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摘要翻译：
本文主要研究斐波那契序列及其q变形或量子扩展在遗传密码研究中的相关性和应用可能性。首先，在提出一个新的公式后，由前6个Fibonacci数组成的索引双Fibonacci序列描述了20个氨基酸多重序列及其简并性，并给出了61个有意义密码子的特征模式。其次，根据原子数（碳、氮、氧和硫）的增加，这20个氨基酸呈现出几种斐波那契序列模式。给出了几种数学关系，描述了各种原子数模式。最后，用一个简单的唯象模型，以q为实形变参数，统一地描述了当q=1时的标准遗传密码，以及当q~1时的所有已知遗传密码的微小变异，以及当q~1时的第21个氨基酸（硒半胱氨酸）和第22个氨基酸（吡咯赖氨酸）的情况。作为这个基本模型的副产品，我们还表明，在极限q=0时，氨基酸的数量达到了6的值，这与古老的、仍然持续存在的说法是一致的，即生命在其早期发展中可能只使用少量氨基酸。
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英文标题：
《A Mathematical Model for the Genetic Code(s) Based on Fibonacci Numbers
and their q-Analogues》
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作者：
Tidjani Negadi
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最新提交年份：
2015
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分类信息：
一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
This work aims at showing the relevance and the applications possibilities of the Fibonacci sequence, and also its q-deformed or quantum extension, in the study of the genetic code(s). First, after the presentation of a new formula, an indexed double Fibonacci sequence, comprising the first six Fibonacci numbers, is shown to describe the 20 amino acids multiplets and their degeneracy as well as a characteristic pattern for the 61 meaningful codons. Next, the twenty amino acids, classified according to their increasing atom-number (carbon, nitrogen, oxygen and sulfur), exhibit several Fibonacci sequence patterns. Several mathematical relations are given, describing various atom-number patterns. Finally, a q-Fibonacci simple phenomenological model, with q a real deformation parameter, is used to describe, in a unified way, not only the standard genetic code, when q=1, but also all known slight variations of this latter, when q~1, as well as the case of the 21st amino acid (Selenocysteine) and the 22nd one (Pyrrolysine), also when q~1. As a by-product of this elementary model, we also show that, in the limit q=0, the number of amino acids reaches the value 6, in good agreement with old and still persistent claims stating that life, in its early development, could have used only a small number of amino acids.
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PDF链接：
https://arxiv.org/pdf/1510.01278
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