Models for Growth, Decline and Regrowth of the Dendrites of Rat Purkinje Cells Induced from Magnitude and Link-length Analysis

This study examines Purkinje neurons of rats aged 1, 10, 18 and 28 months to investigate growth and decline in the magnitude of the dendritic tree, i.e. the number of exterior links (terminal segments) per cell. Growth in the mean number of exterior links was observed from 1 to 10 months, decline at 18 months and regrowth at 28 months. At 10, 28, and especially at 18 months, the cell size frequency distribution indicates two groups of cells, one of small and the other of large sized cells. The study also examines the relationship of age to lengths of topologically defined links of various types. For each age group we find that exterior links are longer than interior links (non-terminal or intermediate segments). Analysis of the geometric mean lengths of subtypes of exterior and interior links at maturity (10 months) indicates that they follow a Fibonacci series of link lengths, such that mean lengths of topologically defined types of mean exterior links are either about 13 or 8 μm long, while interior links are about 5 μm long. A sequential growth model for adding exterior links is suggested to illustrate a style of growth which could account for the various mean link lengths and the Fibonacci ratio (1·618) between their lengths. Interior link lengths are also dependent on the generation of exterior links from the sides of pre-existing interior links. If the Strahler branching ratio, R b , should increase owing to growth of terminals from interior links, then mean interior link length would decline. During a period of regression, mean exterior link lengths become shorter and mean interior link lengths become longer. Changes in mean interior link length are much less affected by changes in R b during regression than is the situation during growth. Finally, the changes in link lengths dictate that the ratio of mean exterior to mean interior link length increases during growth phases from 1 to 10 and 18 to 28 months, and declines during regression from 10 to 28 months. The lowest values of the ratio of mean exterior to mean interior lengths are found at 1 month. This is the period of most intense growth. During this period, the rate of development of new exterior links outbalances the rate at which the links increase in length.