My colleagues and I have been working through this intriguing paper  from a few weeks ago:
Yan, G., Vértes, P.E., Towlson, E.K., Chew, Y.L., Walker, D.S., Schafer, W.R., and Barabási, A.-L. (2017). Network control principles predict neuron function in the Caenorhabditis elegans connectome. Nature advance online publication.
This seems like a very important contribution. It promises detailed insights about the function of a neural circuit based on its connectome alone, without knowing any of the synaptic strengths. The predictions extend to the role that individual neurons play for the circuit’s operation. Seeing how a great deal of effort is now going into acquiring connectomes  – mostly lacking annotations of synaptic strengths – this approach could be very powerful.
The starting point is Barabási’s “structural controllability theory” , which makes statements about the control of linear networks. Roughly speaking a network is controllable if its output nodes can be driven into any desired state by manipulating the input nodes. Obviously controllability depends on the entire set of connections from inputs to outputs. Structural controllability theory derives some conclusions from knowing only which connections have non-zero weight. This seems like a match made in heaven for the structural connectomes of neural circuits derived from electron microscopic reconstructions. In these data sets one can tell which neurons are connected but not what the strength is of those connections, or even whether they are excitatory or inhibitory. Unfortunately the match is looking more like a forced marriage… Continue reading “Control theory meets connectomes?”