Universal features of dendrites through centripetal branch ordering

Authors:
Open Access
Publisher website
Google Scholar
Abstract
Dendrites form predominantly binary trees that are exquisitely embedded in the networks of the brain. While neuronal computation is known to depend on the morphology of dendrites, their underlying topological blueprint remains unknown. Here, we used a centripetal branch ordering scheme originally developed to describe river networks—the Horton-Strahler order (SO)–to examine hierarchical relationships of branching statistics in reconstructed and model dendritic trees. We report on a number of universal topological relationships with SO that are true for all binary trees and distinguish those from SO-sorted metric measures that appear to be cell type-specific. The latter are therefore potential new candidates for categorising dendritic tree structures. Interestingly, we find a faithful correlation of branch diameters with centripetal branch orders, indicating a possible functional importance of SO for dendritic morphology and growth. Also, simulated local voltage responses to synaptic inputs are strongly correlated with SO. In summary, our study identifies important SO-dependent measures in dendritic morphology that are relevant for neural function while at the same time it describes other relationships that are universal for all dendrites. Similarly to river beds, dendritic trees of nerve cells form elaborate networks that branch out to cover extensive areas. In the 1940s, ecologist Robert E. Horton developed an ordering system for branches in river networks that was refined in the 1950s by geoscientist Arthur N. Strahler, the Horton-Strahler order (SO). Branches at the tips start with order 1 and increase their order in a systematic way when encountering new branches on the way to the root. SO relationships have recently become popular for quantifying dendritic morphologies. Various branching statistics can be studied as a function of SO. Here we describe that topological measures such as the number of branches, the branch bifurcation ratio and the size of subtrees exhibit stereotypical relations with SO in dendritic trees independently of cell type, mirroring universal features of binary trees. Other functionally more relevant features such as mean branch lengths, local diameters and simulated voltage responses to synaptic inputs directly correlate with SO in a cell type-specific manner, indicating the importance of SO for understanding dendrite growth as well as neural computation.
Funding Information
  • Bundesministerium für Forschung, Technologie und Raumfahrt (01GQ1406)

This publication has 75 references indexed in Scilit: