期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1999
卷号：96
期号：23
页码：12974-12979
DOI：10.1073/pnas.96.23.12974
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Two variables define the topological state of closed double-stranded DNA: the knot type, K, and {Delta}Lk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P({Delta}Lk, K), is related to two conditional distributions: P({Delta}Lk|K), the distribution of {Delta}Lk for a particular K, and P(K|{Delta}Lk) and also to two simple distributions: P({Delta}Lk), the distribution of {Delta}Lk irrespective of K, and P(K). We explored the relationships between these distributions. P({Delta}Lk, K), P({Delta}Lk), and P(K|{Delta}Lk) were calculated from the simulated distributions of P({Delta}Lk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|{Delta}Lk), the distribution of knot types for a particular value of {Delta}Lk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of {Delta}Lk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |{Delta}Lk| > 12, only one or two knot types dominate the P(K|{Delta}Lk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.
