Article Figures & Data
Figures
- Figure 1.
Assumptions of ∼1 Hz synchrony in nonREM are contradicted in some pairs of neurons. A, Example of data from rat cortical multineuronal spiking during nonREM sleep (top) and the corresponding LFP activity (bottom). Note the prominent LFP delta waves (upgoing) that temporally correspond with periods of relative spiking silence. B, Schematic of neuronal spiking activities during DOWN and UP states (note that LFP fluctuations are inverted relative to the membrane potential for which UP and DOWN states are named). C, Traditional lag analysis does not capture the dynamics needed to predict true cross-correlations between pairs of neurons in nonREM sleep. i, The spike count histograms of two neurons collected from all the UP states in a recording. Shown is a probability distribution of spikes at different phases of the UP state ranging from 0% (start of UP state) to 100% (end of UP state). This data was used to seed our simulation. ii, Cross-correlogram (CCG) calculated from two simulated UP state spike trains based on the distribution of the spike count histogram from the neuron 1 and 2 shown in i. This simulation predicts a positive correlation of spiking between pairs of neurons since neurons tend to fire more in UP states than DOWN states. iii, The actual CCG for the neuron 1 and 2 shown in i and ii. Note that the true CCG from nonsimulated spike trains shows a trough at zero lag, indicating anticorrelation rather than positive correlation. D, Left, All the CCGs with a statistically significant trough from the entire dataset are stacked vertically and sorted by central trough amplitude from baseline (measured by “difference between center and edge” (DCE—see Materials and Methods). Color denotes amplitude of CCG. Right, The corresponding simulations are shown with the same neuron pairs in each row of both plots. E, Comparison of DCE (see Materials and Methods) between experiment and simulation among these pairs with significant troughs in the experiment. All the DCEs in simulation are non-negative.
- Figure 2.
CCG normalization and DCE calculation. A, An example original CCG. B, Averaged CCG with shuffled spike trains (3 times) using 0.5 s jittered window (blue) and the CCG after convolution (1 s triangular window). C, The normalized CCG is defined as log(Original CCG/Convoluted CCG). Illustration of DCE calculation is also demonstrated here.
- Figure 3.
NonREM sleep shows higher amplitude hundreds of millisecond timescale cross-correlations in both positive and negative directions. A, Stacked CCGs with statistically significantly nonzero DCE (either positive or negative) from the full dataset. Left, Top is an example CCG from a pair of neurons showing a peaky (positive correlation) CCG in nonREM; bottom is a CCG from a pair with CCG dominated by a trough (anticorrelation). Right, Stacked CCGs in wake and REM states are sorted by the same DCE in nonREM ranking (horizontal lines continue to represent the same pairs) but show lower amplitude peak/trough for the same pair of neurons. Extended Data Figure 3-1 shows a similar display but including all pairs from this recording (not only those with significant peak/trough). B, DCE variation with the same pairs over states. Only pairs with nonzero DCEs in all three states are included. The mean of the absolute value of DCE in nonREM is significantly larger than wake (p = 0.005) and REM (p = 0.009), but DCE in wake is not larger than REM (p = 0.97; Tukey–Kramer). C, Quantifying state-wise effects via proportion of pairs showing significant correlation patterns. The statistics of trough and peak percentage of all neuron pairs averaged across all our animals. Gray lines indicate connections between percentage values for individual recordings. D, Example neuron pairs demonstrating greater troughs in nonREM. Extended Data Figure 3-2 shows stacked CCGs sorted by different sleep states: same data as 3–1, but sorting order is changed. Extended Data Figure 3-3 shows cross-state comparisons of CCGs of neurons shown in one recording. Extended Data Figure 3-4 shows CCGs of neurons with significantly nonzero DCEs in both wake and nonREM in one recording. Extended Data Figure 3-5 shows downsampled versions of all pairs in the recording to compensate for spike rate differences. Our observation of peaks and troughs in nonREM being stronger remains, indicating lack of evidence for a differential sampling effect.
- Figure 4.
The amplitude of cross-correlations is positively correlated with power of low-frequency oscillations and negatively correlated with power of high-frequency oscillations. A, Relation between the absolute value of DCE and normalized LFP power within nonREM sleep—in two example frequency bands (left and right). Shown are density plots of population DCE versus LFP power in each 3 h of all recordings within our dataset. Density plots are used instead of standard x–y scatterplots to better show relative densities of many very dense points. The recordings are divided into epochs of 3 h. DCEs are calculated for all pairs with negative DCE during nonREM found within each 3 h epoch. The corresponding LFP power during those epochs are calculated and they are normalized over the time axis within each recording, to compare between recordings. The examples shown are data for the 3.5–4.3 Hz (left) and 49–60 Hz (right) frequency bands. At 3.5–4.3 Hz, the Spearman correlation coefficient R = 0.11 (p = 7.1 × 10−15), and at 49–60 Hz R = −0.06 (p = 9.6 × 10−5). See red lines of best linear fit. Full spectrum density plots are shown in Extended Data Figure 4-2. B, Relation between the R value calculated based on the process shown in A for each of many frequency bands. Significant R values are denoted with red asterisks (p < 0.05).
