Pca Based Reactivation Strength

06 Apr 2020

I was recently reading a paper titled Replay of rule-learning related neural patterns in the prefrontal cortex during sleep by Peyrache et al. 2009. It is an amazing paper that demonstrates memory trace reactivation during sleep in the medial Prefrontal Cortex (mPFC) and how it is coupled to the hippocampus sharp-wave ripple (SWRs). This is a must paper to read for anyone interested in the hippocampus-cortical interaction and reactivation during sleep.

The paper uses a PCA-based analysis to compute reactivation strengths. This post is just an attempt to try to replicate the algorithms used in the paper.

Algorithm

There are two parts of the algorithm: Part I: Template Epoch

  1. Get the spike raster for the cell ensemble.

  2. Bin the spike trains in 25ms bin. The authors used 100ms bins. Binned spike trains are then z-transformed.

  3. Compute the correlation matrix on the z-transformed binned spike trains.

  4. Compute the principal components of the correlation matrix.

  5. Compute PCA projector operators P1,P2….,Pn as the external product of the component vector with itself. The sum of these projector operators, weighted by their respective eigenvalues, yields the correlation matrix (shown in right). The projector matrices will be used as our templates.

Part II: Target Epoch

  1. Get the binned spike train from sleep epochs or epochs that you want to match templates to.

  2. Each template computed above is separately applied on the target epoch: for each time t, the binned spike trains is left and right multiplied on the projector matrix. This gives us the reactivation strength at time t between the population vector (binned spike count at time t) and the template.

  3. Repeat this process for each time bin in the target epoch. This will yield a time course for the reactivation strength for each time bin in the target epoch, yielding a time course for the reactivation strength. Reactivation strength computed from two randomly chosen templates:


One can now compare the reactivation strength between NREM, REM epochs or pre-task/ post-task sleep. There are multiple other ways to look at reactivation which I will post about in the future. Good luck!