Skip to main content Accessibility help
×
Home

Precise Self-tuning of Spiking Patterns in Coupled Neuronal Oscillators

  • I.Y. Tyukin (a1) (a2) and V.B. Kazantsev (a3) (a4)

Abstract

In this work we discuss and analyze spiking patterns in a generic mathematical model of two coupled non-identical nonlinear oscillators supplied with a spike-timing dependent plasticity (STDP) mechanism. Spiking patterns in the system are shown to converge to a phase-locked state in a broad range of parameters. Precision of the phase locking, i.e. the amplitude of relative phase deviations from a given reference, depends on the natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanisms. The deviations, however, can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. The scheme applies to systems in which individual oscillators operate in the oscillatory mode. If the dynamics of oscillators becomes bistable then relative phase may fail to converge to a given value giving rise to the emergence of complex spiking sequences.

Copyright

Corresponding author

Corresponding author. E-mail: I.Tyukin@le.ac.uk

References

Hide All
[1] Abraham, W.C.. Metaplasticity: tuning synapses and networks for plasticity. Nature Reviews Neuroscience, 9 (2008), 387399.
[2] Bem, T., Rinzel, J.. Short duty cycle destabilizes a half-center oscillator, but gap junctions can restabilize the anti-phase pattern. Journal of Neurophysiology, 91 (2004), 693703.
[3] Diana, M.A., Bregestovski, P.. Calcium and endocannabinoids in the modulation of inhibitory synaptic transmission. Cell Calcium, 37 (2005), 497505.
[4] Dityatev, A., Rusakov, D.A.. Molecular signals of plasticity at the tetrapartite synapse. Current Opinion in Neurbiology, 21 (2011), 353359.
[5] Gerstner, W., Kempter, R., van Hemmen, J.L., Wagner, H.. A neuronal learning rule for sub-millisecond temporal coding. Nature, 386 (1996), 7678.
[6] J. Guckenheimer, P. Holmes. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer-Verlag, 1986.
[7] Gordleeva, S.Yu., Stasenko, S.V., Semyanov, A.V., Dityatev, A.E., Kazantsev, V.B. Bi-directional astrocytic regulation of neuronal activity within a network. Frontiers of Computational Neuroscience, 6 (2012), article 92.
[8] F.C. Hoppensteadt, E.M. Izhikevich. Weakly connected neural networks. Springer-Verlag, 1997.
[9] Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D., Yuste, R.. Synfire chains and cortical songs: Temporal modules of cortical activity. Science, 304 (2004), 559564.
[10] Izhikevich, E.M.. Polychronization: Computation with spikes. Neural Computation, 18 (2006), 245282.
[11] E.M. Izhikevich. Dynamical systems in neuroscience. The geometry of excitability and bursting. MIT Press, 2007.
[12] Izhikevich, E.M.. Solving the distal reward problem through linkage of STDP and dopamine signaling. Cerebral Cortex, 17 (2007), 24432452.
[13] Kayser, C., Montemurro, M.A., Logothetis, N.K., Panzeri, S.. Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns. Neuron, 61 (2009), 597608.
[14] Kazantsev, V., Tyukin, I.. Adaptive and phase selective spike timing dependent plasticity in synaptically coupled neuronal oscillators. PLOS ONE, 7 (2012), e30411.
[15] Kazantsev, V., Gordleeva, S.Yu., Stasenko, S.V., Dityatev, A.E.. A homeostatic model of neuronal firing governed by feedback signals from extracellular matrix. PLOS ONE, 7 (2012), e41646.
[16] Kazantsev, V.B., Nekorkin, V.I., Binczak, S., Jacquir, S., Bilbault, J.M.. Spiking dynamics of interacting oscillatory neurons. Chaos, 15 (2005), 023103.
[17] Koester, H.J., 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 (1998), 95969601.
[18] Lanore, F., Rebola, N., Carta, M.. Spike-timing-dependent plasticity induces presynaptic changes at immature hippocampal mossy fiber synapses. The Journal of Neuroscience, 29 (2009), 82998301.
[19] Ohno-Shosakua, T., Hashimotodania, Y., Maejima, T., Kano, M.. Calcium signaling and synaptic modulation: Regulation of endocannabinoid-mediated synaptic modulation by calcium. Cell Calcium, 38 (2005), 369374.
[20] A. Pikovsky, M. Rosenblum, J. Kurths. Synchronization: a unified concept in nonlinear sciences. Cambridge University Press, 2001.
[21] Rolston, J.D., Wagenaar, S.M., D.A.and Potter. Precisely timed spatiotemporal patterns of neural activity in dissociated cortical cultures. Neuroscience, 148 (2007), 294303.
[22] Rowat, P.F., Selverston, A.I.. Modeling the gastric mill central pattern generator with a relaxation-oscillator network. Journal of Neurophysiology, 70 (1993), 10301053.
[23] L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, L.O. Chua. Methods of qualitative theory in nonlinear dynamics. World Scientific, 2001.
[24] Sjostrom, P.J., Rancz, E.A., Roth, A., Hausser, M.. Dendritic excitability and synaptic plasticity. Physiological Reviews, 88 (2008), 769840.
[25] Song, S., Miller, K.D., Abbott, L.F.. Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nature Neuroscience, 3 (2000), 919926.
[26] I. Tyukin. Adaptation in dynamical systems. Cambridge University Press, 2011.
[27] Tyukin, I., Steur, E., Neijmeijer, H., van Leeuwen, C.. Small-gain theorems for systems with unstable invariant sets. SIAM Journal on Control and Optimization, 47 (2008), 849882.
[28] Whitehead, A., Rabinovich, M.I., Huerta, R., Zhigulin, V.P., Abarbanel, H.D.I.. Dynamical synaptic plasticity: a model and connection to some experiments. Biological Cybernetics, 88 (2003), 229235.

Keywords

Precise Self-tuning of Spiking Patterns in Coupled Neuronal Oscillators

  • I.Y. Tyukin (a1) (a2) and V.B. Kazantsev (a3) (a4)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.