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Interplay of the magnitude and time-course of postsynaptic Ca2 +  concentration in producing spike timing-dependent plasticity

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Abstract

Synaptic strength can be modified by the relative timing of pre- and postsynaptic activity, a phenomenon termed spike timing-dependent plasticity (STDP). Studies of neurons in the hippocampus and in other regions have found that when presynaptic activity occurs within a narrow time window, typically 10 or 20 ms, before postsynaptic activity, long-term potentiation (LTP) is induced, while if presynaptic activity occurs within a similar time window after postsynaptic activity, long-term depression (LTD) results. The mechanisms underlying these modifications are not completely understood, although there is strong evidence that the postsynaptic Ca 2 +  concentration plays a central role. Some previous modeling of STDP has focused on the dynamics of the postsynaptic Ca 2 +  concentration, while other work has studied biophysical mechanisms of how a synapse can exist in, and switch between, different states corresponding to LTP and LTD. Building on previous work in these two areas we have developed the first low level STDP model of a tristable biochemical system that incorporates induction and maintenance of both LTP and LTD. Our model is able to explain the STDP observed in hippocampal neurons in response to pre- and postsynaptic pulse pairs, using only parameters derived from previous work and without the need for parameter fine-tuning. Our results also give insight into how and why the time course of the postsynaptic Ca 2 +  concentration can lead to either LTP or LTD, and suggest that voltage dependent calcium channels play a key role.

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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 

  • Abraham, W. C., & Williams, J. M. (2003). Properties and mechanisms of LTP maintenance. Neuroscientist, 9, 463–474.

    Article  PubMed  CAS  Google Scholar 

  • Barria, A., Muller, D., Derkach, V., Griffith, L. C., & Soderling, T. R. (1997). Regulatory phosphorylation of AMPA-type glutamate receptors by CaMKII during long-term potentiation. Science, 276, 2042–2045.

    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 

  • Bhalla, U. S., & Iyengar, R. (1999). Emergent properties of networks of biological signaling pathways. Science, 283, 381–387.

    Article  PubMed  CAS  Google Scholar 

  • Bi, G. Q., & Poo, G. (1998). Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience, 18, 10464–10472.

    PubMed  CAS  Google Scholar 

  • Bolshakov, V. Y., & Siegelbaum, S. A. (1994). Postsynaptic induction and presynaptic expression of hippocampal long-term depression. Science, 264, 1148–1152.

    Article  PubMed  CAS  Google Scholar 

  • Bredt, D. S., & Nicoll, R. A. (2003). AMPA receptor trafficking at excitatory synapses. Neuron, 40, 361–379.

    Article  PubMed  CAS  Google Scholar 

  • Carmignoto, G., & Vicini, S. (1992). Activity-dependent decrease in NMDA receptor responses during development of the visual cortex. Science, 258, 1007–1011.

    Article  PubMed  CAS  Google Scholar 

  • Caporale, N., & Dan, Y. (2008). Spike timing-dependent plasticity: A hebbian learning rule. Annual Review of Neuroscience, 31, 25–46.

    Article  PubMed  CAS  Google Scholar 

  • Castellani, G. C., Bazzani, A., & Cooper, L. N. (2009). Toward a microscopic model of bidirectional synaptic plasticity. Proceedings of the National Academy of Science of the United States of America, 106, 14091–14095.

    Article  CAS  Google Scholar 

  • Castellani, G. C., Quinlan, E. M., Bersani, F., Cooper, L. N., & Shouval, H. Z. (2005). A model of bidirectional synaptic plasticity: From signaling network to channel conductance. Learning and Memory, 12, 423–432.

    Article  PubMed  Google Scholar 

  • Castellani, G. C., Quinlan, E. M., Cooper, L. N., & Shouval, H. Z. (2001). A biophysical model of bidirectional synaptic plasticity: Dependence on AMPA and NMDA receptors. Proceedings of the National Academy of Science of the United States of America, 98, 12772–12777.

