Neocortical Axon Arbors Trade-off Material and Conduction Delay Conservation

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Abstract
The brain contains a complex network of axons rapidly communicating information between billions of synaptically connected neurons. The morphology of individual axons, therefore, defines the course of information flow within the brain. More than a century ago, Ramón y Cajal proposed that conservation laws to save material (wire) length and limit conduction delay regulate the design of individual axon arbors in cerebral cortex. Yet the spatial and temporal communication costs of single neocortical axons remain undefined. Here, using reconstructions of in vivo labelled excitatory spiny cell and inhibitory basket cell intracortical axons combined with a variety of graph optimization algorithms, we empirically investigated Cajal's conservation laws in cerebral cortex for whole three-dimensional (3D) axon arbors, to our knowledge the first study of its kind. We found intracortical axons were significantly longer than optimal. The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors. We discovered that cortical axon branching appears to promote a low temporal dispersion of axonal latencies and a tight relationship between cortical distance and axonal latency. In addition, inhibitory basket cell axonal latencies may occur within a much narrower temporal window than excitatory spiny cell axons, which may help boost signal detection. Thus, to optimize neuronal network communication we find that a modest excess of axonal wire is traded-off to enhance arbor temporal economy and precision. Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations. Within the grey matter of cerebral cortex is a complex network formed by a dense tangle of individual branching axons mostly of cortical origin. Yet remarkably when presented with a barrage of complex, noisy sensory stimuli this convoluted network architecture computes accurately and rapidly. How does such a highly interconnected though jumbled forest of axonal trees process vital information so quickly? Pioneering neuroscientist Ramón y Cajal thought the size and shape of individual neurons was governed by simple rules to save cellular material and to reduce signal conduction delay. In this study, we investigated how these rules applied to whole axonal trees in neocortex by comparing their 3D structure to equivalent artificial arbors optimized for these rules. We discovered that neocortical axonal trees achieve a balance between these two rules so that a little more cellular material than necessary was used to substantially reduce conduction delays. Importantly, we suggest the nature of arbor branching balances time and material so that neocortical axons may communicate with a high degree of temporal precision, enabling accurate and rapid computation within local cortical networks. This approach could be applied to other neural structures to better understand the functional principles of brain design.