Biological Cybernetics

, Volume 73, Issue 5, pp 389–400 | Cite as

Local lateral inhibition: a key to spike synchronization?

  • Alfred Nischwitz
  • Helmut Glünder
Original Papers
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Accepted:

Abstract

Starting from the idea that neural group activity as such is unlikely to be immediately relevant for neural synchronization, we investigate mechanisms that act at the level of individual nerve impulses (spikes). Hence, we consider populations of formal spike-emitting ‘leaky integrate and fire’ neurons instead of networks built from non-spiking oscillators. After outlining the principle of synchronization for basic forms of recurrent impulse coupling by using a pair of simplified formal neurons, we show that local lateral inhibition results in robust impulse synchronization in networks with nonvanishing transmission delays.

Keywords

Group Activity Basic Form Lateral Inhibition Transmission Delay Nerve Impulse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. Adrian ED (1935) The electrical activity of the cortex. Proc R Soc Med 29:197–200Google Scholar
  2. Atiya A, Baldi P (1989) Oscillations and synchronizations in neural networks: an exploration of the labeling hypothesis. Int J Neural Syst 1:103–124CrossRefGoogle Scholar
  3. Braitenberg V, Schüz A (1991) Anatomy of the cortex: statistics and geometry. Springer, Berlin Heidelberg New YorkGoogle Scholar
  4. Buck J (1988) Synchronous rhythmic flashing of fireflies. II. Q Rev Biol 63:265–289CrossRefPubMedGoogle Scholar
  5. Bush PC, Douglas RJ (1991) Synchronization of bursting action potenial discharge in a model network of neocortical neurons. Neural Comput 3:19–30Google Scholar
  6. Cairns DE, Baddeley RJ, Smith LS (1993) Constraints on synchronizing oscillator networks. Neural Comput 5:260–266Google Scholar
  7. Coultrip R, Granger R, Lynch G (1992) A cortical model of winnertake-all competition via lateral inhibition. Neural Networks 5:47–54CrossRefGoogle Scholar
  8. Deppisch J, Bauer H-U, Schillen T, König P, Pawelzik K, Geisel T (1992) Stochastic and oscillatory burst activities in a model of spiking neurons. In: Aleksander I, Taylor J (eds) Artificial neural networks 2. Elsevier, Amsterdam, pp 921–924Google Scholar
  9. 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? Biol Cybern 60:121–130CrossRefPubMedGoogle Scholar
  10. Eckhorn R, Reitboeck HJ, Arndt M, Dicke P (1990) Feature linking via synchronization among distributed assemblies: simulations of results from cat visual cortex. Neural Comput 2:293–307Google Scholar
  11. Eckhorn R, Frien A, Bauer R, Woelbern T, Kehr H (1993) High frequency (60–90 Hz) oscillations in primary visual cortex of awake monkey. Neuroreport 4:243–246PubMedGoogle Scholar
  12. Engel AK, König P, Gray CM, Singer W (1990) Stimulus-dependent neuronal oscillations in cat visual cortex: inter-columnar interaction as determined by cross-correlation analysis. Eur J Neurosci 2:588–606PubMedGoogle Scholar
  13. Engel AK, König P, Singer W (1991) Direct physiological evidence for scene segmentation by temporal coding. Proc Natl Acad Sci USA 88:9136–9140PubMedGoogle Scholar
  14. Engel AK, König P, Singer W (1993) Bildung repräsentationaler Zustände im Gehirn. Spektrum Wiss, no 9:42–47Google Scholar
  15. Freeman WJ (1975) Mass action in the nervous system. Academic Press, New YorkGoogle Scholar
  16. French AS, Stein RB (1970) A flexible neural analog using integrated circuits. IEEE Trans Biomed Eng 17:248–253PubMedGoogle Scholar
  17. Gerstner W, Hemmen JL van (1992) Associative memory in a network of ‘spiking’ neurons. Network 3:139–164Google Scholar
  18. Gerstner W, Ritz R, Hemmen JL van (1993a) A biologically motivated and analytically soluble model of collective oscillations in the cortex. I. Theory of weak locking. Biol Cybern 68:363–374CrossRefPubMedGoogle Scholar
  19. Gerstner W, Ritz R, Hemmen JL van (1993b) Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns. Biol Cybern 69:503–515CrossRefPubMedGoogle Scholar
  20. Glünder H, Antesberger M (1995) Same network — different formal neurons. Two network implementations for competitive motion analysis. In: Elsner N, Menzel R (eds) Learning and memory. Göttingen Neurobiology Report 1995. Thieme, Stuttgart, p 895Google Scholar
  21. Glünder H, Nischwitz A (1993) On spike synchronization. In: Aertsen A (eds) Brain theory. Spatio-temporal aspects of brain function. Elsevier, Amsterdam, pp 251–258Google Scholar
  22. Glünder H, Nischwitz A (1994) Single unit (SUA) and group activity (MUA) in simulated populations of impulse coupled neurons with lateral inhibition. In: Elsner N, Breer H (eds) Sensory transduction. Göttingen Neurobiology Report 1994. Thieme, Stuttgart, p 864Google Scholar
  23. 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 338:334–337CrossRefPubMedGoogle Scholar
  24. Hartmann G, Drüe S (1990) Self organization of a network linking features by synchronization. In: Eckmiller R, Hartmann G, Hauske G (eds) Parallel processing in neural systems and computers. Elsevier, Amsterdam, pp 361–364Google Scholar
  25. Hebb DO (1949) The organization of behaviour. Wiley, New YorkGoogle Scholar