    Article  CAS  Google Scholar 

  • Dalby, N. O., & Mody, I. (2003). Activation of NMDA receptors in rat dentate gyrus granule cells by spontaneous and evoked transmitter release. Journal of Neurophysiology, 90, 786–797.

    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 

  • Gerstner, W., Kempter, R., Van Hemmen, J. L., & Wagner, H. (1996). A neuronal learning rule for sub-millisecond temporal coding. Nature, 383, 76–78.

    Article  PubMed  CAS  Google Scholar 

  • Giordano, N. J., & Nakanishi, H. (2005). Computational physics (2nd Ed.). Saddle River: Prentice-Hall.

    Google Scholar 

  • Graupner, M., & Brunel, N. (2007). STDP in bistable synapse model based on CaMKII and associated signaling pathways. PloS Computational Biology, 3, 2299–2323.

    Article  CAS  Google Scholar 

  • Hartley, M., Taylor, N., & Taylor, J. (2006). Understanding spike-time-dependent plasticity: A biologically motivated computational model. Neurocomputing, 69, 2005–2016.

    Article  Google Scholar 

  • Hebb, D. O. (1949). The organization of behavior. New York: Wiley.

    Google Scholar 

  • Jahr, C. E., & Stevens, C. F. (1990). Voltage dependence of NMDA-activated macroscopic conductances predicted by single-channel kinetics. Journal of Neuroscience, 10(9), 3178–3182.

    PubMed  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 

  • Kelso, S. R., Ganong, A. H., & Brown, T. H. (1986). Hebbian synapses in hippocampus. Proceedings of the National Academy of Science of the United States of America, 83, 5326–5330.

    Article  CAS  Google Scholar 

  • Lee, S. H., Liu, L., Wang, Y. T., & Sheng, M. (2002). Clathrin adaptor AP2 and NSF interact with overlapping sites of GluR2 and play distinct roles in AMPA receptor trafficking and hippocampal LTD. Neuron, 36, 661–674.

    Article  PubMed  CAS  Google Scholar 

  • Lee, S. R., Escobedo-Lozoya, Y., Szatmari, E. M., & Yasuda, R. (2009). Activation of CaMKII in single dendritic spines during long-term potentiation. Nature, 458, 299–306.

    Article  PubMed  CAS  Google Scholar 

  • Lin, J. W., Ju, W., Foster, K., Lee, S. H., Ahmadian, G., Wyszynski, M., et al. (2000). Distinct molecular mechanisms and divergent endocytotic pathways of AMPA receptor internalization. Nature Neuroscience, 3, 1282–1290.

    Article  PubMed  CAS  Google Scholar 

  • Linden, D.J. (1997). Long-term potentiation of glial synaptic currents in cerebellar culture. Neuron, 18, 983–994.

    Article  PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • Luthi, A., Chittajallu, R., Duprat, F., Palmer, M. J., Benke, T. A., Kidd, F. L., et al. (1999). Hippocampal LTD expression involves a pool of AMPARs regulated by the NSF-GluR2 interaction. Neuron, 24, 389–399.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Malinow, R., & Malenka, R. C. (2002). AMPA receptor trafficking and synaptic plasticity. Annual Review of Neuroscience, 25, 103–126.

    Article  PubMed  CAS  Google Scholar 

  • Malinow, R., & Miller, J. P. (1986). Postsynaptic hyperpolarization reversibly blocks induction of long-term potentiation. Nature, 320, 529–530.

    Article  PubMed  CAS  Google Scholar 

  • Man, H. Y., Lin, J. W., Ju, W. H., Ahmadian, G., Liu, L., Becker, L. E., et al. (2000). Regulation of AMPA receptor-mediated synaptic transmission by clathrin-dependent receptor internalization. Neuron, 25, 649–662.

