Comparison of Electrical Oscillations in Neurons with Induced or Spontaneous Cellular Rhythms due to Biochemical Regulation

  • Albert Goldbeter
Part of the Brain Dynamics book series (BD)


Biological rhythms can be classified broadly into different categories, according to the way in which they occur. Thus, they can arise spontaneously in a given set of experimental conditions, as exemplified by rhythmic activity in nodal tissues of the heart, or they can be driven by some external periodic process. In the latter case, the biological rhythm is generally entrained in a certain range at the frequency of the forcing stimulus. Oscillations can also occur as a result of a change in external conditions that brings about the transition from a stable steady state to an oscillatory regime. The latter situations relate to different sorts of induced rhythms; indeed (see the introductory chapter by Bullock), induced rhythms are either triggered from silence or modulated from an ongoing rhythm by an external event, transient or sustained.


Dictyostelium Discoideum Stable Steady State Thalamic Neuron Neuronal Oscillation Phase Plane Analysis 
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  1. Adams WB, Benson JA (1985): The generation and modulation of endogenous rhythmicity in the Aplysia bursting pacemaker neurone R15. Prog Biophys Mol Biol 46:1–49CrossRefGoogle Scholar
  2. Adams WB, Benson JA (1989): Rhythmic neuronal burst generation: experiment and theory. In: Cell to Cell Signalling: From Experiments to Theoretical Models, Goldbeter A, ed. London: Academic Press, pp 29–45Google Scholar
  3. Aihara K, Matsumoto G (1982): Temporally coherent organization and instabilities in squid giant axon. J Theor Biol 95:697–720CrossRefGoogle Scholar
  4. Babloyantz A, Destexhe A (1986): Low-dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci USA 83:3513–3517CrossRefGoogle Scholar
  5. Berridge MJ, Galione A (1988): Cytosolic calcium oscillators. FASEB J 2:3074–3082Google Scholar
  6. Berridge MJ, Rapp PE (1979): A comparative survey of the function, mechanism and control of cellular oscillations. J Exp Biol 81:217–279Google Scholar
  7. Cazalis M, Dayanithi G, Nordmann JJ (1985): The role of patterned burst and interburst interval on the excitation-coupling mechanism in the isolated rat neural lobe. J Physiol 369:45–60Google Scholar
  8. Cuthbertson KSR (1989): Intracellular calcium oscillators. In: Cell to Cell Signalling: From Experiments to Theoretical Models, Goldbeter A, ed. London: Academic Press, pp 435–447.Google Scholar
  9. Decroly O, Goldbeter A (1982): Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system. Proc Natl Acad Sci USA 79: 6917–6921CrossRefGoogle Scholar
  10. Decroly O, Goldbeter A (1987): From simple to complex oscillatory behaviour: analysis of bursting in a multiply regulated biochemical system. J Theor Biol 124:219–250CrossRefGoogle Scholar
  11. Devreotes PN (1982): Chemotaxis. In: The Development of Dictyostelium discoideum, Loomis WF, ed. New York: Academic Press, pp 117–168Google Scholar
  12. Dupont G, Berridge M J, Goldbeter A (1991): Signal-induced Ca2+ oscillations: Properties of a model based on Ca2+-induced Ca2+ release. Cell Calcium 12:73–85CrossRefGoogle Scholar
  13. Durston AJ (1974): Pacemaker mutants of Dictyostelium discoideum. Dev Biol 38:308–319CrossRefGoogle Scholar
  14. Eckhorn R, Bauer R, Jordan W, Brosch M, Kruse W, Munk M, Reitboeck HJ (1988): Coherent oscillations: a mechanism of feature linking in the visual cortex? Multiple electrode and correlation analyses in the cat. Biol Cybern 60:121–130CrossRefGoogle Scholar
  15. Fitzhugh R (1961): Impulses and physiological states in theoretical models of nerve membranes. Biophys J 1: 445–466CrossRefGoogle Scholar
