With the growing amount of connectome data being gathered, it behooves us to develop systems-theoretic methods to analyze this data so as to provide insights into the function of neuronal circuits. Here, we develop models and compute capacities for gap junction synapses. We develop information-theoretic lower bounds on computation speed arising from limitations of anatomical connectivity and physical noise. For the nematode Caenorhabditis elegans, these bounds are predictive of biological timescales. Moreover, the hub-and-spoke architecture of C. elegans functional subcircuits are optimal under constraint on number of synapses.