Calcium control of triphasic hippocampal STDP

Abstract

Synaptic plasticity is believed to represent the neural correlate of mammalian learning and memory function. It has been demonstrated that changes in synaptic conductance can be induced by approximately synchronous pairings of pre- and post- synaptic action potentials delivered at low frequencies. It has also been established that NMDAr-dependent calcium influx into dendritic spines represents a critical signal for plasticity induction, and can account for this spike-timing dependent plasticity (STDP) as well as experimental data obtained using other stimulation protocols. However, subsequent empirical studies have delineated a more complex relationship between spike-timing, firing rate, stimulus duration and post-synaptic bursting in dictating changes in the conductance of hippocampal excitatory synapses. Here, we present a detailed biophysical model of single dendritic spines on a CA1 pyramidal neuron, describe the NMDAr-dependent calcium influx generated by different stimulation protocols, and construct a parsimonious model of calcium driven kinase and phosphatase dynamics that dictate the probability of stochastic transitions between binary synaptic weight states in a Markov model. We subsequently demonstrate that this approach can account for a range of empirical observations regarding the dynamics of synaptic plasticity induced by different stimulation protocols, under regimes of pharmacological blockade and metaplasticity. Finally, we highlight the strengths and weaknesses of this parsimonious, unified computational synaptic plasticity model, discuss differences between the properties of cortical and hippocampal plasticity highlighted by the experimental literature, and the manner in which further empirical and theoretical research might elucidate the cellular basis of mammalian learning and memory function.

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References

  1. Abarbanel, H. D. I., Gibb, L., Huerta, R., & Rabinovich, M. I. (2003). Biophysical model of synaptic plasticity dynamics. Biological Cybernetics, 89, 214–226.

    PubMed  Article  Google Scholar 

  2. Abarbanel, H. D. I., Talathi, S. S., Gibb, L., & Rabinovich, M. I. (2005). Synaptic plasticity with discrete state synapses. Physical Review E, 72, 031914.

    Article  CAS  Google Scholar 

  3. Aihara, T., Abiru, Y., Yamazaki, Y., Watanabe, H., Fukushima, Y., & Tsukuda, M. (2007). The relation between spike-timing dependent plasticity and Ca2+ dynamics in the hippocampal CA1 network. Neuroscience, 145, 80–87.

    PubMed  CAS  Article  Google Scholar 

  4. Artola, A., & Singer, W. (1993). Long-term depression of excitatory synaptic transmission and its relationship to long-term potentiation. Trends in Neuroscience, 16, 480–487.

    CAS  Article  Google Scholar 

  5. Bagal, A. A., Kao, J., Tang, C.-M., & Thompson, S. M. (2005). Long-term potentiation of exogenous glutamate responses at single dendritic spines. PNAS, 102, 14434–14439.

    PubMed  CAS  Article  Google Scholar 

  6. Bender, V. A., Bender, K. J., Brasier, D. J., & Feldman, D. E. (2006). Two coincidence detectors for spike timing-dependent plasticity in somatosensory cortex. Journal of Neuroscience, 26, 4166–4177.

    PubMed  CAS  Article  Google Scholar 

  7. Bi, G.-Q., & Poo, M.-M. (1998). Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience, 77, 551–555.

    Google Scholar 

  8. Bienenstock, E. L., Cooper, L. N., & Munro, P. W. (1982). Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. Journal of Neuroscience, 2, 32–48.

    PubMed  CAS  Google Scholar 

  9. Bliss, T., Collingridge, G., & Morris, R. (2007). Synaptic plasticity in the hippocampus. In P. Andersen, R. Morris, D. Amaral, T. Bliss, J. O’Keefe (Eds.), The hippocampus book (pp. 343–474). Oxford University Press.

  10. Buchanan, K. A., & Mellor, J. R. (2007). The development of synaptic plasticity induction rules and the requirement for postsynaptic spikes in rat hippocampal CA1 pyramidal neurones. The Journal of Physiology, 585, 429–445.

    PubMed  CAS  Article  Google Scholar 

  11. Buchanan, K. A., & Mellor, J. R. (2010). The activity requirements for spike timing-dependent plasticity in the hippocampus. Frontiers in Synaptic Neuroscience, 2, 11.

