On the methods for reactivation and replay analysis

Abstract

A major task in the history of neurophysiology has been to relate patterns of neural activity to ongoing external stimuli. More recently, this approach has branched out to relating current neural activity patterns to external stimuli or experiences that occurred in the past or future. Here, we aim to review the large body of methodological approaches used towards this goal, and to assess the assumptions each makes with reference to the statistics of neural data that are commonly observed. These methods primarily fall into two categories, those that quantify zero-lag relationships without examining temporal evolution, termed reactivation, and those that quantify the temporal structure of changing activity patterns, termed replay. However, no two studies use the exact same approach, which prevents an unbiased comparison between findings. These observations should instead be validated by multiple and, if possible, previously established tests. This will help the community to speak a common language and will eventually provide tools to study, more generally, the organization of neuronal patterns in the brain. This article is part of the Theo Murphy meeting issue 'Memory reactivation: replaying events past, present and future'.

Keywords: memory; neuronal dynamics; population coding; sleep.

Figure 1.

Phylogeny of method development. We have attempted to trace out when new methods were developed, and what phenomenon (reactivation or replay) they quantify. Red traces indicate phylogenetic branches of reactivation method development. Blue traces indicate branches of replay method development. Grey traces indicate branches using ‘decoding’ methods. Abbreviations: Bayes, Bayesian decoding; EV/REV, explained variance/reverse explained variance; GLM, generalized linear models; HPC, hippocampus; mPFC, medial prefrontal cortex; NC, neocortex; PoP States, population states; PPC, posterior parietal cortex; Seq. Temp., sequence template; Temp. Bias, temporal bias; V1, primary visual cortex; XCorr, cross-correlation. (Online version in colour.)

Figure 2.

Reactivation. The first step in reactivation methods is to determine the number of significant components (i.e. linear combination of the binned spike trains) that explain more variance than what is expected by chance in the reference epoch. This is done by decomposing the correlation matrix of the binned spike trains of the reference epoch into its eigenvectors (i.e. PCA) and determining the number of its eigenvalues (λ) that are greater than the theoretical upper bound of the eigenvalue spectrum (the Marchenko–Pastur bound, λ_max). Then, the binned spike trains are decomposed into their significant projection matrices (three in this example), which are equal to the outer product of the correlation matrix eigenvectors (or principal components, PCs) or of the independent components (ICs) (see text). Then, the data of the target epoch are binned, z-scored and projected onto the projection matrices, resulting in reaction strengths (R) that track the time-resolved reactivation of target neuronal ensembles relative to the reference epoch. The diagonal of the projection matrices is set to 0 to make the reactivation strength more robust to the fluctuation of single-neuron activity. (Online version in colour.)

Figure 3.

Replay. (a) Example recordings of hippocampal neurons with place tuning, as an animal traverses a maze. (b) Upper: example candidate replay events. R-values are the linear weighted correlations between each event and the template generated from maze traversals. Cells are sorted and coloured to match figure 1a. Lower: histogram of weighted correlation values for all candidate replay events. (c) Histogram of correlation values when comparing linear weighted correlations with the rank-order correlation method for all candidate replay events. (d) Upper: histogram of correlation values when comparing linear weighted correlations with the integral of the line of best fit, using the radon transform method, for all candidate replay events. Lower: histogram of correlation values when comparing linear weighted correlations with the slope of the line of best fit, using the radon transform method, for all candidate replay events. (e) Upper: histogram of correlation values when comparing rank order correlations with the integral of the line of best fit, using the radon transform method, for all candidate replay events. Lower: histogram of correlation values when comparing rank-order correlations with the slope of the line of best fit, using the radon transform method, for all candidate replay events. (Online version in colour.)

Figure 4.

Simulations of candidate events. (a) Rank-order correlation (i) and radon integral (ii) for a set of simulated replay events (n = 100 cells, one spike each per event). x-axis is the number of randomly inserted ‘noise’ spikes. y-axis is the number of randomly removed ‘real’ spikes. These spikes are added and removed from a ‘perfect’ replay event where every cell fires one spike in the same order as a template. (b) Reactivation strength using PCA (i) and reactivation strength using ICA (ii) for the same set of events shown in (a). (Online version in colour.)