Fig. 1. Structural analysis of axons segmented from female mouse brain corpus callosum EM reveals that the 1d placement of caliber variations exhibits short-range disorder, characterized by a finite correlation length.

a 3d EM image with segmented axons passing through the central slice. b 3d representation of the intra-axonal space (IAS) segmentation yielding 227 axons that are long enough to pass through all slices (>20 μm). c Radius variation r(z) and d normalized radius variation $\tilde{r}\left(z\right)$ along seven selected axons. e Histogram of distances a between local radius maxima along all 227 segmented axons. f The power spectrum Γ_1d(k_z) along all axons (blue curve, truncated at k_z ~ 1/L due to limited individual axon’s length L) shows a plateau at low k_z $\ll 1/ā$ with $ā$ the mean distance between restrictions (blue dashed line), indicating a structural exponent p = 0, which corresponds to the short-range disorder and leads to the dynamical exponent ϑ = 1/2 in Eq. (1), cf. Eq. (2). Serving as a reference, the red curve shows the power spectrum Γ_pos(k_z) of the restriction positions¹⁵ with a plateau at low k_z as well. Panels a and b are adapted from ref. ²³ by permission from Springer Nature: Brain Structure and Function, Copyright, 2019.