On the Generation of Random Dendritic Shapes

Abstract

Dendritic branching patterns are complex and show a large degree of variation in their shapes. This variation can be found in typical shape parameters, such as the number, length and connectivity pattern (topological structure) of the constituent segments. Den- dritic branching patterns emerge during neuronal development from the behavior of growth cones which determine the processes of branching and lengthening of segments (e.g., Bray, 1992). This dynamic behavior of growth cones is the result of cellular re- sponses to the local environments (e.g., Kater et a!., 1994; Letourneau et a!., 1994). Many mechanisms are involved in growth cone behavior, making it plausible to hypothesize that dendritic arborizations emerge from stochastic behavior of growth cones. A crucial test for this hypothesis is to show that the characteristic variations in dendritic morphologies can be reproduced by a process of random branching. This study concentrates on the variation in the number of segments and their connectivity patterns in the trees. Metrical properties will be ignored and dendrites are reduced to their skeleton of segments and bifurcation points.