    Article  PubMed  CAS  Google Scholar 

  • Markram, H., Helm, P. J., & Sakmann, B. (1995). Dendritic calcium transients evoked by single back-propagating action potentials in rat neocortical pyramidal neurons. Journal of Physiology, 485, 1–20.

    PubMed  CAS  Google Scholar 

  • Markram, H., Lubke, J., Frotscher, M., & Sakmann, B. (1997). Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science, 275, 213–215.

    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 

  • Nicoll and Malenka(1995). Contrasting properties of two forms of long-term potentiation in the hippocampus. Nature, 377, 115–118.

    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 produced the tristability required for long-term potentiation and long-term depression. Journal of Neuroscience, 28, 13132–13138.

    Article  PubMed  CAS  Google Scholar 

  • Pittenger, C., & Kandel, E. R. (2003). In search of general mechanisms for long-lasting plasticity: Aplysia and the hippocampus. Philosophical Transactions of the Royal Society of London B Biological Sciences, 358, 757–763.

    Article  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 

  • Sajikumar, S., & Frey, J. U. (2003). Anisomycin inhibits the late maintenance of long-term depression in rat hippocampal slices in vitro. Neuroscience Letters, 338, 147–150.

    Article  PubMed  CAS  Google Scholar 

  • Shi, S. H., Hayashi, Y., Petralia, R. S., Zaman, S. H., Wenthold, R. J., Svoboda, K., et al.(1999). Rapid spine delivery and redistribution of AMPA receptors after synaptic NMDA receptor activation. Science, 284, 1811–1816.

    Article  PubMed  CAS  Google Scholar 

  • Shouval, H. Z., Bear, M. F., & Cooper, L. N. (2002). A unified model of NMDA receptor-dependent bidirectional synaptic plasticity. Proceedings of the National Academy of Science of the United States of America, 99, 10831–10836.

    Article  CAS  Google Scholar 

  • Sjostrom, 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 

  • 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 

  • Thiels, E., Norman, E. D., Barrionuevo, G., & Klann, E. (1998). Transient and persistent increases in protein phosphatase activity during long-term depression in the adult hippocampus in vivo. Neuroscience, 86, 1023–1029.

    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 

  • Van Rossum, M. C. W., Bi, G. Q., & Turrigiano, G. G. (2000). Stable hebbian learning from spike timing dependent plasticity. Journal of Neuroscience, 20, 8812–8821.

    PubMed  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, 187–194.

    Article  PubMed  CAS  Google Scholar 

  • Wolf, J. A., Moyer, J. T., & Finkel, L. H. (2005). The role of NMDA currents in state transitions of the nucleus accumbens medium spiny neuron. Neurocomputing, 65–66, 565–570.

    Article  Google Scholar 

  • Yuste, R., & Bonhoeffer, T. (2001). Morphological changes in dendritic spines associated with long-term synaptic plasticity. Annual Review of Neuroscience, 24, 1071–1089.

    Article  PubMed  CAS  Google Scholar 

  • Zhuo, M., Zhang, W., Son, H., Mansuy, I., Sobel, R. A., Seidman, J., et al. (1999). A selective role of calcineurin aalpha in synaptic depotentiation in hippocampus. Proceedings of the National Academy of Science of the United States of America, 96, 4650–4655.

    Article  CAS  Google Scholar 

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  1. Department of Physics, Purdue University, 525 Northwestern Ave., West Lafayette, IN, 47907-2036, USA

    Kristofor D. Carlson & Nicholas Giordano

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  1. Kristofor D. Carlson
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  2. Nicholas Giordano
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Correspondence to Kristofor D. Carlson.

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Carlson, K.D., Giordano, N. Interplay of the magnitude and time-course of postsynaptic Ca2 +  concentration in producing spike timing-dependent plasticity. J Comput Neurosci 30, 747–758 (2011). https://doi.org/10.1007/s10827-010-0290-z

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  • DOI: https://doi.org/10.1007/s10827-010-0290-z

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