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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Modelling of Synaptic STDP and Analysis in a Two-Neuron Model

Discontinuity, Nonlinearity, and Complexity 1(2) (2012) 147--159 | DOI:10.5890/DNC.2012.04.002

V. K. Menz$^{1}$; S. Popovych$^{2}$; T.Küpper$^{3}$

$^{1}$ German Primate Center, Research Group Primate Neurobiology, Göttingen, Germany

$^{2}$ University of Cologne, Zoological Institute, Cologne, Germany

$^{3}$ University of Cologne, Mathematical Institute, Cologne, Germany

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Abstract

A mathematical model is developed to describe the behaviour of spiking neurons and adaptation of synaptic weights in the framework of spike-timing-dependent plasticity (STDP) by modifying the model of STDP suggested by Gorchetchnikov, Versace, and Hasselmo [1]. As a result an STDP curve similar to that found experimentally by Bi and Poo [2] is produced. This approach is applied to a system of two integrate-and-fire neurons interacting via adapting synapses and stimulated by a constant external current. The dynamics of the considered system over long time periods is examined for both permanent and short initial stimulations. The obtained results are then compared with real data for in vivo and in vitro neurons.

References

  1. [1]  Gorchetchnikov, A., Versace, M. and Hasselmo, M.E. (2005), A model of STDP based on spatially and temporally local information: Derivation and combination with gated decay, Neural Networks, 18, 458-466.
  2. [2]  Bi, G. and Poo, M.-M. (1998), Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type, Journal of Neuroscience, 18(24), 10464-10472.
  3. [3]  Hebb, D.O. (1949), The Organization of Behaviour: A Neuropsychological Theory, Wiley: New York.
  4. [4]  Bliss, T.V. and Gardner-Medwin, A.R. (1973), Long-lasting potentiation of synaptic transmission in the dentate area of the unanaesthetized rabbit following stimulation of the perforant path, Journal of Neurophysiology, 232, 357-374.
  5. [5]  Bliss, T.V. and Lømo, T. (1973), Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path, Journal of Neurophysiology, 232, 331-356.
  6. [6]  Artola, A. and Singer, W. (1987), Long-term potentiation and NMDA receptors in rat visual cortex, Nature, 330, 649-652.
  7. [7]  Hirsch, J.C., Barrionuevo, G. and Crepel, F. (1992), Homo- and heterosynaptic changes in efficacy are expressed in prefrontal neurons: an in vitro study in the rat, Synapse, 12, 82-85.
  8. [8]  Iriki, A., Pavlides, C., Keller, A. and Asanuma, H. (1989), Long-term potentiation in the motor cortex, Science, 245(4924), 1385-1387.
  9. [9]  Kirkwood, A. and Bear, M.F. (1994), Hebbian synapses in visual cortex, Journal of Neuroscience, 14(3), 1634- 1645.
  10. [10]  Chapman, P.F., Kairiss, E.W., Keenan, C.L. and Brown, T.H. (1990), Long-Term synaptic potentiation in the amygdala, Synapse, 6, 271-278.
  11. [11]  Clugnet, M.C. and LeDoux, J.E. (1990), Synaptic Plasticity in Fear Conditioning Circuits: Induction of LTP in the Lateral Nucleus of the Amygdala by Stimulation of the Medial Geniculate Body, Journal of Neuroscience, 10 (8), 2818-2824.
  12. [12]  Liu, Q.-S., Pu, L. and Poo, M.-M. (2005), Repeated cocaine exposure in vivo facilitates LTP induction in midbrain dopamine neurons, Nature, 437, 1027-1031.
  13. [13]  Pu, L., Liu, Q.-S. and Poo, M.-M. (2006), BDNF-dependent synaptic sensitization in midbrain dopamine neurons after cocaine withdrawal, Nature Neuroscience, 9(5), 605-607.
