Critical Spatial-Temporal Dynamics and Prominent Shape Collapse of Calcium Waves Observed in Human hNT Astrocytes in Vitro

Abstract

Networks of neurons are typically studied in the field of Criticality. However, the study of astrocyte networks in the brain has been recently lauded to be of equal importance to that of the neural networks. To date criticality assessments have only been performed on networks astrocytes from healthy rats, and astrocytes from cultured dissociated resections of intractable epilepsy. This work, for the first time, presents studies of the critical dynamics and shape collapse of calcium waves observed in cultures of healthy human astrocyte networks in vitro, derived from the human hNT cell line. In this article, we demonstrate that avalanches of spontaneous calcium waves display strong critical dynamics, including power-laws in both the size and duration distributions. In addition, the temporal profiles of avalanches displayed self-similarity, leading to shape collapse of the temporal profiles. These findings are significant as they suggest that cultured networks of healthy human hNT astrocytes self-organize to a critical point, implying that healthy astrocytic networks operate at a critical point to process and transmit information. Furthermore, this work can serve as a point of reference to which other astrocyte criticality studies can be compared.

Keywords: astrocyte; calcium waves; criticality; human neuroscience; in vitro; intercellular dynamics; networks; shape collapse.

FIGURE 1

Plots of a typical time-series recording. (A) shows a raster plot of a typical network over the full recording period. (B) is a time-series of a typical cells showing Ca²⁺ waves, there are regular transients of different shapes and frequencies displayed. (C) is an image sequence showing a typical avalanche, the avalanche is initiated in a single cell with the Ca²⁺ wave spreading and activating further afield cells. The avalanche ends when the initial cells become inactive and the wave no longer spreads. This same avalanche is displayed as a heatmap in (D), where cell index relates to cells sorted by distance from the initial point of the avalanche, and as a 3D plot in (E).

FIGURE 2

Duration and size distributions in all networks. (A) shows the duration distributions, the dashed line is a perfect power-law with exponent 2.8. (B) shows the size distributions, the dashed line is a perfect power-law with exponent 2.06. (C,D) are semilog (log y, linear x) plots of the initial parts of both distributions. Network 1 (o), network 2 (x), network 3 (+), network 4 (□), network 5 (▽), and network 6 (◇).

FIGURE 3

Plots for each individual exponent across all six hNT astrocyte networks. (A) Duration distribution exponents ( $\mathit{\alpha }$ ). (B) Size distribution exponent ( $\mathit{\tau }$ ). (C) Shape collapse exponent (B). (D) The Scaling relation $\left(\mathit{q}=\frac{\mathit{\sigma \nu z}\left(\mathit{\alpha }-1\right)}{\left(\mathit{\tau }-1\right)}\right)$ . (Error bars represent the standard deviation in the estimate).

FIGURE 4

Shape collapse of all networks analysed. The top row of images corresponds to network 1, with the subsequent rows corresponding to subsequent networks. All networks show a universal shape similar to a parabola, although the shape has a slight left skew. Network 3, third row, shows the poorest shape collapse.

FIGURE 5

(A) Plot showing the variance of the avalanche temporal profiles before (•), and after collapse (o). Single arrow shows how the behaviour before collapse does actually tend to lower values after collapse which is to be expected in a critical system (Sethna et al., 2001). Network 3, shows a very small decrease in variance after collapse, although its starting variance is low compared to the other networks. (B) Plot showing distance between the shape collapse exponent (B) (□) and size given duration exponent $\left(\frac{1}{\mathit{\sigma \nu z}}\right)$ (△). Double arrows highlight the closeness in proximity that exists in these real-world astrocyte networks which is expected in an ideal critical system to be equal. Network 2, shows very close agreement between the two exponents.