Tian Wei, Lei Xue, Kauffman Louis H, Liang Jie
Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, 60606, USA.
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60606, USA.
Mol Based Math Biol. 2017 Jan;5(1):21-30. doi: 10.1515/mlbmb-2017-0002.
Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are not taken into account in conventional knot polynomials. In this study, we develop a new class of knot polynomials specifically designed to study RNA molecules, which considers stem regions. We demonstrate that our knot polynomials have direct structural relation with RNA molecules, and can be used to classify the topology of RNA secondary structures. Furthermore, we point out that these knot polynomials can be used to model the topological effects of disulfide bonds in protein molecules.
纽结多项式已被用于检测和分类生物分子中的纽结。DNA和蛋白质分子中纽结多项式的计算揭示了纽结结构的存在，并为其拓扑结构提供了重要的见解。然而，传统的纽结多项式不太适合研究RNA分子，因为RNA结构是由茎区决定的，而传统纽结多项式并未考虑茎区。在本研究中，我们开发了一类专门设计用于研究RNA分子的新型纽结多项式，该多项式考虑了茎区。我们证明了我们的纽结多项式与RNA分子具有直接的结构关系，并且可用于对RNA二级结构的拓扑进行分类。此外，我们指出这些纽结多项式可用于模拟蛋白质分子中二硫键的拓扑效应。
