The coherence Cxy(f) of two signals x check details and y is defined as their normalized cross-spectral density. For a given frequency f, the coherence is higher the more stable the phase difference of the signals: Cxy=|Pxy|2PxPy.

Coherence was computed using PSDs by the Welch periodogram method with 256 FFT points. Slope-triggered averages (Figures 4D and 9D) were computed by averaging windows of 40 ms LFP data centered to the times of strongest 10% slopes of each cPSC. Ripple modulation of the resulting averages indicates a consistent phase of the putative EPSC onsets (or putative IPSC onsets, Figure 9D) in the oscillation defined by the extracellular ripple. The presence of the bulk of the signal after the onset (0 ms offset) indicates a tendency for stronger slopes to concentrate at the beginning of the cPSC. cPSCs

with only one strong slope were removed from the analysis. For the analysis shown in Figure 4, a total of 1,085 cPSCs were represented with 5,161 onsets, each cell having an average of 4 to 5 onsets per cPSC. For the complementary analysis presented in Figure 9, a total of 849 cPSCs from 6 cells were represented with 3,037 onsets, Antidiabetic Compound Library cell assay each cell showing an average of 3 to 5 onsets per cPSC. To assign phases with respect to the ripple component of the LFP, we applied a Hilbert transform on the 120–300 Hz-filtered extracellular potential. Each putative EPSC event (or putative IPSC event, Figure 9D) detected by its extremal slope was assigned a Hilbert phase, ϕj. As an indicator for locking quality

of these collected EPSC ADAMTS5 (or IPSC) phases, we use the vector strength (VS) or mean resultant length, which is normalized between 0 and 1: VS(ϕ)=1N|∑j=1Ne−iϕj|. Figures 4E and 9C illustrate the dependence of vector strength and phase (polar plots in insets) as a function of the slope threshold used for EPSC (or IPSC) detection (in the range of 1% to 25%). All vector strengths and phases plotted are significant according to a Rayleigh test for the uniformity of a phase distribution with p < 0.05. Data are presented as means ± standard error of the mean (SEM), unless otherwise stated. Statistical significance was assessed using Wilcoxon’s rank-sum test, the two-sample Kolmogorov-Smirnov test, or the Rayleigh test for circular statistics. Statistical significance was indicated at the given level (p) with α = 0.05 regarded significant, unless otherwise designated. We wish to thank Sarah Shoichet, Anja Gundlfinger, Alexey Ponomarenko, Christian Wozny, José R. Donoso, Nikolai Axmacher, and Robert Schmidt for constructive comments on earlier versions of the manuscript; Peter Barry (UNSW) for advice on estimation of LJPs; Roger D. Traub for valuable discussions; as well as Serena Dudek and Robert J. Bridges for help on establishing recordings with DNDS. We highly appreciate the technical assistance of Susanne Rieckmann and Anke Schönherr.