Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here, we investigate the relation between knotoids differing only by small perturbations of the direction of projection. Since such knotoids are connected by at most a single forbidden move, we characterize forbidden moves in terms of equivariant band attachment between strongly invertible knots and of strand passages between θ-curves. This allows for the determination of the optimal sample size needed to produce a well-approximated knotoid distribution. Based on that and on topological properties of the distribution, we probe the depth of knotted proteins with the trefoil as the predominant knot type without using subchain analysis.

最近的研究通过使用结状结构分析蛋白质的分布来对蛋白质的拓扑结构进行分类。该分布的近似值取决于采样的投影方向的数量。在这里，我们研究了仅因投影方向的微小扰动而不同的结节之间的关系。由于这样的结节最多只能通过一个禁止的动作连接，因此我们用强可逆结之间的等变带附着以及θ之间的钢绞线通道来表征禁止的动作-曲线。这样就可以确定产生良好近似的节形分布所需的最佳样本量。基于此以及分布的拓扑特性，我们无需使用子链分析就可以将以三叶草为主要结型的结蛋白深度进行研究。