Constructions of DNA and polypeptide cages based on plane graphs and odd crossing π-junctions
Constructions of DNA and polypeptide cages based on plane graphs and odd crossing π-junctions
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DOI：
10.1016/j.amc.2022.127773
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发表时间：
2023-04
期刊：
影响因子：
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通讯作者：
Xiao-Sheng Cheng;Qingying Deng;Y. Diao
中科院分区：
文献类型：
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作者：
Xiao-Sheng Cheng;Qingying Deng;Y. Diao
具有单个封闭DNA链和多肽链的三维合成DNA和多肽结构的构造在数学上基于多面体图的强迹。然而，为构建这样的DNA和多肽结构而开发的方法可能会对强迹和多面体图的类型施加额外的限制。本文证明了某些2-连通平面图（允许有多条边）的强迹可以用加厚图（有时称为带状图）得到，加厚图只由两种类型的联结构成：0-交叉联结和特殊d（v）-交叉联结（称为π-联结），其中d（v）是d（v）-交叉联结所处顶点v的度.π连接仅适用于奇数度（≥ 3）的顶点。我们的特点2-连通平面图，我们的方法可以应用，并提供了一个简短的指导方针，我们的方法的实施。这种方法为设计和构建稳定的DNA和多肽分子提供了理论，以及一组候选者，只需要一种能够在2-连通平面图中创建0-交叉和π-结的方法。
The constructions of three-dimensional synthetic DNA and polypeptide structures with a single closed DNA strand and polypeptide chain are mathematically based on strong traces of polyhedral graphs. However, a method developed for constructing such a DNA and polypeptide structure may impose additional restrictions on the types of strong traces and polyhedral graphs. In this paper, we show that strong traces for certain 2-connected plane graphs (allowed to have multiple edges) can be obtained using thickened graphs (sometimes called ribbon graphs) constructed with only two types of junctions: 0-crossing junction and special d (v)-crossing junction (called π-junction), where d (v) is the degree of the vertex v at which the d (v)-crossing junction is to be placed. The π-junctions are only applicable to vertices with odd degrees (≥ 3). We characterize the 2-connected plane graphs to which our approach can be applied and provide a brief guideline for the implementation of our method. This approach provides the theory, as well as a set of candidates, for designing and constructing stable DNA and polypeptide molecules needing only a method capable of creating the 0-crossing and π-junctions in a 2-connected plane graph.