Definitions

tree morphing

Morphing a tree is the process of mapping new metric length values on an existing tree, while preserving its topology and local angles

adapted from
PLoS supp. material by Hermann Cuntz

← the_topological_gene
→ electrotonic_signature

Segev and colleagues derived a new representation of neuronal trees depending on electrotonic measures. The method used for this representation was called the “Morphoelectrotonic Transform” (Zador et al. 1995, J Neurosci 15(3):1669-82).

In fact, the method used in that case is very generalizable. Any Nx1 vector of length values may be mapped on a tree with N nodes. This is done by scaling the length value l_i of all segments to the new segment lengths while conserving the direction of the segment indicated by the direction vector (arrow below). At each step the entire sub-tree needs to be translated accordingly.

Only in the case of 0-length segments, a direction needs to be picked arbitrarily. A TREES toolbox function (see “morph_tree”), performs this type of morphing operation which can have various applications of which the morpho-electrotonic transform is just one.

On the path sum (see “Pvec_tree”), child sum (see “child_tree”), segment binning (see “bin_tree”) parent daughter ratio (see “ratio_tree”), are further examples of such “meta-functions” which apply an Nx1 vector on a tree structure to result in a wide variety of applications.