If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching s...If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n展开更多
We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mappingtopological current theory.The main purpose of this paper is to present a new theoretical framework,which can di...We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mappingtopological current theory.The main purpose of this paper is to present a new theoretical framework,which can directlygive the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclideanspace R^(2n-1).For the sake of this purpose we introduce a topological tensor current,which can naturally deduce the(n-1)-dimensional topological defect in R^(2n-1) space.If these (n-1)-dimensional topological defects are closed orientedsubmanifolds of R^(2n-1),they are just the (n-1)-dimensional knots.The linking number of these knots is well defined.Using the inner structure of the topological tensor current,the relationship between Hopf invariant and the linkingnumbers of the higher-dimensional knots can be constructed.展开更多
Intrinsically disordered proteins(IDP)are highly dynamic,and the effective characterization of IDP conformations is still a challenge.Here,we analyze the chain topology of IDPs and focus on the physical link of the ID...Intrinsically disordered proteins(IDP)are highly dynamic,and the effective characterization of IDP conformations is still a challenge.Here,we analyze the chain topology of IDPs and focus on the physical link of the IDP chain,that is,the entanglement between two segments along the IDP chain.The Gauss linking number of two segments throughout the IDP chain is systematically calculated to analyze the physical link.The crossing points of physical links are identified and denoted as link nodes.We notice that the residues involved in link nodes tend to have lower root mean square fluctuation(RMSF),that is,the entanglement of the IDP chain may affect its conformation fluctuation.Moreover,the evolution of the physical link is considerably slow with a timescale of hundreds of nanoseconds.The essential conformation evolution may be depicted on the basis of chain topology.展开更多
文摘If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n
基金National Natural Science Foundation of China and Cuiying Project of Lanzhou University
文摘We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mappingtopological current theory.The main purpose of this paper is to present a new theoretical framework,which can directlygive the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclideanspace R^(2n-1).For the sake of this purpose we introduce a topological tensor current,which can naturally deduce the(n-1)-dimensional topological defect in R^(2n-1) space.If these (n-1)-dimensional topological defects are closed orientedsubmanifolds of R^(2n-1),they are just the (n-1)-dimensional knots.The linking number of these knots is well defined.Using the inner structure of the topological tensor current,the relationship between Hopf invariant and the linkingnumbers of the higher-dimensional knots can be constructed.
基金National Natural Science Foundation of China,Grant/Award Numbers:12175195,32371299。
文摘Intrinsically disordered proteins(IDP)are highly dynamic,and the effective characterization of IDP conformations is still a challenge.Here,we analyze the chain topology of IDPs and focus on the physical link of the IDP chain,that is,the entanglement between two segments along the IDP chain.The Gauss linking number of two segments throughout the IDP chain is systematically calculated to analyze the physical link.The crossing points of physical links are identified and denoted as link nodes.We notice that the residues involved in link nodes tend to have lower root mean square fluctuation(RMSF),that is,the entanglement of the IDP chain may affect its conformation fluctuation.Moreover,the evolution of the physical link is considerably slow with a timescale of hundreds of nanoseconds.The essential conformation evolution may be depicted on the basis of chain topology.
