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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.

No MeSH data available.


Complexity is independent of precise spiking relationships in culture data, but dependent on firing rate. (A) Comparison of complexity in real data and complexity in spike swapped randomized data for each culture data set. Note the strong correlation between the complexity values and the fact that most cultures fell near the equality line. This indicates that spiking relationships (which are disrupted to some extent by spike swapping) did not strongly affect complexity. (B) Comparison of complexity in real data and complexity in shuffled data for each culture data set. Note that the complexity values were strongly correlated, but complexity in the real data tended to be greater than the complexity in the shuffled data.
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Figure 12: Complexity is independent of precise spiking relationships in culture data, but dependent on firing rate. (A) Comparison of complexity in real data and complexity in spike swapped randomized data for each culture data set. Note the strong correlation between the complexity values and the fact that most cultures fell near the equality line. This indicates that spiking relationships (which are disrupted to some extent by spike swapping) did not strongly affect complexity. (B) Comparison of complexity in real data and complexity in shuffled data for each culture data set. Note that the complexity values were strongly correlated, but complexity in the real data tended to be greater than the complexity in the shuffled data.

Mentions: Surprisingly, we found that the complexity did not change substantially under spike swapping (Figure 12A), but the complexity did decrease somewhat under shuffling (Figure 12B). Furthermore, we found strong correlations between complexity in the real data and complexity in the spike swapped data (Figure 12A), as well as between complexity in the real data and the complexity in the shuffled data (Figure 12B). Recall that spike swapping preserves avalanche profiles and individual firing rates, but disrupts neuron/spike pairing to some extent, this result implies that precise spiking relationships between neurons did not strongly contribute to complexity in these neural systems. The fact that complexity decreased under shuffling indicates that neuron firing rates (which are not preserved by shuffling) did affect complexity in these neural systems.


Criticality Maximizes Complexity in Neural Tissue
Complexity is independent of precise spiking relationships in culture data, but dependent on firing rate. (A) Comparison of complexity in real data and complexity in spike swapped randomized data for each culture data set. Note the strong correlation between the complexity values and the fact that most cultures fell near the equality line. This indicates that spiking relationships (which are disrupted to some extent by spike swapping) did not strongly affect complexity. (B) Comparison of complexity in real data and complexity in shuffled data for each culture data set. Note that the complexity values were strongly correlated, but complexity in the real data tended to be greater than the complexity in the shuffled data.
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Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC5037237&req=5

Figure 12: Complexity is independent of precise spiking relationships in culture data, but dependent on firing rate. (A) Comparison of complexity in real data and complexity in spike swapped randomized data for each culture data set. Note the strong correlation between the complexity values and the fact that most cultures fell near the equality line. This indicates that spiking relationships (which are disrupted to some extent by spike swapping) did not strongly affect complexity. (B) Comparison of complexity in real data and complexity in shuffled data for each culture data set. Note that the complexity values were strongly correlated, but complexity in the real data tended to be greater than the complexity in the shuffled data.
Mentions: Surprisingly, we found that the complexity did not change substantially under spike swapping (Figure 12A), but the complexity did decrease somewhat under shuffling (Figure 12B). Furthermore, we found strong correlations between complexity in the real data and complexity in the spike swapped data (Figure 12A), as well as between complexity in the real data and the complexity in the shuffled data (Figure 12B). Recall that spike swapping preserves avalanche profiles and individual firing rates, but disrupts neuron/spike pairing to some extent, this result implies that precise spiking relationships between neurons did not strongly contribute to complexity in these neural systems. The fact that complexity decreased under shuffling indicates that neuron firing rates (which are not preserved by shuffling) did affect complexity in these neural systems.

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.

No MeSH data available.