- Figure 5.
Spiking details across neurons within each UP state play a role in forming anticorrelations. A, Diagrams of testing methods to determine the role of UP state spikes in nonREM cross-correlations. Top, “UP” analysis: CCGs are calculated for each neuron pair within each UP state, but not within DOWN states or any non-UP state epoch of nonREM. CCGs are then summed over all the UP states within a recording. Bottom, “UPnext-only” analysis: CCGs are calculated between the spike train of one neuron from UP state N and the spike train of a second neuron from UP state N + 1 (next UP state). Again, CCGs are then summed over all the UP states. As shown in Figure 1C, we know that neurons have typical lags in their firing relative to UP states, but we know less about the importance of any inter-UP state variation in that typical lag. These analyses test the importance of the simultaneous dynamics within each UP state across neurons. B, Comparison of the stacked CCGs between different analyses. At left are the raw nonREM CCGs showing both significant peaks (top) and troughs (bottom). The center shows the UP analysis: CCG patterns are similar to nonREM state, despite the exclusion of any spikes during DOWN states or non-UP state times. The UP states here are trimmed to compare with the scrambled UP states (see Materials and Methods). This indicates that UP state spiking dynamics themselves can create both positive and negative CCGs. However, in the “UPnext-only” analysis, the nonREM CCG patterns are destroyed, indicating that details of simultaneous spiking between pairs of neurons in simultaneous UP states are needed for negative cross-correlations. See Extended Data Figure 5-1 for all pairs, rather than only significantly correlated/anticorrelated pairs. C, DCE Pairwise comparison between UP states and the corresponding scrambled UP states (“UPnext-only”). i, Only negative DCEs in UP states are selected. The corresponding DCEs in “UPnext-only” states are non-negative and significantly different (p = 1.03 × 10−21). ii, Only positive DCEs in UP states are selected. DCEs in “UPnext-only” states are non-negative and significantly smaller (p < 5 × 10−324) with a mean reduction of 23%.
- Figure 6.
Dissecting within-UP state interactions that influence anticorrelation: Role of differences in in UP state-based spiking lag between pairs of neurons. A, Diagram of comparisons used. Top, Difference of first spike time between pairs of neurons, calculated in each UP state. Bottom, Difference of mean spike time between pairs in each UP state are also calculated. B, Quantification of comparisons used: The differences calculated in A are collected across all UP states for each pair of neurons. Results for one pair is shown. The mean and the standard deviation (SD) can be calculated for each neuron pair for each metric in A. C, Comparison of the described metrics between all the pairs with negative DCE (trough) and positive DCE (peak) in the full dataset. The SD of difference of first spike time per UP state is higher for pairs in trough than in peak (p = 5.8 × 10−6). The mean of the difference of mean spike time mean is higher for pairs with troughs (p = 1.6 × 10−9), as is the SD of the difference of mean spike times higher for pairs in trough (p = 9.2 × 10−13). Thus, standard deviations of timing differences are consistently higher in trough pairs than peak pairs, indicating that variable timing may lead to toughs.
- Figure 7.
Removal of burst spikes decreases anticorrelations between pairs of neurons in nonREM sleep. A, Examples of ISI histograms in log timescale from two single neurons. Many neurons display bimodal distribution in log timescale as shown here. We defined the burst spikes as the spikes with ISI less than the set threshold (see Materials and Methods). B, DCEs are recalculated after removing burst spikes (right) or after removing the same amount of spikes in random fashion (middle). Only pairs with negative DCE originally are shown. Burst spike removal renders significantly lower amplitude anticorrelations (less negative DCE) than the original spike trains (p = 9.6 × 10−10) and random spikes removal (p = 5.6 × 10−3). Random removed pairs have significantly lower amplitude negative DCE than the original pairs (p = 9.6 × 10−10). C, Temporal properties of spike trains resulting from burst removal versus random removal. We found that burst removal mainly affected difference of first spike time mean (p = 5.1 × 10−12) and SD (2.4 × 10−10), but not the difference of mean spike time (mean p = 0.62, SD p = 0.09). D, We removed burst spikes in different ways to examine differential effects. Burst spikes were removed either by changing interspike interval used as the burst threshold (middle panel) or removing a numerically equivalent number of spikes but doing so by setting a percentage of burst spikes to remove in a random fashion equivalent the set threshold shown in Figure 6A (right panel). We progressively removed more spikes to uncover any progressive “dose effects.” The number of spikes removed in the left and right panel are equivalent to the number removed by moving the burst threshold (middle panel). DCE relative to real DCE (see Materials and Methods) is calculated so that the lower the value, the greater the effect of removing spikes on reducing the anticorrelation. The results from one of the representative datasets are shown here. E, Collecting the mean and the slope of the DCE relative to real DCE from the full dataset, we found no significant difference between burst removal by threshold and burst removal by percentage (mean p = 0.1; slope p = 0.3). But they are both significantly lower than random spike removal. (random vs burst removal by threshold: mean p = 9.6 × 10−10; slope p = 9.6 × 10−10; random vs burst removal by percentage: mean p = 1.6 × 10−9; slope p = 2.1 × 10−9).
