Abstract
Abstract
Biopolymers, like chromatin, are often confined in small volumes. Confinement has a great effect on polymer conformations, including polymer entanglement. Polymer chains and other filamentous structures can be represented by polygonal curves in three-space. In this manuscript, we examine the topological complexity of polygonal chains in three-space and in confinement as a function of their length. We model polygonal chains by equilateral random walks in three-space and by uniform random walks (URWs) in confinement. For the topological characterization, we use the second Vassiliev measure. This is an integer topological invariant for polygons and a continuous functions over the real numbers, as a function of the chain coordinates for open polygonal chains. For URWs in confined space, we prove that the average value of the Vassiliev measure in the space of configurations increases as O(n
2) with the length of the walks or polygons. We verify this result numerically and our numerical results also show that the mean value of the second Vassiliev measure of equilateral random walks in three-space increases as O(n). These results reveal the rate at which knotting of open curves and not simply entanglement are affected by confinement.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference39 articles.
1. Sampling large random knots in a confined space;Arsuaga;J. Phys. A: Math. Theor.,2007
2. Linking of uniform random polygons in confined spaces;Arsuaga;J. Phys. A: Math. Theor.,2007
3. Mathematical methods in DNA topology: applications to chromosome organization and site-specific recombination;Arsuaga,2009
4. Stretched polygons in a lattice tube;Atapour;J. Phys. A: Math. Theor.,2009
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. The Jones polynomial of collections of open curves in 3-space;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2022-11