2018/10/08 by Lin, Congping, Huang, Yuanfei, Quan, Tingwei +1
#Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Neurons and Cognition (q-bio.NC) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1810.03262
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.