Measuring spike train synchrony between neuronal populations

With the increasing availability of multi-unit recordingsthe focus of attention starts to shift from bivariate meth-ods towards methods that provide the possibility to studypatterns of activity across many neurons. Measures ofmulti-neuron spike train synchrony are becoming indis-pensable tools for addressing issues such as network syn-chronization, spike timing reliability and neuronalcoding. However, many multi-neuron synchrony meas-ures are extensions of bivariate measures. Two of the mostprominent bivariate approaches are the spike train metricsby Victor-Purpura and van Rossum [1,2]. The former eval-uates the cost needed to transform one spike train into theother using only certain elementary steps [1], while thelatter measures the Euclidean distance between the twospike trains after convolution of the spikes with an expo-nential function [2]. Both methods involve one parameterthat sets the time scale. In contrast, a more recent bivariateapproach, the ISI-distance [3], is time scale independentand self-adaptive. Another essential difference is that theISI-distance relies on the relative length of interspike inter-vals (ISI) and not on the timing of spikes. Finally, thismethod also allows the visualization of the relative firingpattern in a time-resolved manner.Recently, the Victor-Purpura and the van Rossum dis-tances have been extended to quantify dissimilaritiesbetween multi-unit responses [4,5]. To calculate themulti-unit Victor-Purpura metric, simultaneous spikes arelabeled by the neuron that fired them, but this label canbe changed at an additional cost which is determined bya second parameter. By varying this population parameterthe metric is shifted from a "labeled line" (LL) code metricin which the distance is defined as the sum of the dis-tances of the single neurons, to a "summed population"(SP) code metric in which the spike trains are superim-posed before the distance is calculated [4]. In the extendedvan Rossum metric, the spike trains of each populationare located in a space of vector fields (with a different unitvector assigned to each neuron). In this case interpolationbetween the LL and the SP coding is achieved by varyingthe angle (a second parameter) between unit vectors [5].Here we present an analogous extension for the ISI-dis-tance [6] that also interpolates between the LL and the SPcodes. This multi-neuron ISI-distance inherits all the basicproperties of the bivariate ISI-distance described above; inparticular, it is also time scale independent and thus, incontrast to the other two multi-neuron metrics, dependson one population parameter only. In this study we com-pare all three multi-neuron distances using both control-led simulations and real data. We stress the advantages ofour extension with respect to visualization, computa-tional cost and applicability to larger numbers of spiketrains with higher numbers of spikes.