Gonzalez Diego L
St. George School Foundation and National Research Council of Italy, Isola di San Giorgio Maggiore, Venice, Italy.
Med Sci Monit. 2004 Apr;10(4):HY11-7.
From a mathematical point of view, the genetic code is a surjective mapping between the set of the 64 possible three-base codons and the set of 21 elements composed of the 20 amino acids plus the Stop signal. Redundancy and degeneracy therefore follow. In analogy with the genetic code, non-power integer-number representations are also surjective mappings between sets of different cardinality and, as such, also redundant. However, none of the non-power arithmetics studied so far nor other alternative redundant representations are able to match the actual degeneracy of the genetic code. In this paper we develop a slightly more general framework that leads to the following surprising results: i) the degeneracy of the genetic code is mathematically described, ii) a new symmetry is uncovered within this degeneracy, iii) by assigning a binary string to each of the codons, their classification into definite parity classes according to the corresponding sequence of bases is made possible. This last result is particularly appealing in connection with the fact that parity coding is the basis of the simplest strategies devised for error correction in man-made digital data transmission systems.
从数学角度来看，遗传密码是64种可能的三联体密码子集合与由20种氨基酸加终止信号组成的21种元素集合之间的满射映射。因此存在冗余和简并性。与遗传密码类似，非幂整数表示也是不同基数集合之间的满射映射，同样存在冗余。然而，到目前为止所研究的非幂算术以及其他替代的冗余表示都无法与遗传密码实际的简并性相匹配。在本文中，我们开发了一个稍微更通用的框架，得出了以下惊人结果：i）从数学上描述了遗传密码的简并性，ii）在这种简并性中发现了一种新的对称性，iii）通过为每个密码子分配一个二进制字符串，使得能够根据相应的碱基序列将它们分类到确定的奇偶类中。鉴于奇偶编码是人造数字数据传输系统中设计的最简单纠错策略的基础，最后这个结果特别有吸引力。
