Are FRs “chance activities” or “distinct phenomena”?

(a) Fast-ripples (FRs) can arise by the chance plesiochronous firing of neurons or can be generated as distinct entities akin to a pathological motif. Similarly, words can emerge either by chance when tapping randomly on a typewriter, or as individual lexical entities. (b) To investigate the relative proportion of true and chance FRs, we shuffled EEG signals within the frequency band of interest (250-500 Hz). This disrupts any ‘true’ FRs and therefore allows us to estimate the incidence of chance FRs. The black rectangles on the left are filtered and expanded on the right.

Fast-ripples (FRs) can arise from stochastic neural firing

(a) Example of 5-s activity from 2 signals with inserted action potentials (APs). Across their entire length (480-s), both signals contain a similar number of APs but the upper trace displays more synchrony than the lower trace, where firing is even. The blue squares highlight a burst of highly synchronized APs. (b) Identification of FRs in simulated signals. (c) Time-frequency representation of detected FRs in simulated signals. (d) Spectrogram of detected FRs in simulated signals. The left peak (blue arrow) reflects FRs and the right peak (red arrow) reflects individual APs. (e) Number of simulations (y-axis) per FRs rate (x-axis). (f) Number of detected FRs across all simulations (50x50x50=125,000) with varying numbers of neurons, mean firing frequency, and synchronization. FRs do not occur randomly; a pattern can be identified, indicating that these three parameters control the expression of FRs. (g-i) Solution points for > 50 FRs to better highlight the pattern of expression. n=neuronal count, f=firing rate, s=synchronization.

Neural count, firing frequency and synchronization constrain the emergence of FRs

(a) Density of FRs across the 125,000 solution points of the simulation. (b) Density of FRs across the 125,000 solution points predicted by a gradient boosted tree (GBT). The distribution is very similar to (a). (c) All solution points predicted by the GBT (y-axis) along corresponding solution points of the original simulation (x-axis). The correlation is significant (r2=0.73, p<0.0001). (d) Blue Performance of the GBT to predict FR number, should FRs be randomly distributed across values of neural count, firing frequency and synchronization (500 permutations). Orange Performance of the GBT to predict FR number in actual simulations. (e) Performance of the GBT classifier using cross-validation (training: 80% of data; test: 20% remaining) using original (orange) and shuffled (blue) data. The difference is significant (paired t-test, p<0.0001).

FRs in neural culture

(a) Example of a detected FR in an MEA recording of neural culture. (b) In the MEA recordings, there are no more FRs than expected by chance (‘shuffle’) during baseline or in a pro-epileptic state following application of picrotoxin

The proportion of FRs as distinct entities varies across the sleep-wake cycle

(a) Incidence of FRs in the original signal (orange trace), shuffled signal (blue), the ratio of FR incidence in the original to shuffled signals (purple), delta amplitude (black) and predicted incidence of FRs across time. Here and after, these metrics are sampled at a rate of h-1. (b) Periodogram of delta amplitude across days. A clear peak at 24 hours is seen in original (black) but not shuffled (grey) data. (c) Fluctuation of FR incidence across days in the data (orange) and as predicted by the model (green), overlaid on fluctuations in delta amplitude. (d) AUC of the model to predict high (above median) and low (below median of individual rats’ FR incidence rate) values of FR incidence rate. The AUC is significantly above chance level, i.e., 0.5 (mean±SD: 0.58±0.05, p=0.003, one-sampled t-test). Each grey line is one animal, the green line is the average across animals. (e) Two-way ANOVA comparing the ratio of FR incidence rate in original to shuffled signals, before and after kainate injection, sampled at delta peaks (max delta) and troughs (min delta). There is a significant kainate * delta interaction (F(1,7)=17.1, p=0.004) and post-hoc tests show that the ratio is different before and after kainate injection only at delta peaks (mean difference, 95%: 0.24, [0.10-0.38], p=0.02). (f) Two-way ANOVA comparing the incidence rate of FRs before and after kainate injection, sampled at delta peaks and troughs. We observed a significant kainate * delta interaction (F(1,7)=14.7, p=0.006). The incidence rate after kainate injection increased only when sampled at delta troughs (12.6 min-1, [9.0-16.3], p<0.001) and not peaks (4.2 min-1, [0.5-7.9], p=0.12).

