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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) The size power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (B) The size power-law fit exponent τ increased under randomization indicating the size distribution became steeper. (C) The duration power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (D) The duration power-law fit exponent α increased under randomization indicating the duration distribution became steeper. Note that the fit results 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 11: Markers of criticality decreased under randomization in culture data. (A) The size power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (B) The size power-law fit exponent τ increased under randomization indicating the size distribution became steeper. (C) The duration power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (D) The duration power-law fit exponent α increased under randomization indicating the duration distribution became steeper. Note that the fit results 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: Next, we examined the size and duration fit ranges, as well as the associated fit exponents measured using all of the data (Figure 11) (see Section 2.10). We found that the fit ranges decreased for strong forms of randomization (e.g., Poisson randomization), but showed slight increases for 10 bin jittering (Figures 11A,C). We believe this may be due to errors associated with determining the characteristic time scale for the system. We found a correlation of 0.296 between the complexity and the size fit ranges of the recordings and a correlation of 0.197 between the complexity and the duration fit ranges of the recordings (see Figure S9). We also found that the power-law fit exponents increased under randomization because randomization tends to remove large or long avalanches and produce a shorter and steeper distribution of avalanche sizes or durations (Figures 11B,D).


Criticality Maximizes Complexity in Neural Tissue
Markers of criticality decreased under randomization in culture data. (A) The size power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (B) The size power-law fit exponent τ increased under randomization indicating the size distribution became steeper. (C) The duration power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (D) The duration power-law fit exponent α increased under randomization indicating the duration distribution became steeper. Note that the fit results 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 11: Markers of criticality decreased under randomization in culture data. (A) The size power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (B) The size power-law fit exponent τ increased under randomization indicating the size distribution became steeper. (C) The duration power-law fit range decreased under randomization, with the exception of the 10 bin jittering. (D) The duration power-law fit exponent α increased under randomization indicating the duration distribution became steeper. Note that the fit results 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: Next, we examined the size and duration fit ranges, as well as the associated fit exponents measured using all of the data (Figure 11) (see Section 2.10). We found that the fit ranges decreased for strong forms of randomization (e.g., Poisson randomization), but showed slight increases for 10 bin jittering (Figures 11A,C). We believe this may be due to errors associated with determining the characteristic time scale for the system. We found a correlation of 0.296 between the complexity and the size fit ranges of the recordings and a correlation of 0.197 between the complexity and the duration fit ranges of the recordings (see Figure S9). We also found that the power-law fit exponents increased under randomization because randomization tends to remove large or long avalanches and produce a shorter and steeper distribution of avalanche sizes or durations (Figures 11B,D).

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