Axons in cat visual cortex are topologically self-similar

The axonal arbors of the different types of neocortical and thalamic neurons appear highly dissimilar when viewed in conventional 2D reconstructions. Nevertheless, we have found that their one-dimensional metrics and topologies are surprisingly similar. To discover this, we analysed the axonal branching pattern of 39 neurons (23 spiny, 13 smooth and three thalamic axons) that were filled intracellularly with horseradish peroxidase (HRP) during in vivo experiments in cat area 17. The axons were completely reconstructed and translated into dendrograms. Topological, fractal and Horton-Strahler analyses indicated that axons of smooth and spiny neurons had similar complexity, length ratios (a measure of the relative increase in the length of collateral segments as the axon branches) and bifurcation ratios (a measure of the relative increase in the number of collateral segments as the axon branches). We show that a simple random branching model (Galton-Watson process) predicts with reasonable accuracy the bifurcation ratio, length ratio and collateral length distribution of the axonal arbors.