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Criticality Maximizes Complexity in Neural Tissue

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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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Power-law exponents in culture data. (A) Size distribution critical exponent (τ) values for all culture recordings analyzed. (B) Duration distribution critical exponent (α) values for all culture recordings analyzed. (C) Average size given duration data critical exponent (1/σνz) values for all culture recordings analyzed. (D) Shape collapse critical exponent (1/σνz) values for all culture recordings analyzed. In all subfigures, the quoted critical exponent value is mean ± standard deviation. Also, histogram bin sizes optimized using methods established in Terrell and Scott (1985).
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Figure 8: Power-law exponents in culture data. (A) Size distribution critical exponent (τ) values for all culture recordings analyzed. (B) Duration distribution critical exponent (α) values for all culture recordings analyzed. (C) Average size given duration data critical exponent (1/σνz) values for all culture recordings analyzed. (D) Shape collapse critical exponent (1/σνz) values for all culture recordings analyzed. In all subfigures, the quoted critical exponent value is mean ± standard deviation. Also, histogram bin sizes optimized using methods established in Terrell and Scott (1985).

Mentions: We calculated the critical exponents using the MLE power-law search algorithm (for size distributions, duration distributions, and average size given duration data), using the full shape collapse analysis, and using sub-sampling methods (Figure 8) (Marshall et al., 2016). We found lower values of τ and α using the sub-sampling analysis, as well as lower errors (Figures 8A,B). The values of 1/σνz showed little change between sub-sampling and the analysis of the full system (Figures 8C,D). The exponents found using the sub-sampling method agreed best with previously reported values for the critical exponents in neural avalanches (Mazzoni et al., 2007; Pasquale et al., 2008; Friedman et al., 2012). Note that the values of 1/σνz found using distinct methods (average size given duration fits and shape collapse) agree within error. Furthermore, note that the critical exponents satisfy the general relationship given in Equation (4) using both the search algorithm and the sub-sampling method. However, we also found that randomized data satisfied the critical exponent relationship, though with different exponent values (data not shown). This result casts doubt on the importance of the critical exponent relationship as a marker for critical systems.


Criticality Maximizes Complexity in Neural Tissue
Power-law exponents in culture data. (A) Size distribution critical exponent (τ) values for all culture recordings analyzed. (B) Duration distribution critical exponent (α) values for all culture recordings analyzed. (C) Average size given duration data critical exponent (1/σνz) values for all culture recordings analyzed. (D) Shape collapse critical exponent (1/σνz) values for all culture recordings analyzed. In all subfigures, the quoted critical exponent value is mean ± standard deviation. Also, histogram bin sizes optimized using methods established in Terrell and Scott (1985).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5037237&req=5

Figure 8: Power-law exponents in culture data. (A) Size distribution critical exponent (τ) values for all culture recordings analyzed. (B) Duration distribution critical exponent (α) values for all culture recordings analyzed. (C) Average size given duration data critical exponent (1/σνz) values for all culture recordings analyzed. (D) Shape collapse critical exponent (1/σνz) values for all culture recordings analyzed. In all subfigures, the quoted critical exponent value is mean ± standard deviation. Also, histogram bin sizes optimized using methods established in Terrell and Scott (1985).
Mentions: We calculated the critical exponents using the MLE power-law search algorithm (for size distributions, duration distributions, and average size given duration data), using the full shape collapse analysis, and using sub-sampling methods (Figure 8) (Marshall et al., 2016). We found lower values of τ and α using the sub-sampling analysis, as well as lower errors (Figures 8A,B). The values of 1/σνz showed little change between sub-sampling and the analysis of the full system (Figures 8C,D). The exponents found using the sub-sampling method agreed best with previously reported values for the critical exponents in neural avalanches (Mazzoni et al., 2007; Pasquale et al., 2008; Friedman et al., 2012). Note that the values of 1/σνz found using distinct methods (average size given duration fits and shape collapse) agree within error. Furthermore, note that the critical exponents satisfy the general relationship given in Equation (4) using both the search algorithm and the sub-sampling method. However, we also found that randomized data satisfied the critical exponent relationship, though with different exponent values (data not shown). This result casts doubt on the importance of the critical exponent relationship as a marker for critical 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.


Related in: MedlinePlus