Information sharing networks and strengths
This protocol is extracted from research article:
Computing hubs in the hippocampus and cortex
Sci Adv, Jun 26, 2019; DOI: 10.1126/sciadv.aax4843

Within each time window, we computed time-lagged mutual information MI[i(t), j(t − τ)] between all pairs of spike density time series for different single units i and j [evaluated via the same binning method for determining the Firing(t) descriptive feature vector]. Although MI is not a directed measure, a pseudo-direction of sharing is introduced by the positive time lag, supposing that information cannot be causally shared from the future. Thus, for every directed pair of single units i and j (including autointeractions, with i = j), we defined pseudo-directed information sharing asIshared(ji)=Στ MI[i(t),j(tτ)]where the lag τ was varying in the range 0 ≤ τ ≤ 0.5 Tθ, where Tθ is the phase of the THE cycle. Once again, we estimated MI terms via direct plug-in estimators on binarized spike trains, as with storage, subtracting a significance threshold (95th percentile of MI estimated on shuffled binarized trains, 400 replicas) and zeroing not significant terms. All these Ishared (ji) entries were interpreted as weights in the adjacency matrix of an information sharing directed functional network, and we defined as sharing assembly formed by a neuron i the star-subgraph of the information sharing network composed of i and all its immediate neighbors. We compiled all the overall N2 different values of Ishared (ji) into time-dependent feature vectors Sharing_A(t), thus describing all the possible sharing assemblies at a given time. We then also computed information sharing strengths by integrating the total amounts of information that each single unit was sharing with the past activity of other units in the network (“sharing-in”)Ishared(i)=Σj Ishared (ji)or with the future activity of other units in the network (“sharing-out”)Ishared (i)=Σj Ishared (ij)

That is, the integrated amount of shared information was given by the in-strength and the out-strength of a node in the information sharing network with individual link weights Ishared (ji). We compiled the N incoming Ishared (→ i) and N outgoing Ishared (i →) values into time-dependent vectors Sharing_S(t). We computed separate Sharing_A(t) and Sharing_S(t) for each of the simultaneously recorded regions. We then performed as before unsupervised clustering based on the associated Msim matrices to extract sharing substates. Because the block structure displayed by these Msim matrices for sharing assemblies and strengths are nearly perfectly overlapping, we conducted all substate analyses based on Sharing_S(t) vectors only. We defined a neuron to be a sharing hub in a given state if its Ishared (*i) and/or Ishared (i*) values in the state prototype vector were higher than the 95% percentile of all concatenated cluster prototypes entries (again protecting against false-positive detection).

The relative comparisons of information sharing between SO and THE (REM and nonREM) epochs for different recordings shown in fig. S5 are based, as in the case of AIS in fig. S5, on averaged and scaled values. We first averaged the total Ishared (i.e., sharing in plus sharing out) over all the units within a specific anatomic layer. We then normalized these average total Ishared values by dividing them by the average total Ishared value in the SO state (in anesthesia) or the nonREM state (in natural sleep) for the specifically considered recording and layer.

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