Tables
Rat's codename Recording duration (h) # of units # of excitatory units # of inhibitory units # of pairs # of significantly correlated pairs # of significantly anticorrelated pairs # of nonREM epochs # of wake epochs # of REM epochs ‘BWRat20_101513' 31.9 59 54 5 1,711 56 7 303 385 133 ‘Bogey_012915' 29.8 64 61 3 2,016 133 46 321 415 158 ‘Dino_080114' 30.6 71 62 9 2,485 226 24 314 390 124 ‘J3_180421' 24.4 101 71 30 5,050 185 98 391 443 122 ‘Splinter_021015' 23.6 55 13 42 1,485 199 122 327 388 167 ‘c3po_160208' 24.0 57 44 13 1,596 328 70 327 365 136 - Table 2.
The statistics of trough and peak percentage of all neuron pairs averaged across all our animals
Trough % Peak % nonREM Wake REM nonREM Wake REM 3.6 ± 3.4 1.5 ± 1.8 0.2 ± 0.2 10.8 ± 6.3 2.0 ± 1.6 0.7 ± 0.7
Extended Data
Download Extended Data, ZIP file.
Figure 3-1
CCG Pairwise comparison between sleep states from all recordings.
(A) Pairwise comparison between nonREM and wake on all the pairs in the dataset that have nonzero values in these two states (P = 2.58 × 10−36).
(B) Pairwise comparison between nonREM and REM on all the pairs in the dataset that have nonzero values in these two states (P = 2.01 × 10−14).
(C) Pairwise comparison between wake and REM on all the pairs in the dataset that have nonzero values in these two states (P = 0.5).
(D) Stacked CCGs from full dataset. Each stack is sorted by its own middle amplitudes.
Download Figure 3-1, TIF file.
Figure 3-2
Stacked CCGs between sleep states from all recordings sorted by different sleep states.
(A) All the Stacked CCGs are sorted by nonREM.
(B) All the Stacked CCGs are sorted by wake.
(C) All the Stacked CCGs are sorted by REM.
Download Figure 3-2, TIF file.
Figure 3-3
Comparison of CCG samples between states in one recording. CCGs with their DCEs shown in Figure 3B are displayed here. The CCGs are sorted by the DCEs in nonREM. Each column of three CCGs is from one neuron pair. The red dot-lines in the top left panels denote the width of trough in Wake. CCGs were Gaussian smoothed at width 10 ms. Download Figure 3-3, TIF file.
Figure 3-4
Comparison of CCG between nonREM and Wake in example pairs. All the pairs with nonzero DCE in both nonREM and Wake in one recording are compared. Each column of two CCGs is from one neuron pair. The CCGs are sorted by the DCEs in nonREM. CCGs were Gaussian smoothed at width 10 ms. Download Figure 3-4, TIF file.
Figure 3-5
Downsampled CCG Pairwise comparison between sleep states from all recordings.
(A) Stacked and downsampled CCGs across sleep/wake states from full dataset to demonstrate the range of correlation structures. Each stack is sorted by nonREM CCGs’ middle amplitudes. All CCGs are shown including zero and nonzero DCE.
(B) Comparison between nonREM, wake, and REM on all the pairs in the dataset that have nonzero values in all three states (One-way ANOVA P = 3.17 × 10−11; nonREM VS wake P = 1.83 × 10−9; nonREM VS REM P = 1.13 × 10−9; REM VS wake P = 0.74).
(C) Pairwise comparison between nonREM and wake in all the pairs in the dataset that have nonzero values in these two states (P = 6.25 × 10−12).
(D) Pairwise comparison between nonREM and REM in all the pairs in the dataset that have nonzero values in these two states (P = 7.31 × 10−19).
(E) Pairwise comparison between wake and REM in all the pairs in the dataset that have nonzero values in these two states (P = 0.1).
