Figure 1.
Steps in functional connectivity analysis of multi-electrode array data.
Steps 1–3 and step 5 are based on recommendations from Bullmore & Sporns (Nature Reviews Neuroscience, 2009). Steps 4, 6 and 7 refer to techniques specific to analysis of culture activity recorded from multi-electrode arrays (MEAs, example pictured top right). The 8×8 grid indicates the recording area of the MEA (inset: close-up of two electrodes with visible neurons in their vicinity).
Table 1.
Topological & non-topological network properties for the present study (part 1).
Table 2.
Topological and non-topological network properties for the present study (part 2).
Figure 2.
Basic topological properties of the persistent networks as a function of culture age.
Number of nodes, links and edge density; calculated for 10 cultures at each age (DIV). Left: mean number of nodes and links found in the persistent networks. Note, although the number of nodes is a very different magnitude from the number of links, number of nodes was not found to change significantly (P = 0.272). Results for numbers of links at each age suggested an increase between younger (DIV 14 and DIV 21) and older (DIV 28 and 35) ages, however the increase was not significant (P = 0.074). Right: mean edge density of the persistent networks. Edge density (i.e. link density) quantifies the ‘cost’ of the network in terms of the number of links (m)/the maximum possible number of links ((n*(n−1)), given the number of nodes (n). Edge density was first calculated for each culture and then averaged over all cultures. Mean edge density at DIVs 21 to 35 was significantly higher than at DIV 14 (P = 0.012). In cases where no links were found the data were excluded from the analysis. All statistics quoted are for the n = 5–8 cultures valid for complex network analysis. Error bars represent ± standard error of mean (s.e.m, n = 5 to 8).
Figure 3.
Complex topological properties of the persistent networks as a function of culture age.
Mean path length, clustering coefficient and conservative small-worldness; averages (n = 5–6), were normalized as follows: mean path length (L) and clustering coefficient (C) were normalized against the expected value from an equivalent population of random networks (n = 50) with the same number of nodes and links. Small worldness was calculated conservatively as (Creal/Clattice)/(Lreal/Lrand). Error bars represent ± s.e.m. The average shortest path length and clustering coefficient at DIV 14 were both close to the value expected for a random network. A statistically significant increase in the clustering coefficient was found between DIV 14 and DIV 28. The combination of a short mean path length and high clustering at DIVs 28 and 35 lead to a network classified as ‘small-world’.
Figure 4.
Change in the node degree distribution with culture development.
Node degree distributions, obtained from all the nodes of the persistent networks of all cultures using a bin size of 10%. Panel A: bar graphs represent node degree distributions on a linear scale. Solid lines show the best fitting model at each age, broken lines represent 95th percent confidence interval. Top left: DIV 14, bottom left: DIV 21, top right DIV 28, bottom right: DIV 35. DIVs 14 and 21 show exponential fit on a linear scale, DIVs 28 and 35 show power law fit on a linear scale. Panel B: scatter plots represent node degree distributions on a log-log scale, DIVs 28 and 35 are shown with a linear fit. The fat tailed node degree distribution found at DIVs 28 and 35 is indicative of nodes with a high degree (hubs).
Figure 5.
Change in the link lengths with culture development.
Panel A: Each bar represents the median proportion of links between nodes up to (and including) two electrodes apart (classified as ‘nearby’) and links between nodes greater than two electrodes apart (classified as ‘distant’), diagonal neighbors were included; values were calculated from all cultures at each age. Upwards error bars represent the 75th percentile and downwards bars the 25th percentile. Notably, at DIV 14 there was a significantly higher number of connections between distant nodes. Panel B: Normalized histograms of link lengths at each culture age, constructed from the link lengths of all cultures, measured as the proportion of each culture's links at each length. Median values from all cultures were used for each bin in the histogram. Bin size was based on spacing between electrodes of MEA, with one bin for each electrode distance (i.e. bin 1 is all links between neighboring electrodes - including diagonal neighbors, bin 2 is all links between nodes up to two electrodes distance, and so forth until seven electrodes distance which is the maximum between any two nodes on the MEA). Bin edges (X-axis) specify the start of each bin, measured as the distance between electrodes on the MEA (micrometers). Y-axis is the same for all histograms in panel, only DIV 14 Y-axis is labeled to avoid overcrowding.
