Skip to main content

Advertisement

SpringerLink
Log in

Calcium control of triphasic hippocampal STDP

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

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

    Article  PubMed  Google Scholar 

  • 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 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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 

  • 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.

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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 

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

    Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Google Scholar 

  • 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 

  • 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.

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  • 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 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Google Scholar 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

  1. UCL Institute of Cognitive Neuroscience, London, WC1N 3AR, UK

    Daniel Bush

  2. UCL Institute of Neurology, London, WC1N 3BG, UK

    Daniel Bush

  3. Department of Computing, University of Surrey, Guildford, GU2 7XH, UK

    Yaochu Jin

Authors
  1. Daniel Bush
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yaochu Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Bush.

Additional information

Action Editor: Carson C. Chow

Electronic supplementary material

Below is the link to the electronic supplementary material.

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)

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-012-0397-5

Keywords

Search

Navigation