Link-Vertex Analysis of Purkinje cell dendritic trees from the murine cerebellum

A method of analysis of dendritic trees is described, called Link-Vertex Analysis, which defines the branching patterns (topology) by means of a discontinuous function, the terminal/link (T/L) vertex ratio, computed at all successive vertex orders within a network, and represented as a graphical plot for a given tree. The T/L vertex ratio is defined as the number (n) of terminal (pendant) vertices (Vp) divided by the total number (n) of all link vertices (both dichotomous, Vd, and trichotomous, Vt) multiplied by the number of segments arising from each vertex--i.e., nVp/(2nVd + 3nVt) per vertex order. Hypotheses of growth are simulated by computer modelling and the distributions of computer generated T/L vertex ratios per order compared with those of actual dendritic trees. The differential distribution of T/L vertex ratios per order in trees grown by either random terminal or random segmental branching discriminates between these two forms of growth. Significant advances of this method include the detection of regional variations in growth and remodelling in a tree and the incorporation of Vt with little perturbation of the Vd data. The analytical powers of this method have been tested using the dendritic fields of 20-day-old mouse cerebellar Purkinje cells defining possible temporal sequences and relative contributions of random and non-random terminal growth, and also the frequency of branching over a growth front relative to that of the rest of the tree.