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Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

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Abstract

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows.

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References

  • Abbott, L. F., & Nelson, S. B. (2000). Synaptic plasticity: Taming the beast. Nature Neuroscience Supp., 3, 1178–1183.

    Article  CAS  Google Scholar 

  • Bienenstock, E. (1991). Notes on the growth of a composition machine. In D. Andler, E. Bienenstock, & B. Laks (Eds.), Proceedings of the First Interdisciplinary Workshop on Compositionality in Cognition and Neural Networks (pp. 25–43). Abbaye de Royaumont, France.

    Google Scholar 

  • Bienenstock, E. (1995). A model of neocortex. Network: Computation in Neural Systems, 6, 179–224.

    Article  Google Scholar 

  • Braunstein, L. A., Buldyrev, S. V., Cohen, R., Havlin, S., & Stanley, H. E. (2003). Optimal paths in disordered complex networks. Physical Review Letters, 91, 168701.

    Article  PubMed  Google Scholar 

  • Bell, C. C., Han, V. Z., Sugawara, Y., & Grant, K. (1997). Synaptic plasticity in a cerebellum-like structure depends on temporal order. Nature, 387, 278–281.

    Article  PubMed  CAS  Google Scholar 

  • Bi, G., & Poo, M. (1998). Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience, 18(24), 10464–10472.

    PubMed  CAS  Google Scholar 

  • Buzsáki, G., & Draguhn, A. (2004). Neuronal oscillations in cortical networks. Science, 304, 1926–1929.

    Article  PubMed  Google Scholar 

  • Dan, Y., & Poo, M. (1992). Hebbian depression of isolated neuromuscular synapses in vitro. Science, 256, 1570–1573.

    Article  PubMed  CAS  Google Scholar 

  • Diesmann, M., Gewaltig, M.-O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402, 529–533.

    Article  PubMed  CAS  Google Scholar 

  • Froemke, R. C., & Dan, Y. (2002). Spike-timing-dependent synaptic modification induced by natural spike trains. Nature, 416, 433–438.

    Article  PubMed  CAS  Google Scholar 

  • Gerstner, W., & van Hemmen, J. L. (1993). Coherence and incoherence in a globally coupled ensemble of pulse-emitting units. Physical Review Letters, 71, 312–315.

    Article  PubMed  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 

  • Gerstner, W. (2000) Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking. Neural Computation, 12, 43–89.

    Article  PubMed  CAS  Google Scholar 

  • Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Cambridge: Cambridge University Press.

    Google Scholar 

  • Glass, L., & Mackey, M. C. (1988). From clocks to chaos—The rhythms of life. Princeton: Princeton University Press.

    Google Scholar 

  • Hansel, D., Mato, G., & Meunier, C. (1993). Phase dynamics for weakly coupled Hodgkin–Huxley neurons. Europhysics Letters, 23(5), 367–372.

    CAS  Google Scholar 

  • Hansel, D., Mato, G., & Meunier, C. (1995). Synchrony in excitatory neural networks. Neural Computation, 7, 307–337.

    PubMed  CAS  Google Scholar 

  • Horn, D., Levy, N., Meilijson, I., & Ruppin, E. (2000). Distributed synchrony of spiking neurons in a Hebbian cell assembly. In S. A. Solla, T. K. Leen, & K.-R. Müller (Eds.), Advances in Neural Information Processing Systems, (Vols. 25–43, pp. 129–135). Cambridge, MA: MIT.

    Google Scholar 

  • Hutcheon, B., & Yarom ,Y. (2000). Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends in Neurosciences, 23(5), 216–222.

    Article  PubMed  CAS  Google Scholar 

  • Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6), 1569–1572.

    Article  Google Scholar 

  • Izhikevich, E. M. (2006). Polychronization: Computation with spikes. Neural Computation, 18, 245–282.

    Article  PubMed  Google Scholar 

  • Izhikevich, E. M., Gally, J. A., & Edelman, G.M. (2004). Spike-timing dynamics of neuronal groups. Cerebral Cortex, 14(8), 933–944.

    Article  PubMed  Google Scholar 

  • Jefferys, J. G. R., Traub, R. D., & Whittington, M. A. (1996). Neuronal networks for induced ‘40 Hz’ rhythms. Trends in Neurosciences, 19(5), 202–208.

    Article  PubMed  CAS  Google Scholar 

  • Karbowski, J., & Ermentrout, G. B. (2002). Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. Physical Review E, 65, 031902.

    Article  Google Scholar 

  • Kempter, R., Gerstner, W., & van Hemmen, J. L. (1999). Hebbian learning and spiking neurons. Physical Review E, 59, 4498–4514.

    Article  CAS  Google Scholar 

  • Kori, H. (2003). Slow switching in a population of delayed pulse-coupled oscillators. Physical Review E, 68, 021919.

    Article  Google Scholar 

  • Kori, H., & Kuramoto, Y. (2001). Slow switching in globally coupled oscillators: Robustness and occurrence through delayed coupling. Physical Review E, 63, 046214.

    Article  CAS  Google Scholar 

  • Kori, H., & Mikhailov, A. S. (2004). Entrainment of randomly coupled oscillator networks by a pacemaker. Physical Review Letters, 93, 254101.

