5. Nusbaum M.P., Friesen W.O., Kristian W.B. Jr., and Pierce R.A. Neural mechanisms generating the leech swimming rhythm // J. Comp. Physiol. A. 1987. Vol. 161. P. 355. 6. Ursin R. Serotonin and sleep // Sleep Med. Rev. 2002. Vol. 6. P. 55. 7. Hull E.M., Lorrain D.S., Du J., Matuszewich L., Lumley L.A., Putnam S.K., and Moses J. Hormone-neurotransmitter interactions in the control of sexual behavior // Behav. Brain Res. 1999. Vol. 105. P. 105. 8. Graeff F.G., Guimaraes F.S., De Andrade T.G., and Deakin J.F. Role of 5-HT in stress, anxiety, and depression // Pharmacol. Biochem. Behav. 1996. Vol. 54. P. 129. 9. Jobe P.C., Dailey J.W., and Wernicke J.F. A noradrenergic and serotonergic hypothesis of the linkage between epilepsy and affective disorders // Crit Rev. Neurobiol. 1999. Vol. 13. P. 317. 10. Whitaker-Azmitia P.M. and Peroutka S.J. The neuropharmacology of serotonin. New York: Academic Sciences, 1990. 11. Pineyro G. and Blier P.  ? Autoregulation of serotonin neurons: Role in antidepressant drug action // Pharmacol. Rev. 1999. Vol. 51, P. 533. 12. Stahl S.M., Grady M.M., and Briley M. SNRIs: their pharamocology, clinical efficacy, and tolerability in comparison with other classes of antidepressants // CNS Spectr. 2005. Vol. 10. P. 732. 13. Johnson K.W., Phebus L.A., and Cohen M.L. Serotonin in migraine: theories, animal models and emerging therapies // Prog. Drug Res. 1998. Vol. 51. P. 219. 14. Anderson I.M. Selective serotonin reuptake inhibitors versus tricyclic antidepressants: a meta-analysis of efficacy and tolerability // J. Affect. Disord. 2000. Vol. 58. P. 19. 15. Kish S.J., Furukawa Y., Ang L., Vorce S.P. and Kalasinsky K.S. Striatal serotonin is depleted in brain of a human MDMA (Ecstasy) user // Neurology. 2000. Vol. 55. P. 294. 16. Hornung J.P. The human raphe nuclei and the serotonergic system // J. Chem. Neuroanat. 2003. Vol. 26. P. 331. 17. Schwartz J.H. and Shkolnik L.J. The giant serotonergic neuron of Aplysia: A multi-targeted nerve cell // J. Neurosci. 1981. Vol. 1. P. 606. 18. Kristian M.B. and Nusbaum M.P. Jr. The dual role of serotonin in leech swimming // J. Physiol. 1983. Vol. 78. P. 743. 19. Sahley C.L. What we have learned from the study of learning of the leech // J. Neurobiol. 1995. Vol. 27. P. 434. 20. Kristan W.B.Jr., Calabrese R., Friesen W.O. Neuronal control of leech behavior // Prog. in Neurobiol. 2005. Vol. 76. P. 279. 21. Roth B.L. The Serotonin receptors: From molecular pharmacology to human therapeutics. Humana Press, 2006. 22. Marder E., Calabrese R.L. Principles of rhythmic motor pattern generation // Physiol. Rev. 1996. Vol. 763. P. 687. 23. Special issue on computational models of neuromodulation // Neural Networks. 2002. Vol. 15. 24. Baxter D.A., Canavier C.C., Clark J.W. Jr., and Byrne J.H. Computational model of the serotonergic modulation of sensory neurons in Aplysia // J. of Neurophysiol. 1999. Vol. 82. P. 2914. 25. Fellous J.-M. and Linster Ch. Computational models of neuromodulation // Neural computation. 1998. Vol. 10. P. 771. 26. FitzHugh R.A. Impulses and physiological states in theoretical models of nerve // Biophys. J. 1961. Vol. 1. P. 445. 27. Keener J., and Sneyd J. Mathematical Physiology. New York: Springer, 1998. 28. Lindner B., Garcia-Ojalvo J., Neiman A. and Schimansky-Geier L. Effects of noise in excitable systems // Phys. Rep. 2004. Vol. 392. P. 321. 29. Касаткин Д.В. Эффекты фазовой переустановки в ансамблях взаимодействующих нейронов ФитцХью–Нагумо // Известия высших учебных заведений. Прикладная нелинейная динамика. 2009. Т. 17, No 1. С. 79. 30. Некоркин В.И., Артюхин Д.В. Регулярные и хаотические колебания в системе двух взаимосвязанных, динамически различных элементов ФитцХью–Нагумо // Известия высших учебных заведений. Прикладная нелинейная динамика. 2001. Т. 9, No 6. С. 45. 31. Acebron J.A., Bulsara A.R., Rappel W.J. Динамика глобально связанных нейронных элементов ФитцХью–Нагумо в присутствии шума // Известия высших учебных заведений. Прикладная нелинейная динамика. 2003. Т. 11, No 3. С. 110. 32. Крюков А.К., Осипов Г.В., Половинкин А.