José Marco V, Morgado Eberto R, Govezensky Tzipe
Theoretical Biology Group, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México D.F. 04510, México.
Bull Math Biol. 2007 Jan;69(1):215-43. doi: 10.1007/s11538-006-9119-3. Epub 2006 Nov 2.
An algebraic and geometrical approach is used to describe the primaeval RNA code and a proposed Extended RNA code. The former consists of all codons of the type RNY, where R means purines, Y pyrimidines, and N any of them. The latter comprises the 16 codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type), and the third, (YRN type) reading frames. In each of these reading frames, there are 16 triplets that altogether complete a set of 48 triplets, which specify 17 out of the 20 amino acids, including AUG, the start codon, and the three known stop codons. The other 16 codons, do not pertain to the Extended RNA code and, constitute the union of the triplets YYY and RRR that we define as the RNA-less code. The codons in each of the three subsets of the Extended RNA code are represented by a four-dimensional hypercube and the set of codons of the RNA-less code is portrayed as a four-dimensional hyperprism. Remarkably, the union of these four symmetrical pairwise disjoint sets comprises precisely the already known six-dimensional hypercube of the Standard Genetic Code (SGC) of 64 triplets. These results suggest a plausible evolutionary path from which the primaeval RNA code could have originated the SGC, via the Extended RNA code plus the RNA-less code. We argue that the life forms that probably obeyed the Extended RNA code were intermediate between the ribo-organisms of the RNA World and the last common ancestor (LCA) of the Prokaryotes, Archaea, and Eucarya, that is, the cenancestor. A general encoding function, E, which maps each codon to its corresponding amino acid or the stop signal is also derived. In 45 out of the 64 cases, this function takes the form of a linear transformation F, which projects the whole six-dimensional hypercube onto a four-dimensional hyperface conformed by all triplets that end in cytosine. In the remaining 19 cases the function E adopts the form of an affine transformation, i.e., the composition of F with a particular translation. Graphical representations of the four local encoding functions and E, are illustrated and discussed. For every amino acid and for the stop signal, a single triplet, among those that specify it, is selected as a canonical representative. From this mapping a graphical representation of the 20 amino acids and the stop signal is also derived. We conclude that the general encoding function E represents the SGC itself.
一种代数和几何方法被用于描述原始RNA密码和一种提出的扩展RNA密码。前者由所有RNY类型的密码子组成，其中R表示嘌呤，Y表示嘧啶，N表示它们中的任何一种。后者包括RNY类型的16个密码子，以及通过考虑RNA密码但在第二个（NYR类型）和第三个（YRN类型）阅读框中获得的密码子。在这些阅读框中的每一个中，都有16个三联体，总共构成一组48个三联体，它们指定了20种氨基酸中的17种，包括起始密码子AUG和三个已知的终止密码子。另外16个密码子不属于扩展RNA密码，它们构成了我们定义为无RNA密码的YYY和RRR三联体的并集。扩展RNA密码的三个子集中的每一个子集中的密码子都由一个四维超立方体表示，无RNA密码的密码子集被描绘为一个四维超棱柱。值得注意的是，这四个对称的两两不相交集合的并集恰好构成了已知的由64个三联体组成的标准遗传密码（SGC）的六维超立方体。这些结果表明了一条合理的进化路径，原始RNA密码可能通过扩展RNA密码加上无RNA密码起源于SGC。我们认为，可能遵循扩展RNA密码的生命形式介于RNA世界的核糖生物和原核生物、古细菌和真核生物的最后共同祖先（LCA）之间，即共同祖先。还推导了一个将每个密码子映射到其相应氨基酸或终止信号的通用编码函数E。在64种情况中的45种情况下，这个函数采取线性变换F的形式，它将整个六维超立方体投影到由所有以胞嘧啶结尾的三联体构成的四维超面上。在其余19种情况下，函数E采取仿射变换的形式，即F与一个特定平移的组合。对四个局部编码函数和E进行了图形表示并进行了讨论。对于每一种氨基酸和终止信号，在指定它的那些三联体中选择一个三联体作为典型代表。从这个映射中还得到了20种氨基酸和终止信号的图形表示。我们得出结论，通用编码函数E代表了SGC本身。
