论文标题
折叠分子链的着色不变的增强
Enhancement of the Coloring Invariant for Folded Molecular Chains
论文作者
论文摘要
折叠线性分子链在生物学上无处不在。折叠是由“胶合”链的两个或多个区域“粘合”的链相互作用介导的。所产生的折叠拓扑被普遍认为是生物分子特性和功能的决定因素。最近，已经扩展了结理论，以描述折叠线性链（例如蛋白质和核酸）的拓扑结构。为了对链拓扑进行分类和区分，已经对Quandles的代数结构进行了调整和应用。但是，该方法受到限制，因为显然不同的拓扑可能最终具有相同数量的着色。在这里，我们通过引入Boltzmann重量来增强Quandle着色方法的分辨能力。我们证明，增强的着色不变性可以通过改进的分辨率来区分折叠拓扑。
Folded linear molecular chains are ubiquitous in biology. Folding is mediated by intra-chain interactions that "glue" two or more regions of a chain. The resulting fold topology is widely believed to be a determinant of biomolecular properties and function. Recently, knot theory has been extended to describe the topology of folded linear chains such as proteins and nucleic acids. To classify and distinguish chain topologies, algebraic structure of quandles has been adapted and applied. However, the approach is limited as apparently distinct topologies may end up having the same number of colorings. Here, we enhance the resolving power of the quandle coloring approach by introducing Boltzmann weights. We demonstrate that the enhanced coloring invariants can distinguish fold topologies with an improved resolution.
