Vazquez Mariel, Colloms Sean D, Sumners De Witt
Department of Mathematics, University of California at Berkeley, Berkeley CA 94720-3840, USA.
J Mol Biol. 2005 Feb 18;346(2):493-504. doi: 10.1016/j.jmb.2004.11.055. Epub 2005 Jan 11.
The product of Xer recombination at directly repeated psi sites on a circular unknotted DNA molecule is a right-hand four-noded catenane. Here, we use tangle equations to analyze the topological changes associated with Xer recombination at psi. This mathematical method allows computation of all possible topological pathways consistent with the experimental data. We give a rigorous mathematical proof that, under reasonable biological assumptions, there are only three solutions to the tangle equations. One of the solutions corresponds to a synaptic complex with antiparallel alignment of recombination core sites, the other two correspond to parallel alignment of cores. We show that all three solutions can be unified into a single three-dimensional model for Xer recombination. Thus the three distinct mathematical solutions do not necessarily represent distinct three-dimensional pathways, and in this case the three distinct tangle solutions are different planar projections of the same three-dimensional configuration.
在环状无纽结DNA分子上直接重复的ψ位点处进行Xer重组的产物是一个右手四节点连环体。在此，我们使用缠结方程来分析与ψ位点处Xer重组相关的拓扑变化。这种数学方法能够计算出与实验数据一致的所有可能的拓扑路径。我们给出了一个严格的数学证明，即在合理的生物学假设下，缠结方程仅有三个解。其中一个解对应于重组核心位点反平行排列的突触复合体，另外两个解对应于核心位点的平行排列。我们表明，所有这三个解都可以统一到一个用于Xer重组的单一三维模型中。因此，这三个不同的数学解不一定代表不同的三维路径，在这种情况下，这三个不同的缠结解是同一三维构型的不同平面投影。