    PubMed  Article  Google Scholar 

  12. Buchler, N. E., & Cross, F. R. (2009). Protein sequestration generates a flexible ultrasensitive response in a genetic network. Molecular Systems Biology, 5, 272.

    PubMed  Article  Google Scholar 

  13. Buonomano, D. V. (2005). A learning rule for the emergence of stable dynamics and timing in recurrent networks. Journal of Neurophysiology, 94, 2275–2283.

    PubMed  Article  Google Scholar 

  14. Bush, D., Philippides, A., Husbands, P., & O’Shea, M. (2010). Dual coding with STDP in an auto-associative network model of the hippocampus. PLoS Computational Biology, 6, e1000839.

    PubMed  Article  CAS  Google Scholar 

  15. Buzsáki, G. (2010). Neural syntax: cell assemblies, synapsembles, and readers. Neuron, 68, 362–385.

    PubMed  Article  CAS  Google Scholar 

  16. Canepari, M., Djurisic, M., & Zecevic, D. (2007). Dendritic signals from rat hippocampal CA1 pyramidal neurons during coincident pre- and post- synaptic activity: a combined voltage- and calcium- imaging study. The Journal of Physiology, 580, 463–484.

    PubMed  CAS  Article  Google Scholar 

  17. Caporale, N., & Dan, Y. (2008). Spike timing-dependent plasticity: a Hebbian learning rule. Annual Reviews in Neuroscience, 31, 25–46.

    CAS  Article  Google Scholar 

  18. Christie, B. R., Magee, J. C., & Johnston, D. (1996). The role of dendritic action potentials and Ca2+ influx in the induction of homosynaptic long-term depression in hippocampal CA1 pyramidal neurons. Learning and Memory, 3, 160–169.

    PubMed  CAS  Article  Google Scholar 

  19. Citri, A., & Malenka, R. C. (2008). Synaptic plasticity: multiple forms, functions, and mechanisms. Neuropsychopharmacology, 33, 18–41.

    PubMed  Article  Google Scholar 

  20. Cooke, S. F., & Bliss, T. V. P. (2006). Plasticity in the human central nervous system. Brain, 129, 1659–1673.

    PubMed  CAS  Article  Google Scholar 

  21. Cormier, R. J., Greenwood, A. C., & Connor, J. A. (2001). Bidirectional synaptic plasticity correlated with the magnitude of dendritic calcium transients above a threshold. Journal of Neurophysiology, 85, 399–406.

    PubMed  CAS  Google Scholar 

  22. Dayan, P., & Abbott, L. F. (2001). Theoretical neuroscience (pp. 180–183). London: MIT.

    Google Scholar 

  23. Debanne, D., Gähwiler, B. H., & Thompson, S. M. (1998). Long-term synaptic plasticity between pairs of individual CA3 pyramidal cells in rat hippocampal slice cultures. The Journal of Physiology, 507, 237–247.

    PubMed  CAS  Article  Google Scholar 

  24. Desai, N. S. (2003). Homeostatic plasticity in the CNS: synaptic and intrinsic forms. Journal of Physiology, Paris, 97, 391–402.

    PubMed  Article  Google Scholar 

  25. Destexhe, A., Mainen, Z., & Sejnowski, T. (1994). Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. Journal of Computational Neuroscience, 1, 195–230.

    PubMed  CAS  Article  Google Scholar 

  26. Dudek, S. M., & Bear, M. F. (1992). Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade. PNAS, 89, 4363–4367.

    PubMed  CAS  Article  Google Scholar 

  27. Dudman, J. T., Tsay, D., & Siegelbaum, S. A. (2007). A role for synaptic inputs at distal dendrites: instructive signals for hippocampal long-term plasticity. Neuron, 56, 866–879.

    PubMed  CAS  Article  Google Scholar 

  28. Erreger, K., Dravid, S. M., Banke, T. G., Wyllie, D. J. A., & Traynelis, S. F. (2005). Subunit-specific gating controls rat NR1/NR2A and NR1/NR2B NMDA channel kinetics and synaptic signalling profiles. The Journal of Physiology, 563, 345–358.

