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Criticality Maximizes Complexity in Neural Tissue

View Article: PubMed Central - PubMed

ABSTRACT

The analysis of neural systems leverages tools from many different fields. Drawing on techniques from the study of critical phenomena in statistical mechanics, several studies have reported signatures of criticality in neural systems, including power-law distributions, shape collapses, and optimized quantities under tuning. Independently, neural complexity—an information theoretic measure—has been introduced in an effort to quantify the strength of correlations across multiple scales in a neural system. This measure represents an important tool in complex systems research because it allows for the quantification of the complexity of a neural system. In this analysis, we studied the relationships between neural complexity and criticality in neural culture data. We analyzed neural avalanches in 435 recordings from dissociated hippocampal cultures produced from rats, as well as neural avalanches from a cortical branching model. We utilized recently developed maximum likelihood estimation power-law fitting methods that account for doubly truncated power-laws, an automated shape collapse algorithm, and neural complexity and branching ratio calculation methods that account for sub-sampling, all of which are implemented in the freely available Neural Complexity and Criticality MATLAB toolbox. We found evidence that neural systems operate at or near a critical point and that neural complexity is optimized in these neural systems at or near the critical point. Surprisingly, we found evidence that complexity in neural systems is dependent upon avalanche profiles and neuron firing rate, but not precise spiking relationships between neurons. In order to facilitate future research, we made all of the culture data utilized in this analysis freely available online.

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Markers of criticality decreased under randomization in culture data. (A) Complexity decreased under randomization, with the exception of spike swapping (see Figure 12). (B) The susceptibility decreased under randomization. (C) Avalanche shape collapse curvature decreased under randomization, indicating that the shape collapses became flatter. Note that the susceptibility and shape collapse curvature were not expected to change under spike swapping or shuffling because those randomization methods preserved avalanche profiles. Box Plots: minimum value, 25th percentile, median, 75th percentile, maximum value. Rank Sum Test: (p < 0.05) 1 star, (p < 0.01) 2 stars, and (p < 0.001) 3 stars. Multiple comparisons correction performed using false discovery rate control (Benjamini and Hochberg, 1995; Benjamini and Yekutieli, 2001; Groppe et al., 2011).
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Figure 10: Markers of criticality decreased under randomization in culture data. (A) Complexity decreased under randomization, with the exception of spike swapping (see Figure 12). (B) The susceptibility decreased under randomization. (C) Avalanche shape collapse curvature decreased under randomization, indicating that the shape collapses became flatter. Note that the susceptibility and shape collapse curvature were not expected to change under spike swapping or shuffling because those randomization methods preserved avalanche profiles. Box Plots: minimum value, 25th percentile, median, 75th percentile, maximum value. Rank Sum Test: (p < 0.05) 1 star, (p < 0.01) 2 stars, and (p < 0.001) 3 stars. Multiple comparisons correction performed using false discovery rate control (Benjamini and Hochberg, 1995; Benjamini and Yekutieli, 2001; Groppe et al., 2011).

Mentions: When we compared complexity and several markers of criticality in the full data sets (see Section 2.10) between randomized culture data and real culture data, we found that all metrics decreased substantially after randomization (Figure 10). The complexity and susceptibility decreased most under the strongest forms of randomization (e.g., Poisson randomization) (Figures 10A,B). Notably, the complexity did not decrease under spike swapping (see below). We also found a correlation of 0.23 between the complexity and the susceptibility of the recordings (see Figure S8). The shape collapse curvature decreased under randomization indicating that avalanches shape collapses became flatter (Figure 10C). In total, these results are consistent with the hypothesis that these neural systems were operating at or near a critical point and that complexity is maximized near the critical point.


Criticality Maximizes Complexity in Neural Tissue
Markers of criticality decreased under randomization in culture data. (A) Complexity decreased under randomization, with the exception of spike swapping (see Figure 12). (B) The susceptibility decreased under randomization. (C) Avalanche shape collapse curvature decreased under randomization, indicating that the shape collapses became flatter. Note that the susceptibility and shape collapse curvature were not expected to change under spike swapping or shuffling because those randomization methods preserved avalanche profiles. Box Plots: minimum value, 25th percentile, median, 75th percentile, maximum value. Rank Sum Test: (p < 0.05) 1 star, (p < 0.01) 2 stars, and (p < 0.001) 3 stars. Multiple comparisons correction performed using false discovery rate control (Benjamini and Hochberg, 1995; Benjamini and Yekutieli, 2001; Groppe et al., 2011).
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License
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Figure 10: Markers of criticality decreased under randomization in culture data. (A) Complexity decreased under randomization, with the exception of spike swapping (see Figure 12). (B) The susceptibility decreased under randomization. (C) Avalanche shape collapse curvature decreased under randomization, indicating that the shape collapses became flatter. Note that the susceptibility and shape collapse curvature were not expected to change under spike swapping or shuffling because those randomization methods preserved avalanche profiles. Box Plots: minimum value, 25th percentile, median, 75th percentile, maximum value. Rank Sum Test: (p < 0.05) 1 star, (p < 0.01) 2 stars, and (p < 0.001) 3 stars. Multiple comparisons correction performed using false discovery rate control (Benjamini and Hochberg, 1995; Benjamini and Yekutieli, 2001; Groppe et al., 2011).
Mentions: When we compared complexity and several markers of criticality in the full data sets (see Section 2.10) between randomized culture data and real culture data, we found that all metrics decreased substantially after randomization (Figure 10). The complexity and susceptibility decreased most under the strongest forms of randomization (e.g., Poisson randomization) (Figures 10A,B). Notably, the complexity did not decrease under spike swapping (see below). We also found a correlation of 0.23 between the complexity and the susceptibility of the recordings (see Figure S8). The shape collapse curvature decreased under randomization indicating that avalanches shape collapses became flatter (Figure 10C). In total, these results are consistent with the hypothesis that these neural systems were operating at or near a critical point and that complexity is maximized near the critical point.

View Article: PubMed Central - PubMed

ABSTRACT

The analysis of neural systems leverages tools from many different fields. Drawing on techniques from the study of critical phenomena in statistical mechanics, several studies have reported signatures of criticality in neural systems, including power-law distributions, shape collapses, and optimized quantities under tuning. Independently, neural complexity&mdash;an information theoretic measure&mdash;has been introduced in an effort to quantify the strength of correlations across multiple scales in a neural system. This measure represents an important tool in complex systems research because it allows for the quantification of the complexity of a neural system. In this analysis, we studied the relationships between neural complexity and criticality in neural culture data. We analyzed neural avalanches in 435 recordings from dissociated hippocampal cultures produced from rats, as well as neural avalanches from a cortical branching model. We utilized recently developed maximum likelihood estimation power-law fitting methods that account for doubly truncated power-laws, an automated shape collapse algorithm, and neural complexity and branching ratio calculation methods that account for sub-sampling, all of which are implemented in the freely available Neural Complexity and Criticality MATLAB toolbox. We found evidence that neural systems operate at or near a critical point and that neural complexity is optimized in these neural systems at or near the critical point. Surprisingly, we found evidence that complexity in neural systems is dependent upon avalanche profiles and neuron firing rate, but not precise spiking relationships between neurons. In order to facilitate future research, we made all of the culture data utilized in this analysis freely available online.

No MeSH data available.


Related in: MedlinePlus