Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland.
Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland.
Sci Rep. 2017 Jul 24;7(1):6309. doi: 10.1038/s41598-017-06649-3.
We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely, knotoids are diagrams representing projections of open curves in 3D space, in contrast to knot diagrams which represent projections of closed curves in 3D space. The intrinsic difference with classical knot theory is that the generalization provided by knotoids admits non-trivial topological entanglement of the open curves provided that their geometry is frozen as it is the case for crystallized proteins. Consequently, our approach doesn't require the closure of chains into loops which implies that the geometry of analysed chains does not need to be changed by closure in order to characterize their topology. Our study revealed that the knotoid approach detects protein regions that were classified earlier as knotted and also new, topologically interesting regions that we classify as pre-knotted.
我们通过实施扭结体的概念来研究开放蛋白质链的全局和局部纠缠。扭结体于 2012 年由弗拉基米尔·图雷尔（Vladimir Turaev）引入，作为三维空间中扭结的推广。更准确地说，扭结体是代表三维空间中开放曲线投影的图表，而扭结图则代表三维空间中封闭曲线的投影。与经典纽结理论的内在区别在于，扭结体的推广允许开放曲线的非平凡拓扑纠缠，前提是它们的几何形状是冻结的，就像结晶蛋白质一样。因此，我们的方法不需要将链封闭成环，这意味着为了表征它们的拓扑结构，不需要通过闭合来改变分析链的几何形状。我们的研究表明，扭结体方法检测到了先前被归类为扭结的蛋白质区域，以及我们归类为预扭结的新的、拓扑有趣的区域。
