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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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Example cortical branching model distributions and shape collapse. (A) Size distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. (B) Duration distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. In (A,B), note that the low transmission probability distributions curve downwards, while the high transmission probability distributions curve upwards. This behavior is indicative of sub-critical and super-critical systems. Automatically detected truncated fit regions marked in black (see Section 2.7) (C) Example shape collapses. Note that all three transmission probabilities qualitatively appear to exhibit shape collapse. Quadratic fit of shape collapse shown in black (see Section 2.8).
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Figure 6: Example cortical branching model distributions and shape collapse. (A) Size distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. (B) Duration distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. In (A,B), note that the low transmission probability distributions curve downwards, while the high transmission probability distributions curve upwards. This behavior is indicative of sub-critical and super-critical systems. Automatically detected truncated fit regions marked in black (see Section 2.7) (C) Example shape collapses. Note that all three transmission probabilities qualitatively appear to exhibit shape collapse. Quadratic fit of shape collapse shown in black (see Section 2.8).

Mentions: The cortical branching model (see Section 2.4) produced neural avalanches that were similar to the culture data (see Section 3.3 below). The model produced size and duration distributions that were fit by truncated power-laws after applying minimum size/duration and occurrence cuts (Figures 6A,B, see Section 2.7). In the size and duration distributions, note that the low transmission probability models produced distributions that curved downwards, whereas the high transmission probability models produced distributions that curved upwards. The model with a transmission probability near the infinite system critical transmission probability (ptrans = 0.25) produced the straightest size and duration distributions. This behavior is typical of a sub-critical (ptrans < pcrit), critical (ptrans ≈ pcrit), and super-critical (ptrans > pcrit) system. The cortical branching model also produced shape collapses (Figure 6C, see Section 2.8). Interestingly, the shape collapses qualitatively appear to be of high quality for all transmission probabilities.


Criticality Maximizes Complexity in Neural Tissue
Example cortical branching model distributions and shape collapse. (A) Size distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. (B) Duration distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. In (A,B), note that the low transmission probability distributions curve downwards, while the high transmission probability distributions curve upwards. This behavior is indicative of sub-critical and super-critical systems. Automatically detected truncated fit regions marked in black (see Section 2.7) (C) Example shape collapses. Note that all three transmission probabilities qualitatively appear to exhibit shape collapse. Quadratic fit of shape collapse shown in black (see Section 2.8).
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Figure 6: Example cortical branching model distributions and shape collapse. (A) Size distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. (B) Duration distributions for three example models with low (left), near critical (center), and high (right) transmission probabilities. In (A,B), note that the low transmission probability distributions curve downwards, while the high transmission probability distributions curve upwards. This behavior is indicative of sub-critical and super-critical systems. Automatically detected truncated fit regions marked in black (see Section 2.7) (C) Example shape collapses. Note that all three transmission probabilities qualitatively appear to exhibit shape collapse. Quadratic fit of shape collapse shown in black (see Section 2.8).
Mentions: The cortical branching model (see Section 2.4) produced neural avalanches that were similar to the culture data (see Section 3.3 below). The model produced size and duration distributions that were fit by truncated power-laws after applying minimum size/duration and occurrence cuts (Figures 6A,B, see Section 2.7). In the size and duration distributions, note that the low transmission probability models produced distributions that curved downwards, whereas the high transmission probability models produced distributions that curved upwards. The model with a transmission probability near the infinite system critical transmission probability (ptrans = 0.25) produced the straightest size and duration distributions. This behavior is typical of a sub-critical (ptrans < pcrit), critical (ptrans ≈ pcrit), and super-critical (ptrans > pcrit) system. The cortical branching model also produced shape collapses (Figure 6C, see Section 2.8). Interestingly, the shape collapses qualitatively appear to be of high quality for all transmission probabilities.

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