    Article  PubMed  Google Scholar 

  • Kori, H., & Mikhailov A. S. (2006). Strong effects of network architecture in the entrainment of coupled oscillator systems. Physical Review E, 74, 066115

    Google Scholar 

  • Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer.

    Google Scholar 

  • Kuramoto, Y. (1991). Collective synchronization of pulse-coupled oscillators and excitable units. Physica D, 50, 15–30.

    Article  Google Scholar 

  • Lengyel, M., Kwag, J., Paulsen, O., & Dayan, P. (2005). Matching storage and recall: Hippocampal spike timing-dependent plasticity and phase response curves. Nature Neuroscience, 8, 1677–1683.

    Article  PubMed  CAS  Google Scholar 

  • Levy, N., Horn, D., Meilijson, I., & Ruppin, E. (2001). Distributed synchrony in a cell assembly of spiking neurons. Neural Networks, 14, 815–824.

    Article  PubMed  CAS  Google Scholar 

  • Markram, H., Lübke, 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 

  • Masuda, N., Aihara, K. (2004). Self-organizing dual coding based on spike-time-dependent plasticity. Neural Computation, 16, 627–663.

    Article  PubMed  Google Scholar 

  • Mehring, C., Hehl, U., Kubo, M., Diesmann, M., & Aertsen, A. (2003). Activity dynamics and propagation of synchronous spiking in locally connected random networks. Biological Cybernetics, 88, 395–408.

    Article  PubMed  Google Scholar 

  • Mehta, M. R., Lee, A. K., & Wilson, M. A. (2002). Role of experience and oscillations in transforming a rate code into a temporal code. Nature, 417, 741–746.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Nowotny, T., Zhigulin, V. P., Selverston, A. I., Abarbanel, H. D. I., & Rabinovich, M. I. (2003). Enhancement of synchronization in a hybrid neural circuit by spike-timing dependent plasticity. Journal of Neuroscience, 23(30), 9776–9785.

    PubMed  CAS  Google Scholar 

  • Pikovsky, A., Rosenblum, M., & Kurths, J. (2001). Synchronization—A universal concept in nonlinear sciences. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Plenz, D., & Kitai, S. T. (1999). A basal ganglia pacemaker formed by the subthalamic nucleus and external globus pallidus. Nature, 400, 677–682.

    Article  PubMed  CAS  Google Scholar 

  • Ramirez, J.-M., Tryba, A. K., & Peña, F. (2004). Pacemaker neurons and neuronal networks: An integrative view. Current Opinion in Neurobiology, 14, 665–674.

    Article  PubMed  CAS  Google Scholar 

  • Reyes, A. D. (2003). Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nature Neuroscience, 6(6), 593–599.

    CAS  Google Scholar 

  • Ritz, R., & Sejnowski, T. J. (1997). Synchronous oscillatory activity in sensory systems: New vistas on mechanisms. Current Opinion in Neurobiology, 7, 536–546.

    Article  PubMed  CAS  Google Scholar 

  • Seliger, P., Young, S. C., & Tsimring, L. S. (2002). Plasticity and learning in a network of coupled phase oscillators. Physical Review E, 65, 041906.

    Article  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 Sciences, USA, 99(16), 10831–10836.

    Article  CAS  Google Scholar 

  • Singer, W., Gray, & C. M. (1995). Visual feature integration and the temporal correlation hypothesis. Annual Review of Neuroscience, 18, 555–586.

    Article  PubMed  CAS  Google Scholar 

  • Song, S., & Abbott, L. F. (2001). Cortical development and remapping through spike timing-dependent plasticity. Neuron, 32, 339–350.

    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(9), 919–926.

    Article  PubMed  CAS  Google Scholar 

  • Timme, M., Wolf, F., & Geisel, T. (2002). Prevalence of unstable attractors in networks of pulse-coupled oscillators. Physical Review Letters, 89, 154105.

    Article  PubMed  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(23), 8812–8821.

    PubMed  Google Scholar 

  • Vogels, T. P., & Abbott, L. F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons. Journal of Neuroscience, 25(46), 10786–10795.

    Article  PubMed  CAS  Google Scholar 

  • Winfree, A. T. (1980). The geometry of biological time. New York: Springer.

    Google Scholar 

  • Woodin, M. A., Ganguly, K., & Poo, M. (2003). Coincident pre- and postsynaptic activity modifies GABAergic synapses by postsynaptic changes in Cl transporter activity. Neuron, 39, 807–820.

    Article  PubMed  CAS  Google Scholar 

  • Zhang, L. I., Tao, H. W., Holt, C. E., Harris, W. A., & Poo, M. (1998). A critical window for cooperation and competition among developing retinotectal synapses. Nature, 395, 37–44.

    Article  PubMed  CAS  Google Scholar 

  • Zhigulin, V. P., & Rabinovich, M. I. (2004). An important role of spike timing dependent synaptic plasticity in the formation of synchronized neural ensembles. Neurocomputing, 58–60, 373–378.

  • Zhigulin, V. P., Rabinovich, M. I., Huerta, R., & Abarbanel, H. D. I. (2003). Robustness and enhancement of neural synchronization by activity-dependent coupling. Physical Review E, 67, 021901.

    Article  CAS  Google Scholar 

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Correspondence to Naoki Masuda.

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Masuda, N., Kori, H. Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity. J Comput Neurosci 22, 327–345 (2007). https://doi.org/10.1007/s10827-007-0022-1

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