Many theories of the evolution of the genetic code assume that the genetic code has always evolved in the direction of increasing the supply of amino acids to be encoded (Barbieri, 2019; Di Giulio, 2005; Wong, 1975). In order to reduce the risk of the formation of a non-functional protein due to point mutations, nature is said to have built in control mechanisms. Using graph theory the authors have investigated in Blazej et al. (2019) if this robustness is optimal in the sense that a different codon–amino acid assignment would not generate a code that is even more robust. At present, efforts to expand the genetic code are very relevant in biotechnological applications, for example, for the synthesis of new drugs (Anderson et al., 2004; Chin, 2017; Dien et al., 2018; Kimoto et al., 2009; Neumann et al., 2010). In this paper we generalize the approach proposed in Blazej et al. (2019) and will explore hypothetical extensions of the standard genetic code with respect to their optimal robustness in two ways:

(1) We keep the usual genetic alphabet but move from codons to longer words, such as tetranucleotides. This increases the supply of coding words and thus makes it possible to encode non-canonical amino acids.

(2) We expand the genetic alphabet by introducing non-canonical base pairs. In addition, the approach from Blazej et al. (2019) and Blazej et al. (2018) is extended by incorporating the weights of single point-mutations into the model. The weights can be interpreted as probabilities (appropriately normalized) or degrees of severity of a single point mutation. In particular, this new approach allows us to take a closer look at the wobble effects in the translation of codons into amino acids. According to the results from Blazej et al. (2019) and Blazej et al. (2018), the standard genetic code is not optimal in terms of its robustness to point mutations if the weights of single point mutations are not taken into account. After incorporation into the model weights that mimic the wobble effect, the results of the present work show that it is much more robust, almost optimal in that respect.

We hope, that this theoretical analysis might help to assess extended genetic codes and their abilities to encode new amino acids.

许多遗传密码进化理论假设遗传密码总是朝着增加待编码氨基酸供应的方向进化（Barbieri，2019；Di Giulio，2005；Wong，1975）。为了降低由于点突变而形成非功能性蛋白质的风险，据说自然界已经建立了控制机制。使用图论，作者在 Blazej 等人中进行了研究。（2019）如果这种稳健性在某种意义上是最佳的，即不同的密码子-氨基酸分配不会产生更稳健的代码。目前，扩展遗传密码的努力与生物技术应用非常相关，例如，用于合成新药（Anderson et al., 2004; Chin, 2017; Dien et al., 2018; Kimoto et al., 2009 ; Neumann 等人，2010 年）。在本文中，我们概括了 Blazej 等人提出的方法。（2019）并将探索标准遗传密码的假设扩展，以两种方式实现其最佳稳健性：

(1) 我们保留通常的遗传字母表，但从密码子转移到更长的单词，例如四核苷酸。这增加了编码词的供应，从而使编码非规范氨基酸成为可能。

(2) 我们通过引入非规范碱基对来扩展遗传字母表。此外，Blazej 等人的方法。(2019) 和 Blazej 等人。(2018) 通过将单点突变的权重合并到模型中进行了扩展。权重可以解释为概率（适当归一化）或单点突变的严重程度。特别是，这种新方法使我们能够仔细研究密码子翻译成氨基酸的摆动效应。根据 Blazej 等人的结果。(2019) 和 Blazej 等人。（2018），如果不考虑单点突变的权重，标准遗传密码对点突变的鲁棒性并不是最优的。并入模拟摆动效应的模型权重后，

我们希望，这种理论分析可能有助于评估扩展的遗传密码及其编码新氨基酸的能力。