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Feasibility of long-range synchronization with zero phase lag in a relay network

Atthaphon Viriyopase1, Ingo Bojak1, 2*, Magteld Zeitler1 and C.C.A.M. (Stan) Gielen1
  • 1 Radboud University Nijmegen (Medical Centre), Donders Institute for Brain, Cognition and Behaviour, Netherlands
  • 2 University of Birmingham, School of Psychology, United Kingdom

The long-range synchronization of neuronal activity between brain areas is now well established experimentally, in particular for the beta (14-30 Hz) and gamma (40-80 Hz) frequency bands. It is remarkable that some of the reported synchrony appears to have zero phase lag, given the synaptic and conduction delays inherent in the connections between distant brain areas. This has led to speculations about a possible functional role of zero-lag synchrony in neuronal communication, attention, memory and feature binding (Fries, 2005). However, recent studies using single-unit and local field potential recordings point to synchronization with non-zero phase lags (Uhlhaas et al., 2009). Hence we ask here under which conditions zero-lag synchrony can occur in the brain.
Several theoretical studies have argued that mutual pulse-coupling with delays and excitatory synapses cannot easily lead to zero-lag synchrony (Zeitler et al., 2009). This study therefore uses the second simplest network for interacting neuronal populations: two synchronizing oscillators which interact via a relay oscillator (Fischer et al., 2006; Vicente et al., 2008), where the relay could for example represent the thalamus (Gollo et al., 2010). Analytical results and computer simulations were obtained for both type I Mirollo-Strogatz and type II Hodgkin-Huxley neurons. A main result of our study is that synchronization is easier to achieve with the latter than with the former. Furthermore, we have investigated various types of synaptic coupling and find that alpha synapses with short rise times (typically less than 2 ms) are more suitable for achieving zero-lag synchronization.
We have also considered the potential impact of Spike-Timing Dependent Plasticity (STDP) for various learning windows. In agreement with Knoblauch and Sommer (2003), we found that with STDP the network converges to zero-lag synchronization at a faster rate and for a larger range of synaptic strengths and delays times. However, when the delay times between the two synchronizing oscillators and the relay oscillator are different, zero phase lag is easily lost. Furthermore, adaptation of the synapses often took quite some time (in general more than 500 cycles); considerably more than the observed time range of 200 to 250 ms to generate zero-lag synchrony in the gamma frequency range in visual perception (Rodriguez et al., 1999). Considering the actual conditions present in the brain, our study hence suggests a cautious re-evaluation of the proposed functional role of zero-lag synchrony.

Figure 1: Influence of synaptic rise times. For different conduction delays τ (normed to the intrinsic period) and synaptic weights ε, (A)-(C) show synchronization quality and (D)-(F) convergence promptness, respectively, for Mirollo-Strogatz neurons. The rise time of the alpha synapses is set to 1 ms in (A) and (D), 2 ms in (B) and (E), and 3 ms in (C) and (F).

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Acknowledgements

This project was partly funded by the Netherlands Organization for Scientific Research (NWO 051.02.050).

References

Fischer, I., Vicente, R., Buldú, J. M., Peil, M., Mirasso CR, Torrent, M. C., and García-Ojalvo, M. (2006). Zero-lag long-range synchronization via dynamical relaying. Phys. Rev. Lett. 97, 123901.
Fries, P. (2005). A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends Cogn. Sci. 9, 474-480.
Gollo, L.L., Mirasso, C., and Villa, A.E.P. (2010). Dynamic control for synchronization of separated cortical areas through thalamic relay. NeuroImage 52, 947-955.
Knoblauch, A., and Sommer, F. T. (2003). Synaptic plasticity, conduction delays, and inter-areal phase relations of spike activity in a model of reciprocally connected areas. Neurocomput. 52-4, 301-306.
Rodriguez, E., George, N., Lachaux, J.P., Martinerie, J., Renault, B., and Varela, F.J. (1999). Perception's shadow: long-distance synchronization of human brain activity. Nature 397, 430-433.
Uhlhaas, P.J., Pipa, G., Lima, B., Melloni, L., Neuenschwander, S., Nikolić, D., and Singer, W. (2009). Neural synchrony in cortical networks: history, concept and current status. Front. Integr. Neurosci. 3, 17.
Vicente, R., Gollo, L. L., Mirasso, C. R., Fischer, I., and Pipa, G. (2008). Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays. Proc. Natl. Acad. Sci. U.S.A. 105, 17157-17162.
Zeitler, M., Daffertshofer, A., and Gielen, C. C. A. M. (2009). Asymmetry in pulse-coupled oscillators with delay. Phy. Rev. E 79, 065203.

Keywords: gamma frequency band, long-range synchronization, phase-locking equation, relay network, spike-timing dependent plasticity (STDP), type I Mirollo-Strogatz neuron, type II Hodgkin-Huxley neuron, zero phase lag

Conference: Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012.

Presentation Type: Poster

Topic: Other

Citation: Viriyopase A, Bojak I, Zeitler M and Gielen C (2012). Feasibility of long-range synchronization with zero phase lag in a relay network. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference 2012. doi: 10.3389/conf.fncom.2012.55.00119

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Received: 18 Sep 2012; Published Online: 12 Sep 2012.

* Correspondence: Dr. Ingo Bojak, University of Birmingham, School of Psychology, Birmingham, West Midlands, B15 2TT, United Kingdom, i.bojak@reading.ac.uk