BCM-Type Synaptic Plasticity Model Using a Linear Summation of Calcium Elevations as a Sliding Threshold

  • Hiroki Kurashige
  • Yutaka Sakai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4232)


It has been considered that an amount of calcium elevation in a synaptic spine determines whether the synapse is potentiated or depressed. However, it has been pointed out that simple application of the principle can not reproduce properties of spike-timing-dependent plasticity (STDP). To solve the problem, we present a possible mechanism using dynamically sliding threshold as the linear summation of calcium elevations induced by single pre-synaptic and post-synaptic spikes. We demonstrate that the model can reproduce the timing dependence of biological STDP. In addition, we find that the model can reproduce the dependence of biological STDP on the initial synaptic strength, which is found to be asymmetric for synaptic potentiation and depression, whereas no explicit initial-strength dependence nor asymmetric mechanism are incorporated into the model.


NMDA Receptor Synaptic Plasticity Synaptic Strength Synaptic Depression Calcium Elevation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Markram, H., Lubke, J., Frotscher, M., Sakmann, B.: Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275, 213–215 (1997)CrossRefGoogle Scholar
  2. 2.
    Bi, G.Q., Poo, M.: Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J. Neuroscience 18, 10464–10472 (1998)Google Scholar
  3. 3.
    Zhang, L., Tao, H., Holt, C., Harris, W., Poo, M.: A critical window for cooperation and competition among developing retinotectal synapses. Nature 395, 37–44 (1998)CrossRefGoogle Scholar
  4. 4.
    Froemke, R.C., Dan, Y.: Spike-timing-dependent synaptic modification induced by natural spike trains. Nature 416, 433–438 (2002)CrossRefGoogle Scholar
  5. 5.
    Song, S., Miller, K.D., Abbott, L.F.: Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nature Neurosci. 3, 919–926 (2000)CrossRefGoogle Scholar
  6. 6.
    Song, S., Abbott, L.F.: Cortical development and remapping through spike timing-dependent plasticity. Neuron 32, 339–350 (2001)CrossRefGoogle Scholar
  7. 7.
    Kitano, K., Fukai, T.: Temporal characteristics of the predictive synchronous firing modeled by spike-timing-dependent plasticity. Learning and Memory 11, 267–276 (2004)CrossRefGoogle Scholar
  8. 8.
    Rao, R.P., Sejnowski, T.J.: Spike-timing-dependent hebbian plasticity as temporal difference learning. Neural Computation 13, 2221–2237 (2001)zbMATHCrossRefGoogle Scholar
  9. 9.
    Hebb, D.O.: The Organization of Behavior: A Neuropsychological Theory. Wiley, New York (1949)Google Scholar
  10. 10.
    Artola, A., Singer, W.: Long-term depression of excitatory synaptic transmission and its relationship to long-term potentiation. Trends in Neuroscience 16, 480–487 (1993)CrossRefGoogle Scholar
  11. 11.
    Bienenstock, E., Cooper, L., Munro, P.: Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J. Neuroscience 2, 32–48 (1982)Google Scholar
  12. 12.
    Bi, G.Q.: Spatiotemporal specificity of synaptic plasticity: cellular rules and mechanisms. Biol. Cybern. 87, 319–332 (2002)zbMATHCrossRefGoogle Scholar
  13. 13.
    Sjostrom, P., Nelson, S.: Spike timing, calcium signals and synaptic plasticity. Curr. Opin. Neurobiol. 12, 305–314 (2002)CrossRefGoogle Scholar
  14. 14.
    Kitajima, T., Hara, K.: A generalized hebbian rule for activity-dependent synaptic modifications. Neural Networks 13, 445–454 (2000)CrossRefGoogle Scholar
  15. 15.
    Shouval, H., Bear, M., Cooper, L.: A unified model of nmda receptor-dependent bidirectional synaptic plasticity. Proc. Natl. Acad. Sci. USA. 99, 10831–10836 (2002)CrossRefGoogle Scholar
