Developing neuronal networks: Self-organized criticality predicts the future
Jiangbo Pu1,2, Hui Gong1,2, Xiangning Li1,2 & Qingming Luo1,2*
Britton Chance Center for Biomedical Photonics, Wuhan National Lab for Optoelectronics - Huazhong
University of Science and Technology, Wuhan 430074, China
1
MoE Key Laboratory for Biomedical Photonics, Department of Biomedical Engineering, Huazhong
University of Science and Technology, Wuhan 430074, China
2
*Corresponding author
SUPPLEMENTARY FIGURES AND LEGENDS
Supplementary Figure 1 | Cultured hippocampal networks on 8 × 8 multi-electrode array. a, The
electrode layout (inter-electrode distance: 200 m; electrode diameter: 30 m) and sample electrical
recordings from selected electrodes (indicated by different colors). Electrodes in the 8 × 8 grid are
labeled by column and row number. b, Phase contrast micrograph of central area (indicated by the dotted
box in (a)) of a typical hippocampal culture at 10 days in vitro.
Supplementary Figure 2 | The diversity of firing patterns of cultured neuronal networks during
development. The upper panel of each subplot shows spontaneous array-wide spike detection rates per
second in recordings from one culture at different ages (labeled in top right corner). The spike detection
rate of individual electrodes is showed in grayscale raster plots (one electrode per row). The colorbar
indicates firing rates per second. Data are available online.
Supplementary Figure 3 | Development of functional connectivity at different developmental
stages. a, The organization of network states at different ages (labeled in bottom right corner). Note the
distribution of data points becomes denser (more overlapped) in the middle stages. b, Weighted graphs
for developing network at various ages (labeled below). The colorbar and thickness of individual links
indicate the strength of connection (computed by mutual information). The size of dots indicates degree
of each node (electrode). The dotted boxes indicate hub nodes with high degree and betweenness
centrality.
Supplementary Figure 4 | Correlated changes in network topology parameters and activity
dynamics during network development. Similarity in spatiotemporal activity patterns is reflected by
the tightness of the clusters during development. Propagation of activity is reflected by branching
parameter. Degree distribution correlation of the network is reflected by assortativity coefficient. Please
note the anti-correlated tendency between cluster tightness and assortativity coefficient and the
correlated tendency between assortativity and branching parameter. (Values are expressed in mean ±
S.D., Data were calculated from all networks with clear U-shape trajectories and normalized.)
Supplementary Figure 5 | Hierarchical clustering of active electrodes involved in each state reveals
the existence of different neural ensembles. Each colored frame indicates the electrode which is active
at the state, and electrode numbers were labeled below. The result of hierarchical clustering is shown in
the above panel. Note there is a core population which is activated at most stages, whereas other
assemblies are only activated at one or a few specific stage(s).
Supplementary Figure 6 | Examples of networks with / without developmental trajectory. a,
Profound sequential transient dynamics can be identified in developing hippocampal networks which
operate in the vicinity of a critical state. The arrow indicates the direction of sequential state transitions
during development. b, Reversible transitions (left panel) and irregular changing firing patterns (right
panel) are showed in networks operating at subcritical regime. Please note that some data points were
covered by other points, all the plots were generated using the data from the entire development process.
Supplementary Figure 7 | A repertoire of developmental trajectories. a, Cultures with clear “Ushape” trajectories (17 of 23). All trajectories in the PC space were normalized to [0,1] and overlaid
together to show a common trend. The arrow indicates the direction of sequential state transitions during
development. b, Cultures without clear “U-shape” trajectories (6 of 23).
Supplementary Figure 8 | Different distribution of dots in the PC space (With vs. Without clear
trajectory). a, Overlapping area of the successive developmental stages in the PC space. b, The
coefficient of variation of the distributed dots in each developmental stage. N = 1994. Results were
showed in Mean ± S.E.M., asterisk indicates paired t-test, p = 0.00081 (in a), p = 0.00077 (in b).
Supplementary Figure 9 | Hierarchical clustering of active electrodes involved in each state (With
vs. Without clear trajectory). Each black frame indicates the electrode which is active at the state. a,
Cultures with clear “U-shape” trajectories. b, Cultures without clear trajectories. Please note that the
“core” populations are more easily to be identified and more “stabled” in cultures with U-shape
trajectories (a).
Supplementary Figure 10 | Additional examples showing that disturbing the excitation-inhibition
balance could alter the developmental trajectory. In the PC space, the inherent developmental
sequence is shown by the grayscale trajectory (black to white) and the recovering track left by firing
patterns after washing out drugs is indicated by colorized dots (light yellow to dark red). The green dots
indicate the original firing patterns before the drug was applied. Total recorded life span of the cultured
network in a-c: 133 DIV, Experiment Day: APV: 39 DIV; BIC: 42 DIV, OCT: 65 DIV. Total recorded
life span of the cultured network in d-f: 147 DIV, Experiment Day: APV: 57 DIV; BIC: 71 DIV, OCT:
52 DIV. (DIV: days in vitro)