Fig 1.
Examples of synthetic spike trains used for MSTM validation, illustrating the spanned dimensions of rhythmicity and sequentialness.
Examples of single-scale (A) and dual-scale (B) spike trains either without (upper panels) or with (lower panels) sequential structure. The left (right) column shows pseudo-rhythmic (non-rhythmic) trains. In each panel, the top subpanel shows the dynamic variables that govern the population activity (r for single-scale trains, for dual-scale trains), the middle subpanel shows the instantaneous population firing rate (obtained by convolving each spike train with a Gaussian kernel of bandwidth 0.1 ms and then averaging across neurons), and the bottom subpanel displays the spike train as a raster plot. In the case of sequential single-scale trains, the instantaneous rate variable r is shown for 5 neurons that span the active phase of the cycle, equally spaced with respect to relative phase; shades from blue to green indicate greater phase lag. Parameter values are set as follows:
Hz, m = 1, Dc = 0 or 0.4 (A);
,
, Dc = 0 or 0.4 (B). In all cases,
Hz.
Table 1.
Parameter descriptions and values used throughout this study, unless otherwise stated.
Table 2.
Multineuron spike train measures (MSTMs) evaluated in this study.
Table 3.
Power spectrum and FOOOF (fitting oscillations & one over f) measures evaluated in this study.
Fig 2.
Assessment of synchrony on synthetic spike trains: broad variability across MSTM behavior.
Assessment of the level of synchrony on single-scale (A) and dual-scale (B) synthetic spike trains using 5 illustrative MSTMs. A: Synchrony is plotted as a function of the modulation amplitude m for average firing rate Hz. B: Synchrony is plotted as a function of the population width Σ for spike deletion probability
. Synchrony increases with m in single-scale trains, while it decreases with Σ in dual-scale trains. In all panels, the population rate f0 varies in the grid [4,12,36] Hz and is color-coded, with warmer colors indicating higher f0. Solid lines: pseudo-rhythmic spike trains; dash lines: non-rhythmic spike trains. Corresponding results for a broader set of MSTMs and parameter values are shown in S1 Fig.
Fig 3.
Correlation between each MSTM and each generative parameter.
The absolute value of the Spearman correlation coefficient between each MSTM and each generative parameter is color-coded for the single-scale (A) and dual-scale (B) synthetic spike train families. Correlation values that are not significant (at , uncorrected) are grayed-out. For each spike train family, MSTMs are ordered according to decreasing absolute values of correlation with the generative parameter that determines synchrony, which is shown in the top row. The bottom row for each panel corresponds to the presence or absence of pseudo-rhythmic oscillations. The intermediate rows correspond to potentially confounding factors such as firing rate r0 and population frequency f0.
Fig 4.
Hierarchical clustering of measures.
A: Dendrogram showing the distances between MSTMs as a hierarchical cluster tree. Measures are sorted along the x axis in increasing order of the dendrogrammatic distance of the first nonsingleton cluster they are grouped in. B: Similarity matrix showing the absolute value of the Spearman correlation coefficient between each pair of MSTMs. Measure labels are color-coded to indicate measure type (green: univariate; blue: bivariate; red: multivariate). Corresponding results for the extended set of 131 MSTMs are shown in S2 Fig.
Fig 5.
Effects of time window length and number of neurons for a subset of selected measures.
Effects of sample size variations in time (A) or space (B) for 5 illustrative MSTMs in the case of single-scale non-sequential spike trains with Hz and m = 0.5. A: For each MSTM, the mean value across windows is plotted as a function of window length. Shaded areas indicate the SD across windows. B: As in (A), but sample size varies in space instead of time. Corresponding results for a broader set of MSTMs and parameter values are shown in S3 Fig.
Fig 6.
Visualizing collective dynamic coordination in rat auditory cortex spiking activity through the lens of the highly comparative approach.
A: A dataset comprising 14 recordings is visualized through the highly comparative description, highlighting nonstationarities, pseudo-rhythmic patterns, and recording-wise idiosyncrasies. Each row corresponds to a MSTM, each column to a 30 s time window; values are z-scored across windows. MSTMs are ordered according to the outcome of an average linkage hierarchical clustering procedure over MSTMs. Time windows are ordered chronologically and recordings are concatenated and indicated by the color-coded labels on top, using the same identifiers as in the original dataset [84]. Gray cells indicate time windows where the FOOOF spectral peak parameter was below the significance threshold, hence the corresponding parameters were not assigned. B: The same data shown in A is replotted by ordering time windows according to the outcome of an average linkage hierarchical clustering procedure over time windows as in Fig 7A. Vertical lines on top color-code for recording session as in (A); their length codes for chronological order within each session. In both (A) and (B), values greater than , where SZ indicates a generic MSTM value after z-scoring and the maximum value is taken over MSTMs and time windows, are clipped to that value for improved visualization. Corresponding results for the mouse and monkey datasets are shown in S7 Fig.
