Figure 1

To study the relation between the Shannon entropy $H$ and the genome order index $S$, the values of $H$ [defined in Eq. (13)] and $S$ [defined in Eq. (7)] for more than 1000 genome sequences were calculated, including the human, mouse, rat, $C$. elegans, yeast, Arabidopsis thaliana, more than 100 bacterial and archaeal genomes, and more than 600 virus genomes. This figure shows that the correlation coefficient $R$ between $H$ and $S$ is almost $-1$, indicating that $H$ and $S$ are negatively correlated, also implying that the genome order index $S$ plays a role of some kind of negative entropy.Reuse & Permissions

Figure 2

The negative cumulative $GC$ profiles for human chromosome 21 and chimpanzee chromosome 22 marked with the segmentation points obtained. The notation used here is described as follows. Besides the position coordinates, the order of occurrence for each point in the segmentation process is also labeled in the figure. We use “$f$,” “$l$,” “$r$,” and an integer to label the order of occurrence, where $f$ denotes the first point occurring during the course of segmentation, whereas $l$ and $r$ denote the point to occur in the left- and right subsequence, respectively. The integer denotes the times of segmentation. Take the point $43443502-r^{2}l4$ as an example. The first part 43 443 502 is the position coordinates. The second part “$r^{2}l4$” denotes the order of occurrence. The last integer “4” in the second part means that this point occurs after four times of segmentation. In the symbol “$r^{2}l$,” $r$ appears two times, so we used “$r^2$” instead of “$rr$” for convenience. The bottom four plots show the distributions of the $G+C$ content, $Alu$, $CpG$ island, and gene along human chromosome 21, respectively. Note that all of these distributions are closely correlated with the segmented regions with distinct $G+C$ content. Also note that the coordinate value of each segmentation point has been corrected by taking the gap length into account. For instance, there is a gap occurring at $n_0\to n_0+\Delta$, where $\Delta$ is the gap length. If a segmentation point obtained is situated at $n$, and $n>n_0$, then the actual coordinate of $n$ adopted in this plot is $n+\Delta$. Meanwhile, the gap region $n_0\to n_0+\Delta$ is represented by a blank interval in this plot. Here, $n_0$ and $n$ are the relative coordinates with respect to the contig without gaps. Other gaps are treated with a similar procedure.Reuse & Permissions