Natural variability in the number of dendritic segments: Model-based inferences about branching during neurite outgrowth

Abstract

A study was made of the possible basis for naturally occurring variations in the number of segments in individual dendritic trees. Distributions of the number of terminal segments have been studied in dendrites from rat, cat, and frog motoneurons, basal dendrites from rat visual cortex pyramidal and non-pyramidal neurons, in rat cerebellar Purkinje cell dendritic trees, and in human hippocampal dentate granule cells. By means of a mathematical model for dendritic branching, it was shown that the variation in the number of dendritic segments can be accounted for by assuming that new branches during neurite outgrowth are formed randomly at terminal segments. The observed terminal segment number distributions could be closely approximated by additionally assuming that branching probabilities decline with increasing number of terminal segments in growing dendrites. The pyramidal neuron group differed significantly from the other neuron groups in such a way as to suggest that this decline is stronger than in the dendrites of other types of neurons. By using literature data on the mean number of terminal segments in rat cerebellar Purkinje cells, measured at different times during early development, an estimate could be obtained of the time-course of the branching probabilities. The branching probability of a terminal segment was found to be in the order of 0.002 per hour in the first 4 weeks postnatal with a 5-fold transient increase in the second week.

Universal features of dendrites through centripetal branch ordering

“…For each successive generation, each terminal node of the previous generation is treated in one of the following two ways: (1) with probability P st , growth stops there; (2) with probability P br , the node becomes a branch point, and edges are added with two new terminal nodes (Fig 2F). Terminal growth was previously found to be compatible with the observed topologies in real dendrites [65]. A Galton-Watson process is called critical if P st = 0.5 and P br = 0.5.…”

Self-organizing Mechanism for Development of Space-filling Neuronal Dendrites

“…Many of the previous models assumed that elongation and branching of dendrites are controlled by probability functions, in which each parameter separately codes individual growth rules such as degree- or segment length- dependent rate of elongation and/or branching [19,20]. In contrast, dendritic patterns are autonomously generated without embedding different parameters to control each branching frequency, branch angle, and self-avoidance of dendrites in our model.…”

Competitive Dynamics during Resource-Driven Neurite Outgrowth

“…In the stochastic phenomenological model of Van Pelt et al [45]–[47], each growth cone in the growing tree has a certain probability to branch and elongate. Interestingly, to be able to accurately produce the morphology of a wide range of neuron types, the model needs a competition factor describing how the growth cone's actions depend on the momentary total number of growth cones in the tree.…”