    PubMed  CAS  Article  Google Scholar 

  29. Fan, Y., Fricker, D., Brager, D. H., Chen, X., Lu, H.-C., Chitwood, R. A., & Johnston, D. (2005). Activity-dependent decrease of excitability in rat hippocampal neurons through increases in Ih. Nature Neuroscience, 8, 1542–1551.

    PubMed  CAS  Article  Google Scholar 

  30. Fernandez de Sevilla, D., Fuenzalida, M., Porto Pazos, A. B., & Buno, W. (2007). Selective shunting of the NMDA EPSP component by the slow afterhyperpolarisation in rat CA1 pyramidal neurons. Journal of Neurophysiology, 97, 3242–3255.

    PubMed  CAS  Article  Google Scholar 

  31. Fiete, I. R., Senn, W., Wang, C., & Hahnloser, R. H. R. (2010). Spike time-dependent plasticity and heterosynaptic competition organize networks to produce long scale-free sequences of neural activity. Neuron, 65, 563–576.

    PubMed  CAS  Article  Google Scholar 

  32. Frey, U., & Morris, R. G. (1997). Synaptic tagging and long-term potentiation. Nature, 385, 533–536.

    PubMed  CAS  Article  Google Scholar 

  33. Frick, A., Magee, J., & Johnston, D. (2004). LTP is accompanied by an enhanced local excitability of pyramidal neuron dendrites. Nature Neuroscience, 7, 126–135.

    PubMed  CAS  Article  Google Scholar 

  34. Froemke, R. C., Poo, M. M., & Dan, Y. (2005). Spike-timing-dependent synaptic plasticity depends on dendritic location. Nature, 434, 221–225.

    PubMed  CAS  Article  Google Scholar 

  35. Froemke, R. C., Tsay, I. H., Raad, M., Long, J. D., & Dan, Y. (2006). Contribution of individual spikes in burst-induced long-term synaptic modification. Journal of Neurophysiology, 95, 1620–1629.

    PubMed  Article  Google Scholar 

  36. Froemke, R. C., Debanne, D., & Bi, G. Q. (2010). Temporal modulation of spike-timing-dependent plasticity. Frontiers in Synaptic Neuroscience, 2, 19.

    PubMed  Google Scholar 

  37. Fukunaga, K., Muller, D., Ohmitsu, M., Bako, E., DePaoli-Roach, A. A., & Miyamoto, E. (2000). Decreased protein phosphatase 2A activity in hippocampal long-term potentiation. Journal of Neurochemistry, 74, 807–817.

    PubMed  CAS  Article  Google Scholar 

  38. Gerkin, R. C., Lau, P.-M., Nauen, D. W., Wang, Y. T., & Bi, G.-Q. (2007). Modular competition driven by NMDA receptor subtypes in spike-timing-dependent plasticity. Journal of Neurophysiology, 97, 2851–2862.

    PubMed  CAS  Article  Google Scholar 

  39. Graupner, M., & Brunel, N. (2007). STDP in a bistable synapse model based on CaMKII and associated signalling pathways. PLoS Computational Biology, 3(11), e221.

    PubMed  Article  CAS  Google Scholar 

  40. Graupner, M., & Brunel, N. (2010). Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models. Frontiers in Computational Neuroscience, 4, 136.

    PubMed  Article  Google Scholar 

  41. Hanson, P. I., & Schulman, H. (1992). Neuronal Ca2+ / Calmodulin-dependent protein kinase. Annual Review of Biochemistry, 61, 559–601.

    PubMed  CAS  Article  Google Scholar 

  42. Harris, K. M., & Kater, S. B. (1994). Dendritic spines: cellular specialisations imparting both stability and flexibility to synaptic function. Annual Reviews in Neuroscience, 17, 341–371.

    CAS  Article  Google Scholar 

  43. Harris, K. D., Hirase, H., Leinekugel, X., Henze, D. A., & Buzsaki, G. (2001). Temporal interaction between single spikes and complex spike bursts in hippocampal pyramidal cells. Neuron, 32, 141–149.

