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

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

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

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

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

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

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

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

Physical distance between connected neurons increased with time scale and hubs were closely spaced.

<p>(<b>A</b>) The mean physical connection distance was calculated as the ratio of the mean physical distance between effectively connected neurons in the network to the mean physical distance between all possible pairs of neurons in the sub-network. Cortical networks were found to be significantly larger for several time scales. (<b>B</b>) The mean physical distance between hubs was calculated as the ratio of the mean physical distance between hubs (connected or not connected) to the mean physical distance between all possible pairs of neurons in the sub-network. No significant differences between hippocampal and cortical networks were observed. (<b>C and D</b>) The hubs were significantly more closely spaced than the average connected pair. 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>E and F</b>) Multiple comparisons corrected Mann-Whitney Test p-values between different time scales for the same tissue type for connection distances (E) and hub distances (F). Note that cortical and hippocampal network connections tend to be significantly longer in time scales 3 to 10 in comparison to time scales 1 and 2. Also, note that hub distances generally increase with time scale.</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