__Preparation of organotypic cortical slice cultures__

All procedures were approved by the Animal Care Committee (Eberhard-Karls-University, Tuebingen, Germany) and were in accordance with the institutional and federal guidelines of the German Animal Welfare Act (TierSchG). We put in a great deal of effort to reduce the number and suffering of animals. We prepared organotypic slice cultures from the neocortex of P 3 – 5 rats as described earlier [19, 24]

In brief, six P3 – P5 Sprague-Dawley rat pups of both sexes (Charles River, Sulzfeld, Germany) were put into a see-through plastic container and anesthetized with 4 Vol% halothane using high air flow (Draeger Vapor 19.3, Draegerwerk, Luebeck, Germnany). Animals were decapitated well after loss of righting reflex, but before cardio-respiratory depression occured. We withdrew the cortical hemisphere, removed the meninges, and cut 300 µm thick coronal slices, which we transferred onto glass coverslips and embedded them in a plasma clot. We transferred the coverslips into plastic tubes containing 750 µl of nutrition medium (consisting of horse serum, Hank’s balanced salt solution, basal medium Eagle, glutamine and glucose) to be incubated in a roller drum at 37°C. After one day in culture, we added antimitotics (pyrimidine analog and DNA synthesis inhibitor) and we renewed the suspension and the antimitotics twice a week. For our experiments, we used the cultures after two weeks *in vitro*.

__Electrophysiologic recordings__

We performed the extracellular multi-unit recordings in a recording chamber mounted on an inverted microscope. Therefore, we perfused the slices with artificial cerebrospinal fluid (aCSF) consisting of (in mM) NaCl 120, KCl 3.3, NaH2PO4 1.13, NaHCO3 26, CaCl2 1.8 and glucose 11, bubbled with 95% oxygen and 5% carbon dioxide. We positioned aCSF-filled glass electrodes with a resistance of about 3 to 5 MΩ on the surface of the slices and advanced into the tissue until extracellular spikes exceeding 100 µV in amplitude were visible. All experiments were conducted at 34°C. For preparation of the test solutions we dissolved diazepam (B.Braun, Melsungen, Germany) and ethanol (99%, university pharmacy) in the aCSF to yield the desired concentration. We applied the drugs (diazepam or ethanol) via bath perfusion using syringe pumps (ZAK, Marktheidenfeld, Germany) at a flow rate of approximately 1 ml min-1. After switching to experimental drug-containing solutions, at least 95% of the medium in the experimental chamber was replaced within 2 min. Effects on the spike patterns were stable about 5 min later. To ensure steady state conditions, we carried out the recordings 10 min after commencing the change of the drug-containing perfusate using a personal computer with the Digidata 1200 AD/DA interface and Axoscope 9 software (Axon Instruments, Union City, CA).

__Separation of local field potential and action potential activity and signal preprocessing__

We included n=7 and n=11 cultures in the diazepam and ethanol group, respectively. For each culture, we recorded spontaneous LFP activity during control conditions as well as in the presence of either ethanol or diazepam. The recorded electrophysiological data was band-pass filtered to separate AP activity from LFP activity. Filter settings for AP traces were 200 – 2000 Hz. For the identification of AP spikes and their time of occurrence we used a self-programmed MATLAB routine. The routine annotates the time point of a spike based on a set amplitude threshold that was defined as three times the standard deviation of baseline noise. We also used MATLAB to extract episodes of cortical up-state activity from the LFP recordings. Prior to extraction of the up-states, we resampled the LFP to 500 Hz. We only used recordings with valid data for all concentration levels to have a paired design for statistical analysis. **Figure 1** presents a representative LFP with corresponding spiking activity.

__Action potential frequency__

We plotted the cumulative probability of the frequencies of action potential firing in the first 200 ms of the cortical up-state for each condition. The analysis was based on the action potentials detected by the threshold-based routine. Therefore, we used the empirical cumulative distribution function plot (*cdfplot*) function in MATLAB.

__Analysis of local field potential activity__

The recorded LFP present the cumulative activity of neuronal activity in proximity of the recording electrode. We restricted our analyses to cortical up-states longer 2.5 s to be able to adequately characterize the spectral composition of the oscillatory phase after the initial peak. We excluded the first second of the up-state, i.e., the initial peak from the spectral analysis because of its very dominant amplitude and its non-oscillatory behaviour. Hence, we evaluated the features of the initial peak separately. **Figure 1** describes our approach. We measured the peak-to-peak amplitude of the initial up-state to quantify possible drug-induced effects. For the analysis of the initial up-state amplitude, we had to exclude one diazepam experiment because we only observed short up-states in one concentration stage of this recording. For the same reasons, we excluded four ethanol experiments.

Further, we excluded the last 0.2 s of each up-state to prevent a bias due to the transition back to a cortical down-state at the end of the up-state.

We used the MATLAB *pmtm* function that applies the Thomson’s multitaper method with 256 data points and time-halfbandwidth product to default for PSD calculation. We also calculated the normalized PSD (nPSD), by dividing the total power by the sum of power between 2 Hz and 30 Hz. While this approach provides information regarding changes in the spectral distribution with increasing drug concentrations, we used the information of AP times and LFP phase to evaluate possible changes in AP to LFP-phase locking.

__Action potential probability at distinct field potential phase__

We assessed the LFP phase with the Hilbert transform [25]. Using this method, an analytical signal *X(t)* is generated from the original trace, here the LFP up-state episode. *X(t)* is complex and the real part complies with the original trace and the imaginary part is the original trace after a ninety-degree phase shift. The analytic signal corresponds to the envelope of the original trace. The analytic phase *Φ(t)* can be obtained from . In order to correctly determine *Φ(t)*, the trace has to be filtered to a narrow frequency range. Here, we analysed frequencies up to 16 Hz in non-overlapping 2 Hz steps. We followed a 5-degree raster of binning the AP to the phase. By matching the AP to the analytic phase we are able to evaluate possible (de-) synchronizing effects between AP and LFP-phase.

__Statistical analysis__

To describe diazepam- or ethanol induced effects on cortical up-state activity we applied different statistical approaches. To statistically describe possible changes in peak-to-peak amplitude of the initial LFP-spike, the number of AP, as well as in PSD and nPSD, we applied the Friedman test with pairwise Wilcoxon signed rank tests and a Bonferroni correction. For unpaired comparisons, we used the Mann-Whitney U test. For outlier analysis, we applied the MATLAB *isoutlier* function, defining elements that are greater than three scaled median absolute deviations away from the median as outlier. For changes in PSD and nPSD we only considered changes to be significant if they occurred in at least two neighboring frequencies [26]. We used Kolmogorov-Smirnov test to find differences in the probability distribution of AP frequency. Being aware of the limited sample size in our experiments, wesupplemented the signed rank test with Hedges’ g tests as effect size using the MATLAB-based MES toolbox [27]. We further used the Kolmogorov-Smirnov test to detect changes in the distribution of action potentials in relation to the LFP phase as well as differences in the distribution of AP frequency.

We performed all descriptive and inference statistical tests with MATLAB. We used the MATLAB boxplot function for visualization of the data. In the boxplots the central horizontal line indicates the median whereas lower and upper box limits indicate the 25th and 75th percentiles. The whiskers span between the most extreme data points not considered outliers.