    PubMed  CAS  Article  Google Scholar 

  44. Hebb, D. O. (1949). The organisation of behaviour. New York: Wiley.

    Google Scholar 

  45. Jahr, C. E., & Stevens, C. F. (1990). A quantitative description of NMDA receptor-channel kinetic behaviour. Journal of Neuroscience, 10, 1830–1837.

    PubMed  CAS  Google Scholar 

  46. Johnston, D., Christie, B. R., Frick, A., Gray, R., Hoffman, D. A., Schexnayder, L. K., Watanabe, S., & Yuan, L.-L. (2003). Active dendrites, potassium channels and synaptic plasticity. Philosophical Transactions of the Royal Society B, 358, 667–674.

    CAS  Article  Google Scholar 

  47. Kampa, B. M., Letzkus, J. J., & Stuart, G. J. (2007). Dendritic mechanisms controlling spike-timing dependent plasticity. Trends in Neuroscience, 30, 456–463.

    CAS  Article  Google Scholar 

  48. Karmarkar, U. R., & Buonomano, D. V. (2002). A model of spike-timing dependent plasticity: one or two coincidence detectors? Journal of Neurophysiology, 88, 507–513.

    PubMed  Google Scholar 

  49. Krug, M., Lossner, B., & Ott, T. (1984). Anisomycin blocks the late phase of long-term potentiation in the dentate gyrus of freely moving rats. Brain Research Bulletins, 13, 39–42.

    CAS  Article  Google Scholar 

  50. Larkum, M. E., Zhu, J. J., & Sakmann, B. (2001). Dendritic mechanisms underlying the coupling of the dendritic with the axonal action potential initiation zone of adult rat layer 5 pyramidal neurons. The Journal of Physiology, 533, 447–466.

    PubMed  CAS  Article  Google Scholar 

  51. Larson, J., Wong, D., & Lynch, G. (1986). Patterned stimulation at the theta frequency is optimal for the induction of hippocampal long-term potentiation. Brain Research, 368, 347–350.

    PubMed  CAS  Article  Google Scholar 

  52. Lazar, A., Pipa, G., & Triesch, J. (2009). SORN: a self-organizing recurrent neural network. Frontiers in Computational Neuroscience, 3, 23.

    PubMed  Google Scholar 

  53. Lee, H.-K., Barbarosie, M., Kameyama, K., Bear, M. F., & Huganir, R. L. (2000). Regulation of distinct AMPA receptor phosphorylation sites during bidirectional synaptic plasticity. Nature, 405, 955–959.

    PubMed  CAS  Article  Google Scholar 

  54. Legenstein, R., & Maass, W. (2011). Branch-specific plasticity enables self-organisation of nonlinear computation in single neurons. Journal of Neuroscience, 31, 10787–10802.

    PubMed  CAS  Article  Google Scholar 

  55. Lisman, J. (1989). A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory. PNAS, 86, 9574–9578.

    PubMed  CAS  Article  Google Scholar 

  56. Lisman, J. E. (1997). Bursts as a unit of neural information: making unreliable synapses reliable. Trends in Neurosciences, 20, 38–43.

    PubMed  CAS  Article  Google Scholar 

  57. Lisman, J., & Spruston, N. (2005). Postsynaptic depolarisation requirements for LTP and LTD: a critique of spike-timing dependent plasticity. Nature Neuroscience, 8, 839–841.

    PubMed  CAS  Google Scholar 

  58. Lomo, T., & Bliss, T. V. (1973). Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. The Journal of Physiology, 232, 331–356.

    PubMed  Google Scholar 

  59. Losonczy, A., Makara, J. K., & Magee, J. C. (2008). Compartmentalised dendritic plasticity and input feature storage in neurons. Nature, 452, 436–441.

    PubMed  CAS  Article  Google Scholar 

  60. Magee, J. C., & Johnston, D. (1997). A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons. Science, 275, 209–213.

    PubMed  CAS  Article  Google Scholar 

  61. Malenka, R. C., & Bear, M. F. (2004). LTP and LTD: an embarrassment of riches. Neuron, 44, 5–21.

    PubMed  CAS  Article  Google Scholar 

  62. Malenka, R. C., & Nicoll, R. A. (1999). Long-term potentiation—a decade of progress? Science, 285, 1870–1874.

    PubMed  CAS  Article  Google Scholar 

  63. Malenka, R. C., Kauer, J. A., Perkel, D. J., Mauk, M. D., Kelly, P. T., Nicoll, R. A., & Waxham, M. N. (1989). An essential role for postsynaptic calmodulin and protein kinase activity in long-term potentiation. Nature, 340, 554–557.

