Arquès D G, Michel C J
Université de Franche-Comté, Besançon, France.
Bull Math Biol. 1993 Nov;55(6):1025-38. doi: 10.1007/BF02460698.
Recently, we proposed a new model of DNA sequence evolution (Arquès and Michel. 1990b. Bull. math. Biol. 52, 741-772) according to which actual genes on the purine/pyrimidine (R/Y) alphabet (R = purine = adenine or guanine, Y = pyrimidine = cytosine or thymine) are the result of two successive evolutionary genetic processes: (i) a mixing (independent) process of non-random oligonucleotides (words of base length less than 10: YRY(N)6, YRYRYR and YRYYRY are so far identified; N = R or Y) leading to primitive genes (words of several hundreds of base length) and followed by (ii) a random mutation process, i.e., transformations of a base R (respectively Y) into the base Y (respectively R) at random sites in these primitive genes. Following this model the problem investigated here is the study of the variation of the 8 R/Y codon probabilities RRR, ..., YYY under random mutations. Two analytical expressions solved here allow analysis of this variation in the classical evolutionary sense (from the past to the present, i.e., after random mutations), but also in the inverted evolutionary sense (from the present to the past, i.e., before random mutations). Different properties are also derived from these formulae. Finally, a few applications of these formulae are presented. They prove the proposition in Arquès and Michel (1990b. Bull. math. Biol. 52, 741-772), Section 3.3.2, with the existence of a maximal mean number of random mutations per base of the order 0.3 in the protein coding genes. They also confirm the mixing process of oligonucleotides by excluding the purine/pyrimidine contiguous and alternating tracts from the formation process of primitive genes.
最近，我们提出了一种新的DNA序列进化模型（Arquès和Michel，1990b，《数学生物学通报》52卷，741 - 772页），根据该模型，嘌呤/嘧啶（R/Y）字母表（R = 嘌呤 = 腺嘌呤或鸟嘌呤，Y = 嘧啶 = 胞嘧啶或胸腺嘧啶）上的实际基因是两个连续进化遗传过程的结果：（i）一个非随机寡核苷酸的混合（独立）过程（碱基长度小于10的片段：到目前为止已鉴定出YRY(N)6、YRYRYR和YRYYRY；N = R或Y），产生原始基因（几百个碱基长度的片段），随后是（ii）一个随机突变过程，即这些原始基因中随机位点上的碱基R（分别为Y）随机转变为碱基Y（分别为R）。按照这个模型，这里研究的问题是在随机突变下8个R/Y密码子概率RRR、……、YYY的变化研究。这里求解的两个解析表达式不仅允许从经典进化意义上（从过去到现在，即随机突变之后）分析这种变化，也允许从反向进化意义上（从现在到过去，即随机突变之前）进行分析。从这些公式还推导得出了不同的性质。最后，给出了这些公式的一些应用。它们证明了Arquès和Michel（1990b，《数学生物学通报》52卷，741 - 772页）第3.3.2节中的命题，即蛋白质编码基因中每个碱基的随机突变平均数量存在一个约为0.3的最大值。它们还通过从原始基因形成过程中排除嘌呤/嘧啶连续和交替片段，证实了寡核苷酸的混合过程。