  26. Hemmen JL van, Gerstner W, Ritz R (1992) A ‘microscopic’ model of collective oscillations in the cortex. In:Taylor JG, Caianiello EK, Cotterill RNJ, Clark JW (eds) Neural network dynamics. Springer, Berlin Heidelberg New York, pp 139–164Google Scholar
  27. Kirillov AB, Woodward DJ (1993) Synchronization of spiking neurons: transmission delays, noise and NMDA receptors. In: Proceedings of the World Congress on Neural Networks, Portland, Ore, pp 594–597Google Scholar
  28. König P, Schulen TB (1991) Stimulus-dependent assembly formation of oscillatory responses. I. Synchronization. Neural Comput 3:155–166Google Scholar
  29. Kraut U, Nischwitz A, Waschulzik T (1993) Temporal resolution: a critical parameter in simulations of pulse-coupled neural networks. In: Okabe Y (eds) Proceedings of the International Joint Conference on Neural Networks '93. Nagoya, Japan, pp 1116–1119Google Scholar
  30. Kuramoto Y (1991) Collective synchronization of pulse-coupled oscillators and excitable units. Physica D 50:15–30CrossRefGoogle Scholar
  31. Lytton WW, Sejnowski TJ (1991) Simulations of cortical pyramidal neurons synchronized by inhibitory interneurons. J Neurophysiol 66:1059–1079PubMedGoogle Scholar
  32. MacGregor RJ, Palasek RL (1974) Computer simulation of rhythmic oscillations in neuron pools. Kybernetik 16:79–86CrossRefPubMedGoogle Scholar
  33. Milner PM (1974) A model for visual shape recognition. Psychol Rev 81:521–535PubMedGoogle Scholar
  34. Mirollo RE, Strogatz SH (1990) Synchronization of pulse-coupled biological oscillators. SIAM J Appl Math 50:1645–1662CrossRefGoogle Scholar
  35. Niebur E, Schuster HG, Kammen DM (1991) Collective frequencies and metastability in networks of limit-cycle oscillators with time elay. Phys Rev Lett 67:2753–2756CrossRefPubMedGoogle Scholar
  36. Nischwitz A (1994) Impuls-Synchronisation in neuronalen Netzwerken. Harri Deutsch, ThunGoogle Scholar
  37. Nischwitz A, Glünder H (1992) Gibt es ein zur starken Wechselwirkung analoges Prinzip bei der neuronalen Informationsverarbeitung? In: Krönig D, Lang M (eds) Physik und Informatik Informatik und Physik. Springer, Berlin Heidelberg New York, pp 143–144Google Scholar
  38. Nischwitz A, Glünder H (1993) Letter to the editor. Spektrum Wiss, no 1:8Google Scholar
  39. Nischwitz A, Glünder H, Klausner P (1991) Synchronization of spikes in populations of laterally coupled model neurons. In: Kohonen T, Mäkisara K, Simula O, Kangas J (eds) Artificial neural networks. Elsevier, Amsterdam, pp 1771–1774Google Scholar
  40. Nischwitz A, Glünder H, Oertzen A von, Klausner P (1992) Synchronization and label-switching in networks of laterally coupled model neurons. In: Aleksander I, Taylor J (eds) Artificial neural networks 2. Elsevier, Amsterdam, pp 851–854Google Scholar
  41. Peskin CS (1975) Mathematical aspects of heart physiology. Courant Institute of Mathematical Sciences, New York University, New YorkGoogle Scholar
  42. Pittendrigh CS, Bruce VG (1957) An oscillator model for biological clocks. In: Rudnick D (ed) Rhythmic and synthetic processes in growth. Princeton University Press, Princeton, NJ, pp 75–109Google Scholar
  43. Pöppel E (1971) Oscillations as possible basis for time perception. Stud Gen 24:85–107Google Scholar
  44. Rall W (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: Reiss RF (eds) Neural theory and modelling. Stanford University Press, Stanford, Calif, pp 73–97Google Scholar
  45. Sayer RJ, Friedlander MJ, Redman SJ (1990) The time course and amplitude of EPSPs evoked at synapses between pairs of CA3/CA1 neurons in the hippocampal slice. J Neurosci 10:826–836PubMedGoogle Scholar
  46. Schuster HG, Wagner P (1989) Mutual entrainment of two limit cycle oscillators with time delayed coupling. Prog Theor Phys 81:939–945Google Scholar
  47. Sejnowski TJ, Lytton WW (1992) Inhibitory interneurons can synchronize cortical pyramidal neurons. In: Elsner N, Richter DW (eds) Rhythmogenesis in neurons and networks. Thieme, Stuttgart, pp 173–185Google Scholar
  48. Smith LS, Cairns DE, Nischwitz A (1994) Synchronization of integrateand-fire neurons with delayed inhibitory lateral connections. In: Marinaro M, Morasso PG (eds) Proceedings of the International Conference on Artificial Neural Networks '94. Springer, Berlin Heidelberg New York, pp 142–145Google Scholar
  49. Traub RD, Miles R, Wong RKS, Schulman LS, Schneiderman JH (1987) Models of synchronized hippocampal bursts in the presence of inhibition. II. Ongoing spontaneous population events. J Neurophysiol 58:752–764PubMedGoogle Scholar
  50. Vreeswijk C van, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J Comput Neurosci 1:313–321CrossRefPubMedGoogle Scholar
  51. Wang X, Blum EK (1992) Discrete-time versus continuous-time models of neural networks. J Comput Syst Sci 45:1–19CrossRefGoogle Scholar
  52. Wiener N (1961) Cybernetics or control and communication in the animal and the machine. MIT Press, Cambridge, MassGoogle Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Alfred Nischwitz
    • 1
  • Helmut Glünder
    • 2
  1. 1.Lehrstuhl für Nachrichtentechnik, Technische Universität MünchenMünchenGermany
  2. 2.Institut für Medizinische Psychologie, Ludwig-Maximilians-UniversitätMünchenGermany

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