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《Acta Zoologica Sinica》 1992-03
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HUANG JING-FEI LIU CI-QUAN WANG YING(Laboratory of Cellular and Molecular Evolution Kunming Institute of Zoology, Academio Sinica Kunming 650107,Yunnan)  
In the recent years, some persons have done a serious of theoretical and experimental studies on the fractal problems of biological macromolecular structures and got some greater progresses.In view of biosystem being a non-linear sy tem, organic evolution being a non-linear procedure and fractals being one of the non-linear features, we consider that do further the detail research on the relationship between molecular evolution of homologous biological macromo-lecules and their fractal dimensions to be necessary. In this work, we calculated that the fractal dimensions of more than 80 kinds of 5S rRNA including animals, plants and bacteria, based on using the principles of fractal theory and improving the theoretical computing methods of ma-cromolecular fractals, and investigated the relations of 5S rRNA fractal dimensions with molecular evolution.The results indicated that during the evolution from simple eukaryotes (e. g., bacteria) to complex eukaryotes, on the one hand, because 5S rRNA structure tends toward complex, its average fractal dimension is increased; on the other hand, during the evolution from lower eukaryotes to higher eukaryotes, because the order degree of 5S rRNA structure is increased, it also make the sequence average fractal dimension occur a decreasing tendency. The fluctuation of 5S rRNA sequence structural fractal dimensions reflects the complexity and non-linearity during molecular evolution.The authors suggest that the relationship between the fractal dimensions of 5S rRNA sequences and molecular evolution is a complex non-linear relation. The sequence fractal dimensions during the evolution are not the simple increase or decrease with molecular evolution, but there is a fluctuation, and the fluctuation is stochastic. Therefore, the structural change of 5S rRNA sequence in two-dimensional base space is also stochastic. We consider that the case may be resulted from gene random drift causing the stochastic change of the sequence structure.
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