Communication Subspaces

The brain is composed of networks of circuits that constantly communicate in time and space. This blog post is about a project that I did with Jean Simonnet and Xin Wei Chia over the course of the NeuroMatch Academy summer school. The project was supervised by Matthew Kaufman. We worked on Neuropixel probes data set from Nick Steinmetz. We focused our investigations on the communication between the frontal brain and midbrain of one experimental animal. The project code can be found here https://github.com/mariakesa/ConnectedLizards_NeuroMatch2020

We used linear regression and PCA to predict neural activity in a midbrain circuit from a forebrain circuit. The dimensions of the source area activity that are predictive of the activity of the tartget circuit are called the communication subspace (Semedo et al, 2019). We were interested in whether dimensions that contain the communication subspace between these areas are also dimensions along which activity best correlates with behavior of the animal (for this blog post we used the face motion energy as behavior, because that's the part of the data that I specifically worked on). 

To investigate this questions of how behavioral information is transmitted between the frontal and midbrain circuits we used the following algorithm.

Communication Subspace Algorithm:
1. Split data into train and test. 
1. Take the principal components of trial averaged neural data in the training set (or potentially multiple trials concatenated together into one long vector, depending on the question) from the frontal circuit, midbrain circuit. Take principal components over behavior matrix (trials x time points). Project the data onto PC dimensions for the test set (transform function in sklearn). 
2. Use linear regression (more specifically regularized linear regression, e.g. ridge regression) to find a projection matrix that maps linearly the PC's from the frontal brain to the PC's of the midbrain.
3. Find the the top vectors from the linear regression projection matrix that when combined with frontal PC's explain the most variance in the midbrain PC's time series. Of course, use the test set to evaluate the best directions (e.g. data you didn't use for fitting the model). 
4. Do ridge regression to find a mapping between the projection of the frontal PC's onto the dimensions of the linear regression matrix (found in the previous step) to predict behavior. 
5. Find the null space of the frontal-midbrain linear regression matrix and project the frontal PC's onto its dimensions and use the found vectors to predict behavior.


What did we find?

When we subset the data to brain areas MOS in the frontal cortex and SCs in the midbrain, there are indeed PC's in the frontal cortex that very well predict a PC in the midbrain. This figure:

The dimensions that explain the most variance in the midbrain PC's can predict behavior. See this figure:

There's a dimension in the null space that predicts behavior really well. See this figure:
Other dimensions in the null space don't predict behavior well. See this figure: 

We're working on a presentation now. The question is how to visualize the results in the most insightful way and generalize to other midbrain and frontal brain regions. 

Thanks for reading!

References
Steinmetz et al, "Distributed coding of choice, action and engagement across the mouse brain", Nature, 2019

Kaufman et al,"Cortical activity in the null space: permitting preparation without movement", Nature Neuroscience, 2014

Semedo et al, "Cortical areas interact through a communication subspace", Neuron, 2019



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