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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.


Neural complexity. (A) Short segments of example spike rasters for three types of chain model data (see Section 2.4, c = 0 (random), c = 0.8 (complex), c = 1 (ordered)). (B) Integration curves with linear approximations for different subset sizes. Note that random data shows no integration, while ordered data shows high integration. Complex data shows high integration that varies non-linearly with subset size. (C) Complexity values. Only the complex data shows non-zero complexity.
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Figure 3: Neural complexity. (A) Short segments of example spike rasters for three types of chain model data (see Section 2.4, c = 0 (random), c = 0.8 (complex), c = 1 (ordered)). (B) Integration curves with linear approximations for different subset sizes. Note that random data shows no integration, while ordered data shows high integration. Complex data shows high integration that varies non-linearly with subset size. (C) Complexity values. Only the complex data shows non-zero complexity.

Mentions: The complexity as expressed in Equation (10) can be difficult to interpret. Therefore, it is helpful to evaluate the complexity in a simple system such as a small chain model (see Section 2.4, Figure 3). Complexity requires some degree of coordinated variability across many scales in the system. In Figure 3, we show three types of models: a random model, a complex model, and an ordered model. The behaviors of the models are apparent from a brief segment of representative spike rasters (Figure 3A). The random data contain no correlations, while the ordered data contain no variability. The complex data show some balance between these states. When the integration curves are plotted (Figure 3B), the random data produce zero integration, while the ordered data produce high integration. However, the complex data produce a non-linear integration curve, suggesting varying correlations across scales and non-zero complexity.


Criticality Maximizes Complexity in Neural Tissue
Neural complexity. (A) Short segments of example spike rasters for three types of chain model data (see Section 2.4, c = 0 (random), c = 0.8 (complex), c = 1 (ordered)). (B) Integration curves with linear approximations for different subset sizes. Note that random data shows no integration, while ordered data shows high integration. Complex data shows high integration that varies non-linearly with subset size. (C) Complexity values. Only the complex data shows non-zero complexity.
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Figure 3: Neural complexity. (A) Short segments of example spike rasters for three types of chain model data (see Section 2.4, c = 0 (random), c = 0.8 (complex), c = 1 (ordered)). (B) Integration curves with linear approximations for different subset sizes. Note that random data shows no integration, while ordered data shows high integration. Complex data shows high integration that varies non-linearly with subset size. (C) Complexity values. Only the complex data shows non-zero complexity.
Mentions: The complexity as expressed in Equation (10) can be difficult to interpret. Therefore, it is helpful to evaluate the complexity in a simple system such as a small chain model (see Section 2.4, Figure 3). Complexity requires some degree of coordinated variability across many scales in the system. In Figure 3, we show three types of models: a random model, a complex model, and an ordered model. The behaviors of the models are apparent from a brief segment of representative spike rasters (Figure 3A). The random data contain no correlations, while the ordered data contain no variability. The complex data show some balance between these states. When the integration curves are plotted (Figure 3B), the random data produce zero integration, while the ordered data produce high integration. However, the complex data produce a non-linear integration curve, suggesting varying correlations across scales and non-zero complexity.

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.