by Wesley Clawson, Aix-Marseille University, Institute of Systems Neuroscience
in collaboration with Pascale Quilichini, Christophe Bernard, Demian Battaglia
Neural computation occurs across networks of neurons whose dynamics can be described by reoccurring substates of information processing activity. It was shown that the organization of these substates is complex and partially constrained by large scale oscillations. However, it is unknown how this organization changes in a diseased state such as epilepsy. Using high density recordings in the hippocampus and medial entorhinal cortex of epileptic rats under anesthesia, we confirm that the basic composition of substates are still present. We find however, that many aspects of their organization both internal and external are disturbed. All observed disruptions of this organization point towards a shift away from control organization and towards a more random regime. We propose that this disruption of organization towards randomness is indicative of a warped form of neural computation and may underlie many observed comorbidities in the epileptic condition.
Intro (Left Side): Epilepsy represents a functional, albeit abnormal state of brain dynamics. People with epilepsy don’t die the moment they develop the disease, they continue to live (function) and while the main component of the disease is seizures, there sadly a host of other cognitive co-morbidities. Many times, long term patients report that the co-morbidities are worse than the seizures. So, there must be something at a fundamental level in the network that is disrupted that could be the root cause of so many varying issues. In previous work we published, we observe that in control states for both natural sleep and anesthesia, neural activity ‘switches’ between varying information processing substates (IPSs). IPSs represent periods of time, often reoccurring throughout a recording, of specific collective coordinated neural firing activity. We posit in this previous paper that these IPSs can be thought of as an algorithmic level of computation and therefore, if these IPSs were disturbed in epilepsy, many things would degrade as a result.
Data (Right Side): We use data from control and epileptic rats under anesthesia (n = 5 and 6, respectively) where we record data taken from implanted silicon electrode probes in CA1 of HPC and mEC. The resulting data is the local field potential (top of white box) as well as spikes (bottom of white box). Importantly, note that we binarize the spike trains, and therefore this activity is reduced to sequences of 0s and 1s. In a similar style to our previous work, we use a sliding window technique (window = 10 s, slide = 1s) to measure four aspects of the network.
- Spectra: the dominate spectral frequency of the network. In anesthesia, this is either slow oscillations (1-2 Hz, SO) or theta oscillations (3-5 Hz, THE)
- Firing: The firing rates of all neurons within the window
- Storage: Active information storage, analogous to autocorrelation, we measure the mutual information between the binarized spike trains between two windows for each neuron
- Sharing: Similar to crosscorrelation, we measure the mutual information between the spike train of one neuron, to all others in the following window, repeated for all neurons
We believe these 4 aspects capture the complex spatiotemporal dynamics of the population.
Clustering (Left side, top): We cluster these 4 features separately using k-means. A resultant IPS table is shown here. The top row represents the clusters of spectra (SO and THE), the second, firing, the third, storage and the fourth, sharing.
Contrast (Left side, large, bottom): To investigate the population activity within the states found by k-means, we measure the contrast. Contrast here is defined as the mean activity of a neuron divided by the neuron’s mean global, i.e. the entire recording, activity. This measure is represented by the black bars. Each row is a given feature. The individual graphs, color coded to show the relation to the example table, shows the varying contrast values across the population within different states. We see that the population changes its behavior drastically between different states for all features.
Cluster Sweep (Left side, small, bottom): How do define how many k? As we were unsure on the effect of epilepsy on clustering, and to also make our analysis agnostic to k, we cluster over a large range of k (3-10) for each feature. Here, we show an example clustering sweep for the storage feature for a recording. We see the states of SO and THE on the left, and the varying different resulting clusters as we increase k.
IPS Table Library (Right side, top): As a result of this cluster sweep, we have many possible resultant IPS tables. We therefore build an IPS library, the collection of the overall 83 = 512 state switching tables, given the many different combinations of all the different clusters. We therefore present most analysis over the library, ranging from ktot = 11 to 32.
Contrast over the varying K (Right side, bottom): Here we show how k and control v epilepsy affects our measure of contrast for mEC. We present a distribution of mean differences between contrast values found in control recordings and epileptic recordings. The black dots are the mean, the thick bars are the 25-75th percentile, and the thin bars are 1-99th percentile. We see that regardless of k, and for all features, all of these distributions are in the negative – meaning that substates in epilepsy are MORE contrasted than in control.