  16. 16.
    Feldman, D.E.: Timing-based ltp and ltd at vertical inputs to layer ii/iii pyramidal cells in rat barrel cortex. Neuron 27, 45–56 (2000)CrossRefGoogle Scholar
  17. 17.
    Nishiyama, M., Hong, K., Mikoshiba, K., Poo, M.-m., Kato, K.: Calcium release from internal stores regulates polarity and input specificity of synaptic modification. Nature 408, 584–588 (2000)CrossRefGoogle Scholar
  18. 18.
    Tsukada, M., Aihara, T., Kobayashi, Y., Shimazaki, H.: Spatial analysis of spike-timing-dependent ltp and ltd in the ca1 area of hippocampal slices using optical imaging. Hippocampus 15, 104–109 (2005)CrossRefGoogle Scholar
  19. 19.
    Schiller, J., Schiller, Y., Clapham, D.: NMDA receptors amplify calcium influx into dendritic spines during associative pre- and postsynaptic activation. Nat. Neurosci. 1, 114–118 (1998)CrossRefGoogle Scholar
  20. 20.
    Koester, H., Sakmann, B.: Calcium dynamics in single spines during coincident pre- and postsynaptic activity depend on relative timing of back-propagating action potentials and subthreshold excitatory postsynaptic potentials. Proc. Natl. Acad. Sci. USA 95, 9596–9601 (1998)CrossRefGoogle Scholar
  21. 21.
    Abraham, W., Tate, W.: Metaplasticity: a new vista across the field of synaptic plasticity. Progress in neurobiology 52, 303–323 (1997)CrossRefGoogle Scholar
  22. 22.
    Solger, J., Wozny, C., Manahan-Vaughan, D., Behr, J.: Distinct mechanisms of bidirectional activity-dependent synaptic plasticity in superficial and deep layers of rat entorhinal cortex. Eur. J. Neurosci. 19, 2003–2007 (2004)CrossRefGoogle Scholar
  23. 23.
    Toyoizumi, T., Pfister, J., Aihara, K., Gerstner, W.: Generalized bienenstockcooper- munro rule for spiking neurons that maximizes information transmission. Proc. Natl. Acad. Sci. USA 102, 5239–5244 (2005)CrossRefGoogle Scholar
  24. 24.
    Noguchi, J., Matsuzaki, M., Ellis-Davies, G., Kasai, H.: Spine-neck geometry determines nmda receptor-dependent ca2+ signaling in dendrites. Neuron 46, 609–622 (2005)CrossRefGoogle Scholar
  25. 25.
    Gasparini, S., Migliore, M., Magee, J.: On the initiation and propagation of dendritic spikes in ca1 pyramidal neurons. J. Neurosci. 24, 11046–11056 (2004)CrossRefGoogle Scholar
  26. 26.
    van Rossum, M.C.W., Bi, G.Q., Turrigiano, G.G.: Stable hebbian learning from spike timing-dependent plasticity. J. Neuroscience 20, 8812–8821 (2000)Google Scholar
  27. 27.
    Rubin, J., Lee, D.D., Sompolinsky, H.: Equilibrium properties of temporally asymmetric Hebbian plasticity. Physical Review Letters 86, 364–367 (2001)CrossRefGoogle Scholar
  28. 28.
    Gütig, R., Aharonov, R., Rotter, S., Sompolinsky, H.: Learning input correlations through nonlinear temporally asymmetric hebbian plasticity. J. Neuroscience 23, 3697–3714 (2003)Google Scholar
  29. 29.
    Sakai, Y., Nakano, K., Yoshizawa, S.: Synaptic regulation on various stdp rules. Neurocomputing 58-60, 351–357 (2004)CrossRefMathSciNetGoogle Scholar
  30. 30.
    Shouval, H., Kalantzis, G.: Stochastic properties of synaptic transmission affect the shape of spike time-dependent plasticity curves. J. Neurophysiol. 93, 1069–1073 (2005)CrossRefGoogle Scholar
  31. 31.
    Rubin, J., Gerkin, R., Bi, G.Q., Chow, C.: Calcium time course as a signal for spike-timing-dependent plasticity. J. Neurophysiol. 93, 2600–2613 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hiroki Kurashige
    • 1
  • Yutaka Sakai
    • 2
  1. 1.Graduate school of EngineeringTamagawa UniversityTokyoJapan
  2. 2.Faculty of EngineeringTamagawa UniversityTokyoJapan

Personalised recommendations