Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV

Structuring synaptic pathways among recurrent connections


In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network.

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  1. Appleby PA, Elliott T (2006) Stable competitive dynamics emerge from multispike interactions in a stochastic model of spike-timing-dependent plasticity. Neural Comput 18(10): 2414–2464

  2. Bi GQ, Poo MM (2001) Synaptic modification by correlated activity: Hebb’s postulate revisited. Annu Rev Neurosci 24: 139–166

  3. Burkitt AN (2006) A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol Cybern 95(1): 1–19

  4. Burkitt AN, Meffin H, Grayden DB (2004) Spike-timing-dependent plasticity: the relationship to rate-based learning for models with weight dynamics determined by a stable fixed point. Neural Comput 16(5): 885–940

  5. Burkitt AN, Gilson M, van Hemmen JL (2007) Spike-timing-dependent plasticity for neurons with recurrent connections. Biol Cybern 96(5): 533–546

  6. Câteau H, Kitano K, Fukai T (2008) Interplay between a phase response curve and spike-timing-dependent plasticity leading to wireless clustering. Phys Rev E 77(5): 051909

  7. Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383(6595): 76–78

  8. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009a) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks I: input selectivity–strengthening correlated input pathways. Biol Cybern 101(2): 81–102

  9. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009b) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks II: input selectivity–symmetry breaking. Biol Cybern 101(2): 103–114

  10. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009c) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III: partially connected neurons driven by spontaneous activity. Biol Cybern doi:10.1007/s00422-009-0343-4

  11. Gütig R, Aharonov R, Rotter S, Sompolinsky H (2003) Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. J Neurosci 23(9): 3697–3714

  12. Hawkes AG (1971) Point spectra of some mutually exciting point processes. J Roy Stat Soc Ser B 33(3): 438–443

  13. Hebb DO (1949) The organization of behavior: a neuropsychological theory. Wiley, New York

  14. Iglesias J, Eriksson J, Grize F, Tomassini M, Villa A (2005) Dynamics of pruning in simulated large-scale spiking neural networks. Biosystems 79: 11–20

  15. Izhikevich EM, Gally JA, Edelman GM (2004) Spike-timing dynamics of neuronal groups. Cereb Cortex 14: 933–944

  16. Karbowski J, Ermentrout GB (2002) Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. Phys Rev E 65(3): 031902

  17. Kempter R, Gerstner W, van Hemmen JL (1999) Hebbian learning and spiking neurons. Phys Rev E 59(4): 4498–4514

  18. Lubenov EV, Siapas AG (2008) Decoupling through synchrony in neuronal circuits with propagation delays. Neuron 58(1): 118–131

  19. Markram H, Lübke J, Frotscher M, Roth A, Sakmann B (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J Physiol (Lond) 500(2): 409–440

  20. Masuda N, Kori H (2007) Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity. J Comput Neurosci 22(3): 327–345

  21. Meffin H, Besson J, Burkitt AN, Grayden DB (2006) Learning the structure of correlated synaptic subgroups using stable and competitive spike-timing-dependent plasticity. Phys Rev E 73(4): 041911

  22. Moreno-Bote R, Renart A, Parga N (2008) Theory of input spike auto-and cross-correlations and their effect on the response of spiking neurons. Neural Comput 20(7): 1651–1705

  23. Morrison A, Aertsen A, Diesmann M (2007) Spike-timing-dependent plasticity in balanced random networks. Neural Comput 19(6): 1437–1467

  24. Morrison A, Diesmann M, Gerstner W (2008) Phenomenological models of synaptic plasticity based on spike timing. Biol Cybern 98(6): 459–478

  25. Pfister JP, Toyoizumi T, Barber D, Gerstner W (2006) Optimal spike-timing-dependent plasticity for precise action potential firing in supervised learning. Neural Comput 18(6): 1318–1348

  26. Roberts PD (2004) Recurrent biological neuronal networks: the weak and noisy limit. Phys Rev E 69(3): 031910

  27. van Hemmen JL (2001) Theory of synaptic plasticity. In: Moss F, Gielen S (eds) Handbook of biological physics, vol 4: Neuro-informatics and neural modelling. Elsevier, Amsterdam, pp 771–823

  28. van Rossum MCW, Bi GQ, Turrigiano GG (2000) Stable Hebbian learning from spike timing-dependent plasticity. J Neurosci 20(23): 8812–8821

  29. Senn W, Schneider M, Ruf B (2002) Activity-dependent development of axonal and dendritic delays, or, why synaptic transmission should be unreliable. Neural Comput 14(3): 583–619

  30. Sjöström PJ, Turrigiano GG, Nelson SB (2001) Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32(6): 1149–1164

  31. Song S, Abbott LF (2001) Cortical development and remapping through spike timing-dependent plasticity. Neuron 32(2): 339–350

  32. Toyoizumi T, Pfister JP, Aihara K, Gerstner W (2007) Optimality model of unsupervised spike-timing-dependent plasticity: synaptic memory and weight distribution. Neural Comput 19(3): 639–671

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Correspondence to Matthieu Gilson.

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Gilson, M., Burkitt, A.N., Grayden, D.B. et al. Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV. Biol Cybern 101, 427 (2009).

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  • Learning
  • STDP
  • Recurrent neuronal network
  • Spike-time correlation