遗传密码的数学揭示了频率简并导致智人的DNA密码子分布的指数缩放
The mathematics of the genetic code reveal that frequency degeneracy leads to exponential scaling in the DNA codon distribution of Homo sapiens
摘要：
人类基因组中64个DNA密码子的数量分布的性质已经是一个争论了十多年的问题。一些研究小组提出，DNA密码子的数量分布以秩-频率图的形式排列，遵循一个众所周知的幂律，称为齐普夫定律。其他人已经表明，DNA密码子分布最适合指数函数。然而，这种缩放行为的原因尚未得到解决。在本研究中，我们证明了DNA密码子分布的非线性是密码子使用频率重复的直接结果（即，在全基因组水平上密码子使用频率的重复性）。我们发现，如果频率复发是从人类基因组中缺失，密码子的出现频率与密码子等级呈线性关系。我们还表明，DNA密码子的低和高频率的基因组中出现的最佳拟合指数函数，并提供了强有力的证据表明，人类基因组的编码区不遵循齐普夫定律。将信息论方法和熵计算应用于DNA密码子分布，提出了一种新的定量分析DNA密码子分布的方法-
英文摘要：
The nature of the quantitative distribution of the 64 DNA codons in the human genome has been an issue of debate for over a decade. Some groups have proposed that the quantitative distribution of the DNA codons ordered as a rank-frequency plot follows a well-known power law called Zipf's law. Others have shown that the DNA codon distribution is best fitted to an exponential function. However, the reason for such scaling behavior has not yet been addressed. In the present study, we demonstrate that the nonlinearity of the DNA codon distribution is a direct consequence of the frequency recurrence of the codon usage (i.e., the repetitiveness of codon usage frequencies at the whole genome level). We discover that if frequency recurrence is absent from the human genome, the frequency of occurrence of codons scales linearly with the codon rank. We also show that DNA codons of both low and high frequency of occurrence in the genome are best fitted by an exponential function and provide strong evidence to suggest that the coding region of the human genome does not follow Zipf's law. Information-theoretic methods and entropy calculations are applied to the DNA codon distribution and a new approach, called the lariat method, is proposed to quantitatively analyze the DNA codon distribution in Homo sapiens.
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