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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.


Basic dissociated culture properties. (A) Neuron firing rate histogram. The histogram does not appear to be log-normal, though firing rates span multiple orders of magnitude and this distribution could result from the sum of multiple log-normal distributions and low firing rate bias in spike sorting. (B) Recording DIVs (black squares) for all cultures. White squares indicate no recording was performed. Red squares indicate the recordings that were excluded from the analysis due to too few avalanches. All other recordings were fully utilized in the analysis. (C) Histogram of number of recorded neurons across all recordings. (D) Histogram of mean network-wide interspike interval (ISI) across all recordings. Each recording was rebinned to the mean ISI. (E) Histogram of number of observed avalanches in each recording after rebinning to ISI.
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Figure 2: Basic dissociated culture properties. (A) Neuron firing rate histogram. The histogram does not appear to be log-normal, though firing rates span multiple orders of magnitude and this distribution could result from the sum of multiple log-normal distributions and low firing rate bias in spike sorting. (B) Recording DIVs (black squares) for all cultures. White squares indicate no recording was performed. Red squares indicate the recordings that were excluded from the analysis due to too few avalanches. All other recordings were fully utilized in the analysis. (C) Histogram of number of recorded neurons across all recordings. (D) Histogram of mean network-wide interspike interval (ISI) across all recordings. Each recording was rebinned to the mean ISI. (E) Histogram of number of observed avalanches in each recording after rebinning to ISI.

Mentions: Dissociated hippocampal cultures were produced from rats using the procedures detailed in Hales et al. (2010). Briefly, timed pregnant female rats (Sprague-Dawley from Harlan Laboratories) were euthanized using CO2. Embryonic day 18 embryos were removed. Embryonic tissue was used to facilitate the creation of a connected network of neurons following dissociation and plating. The hippocampi of each embyro were extracted and combined from all embryos. The neural tissue was then dissociated and plated on Multichannel Systems 60 electrode arrays (8 X 8 square array with corners removed, 200 μm electrode spacing, 30 μm electrode diameter). We plated cultures with a density of 10,000 cells per μL and we plated a total of approximately 200,000 cells per culture. See Figure 1A for an image of an example low density culture. We recorded from the cultures for days in vitro (DIV) 6 through 35. See Figure 2B for a list of the cultures and recording DIV (total number of recordings: 435). We did not record from the cultures for the first five DIV because activity was not generally stable during those DIV (Wagenaar et al., 2006). We analyzed the first 59 min of each recording, conducted at a sampling rate of 20 kHz.


Criticality Maximizes Complexity in Neural Tissue
Basic dissociated culture properties. (A) Neuron firing rate histogram. The histogram does not appear to be log-normal, though firing rates span multiple orders of magnitude and this distribution could result from the sum of multiple log-normal distributions and low firing rate bias in spike sorting. (B) Recording DIVs (black squares) for all cultures. White squares indicate no recording was performed. Red squares indicate the recordings that were excluded from the analysis due to too few avalanches. All other recordings were fully utilized in the analysis. (C) Histogram of number of recorded neurons across all recordings. (D) Histogram of mean network-wide interspike interval (ISI) across all recordings. Each recording was rebinned to the mean ISI. (E) Histogram of number of observed avalanches in each recording after rebinning to ISI.
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Figure 2: Basic dissociated culture properties. (A) Neuron firing rate histogram. The histogram does not appear to be log-normal, though firing rates span multiple orders of magnitude and this distribution could result from the sum of multiple log-normal distributions and low firing rate bias in spike sorting. (B) Recording DIVs (black squares) for all cultures. White squares indicate no recording was performed. Red squares indicate the recordings that were excluded from the analysis due to too few avalanches. All other recordings were fully utilized in the analysis. (C) Histogram of number of recorded neurons across all recordings. (D) Histogram of mean network-wide interspike interval (ISI) across all recordings. Each recording was rebinned to the mean ISI. (E) Histogram of number of observed avalanches in each recording after rebinning to ISI.
Mentions: Dissociated hippocampal cultures were produced from rats using the procedures detailed in Hales et al. (2010). Briefly, timed pregnant female rats (Sprague-Dawley from Harlan Laboratories) were euthanized using CO2. Embryonic day 18 embryos were removed. Embryonic tissue was used to facilitate the creation of a connected network of neurons following dissociation and plating. The hippocampi of each embyro were extracted and combined from all embryos. The neural tissue was then dissociated and plated on Multichannel Systems 60 electrode arrays (8 X 8 square array with corners removed, 200 μm electrode spacing, 30 μm electrode diameter). We plated cultures with a density of 10,000 cells per μL and we plated a total of approximately 200,000 cells per culture. See Figure 1A for an image of an example low density culture. We recorded from the cultures for days in vitro (DIV) 6 through 35. See Figure 2B for a list of the cultures and recording DIV (total number of recordings: 435). We did not record from the cultures for the first five DIV because activity was not generally stable during those DIV (Wagenaar et al., 2006). We analyzed the first 59 min of each recording, conducted at a sampling rate of 20 kHz.

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.