Mathematical Institute, University of Oxford, Oxford, UK.
Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland.
Sci Adv. 2020 Feb 26;6(9):eaay1458. doi: 10.1126/sciadv.aay1458. eCollection 2020 Feb.
Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether these 2D diagrams can be used to model a complex 3D process such as the topoisomerase-mediated preferential unknotting of DNA molecules. We model here topoisomerase-mediated passages of double-stranded DNA segments through each other using the formalism of grid diagrams. We show that this grid diagram-based modeling approach captures the essence of the preferential unknotting mechanism, based on topoisomerase selectivity of hooked DNA juxtapositions as the sites of intersegmental passages. We show that the grid diagram-based approach provides an important, new, and computationally convenient framework for investigating entanglement in biopolymers.
网格图具有相对简单的数学形式，为生成和模拟各种纽结的投影提供了一种便捷的方法。一个悬而未决的问题是，这些 2D 图是否可以用于模拟拓扑异构酶介导的 DNA 分子优先去纽结等复杂的 3D 过程。我们使用网格图的形式体系来模拟拓扑异构酶介导的双链 DNA 片段相互穿越的过程。我们证明，这种基于网格图的建模方法基于拓扑异构酶对钩状 DNA 毗邻的选择性作为片段间穿越的位点，捕捉到了优先去纽结机制的本质。我们证明，基于网格图的方法为研究生物聚合物中的缠结提供了一个重要的、新的、计算方便的框架。
