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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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Related in: MedlinePlus

Cortical branching models exhibit peaks in complexity and susceptibility, and branching ratios close to 1 near the infinite model critical point. (A,B) Complexity and susceptibility peaked near ptrans = 0.25 indicating that both were maximized in critical systems. Note that complexity (A) also showed divergent behavior for high transmission probabilities. This behavior was due to finite recording length bias (Figure S2). (C) Shape collapse curvature did not peak near ptrans = 0.25, though this was not expected. This indicates that low transmission probability avalanches were more curved and high transmission probability avalanches were more flat. (D) The branching ratios (Equation 13) of the networks were near 1 (critical state) near the transmission probabilities that showed peak complexity (A) and susceptibility (C). In all sub-figures, the black line represents the average value and the red fringe represents ± one standard deviation.
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Figure 7: Cortical branching models exhibit peaks in complexity and susceptibility, and branching ratios close to 1 near the infinite model critical point. (A,B) Complexity and susceptibility peaked near ptrans = 0.25 indicating that both were maximized in critical systems. Note that complexity (A) also showed divergent behavior for high transmission probabilities. This behavior was due to finite recording length bias (Figure S2). (C) Shape collapse curvature did not peak near ptrans = 0.25, though this was not expected. This indicates that low transmission probability avalanches were more curved and high transmission probability avalanches were more flat. (D) The branching ratios (Equation 13) of the networks were near 1 (critical state) near the transmission probabilities that showed peak complexity (A) and susceptibility (C). In all sub-figures, the black line represents the average value and the red fringe represents ± one standard deviation.

Mentions: Now we will examine the combined behavior of all cortical branching models across transmission probabilities (0.2 ≤ ptrans ≤ 0.3) after sub-sampling (see Figure S1 for example sub-sampling fits). When we plotted the complexity and susceptibility vs. the transmission probability, we found both peaked near ptrans ≈ 0.265 (Figures 7A,B). Given that complexity and susceptibility showed maxima near the critical transmission probability for an infinite system (ptrans ≈ 0.25), and susceptibility has been shown to be maximized near criticality (Williams-Garcia et al., 2014), this result is strong evidence that neural complexity is also maximized near criticality. Furthermore, the branching ratio was found to be closest to 1 near this same transmission probability (Figure 7D). A branching ratio of 1 indicates sustained levels of activity necessary for a system to be operating at a critical point, as opposed to branching ratios below one which indicate a system is sub-critical or above one which indicate a system is super-critical.


Criticality Maximizes Complexity in Neural Tissue
Cortical branching models exhibit peaks in complexity and susceptibility, and branching ratios close to 1 near the infinite model critical point. (A,B) Complexity and susceptibility peaked near ptrans = 0.25 indicating that both were maximized in critical systems. Note that complexity (A) also showed divergent behavior for high transmission probabilities. This behavior was due to finite recording length bias (Figure S2). (C) Shape collapse curvature did not peak near ptrans = 0.25, though this was not expected. This indicates that low transmission probability avalanches were more curved and high transmission probability avalanches were more flat. (D) The branching ratios (Equation 13) of the networks were near 1 (critical state) near the transmission probabilities that showed peak complexity (A) and susceptibility (C). In all sub-figures, the black line represents the average value and the red fringe represents ± one standard deviation.
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Related In: Results  -  Collection

License
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Figure 7: Cortical branching models exhibit peaks in complexity and susceptibility, and branching ratios close to 1 near the infinite model critical point. (A,B) Complexity and susceptibility peaked near ptrans = 0.25 indicating that both were maximized in critical systems. Note that complexity (A) also showed divergent behavior for high transmission probabilities. This behavior was due to finite recording length bias (Figure S2). (C) Shape collapse curvature did not peak near ptrans = 0.25, though this was not expected. This indicates that low transmission probability avalanches were more curved and high transmission probability avalanches were more flat. (D) The branching ratios (Equation 13) of the networks were near 1 (critical state) near the transmission probabilities that showed peak complexity (A) and susceptibility (C). In all sub-figures, the black line represents the average value and the red fringe represents ± one standard deviation.
Mentions: Now we will examine the combined behavior of all cortical branching models across transmission probabilities (0.2 ≤ ptrans ≤ 0.3) after sub-sampling (see Figure S1 for example sub-sampling fits). When we plotted the complexity and susceptibility vs. the transmission probability, we found both peaked near ptrans ≈ 0.265 (Figures 7A,B). Given that complexity and susceptibility showed maxima near the critical transmission probability for an infinite system (ptrans ≈ 0.25), and susceptibility has been shown to be maximized near criticality (Williams-Garcia et al., 2014), this result is strong evidence that neural complexity is also maximized near criticality. Furthermore, the branching ratio was found to be closest to 1 near this same transmission probability (Figure 7D). A branching ratio of 1 indicates sustained levels of activity necessary for a system to be operating at a critical point, as opposed to branching ratios below one which indicate a system is sub-critical or above one which indicate a system is super-critical.

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