Fig 7.
Auditory cortex spiking activity exhibits structured variability that is distinctive of each recording.
A: Dendrogram showing the distances between time windows as a hierarchical cluster tree. B: Similarity matrix showing the Spearman correlation coefficient between any pair of time windows. Vertical lines on top color-code for recording session and their length codes for chronological order within each session as in Fig 6B. C: MDS representation of the distance matrix obtained from the values shown in B by taking D = 1 − ρ. Each circle represents a time window, color-coded as in Fig 6. D: Silhouette plot showing for each time window, its mean value in the dataset (red vertical line), and the
significance threshold (gray dashed vertical line). Corresponding results for the mouse and monkey datasets are shown in S8 Fig.
Table 4.
Silhouette scores indicating significant recording-wise distinctiveness in the MSTM space for each spike train dataset.
Silhouette scores are reported for each dataset for both the core(46 MSTMs) and the extended (131 MSTMs) sets of MSTMs (unshaded rows), as well as for their 2D MDS projections (shaded rows), along with their corresponding
significance thresholds
.
Fig 8.
Discriminating wake vs. NREM sleep from individual spike train measures.
A: Univariate decoding accuracies for one recording for each MSTM of the core set of 46 MSTMs. MSTMs are ordered according to decreasing decoding accuracy. Gray dotted lines indicate
significance thresholds, with darker shades of gray indicating more stringent significance levels. Corresponding results for each individual recording and for each MSTM of the extended set of 131 MSTMs are shown in S9 Fig. B: Median univariate decoding accuracies
across recordings for each MSTM (blue bars) are shown together with single-recording decoding accuracies (colored symbols). MSTMs are ordered according to decreasing median decoding accuracy. C: As in B, but across-recording (with LORO cross-validation) decoding accuracies
are shown. Colored symbols show average values for each test recording (with the remaining recordings used for training), blue bars indicate their median values across recordings. D: Violin-scatter plots of selected MSTMs for each recording and class. Gray and black circles indicate median values for wake and NREM respectively, vertical gray lines show the interquartile range.
Fig 9.
Discriminating wake vs. NREM sleep from spike train measure pairs in one recording.
Bivariate decoding accuracies (A) and synergies
(B) for one recording (M1R1) for each MSTM pair in the core set. MSTMs are ordered as in Fig 8A. Corresponding results for each individual recording and for each MSTM of the extended set of 131 MSTMs are shown in S10 Fig; median results across the 4 recordings are shown in S11 Fig.
Fig 10.
Discriminating wake vs. NREM sleep from spike train measure pairs.
A: Cumulative probability density functions of median decoding accuracy for each MSTM pair kind of the extended set of MSTMs. The range of shown corresponds to significant decoding accuracy at
, uncorrected; vertical gray dotted lines indicate more stringent
decoding thresholds. The inset shows the
range corresponding to the most discriminating pairs. B: As in (A), for decoding synergies
. C: Decoding synergies are plotted against accuracies for each MSTM pair in the extended set. Pairs in the top 1% of the most synergistic pairs are highlighted in red. D: Wordcloud plots of the MSTMs included in the top 1% most discriminative (top) and synergistic (bottom) pairs. Numbers displayed at the end of timescale-dependent measures indicate the timescale in milliseconds. For FOOOF spectral measures, 1p (2p) refers to the single-peak (dual-peak) model; in the dual-peak model, the number at the end of the parameter name indicates the corresponding peak.
Fig 11.
Intrinsic dimensionality estimates of the MSTM library.
A: Number of components needed to explain 95% and 99% of the variance for the core (46 MSTMs, left) and the extended (131 MSTMs, right) sets of MSTMs as obtained from a PCA decomposition. In general, the inclusion of additional MSTMs in the extended set increases the intrinsic dimensionality as assessed by PCA only modestly at the 95% threshold, but more notably so at the 99% threshold. The higher increase at the 99% threshold is more conspicuous in biological datasets. B: Intrinsic dimension estimated with a nearest neighbor based method. The intrinsic dimension estimates are shown as a function of distance range for synthetic spike train families (top) and biological datasets (bottom), considering the core set of 46 MSTMs (left) or the extended set of 131 MSTMs (right). Shaded areas indicate s.e.m. as returned by a maximum likelihood estimator. The results shown here were obtained with Gride; TWO-NN returned similar estimates.