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Precise Self-tuning of Spiking Patterns in Coupled Neuronal Oscillators

Published online by Cambridge University Press:  12 December 2012

I.Y. Tyukin  and
V.B. Kazantsev
I.Y. Tyukin*
Affiliation:
Department of Mathematics, University of Leicester, University Road, LE1 7RH, UK Department of Automation and Control Processes, Saint-Petersburg State Electrotechnical University Prof. Popova str. 5, 197376, Russia
V.B. Kazantsev
Affiliation:
Department of Nonlinear Dynamics, Institute of Applied Physics of RAS Nizhny Novgorod, Russia Department of Neurodynamics and Neurobiology, University of Nizhny Novgorod Nizhny Novgorod, Russia
*
⋆ Corresponding author. E-mail: [email protected]
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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.

Keywords

nonlinear phase oscillatorsspike-timing dependent plasticityadaptive controlnonlinear parametrizationconvergenceweak attractorsneural oscillators
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 6: Biological oscillations , 2012 , pp. 67 - 94
Copyright
© EDP Sciences, 2012

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References

Références

Abraham, W.C.. Metaplasticity: tuning synapses and networks for plasticity. Nature Reviews Neuroscience, 9 (2008), 387–399. CrossRefGoogle ScholarPubMed
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), 693–703. CrossRefGoogle Scholar
Diana, M.A., Bregestovski, P.. Calcium and endocannabinoids in the modulation of inhibitory synaptic transmission. Cell Calcium, 37 (2005), 497–505. CrossRefGoogle ScholarPubMed
Dityatev, A., Rusakov, D.A.. Molecular signals of plasticity at the tetrapartite synapse. Current Opinion in Neurbiology, 21 (2011), 353–359. CrossRefGoogle ScholarPubMed
Gerstner, W., Kempter, R., van Hemmen, J.L., Wagner, H.. A neuronal learning rule for sub-millisecond temporal coding. Nature, 386 (1996), 76–78. CrossRefGoogle Scholar
J. Guckenheimer, P. Holmes. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer-Verlag, 1986.
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. CrossRefGoogle ScholarPubMed
F.C. Hoppensteadt, E.M. Izhikevich. Weakly connected neural networks. Springer-Verlag, 1997.
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), 559–564. CrossRefGoogle Scholar
Izhikevich, E.M.. Polychronization: Computation with spikes. Neural Computation, 18 (2006), 245–282. CrossRefGoogle ScholarPubMed
E.M. Izhikevich. Dynamical systems in neuroscience. The geometry of excitability and bursting. MIT Press, 2007.
Izhikevich, E.M.. Solving the distal reward problem through linkage of STDP and dopamine signaling. Cerebral Cortex, 17 (2007), 2443–2452. CrossRefGoogle ScholarPubMed
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), 597–608. CrossRefGoogle Scholar
Kazantsev, V., Tyukin, I.. Adaptive and phase selective spike timing dependent plasticity in synaptically coupled neuronal oscillators. PLOS ONE, 7 (2012), e30411. CrossRefGoogle ScholarPubMed
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. CrossRefGoogle ScholarPubMed
Kazantsev, V.B., Nekorkin, V.I., Binczak, S., Jacquir, S., Bilbault, J.M.. Spiking dynamics of interacting oscillatory neurons. Chaos, 15 (2005), 023103. CrossRefGoogle ScholarPubMed
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), 9596–9601. CrossRefGoogle ScholarPubMed
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), 8299–8301. CrossRefGoogle ScholarPubMed
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), 369–374. CrossRefGoogle Scholar
A. Pikovsky, M. Rosenblum, J. Kurths. Synchronization: a unified concept in nonlinear sciences. Cambridge University Press, 2001.
Rolston, J.D., Wagenaar, S.M., D.A.and Potter. Precisely timed spatiotemporal patterns of neural activity in dissociated cortical cultures. Neuroscience, 148 (2007), 294–303. CrossRefGoogle ScholarPubMed
Rowat, P.F., Selverston, A.I.. Modeling the gastric mill central pattern generator with a relaxation-oscillator network. Journal of Neurophysiology, 70 (1993), 1030–1053. Google ScholarPubMed
L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, L.O. Chua. Methods of qualitative theory in nonlinear dynamics. World Scientific, 2001.
Sjostrom, P.J., Rancz, E.A., Roth, A., Hausser, M.. Dendritic excitability and synaptic plasticity. Physiological Reviews, 88 (2008), 769–840. CrossRefGoogle ScholarPubMed
Song, S., Miller, K.D., Abbott, L.F.. Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nature Neuroscience, 3 (2000), 919–926. Google ScholarPubMed
I. Tyukin. Adaptation in dynamical systems. Cambridge University Press, 2011.
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), 849–882. CrossRefGoogle Scholar
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), 229–235. Google ScholarPubMed