Figure 1
From: An Optimized Structure-Function Design Principle Underlies Efficient Signaling Dynamics in Neurons
Deriving axonal network tree graphs from morphological reconstructions. (A) Representative three dimensional morphological reconstruction of one of the Basket cells in our data set from rat neocortex. Dendritic arbors are in green, axonal arbors in black [data from http://neuromorpho.org/21,22,23]. (B) Graph-based model of the geometric network of an axon and its arborizations. Vertices in the graph are labeled as follows: root vertex vR is located at the initial segment of the axon at the soma; branching vertices vB corresponding to branch points along the axons; terminal vertices vT were synaptic terminals of the axon arborizations. Vertices between branch points reflect measurement points in the original reconstruction, and are denoted as ve,n, with e identifying the edge and n the specific axonal point within that edge. The computation of the convoluted geometric distance between the root vertex vR and a selected terminal vertex \({v}_{{T}_{s}}\) was determined by the sum of all edge distances between ve,n pairs forming the total path that connected the two vertices. The total distance approximates well the edge path length integral (see the Methods) of the tortuous path connecting the axon initial segment to a synaptic terminal in a real neuron (see panel A). (C) Reduced adjacency matrix mapping the connectivity between branching points along the axon tree of the neuron visualized in A. (D) Three dimensional graph of the same axon arbor mapped onto a minimized length network where only root vertex and terminal vertices are considered. The units are microns, as indicated. Metric distances are Euclidean distances from the root vertex at the center of the figure (common point for each branch) to the axonal terminals. The actual terminals are the green points in the figure. The 3D positions of root and terminal vertices (X, Y, Z coordinate values) were obtained from the 3D morphological reconstruction in the NeuroMorpho database. Visually, Euclidean distances are represented by the blue lines connecting the root to the terminal vertices. (E) Biograph of the reduced network of the axon arbor in A, described by the adjacency matrix in C. Each labeled box in the graph stands for an identification number of the reported vertex. Root vertex in yellow, branching vertices in green, and terminal vertices in red.
