BCM and Membrane Potential: Alternative Ways to Timing Dependent Plasticity

  • Johannes Partzsch
  • Christian Mayr
  • Rene Schüffny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5506)


The Bienenstock-Cooper-Munroe (BCM) rule is one of the best-established learning formalisms for neural tissue. However, as it is based on pulse rates, it can not account for recent spike-based experimental protocols that have led to spike timing dependent plasticity (STDP) rules. At the same time, STDP is being challenged by experiments exhibiting more complex timing rules (e.g. triplets) as well as simultaneous rate- and timing dependent plasticity. We derive a formulation of the BCM rule which is based on the instantaneous postsynaptic membrane potential as well as the transmission profile of the presynaptic spike. While this rule is neither directly rate nor timing based, it can replicate BCM, conventional STDP and spike triplet experimental data, despite incorporating only two state variables. Moreover, these behaviors can be replicated with the same set of only four free parameters, avoiding the overfitting problem of more involved plasticity rules.


Spike Train Presynaptic Activity Spike Timing Dependent Plasticity Postsynaptic Spike Presynaptic Spike 
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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  1. 1.
    Koch, C.: Biophysics of computation. Information processing in single neurons. In: Computational Neuroscience. Oxford University Press, Oxford (1999)Google Scholar
  2. 2.
    Morrison, A., Diesmann, M., Gerstner, W.: Phenomenological models of synaptic plasticity based on spike timing. Biological Cybernetics 98, 459–478 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Lisman, J., Spruston, N.: Postsynaptic depolarization requirements for LTP and LTD: a critique of spike timing-dependent plasticity. Nature Neuroscience 8(7), 839–841 (2005)CrossRefGoogle Scholar
  4. 4.
    Pfister, J.P., Gerstner, W.: Triplets of spikes in a model of spike timing-dependent plasticity. Journal of Neuroscience 26(38), 9673–9682 (2006)CrossRefGoogle Scholar
  5. 5.
    Bienenstock, E., Cooper, L., Munro, P.: Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. Journal of Neuroscience 2(1), 32–48 (1982)Google Scholar
  6. 6.
    Dudek, S., Bear, M.: Homosynaptic long-term depression in area CAl of hippocampus and effects of N-methyl-D-aspartate receptor blockade. PNAS 89, 4363–4367 (1992)CrossRefGoogle Scholar
  7. 7.
    Artola, A., Bröcher, S., Singer, W.: Different voltage-dependent thresholds for inducing long-term depression and long-term potentiation in slices of rat visual cortex. Nature 347, 69–72 (1990)CrossRefGoogle Scholar
  8. 8.
    Bi, G.Q., Poo, M.M.: Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience 18(24), 10464–10472 (1998)Google Scholar
  9. 9.
    Froemke, R., Dan, Y.: Spike-timing-dependent synaptic modification induced by natural spike trains. Nature 416, 433–438 (2002)CrossRefGoogle Scholar
  10. 10.
    Sjöström, P., Turrigiano, G., Nelson, S.: Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32, 1149–1164 (2001)CrossRefGoogle Scholar
  11. 11.
    Shouval, H., Bear, M., Cooper, L.: A unified model of NMDA receptor-dependent bidirectional synaptic plasticity. PNAS 99(16), 10831–10836 (2002)CrossRefGoogle Scholar
  12. 12.
    Kurashige, H., Sakai, Y.: BCM-type synaptic plasticity model using a linear summation of calcium elevations as a sliding threshold. In: King, et al. (eds.) ICONIP 2006. LNCS, vol. 4232, pp. 19–29. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Badoual, M., Zou, Q., Davison, A., Rudolph, M., Bal, T., Fregnac, Y., Destexhe, A.: Biophysical and phenomenological models of multiple spike interactions in spike-timing dependent plasticity. International Journal of Neural Systems 16(2), 79–97 (2006)CrossRefGoogle Scholar
  14. 14.
    Izhikevich, E., Desai, N.: Relating STDP to BCM. Neural Computation 15, 1511–1523 (2003)CrossRefzbMATHGoogle Scholar
  15. 15.
    Lu, B., Yamada, W., Berger, T.: Asymmetric synaptic plasticity based on arbitrary pre- and postsynaptic timing spikes using finite state model. In: Proceedings of International Joint Conference on Neural Networks (2007)Google Scholar
  16. 16.
    Gerstner, W., Kistler, W.: Spiking neuron models: single neurons, populations, plasticity. Cambridge University Press, Cambridge (2002)CrossRefzbMATHGoogle Scholar
  17. 17.
    Schreiter, J., Ramacher, U., Heittmann, A., Matolin, D., Schüffny, R.: Cellular pulse coupled neural network with adaptive weights for image segmentation and its VLSI implementation. In: Proceedings 16th International Symposium on Electronic Imaging: Science and Technology, vol. 5298, pp. 290–296 (2004)Google Scholar
  18. 18.
    Schemmel, J., Brüderle, D., Meier, K., Ostendorf, B.: Modeling synaptic plasticity within networks of highly accelerated I&F neurons. In: ISCAS 2007 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Johannes Partzsch
    • 1
  • Christian Mayr
    • 1
  • Rene Schüffny
    • 1
  1. 1.Chair for Parallel VLSI Systems and Neural CircuitsUniversity of Technology DresdenGermany

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