Biological Cybernetics

, 96:615 | Cite as

Computational consequences of experimentally derived spike-time and weight dependent plasticity rules

  • Dominic Standage
  • Sajiya Jalil
  • Thomas TrappenbergEmail author
Original Paper


We present two weight- and spike-time dependent synaptic plasticity rules consistent with the physiological data of Bi and Poo (J Neurosci 18:10464–10472, 1998). One rule assumes synaptic saturation, while the other is scale free. We extend previous analyses of the asymptotic consequences of weight-dependent STDP to the case of strongly correlated pre- and post-synaptic spiking, more closely resembling associative learning. We further provide a general formula for the contribution of any number of spikes to synaptic drift. Asymptotic weights are shown to principally depend on the correlation and rate of pre- and post-synaptic activity, decreasing with increasing rate under correlated activity, and increasing with rate under uncorrelated activity. Spike train statistics reveal a quantitative effect only in the pre-asymptotic regime, and we provide a new interpretation of the relation between BCM and STDP data.


Spike Train Postsynaptic Spike EPSC Amplitude Power Rule Equilibrium Weight 
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.


  1. Abbott LF, Nelson SB (2000) Synaptic plasticity: taming the beast. Nat Neurosci 3:1178–1183CrossRefPubMedGoogle Scholar
  2. Bair W, Koch C, Newsome W, Britten K (1994) power spectrum analysis of bursting cells in area mt in the behaving monkey. J Neurosci 14(5):2870–2892PubMedGoogle Scholar
  3. Bi GQ (2002) Spatiotemporal specificity of synaptic plasticity: cellular rules and mechanisms. Biol Cybern 87:319–332CrossRefPubMedGoogle Scholar
  4. Bi GQ, Poo MM (1998) Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci 18:10464–10472PubMedGoogle Scholar
  5. Bienenstock EL, Cooper LN, Munro PW (1982) Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J Neurosci 2(1):32–48PubMedGoogle Scholar
  6. Bliss TVP, Lømo TJ (1973) Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. J Physiol 232:331–356PubMedGoogle Scholar
  7. Burkitt A, 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 16:885–940CrossRefPubMedGoogle Scholar
  8. Debanne D, Gahwiler BH, Thompson SM (1996) Cooperative interactions in the induction of long-term potentiation and depression of synaptic excitation between hippocampal ca3-ca1 cell pairs in vitro. Proc Natl Acad Sci USA 93:11225–11230CrossRefPubMedGoogle Scholar
  9. Debanne D, Gahwiler BH, Thompson SM (1999) Heterogeneity of synaptic plasticity at unitary ca3-ca1 and ca3-ca3 connections in rat hippocampal slice cultures. J Neurosci 19(24):10664–10671PubMedGoogle Scholar
  10. Dudek SM, Bear MF (1992) Homosynaptic long-term depression in area ca1 of hippocampus and effects of n-methyl-d-aspartate receptor blockade. Proc Natl Acad Sci USA 89:4363–4367CrossRefPubMedGoogle Scholar
  11. Froemke RC, Dan Y (2002) Spike-timing-dependent synaptic modification induced by natural spike trains. Nature 416(6879):433–438CrossRefPubMedGoogle Scholar
  12. Froemke RC, Tsay IA, Raad M, Long JD, Dan Y (2006) Contribution of individual spikes in burst-induced long-term synaptic dification. J Neurophysiol 95:1620–1629CrossRefPubMedGoogle Scholar
  13. Gütig R, Aharonov R, Rotter S, Sompolinsky H (2003) Learning input correlations through nonlinear temporally asymmetric hebbian plasticity. J Neurosci 23:3697–3714PubMedGoogle Scholar