  14. [14]  Artola, A., Bröcher, S. and Singer, W. (1990), Different voltage-dependent thresholds for inducing long-term depression and long-term potentiation in slices of rat visual cortex, Nature, 347, 69-72.
  15. [15]  Dudek, S.M. and Bear, M.F. (1993), Bidirectional Long-Term Modification of Synaptic Effectiveness in the Adult and Immature Hippocampus, Journal of Neuroscience, 13(7), 2910-2918.
  16. [16]  Linden, D.J. and Connor, J.A. (1995), Long-term synaptic depression, Annual Review of Neuroscience, 18, 319- 357.
  17. [17]  Mulkey, R.M. and Malenka, R.C. (1992), Mechanisms underlying induction of homosynaptic long-term depression in area CA1 of the hippocampus, Neuron, 9 (5), 967-975.
  18. [18]  Stanton, P.K. and Sejnowski, T.J. (1989),Associative long-term depression in the hippocampus incuced by hebbian covariance, Nature, 339, 215-218.
  19. [19]  Froemke, R.C. and Dan, Y. (2002), Spike-timing-dependent synaptic modification induced by natural spike trains, Nature, 416, 433-438.
  20. [20]  Zhang, L.I., Tao, H.W., Holt, C.E., Harris, W.A. and Poo, M.-M. (1998) A critical window for cooperation and competition among developing retinotectal synapses, Nature, 395, 37-44.
  21. [21]  Song, S., Miller, K.D. and Abbott, L.F. (2000), Competitive Hebbian learning through spike-timing-dependent synaptic plasticity, Nature Neuroscience, 3(9), 919-926.
  22. [22]  Porr, B., Saudargiene, A. and Wörgötter, F. (2004), Analytical solution of spike-timing dependent plasticity based on synaptic biophysics. In: Thrun, S., Saul, L.K. and Schölkopf, B. (Eds.), Advances in neural information processing systems 16, pp. 1343-1350. Cambridge, MA: MIT Press.
  23. [23]  Kepecs, A., van Rossum, M.C., Song, S. and Tegner, J. (2002), Spike-timing-dependent plasticity: common themes and divergent vistas, Biological Cybernetics, 87, 446-458.
  24. [24]  Stein, R.B. (1967), Some models of neuronal variability, Biophysical Journal, 7(1), 37-68.
  25. [25]  Rauch, A., La Camera, G., Lüscher, H.-R., Senn,W. and Fusi, S. (2003), Neocortical Pyramidal Cells Respond as Integrate-and-Fire Neurons to In Vivo-Like Input Currents, Journal of Neurophysiology, 90, 1598-1612.
  26. [26]  Brunel, N. (2000), Persistent activity and the single-cell frequency-current curve in a cortical network model, Network: Computation in Neural Systems, 11, 261-280.
  27. [27]  Troyer, T.W. and Miller, K.D. (1997), Physiological Gain Leads to High ISI Variability in a Simple Model of a Cortical Regular Spiking Cell, Neural Computation, 9, 971-983.
  28. [28]  Yakovlev, V., Fusi, S., Berman, E. and Zohary, E. (1998), Inter-trial neuronal activity in inferior temporal cortex: a putative vehicle to generate long-term visual associations, Nature Neuroscience, 1(4), 310-317.
  29. [29]  Abbott, L.F. and Nelson, S.B. (2000), Synaptic plasticity: taming the beast, Nature Neuroscience, 3, 1178-1183.
  30. [30]  Creutzfeldt, O.D., Lux, H.D. and Nacimiento, A.C. (1964), Intracelluläre Reizung corticaler Nervenzellen, Pflügers Archiv European Journal of Physiology, 281, 129-151.
  31. [31]  Stevens, C.F. and Zador, A.M. (1998), Input synchrony and the irregular firing of cortical neurons, Nature Neuroscience, 1(3), 210-217.
  32. [32]  Reining, R. and Schweiger, A. (2006), Endlich weniger Schmerzen, Stuttgart: Georg Thieme Verlag.
  33. [33]  Preyer, S. and Bootz, F. (1995), Tinnitusmodelle zur Verwendung bei der Tinnituscouncellingtherapie des chronischen Tinnitus, HNO, 43, 338-351.