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.
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References
Adrian ED (1935) The electrical activity of the cortex. Proc R Soc Med 29:197–200
Atiya A, Baldi P (1989) Oscillations and synchronizations in neural networks: an exploration of the labeling hypothesis. Int J Neural Syst 1:103–124
Braitenberg V, Schüz A (1991) Anatomy of the cortex: statistics and geometry. Springer, Berlin Heidelberg New York
Buck J (1988) Synchronous rhythmic flashing of fireflies. II. Q Rev Biol 63:265–289
Bush PC, Douglas RJ (1991) Synchronization of bursting action potenial discharge in a model network of neocortical neurons. Neural Comput 3:19–30
Cairns DE, Baddeley RJ, Smith LS (1993) Constraints on synchronizing oscillator networks. Neural Comput 5:260–266
Coultrip R, Granger R, Lynch G (1992) A cortical model of winnertake-all competition via lateral inhibition. Neural Networks 5:47–54
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 921–924
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 60:121–130
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 2:293–307
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 4:243–246
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 2:588–606
Engel AK, König P, Singer W (1991) Direct physiological evidence for scene segmentation by temporal coding. Proc Natl Acad Sci USA 88:9136–9140
Engel AK, König P, Singer W (1993) Bildung repräsentationaler Zustände im Gehirn. Spektrum Wiss, no 9:42–47
Freeman WJ (1975) Mass action in the nervous system. Academic Press, New York
French AS, Stein RB (1970) A flexible neural analog using integrated circuits. IEEE Trans Biomed Eng 17:248–253
Gerstner W, Hemmen JL van (1992) Associative memory in a network of ‘spiking’ neurons. Network 3:139–164
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 68:363–374
Gerstner W, Ritz R, Hemmen JL van (1993b) Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns. Biol Cybern 69:503–515
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 895
Glünder H, Nischwitz A (1993) On spike synchronization. In: Aertsen A (eds) Brain theory. Spatio-temporal aspects of brain function. Elsevier, Amsterdam, pp 251–258
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 864
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 338:334–337
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 361–364
Hebb DO (1949) The organization of behaviour. Wiley, New York
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 139–164
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 594–597
König P, Schulen TB (1991) Stimulus-dependent assembly formation of oscillatory responses. I. Synchronization. Neural Comput 3:155–166
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 1116–1119
Kuramoto Y (1991) Collective synchronization of pulse-coupled oscillators and excitable units. Physica D 50:15–30
Lytton WW, Sejnowski TJ (1991) Simulations of cortical pyramidal neurons synchronized by inhibitory interneurons. J Neurophysiol 66:1059–1079
MacGregor RJ, Palasek RL (1974) Computer simulation of rhythmic oscillations in neuron pools. Kybernetik 16:79–86
Milner PM (1974) A model for visual shape recognition. Psychol Rev 81:521–535
Mirollo RE, Strogatz SH (1990) Synchronization of pulse-coupled biological oscillators. SIAM J Appl Math 50:1645–1662
Niebur E, Schuster HG, Kammen DM (1991) Collective frequencies and metastability in networks of limit-cycle oscillators with time elay. Phys Rev Lett 67:2753–2756
Nischwitz A (1994) Impuls-Synchronisation in neuronalen Netzwerken. Harri Deutsch, Thun
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 143–144
Nischwitz A, Glünder H (1993) Letter to the editor. Spektrum Wiss, no 1:8
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 1771–1774
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 851–854
Peskin CS (1975) Mathematical aspects of heart physiology. Courant Institute of Mathematical Sciences, New York University, New York
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 75–109
Pöppel E (1971) Oscillations as possible basis for time perception. Stud Gen 24:85–107
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 73–97
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 10:826–836
Schuster HG, Wagner P (1989) Mutual entrainment of two limit cycle oscillators with time delayed coupling. Prog Theor Phys 81:939–945
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 173–185
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 142–145
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 58:752–764
Vreeswijk C van, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J Comput Neurosci 1:313–321
Wang X, Blum EK (1992) Discrete-time versus continuous-time models of neural networks. J Comput Syst Sci 45:1–19
Wiener N (1961) Cybernetics or control and communication in the animal and the machine. MIT Press, Cambridge, Mass
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Nischwitz, A., Glünder, H. Local lateral inhibition: a key to spike synchronization?. Biol. Cybern. 73, 389–400 (1995). https://doi.org/10.1007/BF00201473
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DOI: https://doi.org/10.1007/BF00201473