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Connectome-constrained Latent Variable Model of Whole-Brain Neural Activity

Brain-wide measurements of activity and anatomical connectivity of the $\textit{C. elegans}$ nervous system in principle allow for the development of detailed mechanistic computational models. However, there are several challenges. We often do not have direct experimental access to important modeling details such as single-neuron dynamics and the signs and strengths of the synaptic connectivity. Further, neural activity can only be measured in a subset of neurons, often indirectly via calcium imaging, and significant trial-to-trial variability has been observed. To overcome these challenges, we introduce a connectome-constrained latent variable model (CC-LVM) of the unobserved voltage dynamics of the entire $\textit{C. elegans}$ nervous system and the observed calcium signals. We used the framework of variational autoencoders to fit parameters of the mechanistic simulation constituting the generative model of the LVM to calcium imaging observations. A variational approximate posterior distribution over latent voltage traces for all neurons is efficiently inferred using an inference network, and constrained by a prior distribution given by the biophysical simulation of neural dynamics. When applied to a recent dataset, we find that connectomic constraints enable our LVM to predict the activity of neurons whose activity were withheld. We explored models with different degrees of biophysical detail, and found that models with conductance-based synapses provide markedly better predictions than current-based synapses for this system.

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