Hierarchical recurrent state space models reveal discrete and continuous dynamics of neural activity inC. elegans

Abstract

Modern recording techniques enable large-scale measurements of neural activity in a variety of model organisms. The dynamics of neural activity shed light on how organisms process sensory information and generate motor behavior. Here, we study these dynamics using optical recordings of neural activity in the nematode C. elegans. To understand these data, we develop state space models that decompose neural time-series into segments with simple, linear dynamics. We incorporate these models into a hierarchical framework that combines partial recordings from many worms to learn shared structure, while still allowing for individual variability. This framework reveals latent states of population neural activity, along with the discrete behavioral states that govern dynamics in this state space. We find stochastic transition patterns between discrete states and see that transition probabilities are determined by both current brain activity and sensory cues.Our methods automatically recover transition times that closely match manual labels of different behaviors, such as forward crawling, reversals, and turns. Finally, the resulting model can simulate neural data, faithfully capturing salient patterns of whole brain dynamics seen in real data. Tonic signaling from O 2 sensors sets neural circuit activity and behavioral state. Nature neuroscience, 15(4):581, 2012. M. Chalfie, J. E. Sulston, J. G. White, E. Southgate, J. N. Thomson, and S. Brenner. The neural circuit for touch sensitivity in Caenorhabditis elegans. Journal of Neuroscience, 5(4):956-964, 1985. C.-B. Chang and M. Athans. State estimation for discrete systems with switching parameters. IEEE Transactions on Aerospace and Electronic Systems, AES-14(3):418-425, 1978. Z. Chen, S. N. Gomperts, J. Yamamoto, and M. A. Wilson. Neural representation of spatial topology in the rodent hippocampus. Neural Computation, 26(1):1-39, 2014. Monte Carlo sampling for tuning-curve analysis. J. Neurophysiol., 103(1):591-602, Jan. 2010. J. P. Cunningham and M. B. Yu. Dimensionality reduction for large-scale neural recordings. Nature neuroscience, 17(11):1500, 2014. P. Dayan and L. F. Abbott. Theoretical neuroscience: computational and mathematical modeling of neural systems. MIT press, 2001. A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM algorithm.

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