In this paper, we propose two four-base related 2D curves of DNA primary sequences (termed as F-B curves) and their corresponding single-base related 2D curves (termed as A-related, G-related, T-related and C-related curves). The constructions of these graphical curves are based on the assignments of individual base to four different sinusoidal (or tangent) functions; then by connecting all these points on these four sinusoidal (tangent) functions, we can get the F-B curves; similarly, by connecting the points on each of the four sinusoidal (tangent) functions, we get the single-base related 2D curves. The proposed 2D curves are all strictly non degenerate. Then, a 8-component characteristic vector is constructed to compare similarity among DNA sequences from different species based on a normalized geometrical centers of the proposed curves. As examples, we examine similarity among the coding sequences of the first exon of beta-globin gene from eleven species, similarity of cDNA sequences of beta-globin gene from eight species, and similarity of the whole mitochondrial genomes of 18 eutherian mammals. The experimental results well demonstrate the effectiveness of the proposed method.

中文翻译：

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基于三角函数的DNA序列的图形表示和相似性分析

在本文中，我们提出了两条 DNA 一级序列的四碱基相关二维曲线（称为 FB 曲线）及其相应的单碱基相关二维曲线（称为 A 相关、G 相关、T 相关和 C 相关）。曲线）。这些图形曲线的构造基于对四个不同正弦（或切线）函数的各个基数的分配；然后通过连接这四个正弦（正切）函数上的所有这些点，我们可以得到FB曲线；类似地，通过连接四个正弦（切线）函数中的每一个上的点，我们得到与单基相关的二维曲线。建议的二维曲线都是严格非退化的。然后，基于所提出曲线的归一化几何中心，构建了一个 8 分量特征向量来比较来自不同物种的 DNA 序列之间的相似性。例如，我们研究了 11 个物种的 β-珠蛋白基因第一个外显子编码序列的相似性、8 个物种的 β-珠蛋白基因 cDNA 序列的相似性以及 18 种真兽类哺乳动物的整个线粒体基因组的相似性。实验结果很好地证明了所提出方法的有效性。