В. Мультистабильность синхронных режимов в ансамблях неидентичных осцилляторов: цепочка и решетка связанных элементов // Известия высших учебных заведений. Прикладная нелинейная динамика. 2009. Т. 17, No 2. С. 29. 33. Binczak S., Jacquir S., Bilbault J.-M., Kazantsev V.B. and Nekorkin V.I. Experimental study of electrical FitzHugh–Nagumo neurons with modified excitability // Neural Networks. 2006. Vol. 19, No 5. P. 684. 34. Aghajanian G.K. and Vandermaelen C.P. Intracellular recordings from serotonergic dorsal raphe neurons: Pacemaker patentials and the effect of LSD // Brain Res. 1982. Vol. 238. P. 463. 35. Mnie-Filalia O., El Mansaria M., Espana A., Sanchez C., and Haddjeri N.  ? Allosteric modulation of the effects of the 5-HT reuptake inhibitor escitalopram on the rat hippocampal synaptic plasticity // Neuroscience letters. 2006. Vol. 395. P. 23. 36. Wang R.Y. and Aghajanian G.K. Correlative firing patterns of serotonergic neurons in rat dorsal raphe nucleus // J. Neurosci. 1982. Vol. 2. P. 11. 37. Berry M.S. and Pentreath V.W. Properties of a symmetric pair of serotonin-containing neurons in the cerebral ganglia of planorbis // J. Exp. Biol. 1976. Vol. 65. P. 361. 38. Moss B.L., Fuller A.D., Sahley C.L., and Burrell B.D. Serotonin modulates axoaxonal coupling between neurons critical for learning in the leech // J. Neurophysiol. 2005. Vol. 94. 2575-25-89. 39. De Miguel F.E. and Trueta C. Synaptic and extrasynaptic secretion of serotonin // Cell. Mol. Neurobiol. 2005. Vol. 25. P. 297. 40. Norekian T.P. and Satterlie R.A. Serotonergic neural system not only activates swimming but also inhibits competing neural centers in a pteropod mollusc // Amer. Zool. 2001. Vol. 41. P. 993. 41. Zhang H., Wainwright M., Byrne J.H., and Cleary L.J. Quantitation of contacts among sensory, motor, and serotonergic neurons in the pedal ganglion of Aplysia // Learning and Memory. 2003. Vol. 10. P. 387. 42. Izhikevich E.M. Resonate-and-fire neurons // Neural Networks J. 2001. Vol. 14. P. 883. 43. Izhikevich E.M. Dynamical systems in Neuroscience: The geometry of excitability and bursting. MIT Press, 2007. 44. Rinzel J. and Ermentrout G.B. Analysis of neural excitability and oscillations // Methods in Neuronal Modeling / Eds C. Koch, I. Segel. Cambridge: MIT Press, 1989. 45. Hodgkin A.L. The local electric changes associated with repetitive action in a nonmedulated axon // J. Physiol. 1948. Vol. 107. P. 165. 46. Izhikevich E.M. Neural Excitability, Spiking, and Bursting // Int. J. Bifur. Chaos. 2000. Vol. 10. P. 1171. 47. Morris C. and Lecar H. Voltage oscillations in the barnacle giant muscle fibre // Biophys. J. 1981. Vol. 35. P. 193. 48. Kopell N., Ermentrout G.B., Whittington M.A., and Traub R.D. Gamma rhythms and beta rhythms have different synchronization properties // Proc. Nat. Acad. Sci. USA. 2000. Vol. 97. P. 1867. 49. Hamon M., Gerschenfeld H.M., and Paupardin-Tritsch D. Release of endogenous serotonin from two identified serotonin-containing neurones and the physiological role of serotonin re-uptake // J. Physiol. 1978. Vol. 274. P. 265. 50. Казанцев В.Б., Некоркин В.И., Велардэ М.Г. Модель нейрона с осцилляторной активностью ниже порога возбуждения // Известия высших учебных заведений. Радиофизика. 1998. Т. 41, No 12. С. 1623. 51. Анищенко В.С., Астахов В.В., Вадивасова Т.Е. Регулярные и хаотические авто-колебания. Синхронизация и влияние флуктуаций. Учебник-монография. М.: Изд-во «Интеллект», 2009. 312 с. 52. Pikovsky A. and Kurths J. Coherence resonance in a noise-driven excitable systems // Phys. Rev. Lett. 1997. Vol. 78. P. 775. 53. Han S.K., Yim T.G., Postnov D.E. and Sosnovtseva O.V. Interacting coherence resonance oscillators // Phys. Rev. Lett. 1999. Vol. 83. P. 1771. 54. Ranganathan R., Cannon S.C., and Horvitz H.R. MOD-1 is a serotonin-gated chloride channel that modulates locomotory behaviour in C. elegans // Nature. 2000. Vol. 408. P. 470. 55. Ali D.W., Catarsi S., and Drapeau P. Ionotropic and metabotropic activation of a neuronal chloride channel by serotonin and dopamine in the leech Hirudo medicinalis // J. Physiol. 1998. Vol. 509. P. 211.  

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