  16. Gadsby DC, Wit AL (1981): Electrophysiologic characteristics of cardiac cells and the genesis of cardiac arrhythmias. In: Cardiac Pharmacology. New York: Academic Press, pp 229–274Google Scholar
  17. Gerisch G, Malchow D, Roos W, Wick U (1979): Oscillations of cyclic nucleotide concentrations in relation to the excitability of Dictyostelium cells. J Exp Biol 81: 33–47Google Scholar
  18. Gerisch G, Wick U (1975): Intracellular oscillations and release of cyclic AMP from Dictyostelium cells. Biochem Biophys Res Commun 65:364–370CrossRefGoogle Scholar
  19. Glass L, Mackey MC (1988): From Clocks to Chaos: The Rhythms of Life. Princeton: Princeton University PressGoogle Scholar
  20. Goldbeter A (1990): Rythmes et chaos dans les systèmes biochimiques et cellulaires. Masson: Paris. (An English translation is to be published by Cambridge University Press under the title Rhythms and chaos in biochemical and cellular systems) Google Scholar
  21. Goldbeter A, Caplan SR (1976): Oscillatory enzymes. Annu Rev Biophys Bioeng 5: 449–476CrossRefGoogle Scholar
  22. Goldbeter A, Dupont G, Berridge MJ (1990): Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci USA 87:1461–1465CrossRefGoogle Scholar
  23. Goldbeter A, Moran F (1988): Dynamics of a biochemical system with multiple oscillatory domains as a clue for multiple modes of neuronal oscillations. Eur Biophys J 15:277–287CrossRefGoogle Scholar
  24. Goldbeter A, Segel LA (1980): Control of developmental transitions in the cyclic AMP signaling system of Dictyostelium discoideum. Differentiation 17:127–135CrossRefGoogle Scholar
  25. Goldbeter A, Wurster B (1989): Regular oscillations in suspensions of a putatively chaotic mutant of Dictyostelium discoideum. Experientia 45:363–365CrossRefGoogle Scholar
  26. Gray CM, König P, Engel AK, Singer W (1989): Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334–337CrossRefGoogle Scholar
  27. Gray CM, Singer W (1989): Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc Natl Acad Sci USA 86:1698–1702CrossRefGoogle Scholar
  28. Guttman R, Lewis S, Rinzel J (1980): Control of repetitive firing in squid axon membrane as a model for a neuroneoscillator. J Physiol (Lond) 305:377–395Google Scholar
  29. Halloy J, Li YX, Martiel JL, Wurster B, Goldbeter A (1990): Coupling chaotic and periodic cells results in a period-doubling route to chaos in a model for cAMP oscillations in Dictyostelium suspensions. Phys Lett A 151:33–36 and 159 : 442CrossRefGoogle Scholar
  30. Hess B, Boiteux A (1971): Oscillatory phenomena in biochemistry. Annu Rev Biochem 40:237–258CrossRefGoogle Scholar
  31. Holden AV, Ed. (1986) Chaos. Manchester: Manchester University PressGoogle Scholar
  32. Holden AV, Winlow W, Haydon PG (1982): The induction of periodic and chaotic activity in a molluscan neurone. Biol Cybern 43:169–173CrossRefGoogle Scholar
  33. Holden AV, Yoda M (1981): Ionic channels density of an excitable membrane can act as bifurcation parameter. Biol Cybern 42:29–38CrossRefGoogle Scholar
  34. Huxley AH (1959): Ion movements during nerve activity. Ann N Y Acad Sci 81: 221—246CrossRefGoogle Scholar
  35. Jacob R (1990): Calcium oscillations in electrically non-excitable cells. Biochim Biophys Acta 1052:427–438CrossRefGoogle Scholar
  36. Jahnsen H, Llinás R (1984): Ionic basis for the electroresponsiveness and oscillatory properties of guinea-pig thalamic neurones in vitro. J Physiol (Lond) 349:227–247Google Scholar
  37. Johnston D, Brown TH (1984): Mechanism of neuronal burst generation. In: Electrophysiology of Epilepsy. New York: Academic Press, pp 277–301Google Scholar
  38. Knobil E (1980): The neuroendocrine control of the menstrual cycle. Rec Prog Horm Res 36:53–88Google Scholar
  39. Kuba K, Takeshita S (1981): Simulation of intracellular Ca2+ oscillation in a sympathetic neurone. J Theor Biol 93:1009–1031CrossRefGoogle Scholar