SSI (bottom, right): To see when these states appear, we compute the state specificity index (SSI). This index is listed on the slide and is bound between 0 (equal probability of occurring in SO and THE) and 1 (limited to SO or THE). This is computed for each features (rows) for mEC and CA1 (columns). The x axis are the varying clusters from 3-10, and the y axis is the SSI. The thick bars represent the mean, and the shaded areas represent a 99% confidence interval.
Computational Hubs (Right side, top): While contrast examines how the population changes from state to state, the measure (or role) of a computational hub examines individual neuronal behavior within states. If we examine the distribution of mean activity for all neurons across all states and take a threshold of the top 10% of that distribution, any neuron that has mean activity within a state ABOVE that threshold is a computational hub. In short, a computational hub is a neuron with exceptionally high firing, storage or sharing within a given state. Here, we have possible states on the x axis, and neurons on the y axis. A blue square means that a neuron was NOT a hub in this state, while a yellow square indicates that that given neuron was a hub in the state. The bar on the far right represents a ‘squashed’ version of the graph on the left – i.e. was a neuron EVER a hub in any state?
% neurons as hubs (Bottom, middle): If we calculate how many neurons were a hub (see above, right graph), we have the percentage of neurons that were hubs in a given recording across the library. Here we show how that value changes across the library. The thick bars represent the mean, and the shaded areas represent a 99% confidence interval. We see an increase in this measure for both mEC and CA1 in the epileptic state
Similarity (bottom, right): We also want to examine how the distribution of hubs across the network and states change. We compute the average hamming distance between the columns of the top left graph (computational hubs). This indicates how different each column is – i.e. how the distribution changes on average between states. 0 would mean that all states are different and 1 would mean that all states have the same. We present these measures over the library for both mEC and CA1. Again, the thick bar represents the mean and the shaded area the 99% confidence interval. We see that in mEC there is a decrease in similarity and in CA1, there is no change.
Between order and randomness (left, top): An example of our complex IPS table (derived from experimental data) lying between the ‘sister’ IPS tables of order and randomness. The ordered table is created by sorting the derived table and the random table is created by randomizing the derived table. This is to give a visual example of the y-axis scaling we use in the follow graphs.
Dictionary (left, bottom): If we treat each state as a symbol, then the IPS, a combination of symbols, can be considered as a word. As there are a set number of symbols, there is an upper limit on how many words could have been expressed, the dictionary. An example of a low dictionary can be seen on the top left, and an example of a high dictionary is on the top right. The rows are the features of firing, storage, and sharing and the varying colors represent the varying possible states. Being lightly shaded represents the given word not being expressed, and the darker colors represent an expressed word. Below, we present the measures of relative dictionary (expressed / total possible) for control and epilepsy for mEC and CA1. Importantly, the y-axis is scaled to order and random. To do this, we rescaled the values such that 0 was the mean relative dictionary of the ordered tables, and 1 was the mean relative dictionary of the random tables. The x axis is the library of state tables. The thick bars are the mean, and the shaded area the 99% confidence interval. We see that for mEC there is a drop (move towards order) in the dictionary while for CA1, there is an increase (move towards randomness) in the dictionary.
Complexity (right): We use a measure of complexity similar to Lempel-Ziv complexity, minimum length description. It is a measure of how long a computer program would need to be to reproduce the sequence of words. It is also a measure that is related to compressibility. Something very compressible means the code would be shorter, and something very uncompressible would require a long program. Here, the y-axis is again scaled such that 0 is the mean complexity of the ordered tables and 1 is the mean complexity of the random tables. The x-axis is the measure of the library of state tables. The thick bar is the mean and the shaded area is the 99% confidence interval. Here, we see that for both mEC and CA1 the complexity shifts up, towards the complexity of something random.
We posit here that the fundamental changes in the network due to epilepsy causes a destructuring of the IPSs and their organization and shift the resulting behavior towards a more random regime. This could underly many cognitive co-morbidities.