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This article is part of the supplement: Eighteenth Annual Computational Neuroscience Meeting: CNS*2009

Open Access Poster presentation

Measuring spike train synchrony between neuronal populations

Thomas Kreuz12*, Daniel Chicharro3 and Ralph G Andrzejak3

Author Affiliations

1 Institute for Nonlinear Sciences, University of California, San Diego, CA, USA

2 Institute for Complex Systems, CNR, Sesto Fiorentino, Italy

3 Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain

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BMC Neuroscience 2009, 10(Suppl 1):P271  doi:10.1186/1471-2202-10-S1-P271


The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/10/S1/P271


Published:13 July 2009

© 2009 Kreuz et al; licensee BioMed Central Ltd.

Poster presentation

With the increasing availability of multi-unit recordings the focus of attention starts to shift from bivariate methods towards methods that provide the possibility to study patterns of activity across many neurons. Measures of multi-neuron spike train synchrony are becoming indispensable tools for addressing issues such as network synchronization, spike timing reliability and neuronal coding. However, many multi-neuron synchrony measures are extensions of bivariate measures. Two of the most prominent bivariate approaches are the spike train metrics by Victor-Purpura and van Rossum [1,2]. The former evaluates the cost needed to transform one spike train into the other using only certain elementary steps [1], while the latter measures the Euclidean distance between the two spike trains after convolution of the spikes with an exponential function [2]. Both methods involve one parameter that sets the time scale. In contrast, a more recent bivariate approach, the ISI-distance [3], is time scale independent and self-adaptive. Another essential difference is that the ISI-distance relies on the relative length of interspike intervals (ISI) and not on the timing of spikes. Finally, this method also allows the visualization of the relative firing pattern in a time-resolved manner.

Recently, the Victor-Purpura and the van Rossum distances have been extended to quantify dissimilarities between multi-unit responses [4,5]. To calculate the multi-unit Victor-Purpura metric, simultaneous spikes are labeled by the neuron that fired them, but this label can be changed at an additional cost which is determined by a second parameter. By varying this population parameter the metric is shifted from a "labeled line" (LL) code metric in which the distance is defined as the sum of the distances of the single neurons, to a "summed population" (SP) code metric in which the spike trains are superimposed before the distance is calculated [4]. In the extended van Rossum metric, the spike trains of each population are located in a space of vector fields (with a different unit vector assigned to each neuron). In this case interpolation between the LL and the SP coding is achieved by varying the angle (a second parameter) between unit vectors [5].

Here we present an analogous extension for the ISI-distance [6] that also interpolates between the LL and the SP codes. This multi-neuron ISI-distance inherits all the basic properties of the bivariate ISI-distance described above; in particular, it is also time scale independent and thus, in contrast to the other two multi-neuron metrics, depends on one population parameter only. In this study we compare all three multi-neuron distances using both controlled simulations and real data. We stress the advantages of our extension with respect to visualization, computational cost and applicability to larger numbers of spike trains with higher numbers of spikes.

Acknowledgements

TK has been supported by the Marie Curie Individual Intra-European Fellowship "DEAN," project No 011434, DC by the I.U.E. Department of the Generalitat of Catalunya and the European Social Fund, and RGA by the Ramón y Cajal program.

References

  1. Victor J, Purpura K: Nature and precision of temporal coding in visual cortex: A metric-space analysis.

    J Neurophysiol 1996, 76:1310-1326. PubMed Abstract | Publisher Full Text OpenURL

  2. van Rossum MCW: A novel spike distance.

    Neural Computation 2001, 13:751-763. PubMed Abstract | Publisher Full Text OpenURL

  3. Kreuz T, Haas JS, Morelli A, Abarbanel HDI, Politi A: Measuring spike train synchronization.

    J Neurosci Methods 2007, 165:151-161. PubMed Abstract | Publisher Full Text OpenURL

  4. Aronov D, Reich DS, Mechler F, Victor JD: Neural coding of spatial phase in V1 of the macaque monkey.

    J Neurophysiol 2003, 89:3304-3327. PubMed Abstract | Publisher Full Text OpenURL

  5. Houghton C, Sen K: A new multineuron spike train metric.

    Neural Computation 2008, 20:1495-1511. PubMed Abstract | Publisher Full Text OpenURL

  6. The Matlab source code for calculating and visualizing all ISI-distances as well as information about their implementation can be found under [http://inls.ucsd.edu/~kreuz/Source-Code/Spike-Sync.html] webcite