Inferring neural population dynamics from multiple partial recordings of the same neural circuit
Simultaneous recordings of the activity of large neural populations are extremely valuable as they can be used to infer the dynamics and interactions of neurons in a local circuit, shedding light on the computations performed. It is now possible to measure the activity of hundreds of neurons using 2-photon calcium imaging. However, many computations are thought to involve circuits consisting of thousands of neurons, such as cortical barrels in rodent somatosensory cortex. Here we contribute a statistical method for "stitching" together sequentially imaged sets of neurons into one model by phrasing the problem as fitting a latent dynamical system with missing observations. This method allows us to substantially expand the population-sizes for which population dynamics can be characterized-beyond the number of simultaneously imaged neurons. In particular, we demonstrate using recordings in mouse somatosensory cortex that this method makes it possible to predict noise correlations between non-simultaneously recorded neuron pairs.
The paper contributes a statistical method to “stitch” 
      together sequentially imaged sets of neurons. Such a method expands the 
      population sizes for which population dynamics can be characterized beyond 
      the number of simultaneously imaged neurons and provide a better image of 
      the circuit which cannot be imaged as a whole for experimental and 
      technical limitations. The method is then applied on simulated data as 
      well as on experimental calcium imaging data in mice. Authors show that 
      they can estimate correlations in variability across two populations which 
      were not imaged simultaneously. The Authors model the problem as 
      fitting a latent dynamical system with missing observations. In this case 
      they used simple linear Gaussian system. Four parameters were defined in 
      the model: a functional coupling matrix, a stimuli receptive fields’ 
      matrix which models the stimulus dependence of the population activity and 
      two covariance matrices for neural and measurement noise. The parameters 
      were estimated from experimental data using a variant of standard EM 
      algorithm. Quality The model works nicely on the simulated 
      data with two non-overlapping populations of neurons but when applying on 
      real data populations must have a certain level of overlap to get 
      reasonable results. It is clear why the greater the overlap the better the 
      results are, the question is why wasn’t overlap necessary in the simulated 
      data example? Also, the authors do not address the source for the 
      great difference in correlation shown when applying the model on simulated 
      data as in fig 2c and on real data as in fig 3b The beauty of the 
      model is the recovery of pairwise correlations between non-simultaneously 
      measured neuron pairs. Clarity The paper is well written, 
      although all figure legends are not descriptive enough and the text 
      related to the figures in the body of the paper does not elaborate enough 
      on the figures. Originality The authors list several works 
      which have addressed the question of inferring functional connectivity 
      from 2-photon imaging data or electrophysiological measurements. However, 
      these works do not infer functional connections of non-simultaneously 
      imaged neurons. Significance There are many fundamental limits 
      to the number of neurons which can be simultaneously imaged. That of 
      course, limits our capabilities to reveal the nature of the neural 
      computation at the level of the circuit (or more than a few hundreds of 
      cells). This paper suggests a method for expanding these limited 
      capabilities.