    PubMed  CAS  Article  Google Scholar 

  64. Malinow, R., Schulman, H., & Tsien, R. W. (1989). Inhibition of postsynaptic PKC or CaMKII blocks induction but not expression of LTP. Science, 245, 862–866.

    PubMed  CAS  Article  Google Scholar 

  65. Martin, S. J., Grimwood, P. D., & Morris, R. G. M. (2000). Synaptic plasticity and memory: an evaluation of the hypothesis. Annual Review of Neuroscience, 23, 649–711.

    PubMed  CAS  Article  Google Scholar 

  66. Meredith, R. M., Floyer-Lea, A. M., & Paulsen, O. (2003). Maturation of long-term potentiation induction rules in rodent hippocampus: role of GABAergic inhibition. Journal of Neuroscience, 23, 11142–11146.

    PubMed  CAS  Google Scholar 

  67. Mizuno, T., Kanazawa, I., & Sakurai, M. (2001). Differential induction of LTP and LTD is not determined solely by instantaneous calcium concentration: an essential involvement of a temporal factor. European Journal of Neuroscience, 14, 701–708.

    PubMed  CAS  Article  Google Scholar 

  68. Morgan, D. O. (2007). The cell cycle: Principles of control. Sunderland: New Science Press.

    Google Scholar 

  69. Mulkey, R. M., Herron, C. E., & Malenka, R. C. (1993). An essential role for protein phosphatases in hippocampal long-term depression. Science, 261, 1104–1107.

    Article  Google Scholar 

  70. Nelson, S. B., & Turrigiano, G. G. (2008). Strength through diversity. Neuron, 60, 477–482.

    PubMed  CAS  Article  Google Scholar 

  71. Neves, G., Cooke, S. F., & Bliss, T. V. P. (2008). Synaptic plasticity, memory and the hippocampus: a neural network approach to causality. Nature Reviews Neuroscience, 9, 65–75.

    PubMed  CAS  Article  Google Scholar 

  72. Nevian, T., & Sakmann, B. (2006). Spine Ca2+ signaling in spike-timing-dependent plasticity. Journal of Neuroscience, 26, 11001–11013.

    PubMed  CAS  Article  Google Scholar 

  73. Ngezahayo, A., Schachner, M., & Artola, A. (2000). Synaptic activity modulates the induction of bidirectional synaptic changes in adult mouse hippocampus. Journal of Neuroscience, 20, 2451–2458.

    PubMed  CAS  Google Scholar 

  74. Nguyen, P. V., Abel, T., & Kandel, E. R. (1994). Requirement of a critical period of transcription for induction of a late phase of LTP. Science, 165, 1104–1107.

    Article  Google Scholar 

  75. Nishiyama, M., Hong, K., Mikoshiba, K., Poo, M. M., & Kato, K. (2000). Calcium stores regulate the polarity and input specificity of synaptic modification. Nature, 408, 584–588.

    PubMed  CAS  Article  Google Scholar 

  76. O’Connor, D. H., Wittenberg, G. M., & Wang, S. S. H. (2005a). Graded bidirectional synaptic plasticity is composed of switch-like unitary events. PNAS, 102, 9679–9684.

    PubMed  Article  CAS  Google Scholar 

  77. O’Connor, D. H., Wittenberg, G. M., & Wang, S. S. H. (2005b). Dissection of bidirectional synaptic plasticity into saturable unidirectional processes. Journal of Neurophysiology, 94, 1565–1573.

    PubMed  Article  Google Scholar 

  78. Palmer, L. M., & Stuart, G. J. (2009). Membrane potential changes in dendritic spines during action potentials and synaptic input. Journal of Neuroscience, 29, 6897–6903.

    PubMed  CAS  Article  Google Scholar 

  79. Perez-Otano, I., & Ehlers, M. D. (2005). Homeostatic plasticity and NMDA receptor trafficking. Trends in Neurosciences, 28, 229–238.

