自1996年以来,由于6种统计方法的发展,已经确定了基因中的循环代码:每帧三核苷酸频率(Arquès和Michel,1996),每帧相关函数(Arquès和Michel,1997),框架置换三核苷酸频率(Frey和Michel,2003,2006),基因群体水平的高级统计功能(米歇尔,2015)和基因水平(米歇尔,2017)。所有这些3帧统计方法分析了3个基因帧中的三核苷酸信息:阅读框和2个移位框。值得注意的是,密码子使用不允许识别循环代码(Michel,2020)。自1996年以来,这一直是一个长期存在的问题,阻碍了生物学家获得循环代码理论。通过考虑由代码理论产生的循环代码条件,特别是置换类的概念,在以前的统计工作的基础上,一种仅基于密码子使用的新统计方法,即1帧统计方法,令人惊讶的是,在细菌基因和平均(细菌,考古,真核)基因,几乎在古细菌基因中。此外,一个新的参数定义表明,细菌和古细菌基因表现出相同数量级的密码子使用分散,但显著高于在真核基因中观察到的。这一统计发现可以解释与细菌和古细菌基因相比,真核基因中密码的变异性更大。这个问题已经公开了很多年。最后,生物学家现在可以在基因组水平(跨给定基因组中的所有基因)和仅使用密码子使用的基因水平上搜索新的(变异)循环代码,不需要分析移位的帧。
Since 1996, circular codes in genes have been identified thanks to the development of 6 statistical approaches: trinucleotide frequencies per frame (Arquès and Michel, 1996), correlation functions per frame (Arquès and Michel, 1997), frame permuted trinucleotide frequencies (Frey and Michel, 2003, 2006), advanced statistical functions at the gene population level (Michel, 2015) and at the gene level (Michel, 2017). All these 3-frame statistical methods analyse the trinucleotide information in the 3 frames of genes: the reading frame and the 2 shifted frames. Notably, codon usage does not allow for the identification of circular codes (Michel, 2020). This has been a long-standing problem since 1996, hindering biologists\' access to circular code theory. By considering circular code conditions resulting from code theory, particularly the concept of permutation class, and building upon previous statistical work, a new statistical approach based solely on the codon usage, i.e. a 1-frame statistical method, surprisingly reveals the maximal C3 self-complementary trinucleotide circular code X in bacterial genes and in average (bacterial, archaeal, eukaryotic) genes, and almost in archaeal genes. Additionally, a new parameter definition indicates that bacterial and archaeal genes exhibit codon usage dispersion of the same order of magnitude, but significantly higher than that observed in eukaryotic genes. This statistical finding may explain the greater variability of codes in eukaryotic genes compared to bacterial and archaeal genes, an issue that has been open for many years. Finally, biologists can now search for new (variant) circular codes at both the genome level (across all genes in a given genome) and the gene level using only codon usage, without the need for analysing the shifted frames.