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Branching rates and growth functions in the outgrowth of dendritic branching patterns

The outgrowth of dendritic branching patterns proceeds by neurite elongation and branching. These actions are supported by growth cones, specialized dynamic structures at the tips of outgrowing neurites, in response to a multitude of intracellular and extracellular signals and mechanisms. Branching rates of growth cones and their temporal patterns thus reflect the extent and changes in these responses. The present study outlines a model framework to relate branching rates of individual growth cones with the growth rate of the entire dendritic tree. The branching rate of an individual growth cone is assumed to depend on the total number of growth cones at any given moment (representing competition between growth cones), on its position along the dendrite, and on a baseline component representing all other factors. Four different strategies are discussed for determining quantitatively these components from experimental data. The methods are applied in the analysis of dendritic trees of Wistar rat multipolar non-pyramidal neurons, quantitatively reconstructed at several developmental stages (Parnavelas J G and Uylings H B M 1980 Brain Res. 193 373–82, Uylings H B M, Parnavelas J G, Walg H and Veltman W A M 1980 Mikroskopie 37 220–4). It is shown that the baseline branching rate is a rapidly decreasing function of time, indicating the largest baseline drive for branching in the early days of outgrowth.