FRs as distinct entities in humans are uncommon

(a) Example of a FR detected in the original signal (orange) and shuffled signal (blue). (b) Incidence of FRs per minute in the original and shuffled signals, across sampling frequencies (3,000; 4,000; 5,000; 6,000; 8,000; 10,000; 15,000 Hz) to assess any possible effect of sampling frequency. We observed only a main effect of signal type (original vs shuffle, F(1, 770.4)=20.62, p<0.001) but no interaction (F(1,770.4)=0.05, p=0.82) or main effect of sampling frequency (F(1,13.2)=0.47, p=0.51). (c) Illustration of the proportion of FRs in the original signal and in the corresponding shuffled signal. This ratio is of 3:5. Hence, distinct FRs account for only 37.5% of all detected FRs.

Fano factor and level of synchronization

The Fano factor, defined as the variance of interspike intervals divided by their mean, is exponentially related to the level of synchronization of the model.

Markers of epileptic activity in MEA recordings increase after picrotoxin (PTX) application

Neuronal subgroup firing events measured by MEA recordings in vitro. (a) Example waveforms before and after picrotoxin treatment, where a burst event is highlighted. (b) Spike frequency, (c) burst frequency, (d) burst duration, and (e) number of spikes per burst (2-way ANOVA, p < 0.001).

Validation of shuffling procedure for high-frequency signals

To verify that our signal shuffling algorithm did not distort high frequency content, we compared the (a) amplitude and (b) oscillatory frequency of signals filtered within the frequency range of FRs (200-500 Hz) between the original and shuffled signals. There were no significant differences in either measure. This validation was performed on human data at a sampling frequency of 3000 Hz.

Distribution of FR incidence along phases of 24-hour delta amplitude fluctuations: group analysis

(a) Circular-to-linear correlation coefficient between the phase of delta amplitude traces and incidence of FRs (left box-and-whiskers). The correlation is significantly higher (r2 coefficient, mean, ± SD: 0.57, [0.10]) than if FR occurrence across days is shuffled (r2 coefficient: 0.03, [0.01], p<0.0001, paired t-test). (b) Circular plots indicating the incidence of FRs at different phases of daily delta amplitude fluctuations (-π to π). Each panel corresponds to one animal. The maximal incidence of FRs is seen at the trough of delta fluctuations. (c) The inverse relationship between FR incidence and delta fluctuations was further assessed with a second, independent HFO detector. One example FR is depicted (left), as well as the daily fluctuations of FR incidence (middle). Consistent with results from the original detector, FR incidence was inversely proportional to delta amplitude. Hence, FR incidence peaked at delta troughs (right, circular histogram including all animals). (d) Beta to delta power ratio across time is superimposed over delta power across time. There is a strong (inverse) correlation between the two time-series (inset), which is confirmed by the correlation coefficient across animals (right).

Examples of FRs in rats

Examples of FRs in different rats and the time-frequency representation of all detected FRs. See Supplementary Figure 6 for an objective assessment of “false FRs”. Scale: windows of 100 ms, 80 μV. 39

Lights ON and OFF are not associated with a different proportion of FRs overlapping with muscle artefact (assayed by broadband high-frequency activity)

We computed the proportion of FRs occurring during periods of broadband high-frequency activity (20-80 Hz) to verify that detected FRs are not “false ripples”. The proportion of such doubtful FRs was very low and, importantly, there was no difference between conditions lights ON and OFF (mean, ± SD, lights ON: 6%, ±2%, lights OFF: 6%, ±2%, p=0.74).

FR periodogram identifies a peak of incidence each 24 hours

The periodogram is obtained by computing a frequency analysis over the time-resolved incidence trace of FRs and converting the frequency unit (x-axis) into periods (in hours). A clear peak at 24 hours can be identified, confirming the visually observed daily fluctuation of FRs.

Periodogram of FRs incidence in simulated EEGs

Similar to the rodent data, the incidence rate of FRs in simulated EEGs also displays a period of 24 hours.

Duration of detected FRs

(a) Distribution of detected FR durations in shuffled (blue) and original (orange) rodent data. The two curves differ significantly from 5 to 25 ms (two-sample Kolmogorov-Smirnov test on averages, p=0.003). (b) The difference observed in (a) is driven by a shorter duration of FRs in shuffled data, as compared to original data in rodents (Wilcoxon test, p=0.002).

FRs are not more frequent than expected by chance when computed with alternative shuffling procedures

We used a (a) Fourier-transform (FT) based, (b) auto-regression (AR), (c) amplitude adjusted Fourier-transform (AAFT), (d) iterative AAFT until convergence of amplitude distribution (IAAFT-1), (e) IAAFT until convergence of spectrum (IAAFT-2) and (f) wavelet-based IAAFT together with preservation of cross-frequency coupling. None displayed a significantly different incidence of FRs between the original and shuffled data.