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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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Culture recording, spike sorting, and avalanche detection. (A) Image of example low density dissociated hippocampal culture plated on the electrode array (50,000 cells, DIV 6). Low density culture produced for testing and imaging purposes. High density cultures (as used in the analysis) were difficult to image due to overlapping cell structure. (B) Example voltage recording from a culture that was utilized in the analysis. Spike sorting identified two neurons. (C) Average spike waveforms for neurons 1 and 2 from (B). Solid line represents mean voltage and fringe represents one standard deviation. (D) A segment of the spike raster for all electrodes in the same culture as the electrode shown in (B). (E) Example neuronal avalanche. Once spikes were found for all electrodes with a temporal resolution of 0.05 ms, the data were rebinned to the mean network-wide interspike interval (ISI). Adjacent periods of activity were then identified as avalanches. This avalanche corresponds to the red vertical line in (D). This avalanche was duration 6 (6 time bins long) and size 12 (12 total neuron activations). (F) Avalanche profile for the example avalanche shown in (E).
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Figure 1: Culture recording, spike sorting, and avalanche detection. (A) Image of example low density dissociated hippocampal culture plated on the electrode array (50,000 cells, DIV 6). Low density culture produced for testing and imaging purposes. High density cultures (as used in the analysis) were difficult to image due to overlapping cell structure. (B) Example voltage recording from a culture that was utilized in the analysis. Spike sorting identified two neurons. (C) Average spike waveforms for neurons 1 and 2 from (B). Solid line represents mean voltage and fringe represents one standard deviation. (D) A segment of the spike raster for all electrodes in the same culture as the electrode shown in (B). (E) Example neuronal avalanche. Once spikes were found for all electrodes with a temporal resolution of 0.05 ms, the data were rebinned to the mean network-wide interspike interval (ISI). Adjacent periods of activity were then identified as avalanches. This avalanche corresponds to the red vertical line in (D). This avalanche was duration 6 (6 time bins long) and size 12 (12 total neuron activations). (F) Avalanche profile for the example avalanche shown in (E).

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
Culture recording, spike sorting, and avalanche detection. (A) Image of example low density dissociated hippocampal culture plated on the electrode array (50,000 cells, DIV 6). Low density culture produced for testing and imaging purposes. High density cultures (as used in the analysis) were difficult to image due to overlapping cell structure. (B) Example voltage recording from a culture that was utilized in the analysis. Spike sorting identified two neurons. (C) Average spike waveforms for neurons 1 and 2 from (B). Solid line represents mean voltage and fringe represents one standard deviation. (D) A segment of the spike raster for all electrodes in the same culture as the electrode shown in (B). (E) Example neuronal avalanche. Once spikes were found for all electrodes with a temporal resolution of 0.05 ms, the data were rebinned to the mean network-wide interspike interval (ISI). Adjacent periods of activity were then identified as avalanches. This avalanche corresponds to the red vertical line in (D). This avalanche was duration 6 (6 time bins long) and size 12 (12 total neuron activations). (F) Avalanche profile for the example avalanche shown in (E).
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Figure 1: Culture recording, spike sorting, and avalanche detection. (A) Image of example low density dissociated hippocampal culture plated on the electrode array (50,000 cells, DIV 6). Low density culture produced for testing and imaging purposes. High density cultures (as used in the analysis) were difficult to image due to overlapping cell structure. (B) Example voltage recording from a culture that was utilized in the analysis. Spike sorting identified two neurons. (C) Average spike waveforms for neurons 1 and 2 from (B). Solid line represents mean voltage and fringe represents one standard deviation. (D) A segment of the spike raster for all electrodes in the same culture as the electrode shown in (B). (E) Example neuronal avalanche. Once spikes were found for all electrodes with a temporal resolution of 0.05 ms, the data were rebinned to the mean network-wide interspike interval (ISI). Adjacent periods of activity were then identified as avalanches. This avalanche corresponds to the red vertical line in (D). This avalanche was duration 6 (6 time bins long) and size 12 (12 total neuron activations). (F) Avalanche profile for the example avalanche shown in (E).
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.


Related in: MedlinePlus