Scaling Principles of Distributed Circuits.

Identifying shared quantitative features of a neural circuit across species is important for 3 reasons. Often expressed in the form of power laws and called scaling relationships [1, 2], they reveal organizational principles of circuits, make insights gleaned from model systems widely applicable, and explain circuit performance and function, e.g., visual circuits [3, 4]. The visual circuit is topographic [5, 6], wherein retinal neurons target and activate predictable spatial loci in primary visual cortex. The brain, however, contains many circuits, where neuronal targets and activity are unpredictable and distributed throughout the circuit, e.g., olfactory circuits, in which glomeruli (or mitral cells) in the olfactory bulb synapse with neurons distributed throughout the piriform cortex [7-10]. It is unknown whether such circuits, which we term distributed circuits, are scalable. To determine whether distributed circuits scale, we obtained quantitative descriptions of the olfactory bulb and piriform cortex in six mammals using stereology techniques and light microscopy. Two conserved features provide evidence of scalability. First, the number of piriform neurons n and bulb glomeruli g scale as n∼g3/2. Second, the average number of synapses between a bulb glomerulus and piriform neuron is invariant at one. Using theory and modeling, we show that these two features preserve the discriminatory ability and precision of odor information across the olfactory circuit. As both abilities depend on circuit size, manipulating size provides evolution with a way to adapt a species to its niche without designing developmental programs de novo. These principles might apply to other distributed circuits like the hippocampus.