Download Figure 3-5, TIF file.
Figure 4-1
Strengths of pairwise correlations across the population are coordinated over time.
(A) Recordings are divided into epochs of three hours. The twenty neurons that are the least synchronized with other neurons (neurons that have the most negative DCE counts during nonREM) are selected for this display. Their DCEs during nonREM at those three-hour epochs are then calculated and shown as the matrix elements. Color scale shows DCE value with each value in the matrix representing the DCE of one neuron pair. Note overall similarity of DCE matrix over multiple hours of recording.
(B) At left, time courses of DCE for fifty example pairs with the most negative DCEs during nonREM. At right, standard deviations respectively were calculated for each pair and were shown sorted by its DCE value during nonREM epoch.
(C) Comparison between the mean std from the original matrix and matrices where values within each three hours are shuffled (Z-test, P = 1.4 × 10−168). The std of the real data is much less than the shuffled, showing the conservation of the correlation structure over time.
(D) Correlation between pairs over time. As one pair of neurons becomes more strongly correlated, do others at the same time? The amplitude of DCE between pairs tends to be positively correlated from one timepoint to the next.
(i) The absolute values of the time courses of DCE for the twenty neurons’ pairs are first taken. The Pearson correlations between the resultant time courses for each pair are then calculated. Only significant correlations are counted (P < 0.05). The absolute values of the correlation coefficient R are taken and the distribution of the negative Rs and positive Rs are shown. Generally, we see many more counts of significant positive correlations than negative correlations.
(ii) Similar approach to (i), but without taking the absolute values of the time courses of DCE. Note the lower amplitude red line in (i), showing that most of the negative Rs are contributed by larger positive DCEs coinciding with smaller negative DCEs.
Download Figure 4-1, TIF file.
Figure 4-2
Full data for Figure 4. Separating three-hour epochs with positive DCE from negative DCE and analyze them independently yields consistent result
(A) Density plots of mean LFP power versus the absolute values of DCE in each frequency band shown in Figure 4. For density plots with statistically significant R (P < 0.05), the best linear fits are drawn as red lines.
(B) Grouping three-hour epochs with positive DCE and find the R values of mean LFP power versus DCE for each of many frequency bands. Relation between the R values and frequency bands are shown. Significant R values are denoted with red asterisks (P < 0.05).
(C) Similar approach to (B) but for epochs with negative DCE.
Download Figure 4-2, TIF file.
Figure 4-3
Alternative analysis to verify the correlation between band power and DCE in nonREM states.
(A) Pearson Correlation between the LFP power and the DCEs calculated in an alternative way. Given a frequency band, each nonREM epoch is ranked into one of four power quartiles and the CCGs are generated for each pair. Correlation between the power and the DCEs calculated from the CCGs in that frequency band can then be calculated. Significant R values are denoted with red asterisks (P < 0.05). Qualitatively similar overall findings to figure 4B, despite different methodology.
(B) Raw data underlying plot in (A). For density plots with statistically significant R (P < 0.05), the best linear fits are drawn in red lines.
Download Figure 4-3, TIF file.
Figure 4-4
NonREM epoch duration is positively correlated with delta power and negatively correlated with gamma power.
(A) We initially found duration of epoch correlates with delta power and negatively correlates with gamma power (similar to 4-4B, but not shown), but to prevent contamination and overly strong findings by ramp-up and ramp-down dynamics, we analyzed only plateaus of each epoch using the following analysis. We found putative contamination of findings by the fact that regardless of epoch duration,timecourse of delta power (i) in the first 200 secs and (ii) in the last 100secs of each nonREM epoch (>200 secs) did not vary. This leads to short duration epochs having low delta and high gamma values not representative of their plateau value, potentially falsely over-driving correlations. Gamma powers are shown in (iii) and (iv). Each power trace is shown as a grey line. Mean values are shown in red lines and standard deviation are denoted by light red area.
(B) After correction: pearson correlation between the duration of nonREM epochs (>200 secs) and the mean LFP power in each frequency band. Band power in the first 120 secs and last 50 secs are removed when averaging. Significant R values are denoted with red asterisks (P < 0.05).
(C) Raw data underlying plot in (B). For density plots with statistically significant R (P < 0.05), the best linear fits are drawn in red lines.
Download Figure 4-4, TIF file.
Figure 5-1
Complete comparison of the stacked CCGs in nonREM, UP-only, and “UPnext-only” states from all dataset (not restricted to significant pairs). Each stack is sorted by nonREM CCGs’ middle amplitudes. All CCGs are shown including zero and nonzero DCE. Results are consistent with significant-only pairs. Download Figure 5-1, TIF file.
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