Topology David Shiuan Department of Life Science

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1 Topology David Shiuan Department of Life Science
Institute of Biotechnology Interdisciplinary Program of Bioinformatics National Dong Hwa University

2 拓 樸 學 (Topology) 拓樸學(Topology)是近代數學的一支,拓樸學研究的是一些圖型經類似拉長或壓縮後皆不變的幾何性質(橡皮幾何學) Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry. Topology begins with a consideration of the nature of space, investigating both its fine structure and its global structure. Topology builds on set theory, considering both sets of points and families of sets.

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9 Homotopy

10 Knot Theory

11 Molecular Knot

12 DNA Topology DNA在結構上主要有三種拓樸構變化：超螺旋（supercoiling） 紐結（knotting）
連鎖（catenation） Topology能夠使DNA在不進行DNA複製與轉錄的時候，維持其緊密性。反之在轉錄或複製過程中，這些拓撲構型將會阻礙反應

13 DNA Topology Circular DNA Supercoiling

14 Topoisomerase 拓樸異構酶 王卓
Type-I topoisomerase 可將雙股螺旋DNA包覆，以破壞phosphodiester bond的方式切斷其中一股DNA，產生一個小缺口，此時另一股完整的DNA將會穿過此缺口，之後重新黏合。Topoisomerase -I 與 -III Type-II topoisomerase 可將雙股螺旋DNA上的兩股DNA皆切斷，產生缺口，使另一條雙股螺旋能夠穿過此缺口，之後再重新黏合。topoisomerase-IIα與IIβ

15 Topo-II Catalyzes the catenation and decatenation