  40. Li YX, Goldbeter A (1989): Frequency specificity in intercellular communication: The influence of patterns of periodic signaling on target cell responsiveness. Biophys J 55:125–145CrossRefGoogle Scholar
  41. Li YX, Goldbeter A (1990): Frequency encoding of pulsatile signals of cyclic AMP based on receptor desensitization in Dictyostelium cells. J Theor Biol 146:355–367CrossRefGoogle Scholar
  42. Li YX, Halloy J, Martiel JL, Wurster B, Goldbeter A (1992): Suppression of chaos by periodic oscillations in a model for cyclic AMP signalling in Dictyostelium cells. Experientia (in press)Google Scholar
  43. Llinás R (1988): The intrinsic electrophysiological properties of mammalian neurons: a new insight into CNS function. Science 242:1654–1664CrossRefGoogle Scholar
  44. Markus M, Hess B (1984): Transitions between oscillatory modes in a glycolytic model system. Proc Natl Acad Sci USA 81: 4394–4398CrossRefGoogle Scholar
  45. Martiel JL, Goldbeter A (1985): Autonomous chaotic behaviour of the slime mould Dictyostelium discoideum predicted by a model for cyclic AMP signaling. Nature 313:590–592CrossRefGoogle Scholar
  46. Martiel JL, Goldbeter A (1987): A model based on receptor desensitization for cyclic AMP signaling in Dictyostelium cells. Biophys J 52:807–828CrossRefGoogle Scholar
  47. Meyer T, Stryer L (1988): Molecular model for receptor-stimulated calcium spiking. Proc Natl Acad Sci USA 85:5051–5055CrossRefGoogle Scholar
  48. Minorsky N (1962): Nonlinear Oscillations. Princeton: Van NostrandGoogle Scholar
  49. Nicolis G, Prigogine I (1977): Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations. New York: WileyGoogle Scholar
  50. Olsen LF, Degn H (1985): Chaos in biological systems. Q Rev Biophys 18:165–225CrossRefGoogle Scholar
  51. Rapp PE (1987): Why are so many biological systems periodic? Prog Neurobiol 29:261–273CrossRefGoogle Scholar
  52. Rapp PE, Bashore TR, Martinerie JM, Albano AM, Mees AI (1989): Dynamics of brain electrical activity. Brain Topogr 2: 99–118CrossRefGoogle Scholar
  53. Rinzel J (1985): Excitation dynamics: insights from simplified membrane models. Fed Proc 44:2944–2946Google Scholar
  54. Rinzel J (1987): A formal classification of bursting mechanisms in excitable systems. Lect Notes Biomath 71: 267–281CrossRefGoogle Scholar
  55. Roschke J, Başar E (1988): The EEG is not simple noise: strange attractors in intracranial structures. In: Dynamics of Sensory and Cognitive Processing in the Brain, Başar E, ed. Berlin: Springer-VerlagGoogle Scholar
  56. Roschke J, Başar E (1988): The EEG is not simple noise: strange attractors in intracranial structures. Springer Series in Brain Dynamics. 1: 203–216CrossRefGoogle Scholar
  57. Rose RM, Hindmarsh JL (1985): A model for a thalamic neuron. Proc R Soc Lond B 225:161–193CrossRefGoogle Scholar
  58. Rose RM, Hindmarsh JL (1989): The assembly of ionic currents in a thalamic neuron. III. The seven-dimensional model. Proc R Soc Lond B 237: 313–334CrossRefGoogle Scholar
  59. Selverston AI, Moulins M (1985): Oscillatory neural networks. Annu Rev Physiol 47: 29–48CrossRefGoogle Scholar
  60. Skarda CA, Freeman WJ (1987): How brain makes chaos in order to make sense of the world. Behav Brain Sci 10:161–195CrossRefGoogle Scholar
  61. Tsien RW, Kass RL, Weingart R (1979): Cellular and subcellular mechanisms of cardiac pacemaker oscillations. J Exp Biol 81: 205–215Google Scholar
  62. Whim MD, Lloyd PE (1989): Frequency-dependent release of peptide cotransmitters from identified cholinergic motor neurons in Aplysia. Proc Natl Acad Sci USA 86: 9034–9038CrossRefGoogle Scholar

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© Springer Science+Business Media New York 1992

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  • Albert Goldbeter

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