中文摘要：

利用纽结理论和缠绕模型来研究环状DNA分子在酶（如拓扑异构酶和重组酶）作用机制下的变化，揭示了其在酶促反应过程中如何断开原有结构并改变端点进行重组，从而改变其拓扑结构的．在整个DNA分子重组实验过程中，相当于进行了一次缠绕手术，用新的缠绕取代了被删除的缠绕，因此研究并分析在此过程中抽象出的缠绕模型显得十分重要．给出某些缠绕方程组的解，从而给出了DNA分子重组的数学模型．

英文摘要：

This paper employs knot theory and the model of tangles to research the change of the circular DNA molecules change under the action of enzymes such as topoisomerases and recombinases. Meanwhile, this paper also reveals how the circular DNA molecules break the original structure and change the endpoints to reconnect them so that they can change the topological structure in the process of enzymatic reaction. In the whole process of recombination experiment of the circular DNA molecule, the role of the enzyme can be viewed as a tangle surgery which replaces the deleted tangles the abstracting model of tangles. We give DNA molecule recombination. by new tangles. Therefore, it is very significant to study and analyze solutions of some tangle system and obtain mathematics model of