Woldenberg M J, O'Neill M P, Quackenbush L J, Pentney R J
Department of Geography, State University of New York at Buffalo, NY 14261.
J Theor Biol. 1993 Jun 21;162(4):403-29. doi: 10.1006/jtbi.1993.1097.
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 microns long, while interior links are about 5 microns 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, Rb, 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 Rb 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.
本研究对1、10、18和28月龄大鼠的浦肯野神经元进行了检测，以研究树突树大小（即每个细胞的外部连接数，也就是末端节段数）的生长和衰退情况。观察到外部连接的平均数量从1月龄到10月龄有所增长，18月龄时下降，28月龄时又重新增长。在10月龄、28月龄，尤其是18月龄时，细胞大小频率分布显示出两组细胞，一组是小细胞，另一组是大细胞。该研究还考察了年龄与各种类型拓扑定义连接长度之间的关系。对于每个年龄组，我们发现外部连接比内部连接（非末端或中间节段）长。对成熟时（10月龄）外部和内部连接亚型的几何平均长度分析表明，它们遵循连接长度的斐波那契数列，即拓扑定义的平均外部连接类型的平均长度约为13微米或8微米，而内部连接约为5微米。我们提出了一个用于添加外部连接的顺序生长模型，以说明一种生长方式，该方式可以解释各种平均连接长度以及它们长度之间的斐波那契比率（1.618）。内部连接长度还取决于从预先存在的内部连接侧面产生的外部连接。如果由于内部连接末端的生长导致斯特拉勒分支比Rb增加，那么平均内部连接长度将会下降。在衰退期，平均外部连接长度变短，平均内部连接长度变长。与生长期间的情况相比，衰退期间平均内部连接长度的变化受Rb变化的影响要小得多。最后，连接长度的变化表明，在1至10月龄以及18至28月龄的生长阶段，平均外部与平均内部连接长度的比率会增加，而在10至28月龄的衰退期则会下降。平均外部与平均内部长度的比率在1月龄时最低。这是生长最旺盛的时期。在此期间，新外部连接的发育速度超过了连接长度增加的速度。
