折叠分子链着色不变量的增强
Enhancement of the Coloring Invariant for Folded Molecular Chains
摘要：
折叠的线性分子链在生物学中普遍存在。折叠是由链内相互作用介导的，其“粘合”链的两个或更多个区域。由此产生的折叠拓扑结构被广泛认为是生物分子性质和功能的决定因素。最近，纽结理论已被扩展到描述折叠线性链的拓扑结构，如蛋白质和核酸。为了对链式拓扑进行分类和区分，量子点的代数结构被采用和应用。然而，该方法是有限的，因为明显不同的拓扑可能最终具有相同数量的着色。在这里，我们通过引入玻尔兹曼权重来提高量子着色方法的分辨率。我们证明了增强的着色不变量可以区分折叠拓扑结构，提高了分辨率。
英文摘要：
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.
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