Strategies for identifying exact structure of neural circuits with broad light microscopy connectivity probes

Dissecting the structure of neural circuits in the brain is one of the central problems of neuroscience. Until present day, the only way to obtain complete and detailed reconstructions of neural circuits was thought to be the serial section Electron Microscopy, which could take decades to complete a small circuit. In this paper, we develop a mathematical framework that allows performing such reconstructions much faster and cheaper with existing light microscopy and genetic tools. In this framework, a collection of genetically targeted light probes of connectivity is prepared from different animals and then used to systematically deduce the circuit's connectivity. Each measurement is represented as mathematical constraint on the circuit architecture. Such constraints are then computationally combined to identify the detailed connectivity matrix for the probed circuit. Connectivity here is understood broadly, such as that between different identifiable neurons or identifiable classes of neurons, etc. This paradigm may be applied with connectivity probes such as ChR2-assisted circuit mapping, GRASP or transsynaptic viruses, and genetic targeting techniques such as Brainbow, MARCM/MADM or UAS/Gal4, in model organisms such as C. Elegans, Drosophila, zerbafish, mouse, etc. In particular, we demonstrate how, by using this paradigm, the wiring diagram between all neurons in C. Elegans may be reconstructed with GRASP and Brainbow and off-the-shelf light microscopy tools in the time span of one week or less. Described approach allows recovering exact connectivity matrix even if neurons may not be targeted individually in ~Np*log(N) time (Np is the number of nonzero entries and N is the size of the connectivity matrix). For comparison, the minimal time that would be necessary to determine connectivity matrix directly by probing connections between individual neurons when one knows a-priory which pairs should be tested, e.g. with whole-cell patches, is ~Np.

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