We present a framework for reconstructing structure of complete neural circuits
in the brain using collections of independent measurements of connectivity
performed with existing anatomical or functional fluorescent probes, and
designed to provide complementary information about neural circuit’s structure
by targeting slightly different its parts either in deterministic or stochastic
succession. We discuss specific implementation of this procedure using
synaptic fluorescent marker GRASP and Cre/Lox system Brainbow to collect
ensemble of observations of the sets of synapses between stochastically labeled
samples of neurons. By representing such measurements mathematically as
weak constraints on circuit’s connectivity matrix and by solving a constrained
optimization problem, we are able to exactly deduce the wiring diagram in C.
Elegans in an in-silico experiment from only ~10,000 measurements. This
offers possibility for routinely reconstructing complete connectivity in smaller
organisms, such as C. Elegans, using exclusively light microscopy instruments
over the span of single weeks
