A Bayesian compressed-sensing approach for reconstructing neural connectivity from subsampled anatomical data

In recent years, the problem of reconstructing the connectivity in large neural circuits ("connectomics") has re-emerged as one of the main objectives of neuroscience. Classically, reconstructions of neural connectivity have been approached anatomically, using electron or light microscopy and histological tracing methods. This paper describes a statistical approach for connectivity reconstruction that relies on relatively easy-to-obtain measurements using fluorescent probes such as synaptic markers, cytoplasmic dyes, transsynaptic tracers, or activity-dependent dyes. We describe the possible design of these experiments and develop a Bayesian framework for extracting synaptic neural connectivity from such data. We show that the statistical reconstruction problem can be formulated naturally as a tractable L₁-regularized quadratic optimization. As a concrete example, we consider a realistic hypothetical connectivity reconstruction experiment in C. elegans, a popular neuroscience model where a complete wiring diagram has been previously obtained based on long-term electron microscopy work. We show that the new statistical approach could lead to an orders of magnitude reduction in experimental effort in reconstructing the connectivity in this circuit. We further demonstrate that the spatial heterogeneity and biological variability in the connectivity matrix--not just the "average" connectivity--can also be estimated using the same method.