A small and consistent percentage of neurons were found to be hubs.

<p>(<b>A</b>) Most data sets exhibited a small, but significant number of hubs across all time scales. Note that the likelihood for a randomly connected neuron to be found to be a hub was set at 10⁻⁴ (see <i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115764#s4" target="_blank">Materials and Methods</a></i>), so these results indicate a roughly two order of magnitude increase in the number of hubs over a random network. Box plots: minimum, 25^th percentile, median, 75^th percentile, maximum data set (recording). No significant differences were found between hippocampal and cortical networks. (<b>B</b>) Multiple comparison corrected Mann-Whitney Test p-values between different time scales for the same tissue type. The number of hubs generally increased with time scale.</p

Time scales.

<p>As the time scale increased, the bin sizes logarithmically increased. The overall state structure with regards to the bins was identical for time scales 2 through 10. Time scale 1 possessed a delay of 0 (d = 0) in order to capture interactions at the smallest resolution of the recordings (0.05 ms).</p><p>Time scales.</p

Binning structure for short time scales on example spike trains.

<p>Note that the time scales overlapped to some degree to capture interactions with all delays and that time scales greater than 1 possessed delays to prevent short time scale interactions from influencing long time scale measurements.</p

Network assortativity decreased with time scale.

<p>(<b>A</b>) Network assortativity generally decreased (disassortativity generally increased) with time scale. Note the significantly higher assortativity for cortical networks at time scale 1 (interaction delays of 0.05 ms to 3 ms), and that the networks were generally disassortative. Box plots: minimum, 25^th percentile, median, 75^th percentile, maximum data set (recording). Differences between hippocampal and cortical networks were assessed with a multiple comparisons corrected Mann-Whitney Test (one dot: p<0.05, two dots: p<0.01, three dots: p<0.001). (<b>B</b>) Multiple comparisons corrected Mann-Whitney Test p-values across different time scales for identical tissue types. Note that the decreasing behavior in (A) was generally significant.</p

Connectivity statistics.

<p>(<b>A</b>) TE p-value histogram for real and randomized data. Real data show many more pairs of neurons with low p-values compared to randomized data. In this analysis, the p-value threshold was set at less than 0.001. The extrema correspond to the time scale with the largest or smallest percentage value for a given p-value. (<b>B</b>) Number of found connections. The number of connections found in each network was at least 4 times larger than expected by chance, with most networks containing 10 to 100 times more connections than expected by chance. (<b>C</b>) Effective N values. The effective N for each network is the number of connected nodes in the network. The mean ± STD in the original data (sub-networks) was 241±103 (42±7) for cortical networks and 128±54 (42±7) for hippocampal networks. (<b>D</b>) Effective k values. The effective k for each network is the average number of connections (degree) per neuron. The mean ± STD in the original data (sub-networks) was 22±30 (3.7±0.7) for cortical networks and 11±18 (3.7±0.8) for hippocampal networks. Note that the sub-network procedure significantly reduced the variability of the effective N and k values, as well as the differences in effective N and k between tissue types.</p

Analysis time scales and basic data properties.

<p>(<b>A</b>) Example spike raster from a cortical recording. (<b>B</b>) Firing rate histogram of neurons in all hippocampal and cortical recordings. (<b>C</b>) Histogram of the number of neurons in each recording. (<b>D</b>) The number of viable data sets or recordings. Data sets were deemed viable if they produced sub-networks with at least 50 neurons and a given average degree (k). We used sub-networks with k = 3 throughout the analysis. (<b>E</b>) Time resolutions for the 10 discrete time scales used in this analysis in comparison to the approximate time scales for various neurological phenomena and measurement methods. Note that some measurement methods (e.g. MEG and EEG (forms of electrophysiology), as well as fMRI) are not capable of recording the activity of individual neurons, unlike calcium imaging or cellular electrophysiology (as was used in this study). The analysis time scales were chosen to logarithmically span many neurological time scales and they allowed us to compare network structure on this wide range of time scales. Note that the analysis time scales overlap to ensure that all phenomena are adequately measured.</p

Long time scale connectivity was independent of short time scale connectivity.