Figure 6.
The persistent network of a representative culture at DIV 14, 21, 28 and 35.
Graphs illustrate the spatial organization of network components at each culture age: the 8 by 8 grid corresponds to positions of the electrodes on the multi-electrode array (MEA). Nodes that are part of the network (i.e. for which a link was identified) are numbered according to their MEA hardware numbers, and the lines between electrodes represent un-directed links between nodes. Panel A: graphs from the networks thresholded at 25% link persistence. Panel B: graphs from the networks thresholded at 15% link persistence, this lower threshold results in more nodes and links.
Figure 7.
Visualization of hubs in a representative culture at DIVs 28 and 35.
Graphs illustrate the location of hubs in the persistent network of a representative culture at two separate ages. The 8 by 8 grid corresponds to positions of the electrodes on the multi-electrode array (MEA). Nodes that are part of the network (i.e. for which a link was identified) are numbered according to their MEA hardware numbers, and the lines between electrodes represent un-directed links between nodes. At DIV 28 (left hand graph), nodes 4 and 38 were classified as hubs in the network, whilst at DIV 35 (right hand graph), nodes 34, 38, 40, 48, 49 and 53 were hubs. Hubs were classified as nodes having a high degree (degree greater than mean node degree plus one standard deviation) and are highlighted with blue circles.
Figure 8.
Basic topological properties of the transient networks as a function of culture age.
Panels A, B: mean number of links and nodes (respectively) in transient networks, averaged over all cultures at a particular age (solid black lines). Error bars represent ± s.e.m. The mean numbers of links at each culture age suggested an increasing trend in the number of links between DIVs 14 and 28, however the trend was not significant (P = 0.087). Likewise the mean numbers of nodes suggested an increasing trend (P = 0.089). The mean numbers of persistent network links and nodes are shown for reference (dotted red lines). Panels C, D: expected coefficient of variation for the numbers of links and nodes (respectively) in each culture's set of transient networks. Error bars represent ± s.e.m. Coefficient of variation for number of links was significantly higher at DIV 21 than DIV 14 (P = 0.021).
Figure 9.
Network-wide burst propagation time as a function of culture age.
Bar chart shows the median burst propagation time (from all transient networks of all cultures at each age), values outside the 5th to 95th percentiles were removed as outliers, giving n = 6–8 for each age). Error bars show 25th and 75th percentiles. A (network-wide) burst was defined as a near-simultaneous (within 250 ms) occurrence of channel bursts on multiple (≥4) channels. A channel was considered to display bursting activity if ≥4 spikes were detected in 100 ms. For each channel included in the burst, recruitment time was the timestamp of the first spike in the ≥4 spikes in 100 ms sequence. Burst propagation time was calculated as the time to recruit all channels in a network-wide burst. At DIVs 28 and 35, this time was significantly lower than at DIV 14.
Figure 10.
An increase in the number of links with high persistence as cultures aged.
Each histogram shows the percentage of links found at each link persistence level for all cultures at each age (normalized count of links found at the persistence value, expressed as the percentage of transient networks (bursts) in which the link was found, bin size 5%, bin edges specify the end of each bin). Top left: DIV 14, bottom left: DIV 21, top right: DIV 28, bottom right: DIV 35. Red (solid) line is the link persistence threshold (link presence in at least 25% of the transient networks). The histograms are cropped to show the detailed distribution, inset histograms show the full scale. At DIV 21, many links were found infrequently (i.e. below the link persistence threshold). The more pronounced tail of the distribution as the cultures matured, reflected a significantly higher contribution of persistent links in the network's of mature cultures.