  14. Hasselmo ME (1995) Neuromodulation and cortical function: modeling the physiological basis of behavior. Behav Brain Res 67:1–27CrossRefPubMedGoogle Scholar
  15. Hebb DO (1949) The organisation of behaviour. Wiley, New YorkGoogle Scholar
  16. Izhikevich EM, Desai NS (2003) Relating stdp to bcm. Neural Comput 15(7):1511–1523CrossRefPubMedGoogle Scholar
  17. Kempter R, Gerstner W, van Hemmen JL (1999) Hebbian learning and spiking neurons. Phys Rev E 59(4):4498–4514CrossRefGoogle Scholar
  18. Kirkwood A, Rioult MG, Bear MF (1996) Experience-dependent modification of synaptic plasticity in visual cortex. Nature 381:526–528CrossRefPubMedGoogle Scholar
  19. Kistler WM, van Hemmen JL (2000) Modeling synaptic plasticity in conjunction with the timing of pre- and post-synaptic action potentials. Neural Comput 12:385–405CrossRefPubMedGoogle Scholar
  20. Kuhn A, Aertsen A, Rotter S (2003) Higher-order statistics of input ensembles and the response of simple model neurons. Neural Comput 15:67–101CrossRefPubMedGoogle Scholar
  21. Levy WB, Steward O (1983) Temporal contiguity requirements for long-term associative potentiation/depression in the hippocampus. Neuroscience 8:791–797CrossRefPubMedGoogle Scholar
  22. Lynch G, Dunwiddie T, Gribkoff V (1977) Heterosynaptic depression: a postsynaptic correlate of long-term potentiation. Nature 266:737–739CrossRefPubMedGoogle Scholar
  23. Markram H, Löbke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic aps and epsps. Science 275(5297):213–215CrossRefPubMedGoogle Scholar
  24. Montgomery JM, Pavlidis P, Madison DV (2001) Pair recordings reveal all-silent synaptic connections and the postsynaptic expression of long-term potentiation. Neuron 29:691–701CrossRefPubMedGoogle Scholar
  25. O’Connor DH, Wittenberg GM, Wang SSH (2005a) Dissection of bidirectional synaptic plasticity into saturable unidirectional processes. J Neurophysiol 94:1565–1573CrossRefPubMedGoogle Scholar
  26. O’Connor DH, Wittenberg GM, Wang SSH (2005b) Graded bidirectional synaptic plasticity is composed of switch-like unitary events. Proc Natl Acad Sci USA 102(27):9679–9684CrossRefPubMedGoogle Scholar
  27. Petersen CC, Malenka RC, Nicoll RA, Hopfield JJ (1998) All-or-none potentiation at ca3-ca1 synapses. Proc Natl Acad Sci USA 95:4732–4737CrossRefPubMedGoogle Scholar
  28. van Rossum MCW, Bi GQ, Turrigiano GG (2000) Stable hebbian learning from spike timing-dependent plasticity. J Neurosci 20(23):8812–8821PubMedGoogle Scholar
  29. Rubin J, Lee DD, Sompolinsky H (2001) Equilibrium properties of temporally asymmetric hebbian plasticity. Phys Rev Lett 86:364CrossRefPubMedGoogle Scholar
  30. Shah NT, Yeung LC, Cooper LN, Cai Y, Shouval HZ (2006) A biophysical basis for the inter-spike interaction of spike-timing-dependent plasticity. Biol Cybern 95:113–121CrossRefPubMedGoogle Scholar
  31. Sjöström PJ, Turrigiano GG, Nelson SB (2001) Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32:1149–1164CrossRefPubMedGoogle Scholar
  32. Song S, Miller KD, Abbott LF (2000) Competitive hebbian learning through spike-timing-dependent synaptic plasticity. Nat Neurosci 3(9):919–926CrossRefPubMedGoogle Scholar
  33. Wang HX, Gerkin RC, Nauen DW, Bi GQ (2005) Coactivation and timing-dependent integration of synaptic potentiation and depression. Nat Neurosci 8(2):187–193CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Dominic Standage
    • 1
  • Sajiya Jalil
    • 1
  • Thomas Trappenberg
    • 1
    Email author
  1. 1.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

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