<p>(<b>A</b>) Connectivity was most correlated at nearby time scales, but uncorrelated at distant time scales. Correlation was measured using all possible pairs of neurons where a connection (lack of connection) was assigned to 1 (0). (<b>B</b>) Chains of indirect connections at short time scales (time scale on vertical axes) were weakly correlated with direct long time scale connections (time scale on horizontal axes). Correlation was measured using all possible pairs of neurons where a connection or chain of indirect connections (lack of connection or chain) was assigned to 1 (0).</p

Hippocampal structures were preserved throughout culturing. Photographs of cortico-hippocampal organotypic cultures.

<p>(<b>A</b>) A bright field image of an example organotypic culture at DIV1. The hippocampal structure is visible without staining. Blue arrows indicate the location of the edge of the recording array. (<b>B</b>) NeuN staining of the culture after data taking and tissue fixation at DIV16. There are missing neurons in CA3 as consistent with a previous report <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115764#pone.0115764-Zimmer1" target="_blank">[111]</a>, but the overall layer structure is well conserved. (<b>C</b>) Overlaid photograph of A and B. Positions and dimensions of the hippocampal structures are well conserved during the incubation period. (<b>D</b>) Overlaid photograph of B, the outline of the array (yellow rectangle), and the estimated locations of the recorded neurons. Light blue circles are manually identified hippocampal neurons and red circles are neurons recorded outside the hippocampal structure. Locations of the recorded neurons match with the granule cell layer and the cell body layer. For complete details on culture preparation, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115764#pone.0115764-Ito2" target="_blank">[48]</a>.</p

Firing rate and degree were correlated.

<p>(<b>A</b>) Neuron firing rate and degree were correlated, especially for short time scales. Hippocampal networks showed higher correlations than cortical networks for middle and long time scales. Box plots: minimum, 25^th percentile, median, 75^th percentile, maximum data set (recording). Differences between hippocampal and cortical networks were assessed with a multiple comparisons corrected Mann-Whitney Test (one dot: p<0.05, two dots: p<0.01, three dots: p<0.001). (<b>B</b>) The correlation between firing rate and degree generally decreased with time scale. Multiple comparison corrected Mann-Whitney Test p-values between different time scales for the same tissue type. (<b>C</b>) Density plots of neuron degrees and firing rates in sub-networks. Note that the real data contain many high degree neurons and the stronger correlation between degree and firing rate for short time scales (top row) in comparison to longer time scales. Also, note that the null model data contained very few non-zero degree neurons. This lack of connectivity in the null model implies that high degrees for high firing rate neurons are not the result of false-positive connections. Vertical line is the approximate degree threshold for hub classification.</p

Hub sharing was limited to adjacent time scales.

<p>(<b>A</b>) We classified each neuron as a hub, non-hub, or unconnected neuron at each time scale. A neuron was considered to be a shared hub or shared non-hub for two time scales if its status as a hub or non-hub was consistent across those time scales. Hubs were defined using a degree threshold set by the likelihood to have a given number of connections in a random network (0.05 in this illustrative diagram and 10⁻⁴ in the full analysis). (<b>B</b>) We calculated the amount of hub and non-hub sharing (see <i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115764#s4" target="_blank">Materials and Methods</a></i>) for each pair of time scales and grouped the results into neighboring (4 or less) and distant (greater than 4) time scales. <i><u>We found that hubs were only shared at a significant level for neighboring time scales, while non-hubs were broadly shared across all time scales</u></i> (multiple comparisons correct Mann-Whitney Test (1, 2, and 3 dots: p<0.05, 0.01, and 0.001 respectively), error bar: standard error of the mean). For each data set, we subtracted the mean sharing values for 500 trials with neuron identities randomized and neuron hub, non-hub, or unconnected status held constant. This null model approximates the amount of sharing expected based only on the number of hubs, non-hubs, and unconnected neurons in the data set, as well as the effect of ignoring the multiplex properties of the networks and considering the time scales to be truly independent networks. We also calculated the mean sharing value of (<b>C</b>) hubs and (<b>E</b>) non-hubs across each pair of time scales for cortical and hippocampal networks. In (B), neighboring time scale pairs are up and to the left of the white line, while distant time scale pairs are down and to the right of the white line. (<b>D and F</b>) Finally, we calculated the multiple comparisons corrected Mann-Whitney Test p-values between sharing results from data and sharing results from the null model.</p