    PubMed  CAS  Article  Google Scholar 

  80. Petersen, C. C. N., Malenka, R. C., Nicoll, R. A., & Hopfield, J. J. (1998). All-or-none potentiation at CA3-CA1 synapses. PNAS, 95, 4732–4737.

    PubMed  CAS  Article  Google Scholar 

  81. Pfister, J.-P., & Gerstner, W. (2006). Triplets of spikes in a model of spike timing-dependent plasticity. Journal of Neuroscience, 26, 9673–9682.

    PubMed  CAS  Article  Google Scholar 

  82. Pi, H. J., & Lisman, J. E. (2008). Coupled phosphatase and kinase switches produce the tristability required for long-term potentiation and long-term depression. Journal of Neuroscience, 28, 13132–13138.

    PubMed  CAS  Article  Google Scholar 

  83. Pike, F. G., Meredith, R. M., Olding, A. W., & Paulsen, O. (1999). Postsynaptic bursting is essential for 'Hebbian' induction of associative long-term potentiation at excitatory synapses in rat hippocampus. The Journal of Physiology, 518, 571–576.

    PubMed  CAS  Article  Google Scholar 

  84. Rackham, O. J. L., Tsaneva-Atanasova, K., Ganesh, A., & Mellor, J. R. (2010). A Ca2+-based computational model for NMDA receptor-dependent synaptic plasticity at individual post-synaptic spines in the hippocampus. Frontiers in Synaptic Neuroscience, 2, 31.

    PubMed  CAS  Google Scholar 

  85. Rodríguez-Moreno, A., & Paulsen, O. (2008). Spike timing-dependent long-term depression requires presynaptic NMDA receptors. Nature Neuroscience, 11, 744–745.

    PubMed  Article  CAS  Google Scholar 

  86. Rubin, J. E., Gerkin, R. C., Bi, G.-Q., & Chow, C. C. (2005). Calcium time course as a signal for spike-timing-dependent plasticity. Journal of Neurophysiology, 93, 2600–2613.

    PubMed  Article  Google Scholar 

  87. Sabatini, B. L., Oertner, T. G., & Svoboda, K. (2002). The life cycle of Ca2+ ions in dendritic spines. Neuron, 33, 439–452.

    PubMed  CAS  Article  Google Scholar 

  88. Shouval, H. Z., & Kalantzis, G. (2005). Stochastic properties of synaptic transmission affect the shape of spike time-dependent plasticity curves. Journal of Neurophysiology, 93, 1069–1073.

    PubMed  Article  Google Scholar 

  89. Shouval, H. Z., Bear, M. F., & Cooper, L. N. (2002). A unified model of NMDA receptor-dependent bidirectional synaptic plasticity. PNAS, 99, 10831–11083.

    PubMed  CAS  Article  Google Scholar 

  90. Shouval, H. Z., Wang, S. S.-H., & Wittenberg, G. M. (2010). Spike timing dependent plasticity: a consequence of more fundamental learning rules. Frontiers in Computational Neuroscience, 4, 19.

    PubMed  Google Scholar 

  91. Sjostrom, P. J., & Nelson, S. B. (2002). Spike timing, calcium signals and synaptic plasticity. Current Opinion in Neurobiology, 12, 305–314.

    PubMed  CAS  Article  Google Scholar 

  92. Sjöström, P. J., Turrigiano, G. G., & Nelson, S. B. (2001). Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron, 32, 1149–1164.

    PubMed  Article  Google Scholar 

  93. Sjöström, P. J., Turrigiano, G. G., & Nelson, S. B. (2003). Neocortical LTD via coincident activation of presynaptic NMDA and cannabinoid receptors. Neuron, 39, 641–654.

    PubMed  Article  Google Scholar 

  94. Sjöström, P. J., Rancz, E. A., Roth, A., & Häusser, M. (2008). Dendritic excitability and synaptic plasticity. Physiological Reviews, 88, 769–840.

    PubMed  Article  CAS  Google Scholar 

  95. Song, S., Miller, K. D., & Abbott, L. F. (2000). Competitive Hebbian learning through spike-timing dependent synaptic plasticity. Nature Neuroscience, 3, 919–926.

