Yu Zu-Guo, Anh Vo, Lau Ka-Sing
Program in Statistics and Operations Research, Queensland University of Technology, GPO Box 2434, Brisbane Q4001, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 1):021913. doi: 10.1103/PhysRevE.68.021913. Epub 2003 Aug 22.
A measure representation of protein sequences similar to the measure representation of DNA sequences proposed in our previous paper [Yu et al., Phys. Rev. E 64, 031903 (2001)] and another induced measure are introduced. Multifractal analysis is then performed on these two kinds of measures of a large number of protein sequences derived from corresponding complete genomes. From the values of the D(q) (generalized dimensions) spectra and related C(q) (analogous specific heat) curves, it is concluded that these protein sequences are not completely random sequences. For substrings with length K=5, the D(q) spectra of all organisms studied are multifractal-like and sufficiently smooth for the C(q) curves to be meaningful. The C(q) curves of all bacteria resemble a classical phase transition at a critical point. But the "analogous" phase transitions of higher organisms studied exhibit the shape of double-peaked specific heat function. But for the classification problem, the multifractal property is not sufficient. When the measure representations of protein sequences from complete genomes are considered as time series, a method based on correlation analysis after removing some memory from the time series is proposed to construct a phylogenetic tree. This construction is shown to be reasonably satisfactory.
引入了一种类似于我们之前论文[Yu等人，《物理评论E》64，031903（2001）]中提出的DNA序列测度表示的蛋白质序列测度表示以及另一种诱导测度。然后对从相应完整基因组中获得的大量蛋白质序列的这两种测度进行多重分形分析。从D（q）（广义维数）谱的值和相关的C（q）（类似比热）曲线可以得出结论，这些蛋白质序列不是完全随机的序列。对于长度K = 5的子串，所有研究生物体的D（q）谱都类似多重分形，并且C（q）曲线足够平滑，有意义。所有细菌的C（q）曲线在临界点处类似于经典相变。但是所研究的高等生物体的“类似”相变呈现出双峰比热函数的形状。但是对于分类问题，多重分形性质是不够的。当将完整基因组中蛋白质序列的测度表示视为时间序列时，提出了一种在从时间序列中去除一些记忆后基于相关分析的方法来构建系统发育树。这种构建显示出相当令人满意的结果。
