Modelling brain-wide neuronal morphology via rooted Cayley trees

TL;DR

This study analyzes brain-wide neuron reconstructions, revealing self-affinity in axons and self-similarity in dendrites, and introduces a stochastic inhomogeneous branching model that captures key topological features of neuronal trees.

Contribution

The paper presents a novel inhomogeneous branching model based on rooted Cayley trees that accurately reproduces the topology of brain-wide neuronal morphology.

Findings

Axonal trees are self-affine.

Dendritic trees are self-similar.

Tree size is independent of dendrite number.

Abstract

Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.