    PubMed  CAS  Article  Google Scholar 

  96. Stuart, G. J., & Sakmann, B. (1994). Active propagation of somatic action potentials into neocortical pyramidal cell dendrites. Nature, 367, 69–72.

    PubMed  CAS  Article  Google Scholar 

  97. Urakubo, H., Honda, M., Froemke, R. C., & Kuroda, S. (2008). Requirement of an allosteric kinetics of NMDA receptors for spike-timing dependent plasticity. Journal of Neuroscience, 28, 3310–3323.

    PubMed  CAS  Article  Google Scholar 

  98. Wang, H. X., Gerkin, R. C., Nauen, D. W., & Bi, G.-Q. (2005). Coactivation and timing-dependent integration of synaptic potentiation and depression. Nature Neuroscience, 8, 187–193.

    PubMed  CAS  Article  Google Scholar 

  99. Watt, A. J., Sjostrom, P. J., Hausser, M., Nelson, S. B., & Turrigiano, G. G. (2004). A proportional but slower NMDA potentiation follows AMPA potentiation in LTP. Nature Neuroscience, 7, 518–524.

    PubMed  CAS  Article  Google Scholar 

  100. Whitlock, J. R., Heynen, A. J., Shuler, M. G., & Bear, M. F. (2006). Learning induces long-term potentiation in the hippocampus. Science, 313, 1093–1097.

    PubMed  CAS  Article  Google Scholar 

  101. Wittenberg, G. M., & Wang, S.-S. H. (2006). Malleability of spike-timing-dependent plasticity at the CA3-CA1 synapse. Journal of Neuroscience, 26, 6610–6617.

    PubMed  CAS  Article  Google Scholar 

  102. Yang, S. N., Tang, Y. G., & Zucker, R. (1999). Selective induction of LTP and LTD by post-synaptic [Ca2+]i elevation. Journal of Neurophysiology, 81, 781–787.

    PubMed  CAS  Google Scholar 

  103. Zhabotinsky, A. M. (2000). Bistability in the Ca2+ / calmodulin-dependent protein kinase-phosphatase system. Biophysical Journal, 79, 2211–2221.

    PubMed  CAS  Article  Google Scholar 

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Acknowledgments

The authors would like to thank Samuel Wang, Gayle Wittenberg and Guoqiang Bi for providing experimental data.

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Correspondence to Daniel Bush.

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Supplementary Fig. 1

Summary of synaptic plasticity data generated with τbAP,s = 55 ms and τNMDA,s = 152 ms. (a) Overall synaptic weight change generated by 100 spike pairings delivered at 5 Hz with βP = 0.45, βD = 0.24, kP = 0.04 and kD = 4 × 10-4, where kinase and phosphatase dynamics are controlled by peaks in intracellular calcium concentration. Horizontal dashed line represents zero change in total synaptic weight. (b) Synaptic weight change generated by 100 triplet pairings delivered at 5 Hz with all other parameter values the same as (a). (c) Synaptic weight change generated by tetanic pre-synaptic stimulation delivered at various firing rates in the presence of stochastic post-synaptic activity that follows the statistics described in (Wittenberg and Wang 2006), and all other parameter values the same as in (a). (d) Synaptic weight change generated by 100 pre-synaptic inputs delivered at 2 Hz while the post-synaptic membrane voltage is held fixed at various levels of depolarisation, and all other parameter values the same as in (a). (e) Synaptic weight change generated by 10 causal pre- and / or post- synaptic burst pairings delivered at 5 Hz in the experimental data from (Pike et al. 1999) (grey) and in the model (red), where all other parameters are the same as in (a). (f) Synaptic weight change generated by 60 triplet pairings with various temporal offsets delivered at 1 Hz in the experimental data from (Wang et al. 2005) (grey) and in the model (red), where all other parameters are the same as in (a). (PDF 32 kb)

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Bush, D., Jin, Y. Calcium control of triphasic hippocampal STDP. J Comput Neurosci 33, 495–514 (2012). https://doi.org/10.1007/s10827-012-0397-5

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Keywords

  • Synaptic plasticity
  • Calcium
  • Learning
  • Memory
  • Hippocampus