论文标题
RNA折叠和结节
RNA foldings and Stuck Knots
论文作者
论文摘要
我们研究了RNA折叠，并使用结理论和嵌入刚性顶点图的组合研究了它们的拓扑。打结理论有助于对生物分子进行建模，但是经典结对生物分子的纠缠而忽略了它们的内部相互作用。我们通过使用卡住的结和链接来解决这个问题，这提供了一种强调其纠缠和内部相互作用的方法。我们首先为定向的卡住链接提供了一组定向的卡住reidementer动作。然后，我们引入一个代数结构，以公理化定向的卡住reidemerster移动。使用这种代数结构，我们定义了链接的着色计数不变性，并提供了不变的明确计算。最后，我们通过使用卡住的链路图来计算RNA折叠的弧形图的计数不变。
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots place emphasis on a biomolecule's entanglement while ignoring their intrachain interactions. We remedy this by using stuck knots and links, which provide a way to emphasize both their entanglement and intrachain interactions. We first give a generating set of the oriented stuck Reidemeister moves for oriented stuck links. We then introduce an algebraic structure to axiomatize the oriented stuck Reidemeister moves. Using this algebraic structure, we define a coloring counting invariant of stuck links and provide explicit computations of the invariant. Lastly, we compute the counting invariant for arc diagrams of RNA foldings through the use of stuck link diagrams.
