Scaling principles of distributed circuits

Distributed circuits like the olfactory cortex, hippocampus, and cerebellum contain sub-circuits whose inputs distribute their axons over the entire circuit creating a puzzle of how information is encoded. One method for approaching the puzzle is to view them as scalable systems. In scalable systems the quantitative relationship between circuit components is conserved across brain sizes, and by mapping circuit size to functional abilities - e.g. visual acuity in the visual circuit - scientists have explained information encoding. This approach has not been applied to anti-map circuits as their scalability is unknown. To address this gap in knowledge, we obtained quantitative descriptions of the olfactory bulb and piriform cortex in six mammals using stereology techniques and light microscopy. We found that the olfactory circuit is scalable as it satisfies three requirements of scalable systems. First, quantitative relationships between circuit components are conserved: the number piriform neurons n scales with bulb glomeruli g as n ~ g3/2. Second, the olfactory circuit has an invariant property: the average number of synapses between a bulb glomerulus and piriform neuron is one. Third, the olfactory circuit is symmorphic, i.e. olfactory ability improves with circuit size. Other distributed circuits with similar properties might also be scalable.