Development of neural population activity toward self-organized criticality

Abstract

Self-organized criticality (SoC), a spontaneous dynamic state established and maintained in networks of moderate complexity, is a universal characteristic of neural systems. Such systems produce cascades of spontaneous activity that are typically characterized by power-law distributions and rich, stable spatiotemporal patterns (i.e., neuronal avalanches). Since the dynamics of the critical state confer advantages in information processing within neuronal networks, it is of great interest to determine how criticality emerges during development. One possible mechanism is developmental, and includes axonal elongation during synaptogenesis and subsequent synaptic pruning in combination with the maturation of GABAergic inhibition (i.e., the integration then fragmentation process). Because experimental evidence for this mechanism remains inconclusive, we studied the developmental variation of neuronal avalanches in dissociated cortical neurons using high-density complementary metal-oxide semiconductor (CMOS) microelectrode arrays (MEAs). The spontaneous activities of nine cultures were monitored using CMOS MEAs from 4 to 30days in vitro (DIV) at single-cell spatial resolution. While cells were immature, cultures demonstrated random-like patterns of activity and an exponential avalanche size distribution; this distribution was followed by a bimodal distribution, and finally a power-law-like distribution. The bimodal distribution was associated with a large-scale avalanche with a homogeneous spatiotemporal pattern, while the subsequent power-law distribution was associated with diverse patterns. These results suggest that the SoC emerges through a two-step process: the integration process accompanying the characteristic large-scale avalanche and the fragmentation process associated with diverse middle-size avalanches.

Keywords: dissociated culture; microelectrode array; neuronal avalanche; self-organized criticality.

Fig. 1. Schematic illustration of possible models of development.

(A and B) illustrate variation of network structures. (C and D) show variation of avalanche size distributions corresponding to (A and B), respectively.

Fig. 2. Spontaneous activity of dissociated cortical cultures at different developmental stages.

(A–C) show spatial maps of action potential amplitude obtained using high-density complementary metal-oxide semiconductor microelectrode arrays (CMOS MEAs). CMOS MEAs from the same culture at 4 days in vitro (DIV) (A), 7 DIV (B), and 16 DIV (C). Black (and green) circles indicate designated recording sites. (D–F) show examples of mean spike waveforms (red lines) detected at the green circles in (A–C), respectively. The gray lines depict all traces of spike waveforms. Raster plots of 120 s of spontaneous spiking activity out of 30 min of recorded data are shown in G–I. Activities were recorded from the same dissociated cortical culture shown in (A–C) at 4 DIV (G), 7 DIV (H), and 16 DIV (I). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Avalanche size distributions obtained from the culture shown in Fig. 2.

This figure shows data from 4 DIV (A), 7 DIV (B), and 16 DIV (C), respectively. The red lines represent power-law distribution fitted to the empirical distributions, where the parameters were estimated by maximum likelihood estimation (MLE). The blue lines are fitted exponential distribution estimated by MLE (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

Fig. 4. Avalanche size distributions in different configurations.

(A) shows avalanche size distributions from the same culture at the same DIV (i.e., 16 DIV) shown in Fig. 3C for different number of electrodes and (B) shows the avalanche size distributions for different sizes of the time bin.

Fig. 5. The developmental variation of avalanche distribution features over time.

A–G illustrate the developmental variation of arraywide firing rates (A), the Kolmogorov–Smirnov (KS) statistic for power-law distribution where size 1 avalanches were excluded (B), the KS statistic for exponential distribution (C), G values (D), the ratio of expR² to powerR² (E), the maximum avalanche sizes (F), and the alpha exponent (G), respectively. Plotted points of the same color indicate features from the same culture on a different DIV. Black lines indicate a moving average (A, G: mean; B, C, D, E, F: median) and gray shades indicate errors (A, G: SD; B, C, D, E, F: first and third quartiles) for each feature, including the day before and after. H–J show comparison of avalanche distribution features (for B–D, respectively) between developmental periods (4–6 DIV, 7–10 DIV and 11–30 DIV). *p < 0.05, **p < 0.01, ***p < 0.001; Mann–Whitney U-test.

Fig. 6. Poisson-like spiking activity in cortical cultures with synaptic blockers.

(A) illustrates a raster plot of spontaneous activity in a culture supplemented with CNQX/AP5 and bicuculline. (B) shows the avalanche size distribution of a culture supplemented with synaptic blockers. (C and D) illustrate the KS statistics for exponential distribution (C) and Fano factors (D) from cultures at 4–6 DIV, cultures older than 6 DIV, and from cultures supplemented with synaptic blockers. The horizontal dashed line in D indicates a point where the Fano factor equals one. **p < 0.01, ***p < 0.001; Mann–Whitney U-test.

Fig. 7

The changing proportion of avalanche distribution over time. This figure displays the proportion of each avalanche distribution type occurring at a specific time point. The details for distribution type classification are described in the Experimental Procedures. The proportions of each day include the day before and after.

Fig. 8. Developmental variations in spatiotemporal patterns.

(A–C) displays the correlation matrices for spatiotemporal patterns in large avalanches, i.e., synchronized bursts. Each matrix was obtained from a culture at 7 DIV (A), 16 DIV (B), and 23 DIV (C), respectively. (D) illustrates the mean correlation and standard deviation of spatiotemporal pattern correlations calculated from five cultures that exhibited high G value (G > 0.39 = 0.13 x 3) during 7–8 DIV.