Packing structure of semiflexible rings

Abstract

Unraveling the packing structure of dense assemblies of semiflexible rings is not only fundamental for the dynamical description of polymer rings, but also key to understand biopackaging, such as observed in circular DNA of viruses or genome folding. Here we use X-ray tomography to study the geometrical and topological features of disordered packings of rubber bands in a cylindrical container. Assemblies of short bands assume a liquid-like disordered structure, with short-range orientational order, and reveal only minor influence of the container. In the case of longer bands, the confinement causes folded configurations and the bands interpenetrate and entangle. Most of the systems are found to display a threading network which percolates the system. Surprisingly, for long bands whose diameter is more than twice the diameter of the container, we found that all bands interpenetrate each other, in a complex fully entangled structure.

Topological Tuning of DNA Mobility in Entangled Solutions of Supercoiled Plasmids

“…It is natural to associate the open-oblate/closed-prolate conformations assumed by DNA plasmids to a larger/smaller (minimal) spanning area, respectively ( 63 ). The size of this area may be relevant for the dynamics because it could be “threaded” by neighbouring plasmids hence hindering the dynamics ( 28, 53, 54, 64 ). To quantify this in more detail we calculated the minimal surface using the algorithm used in Ref.…”

Effects of Topological Constraints on Penetration Structures of Semi-Flexible Ring Polymers

“…The surface of the ring A is composed of triangle 123, while other triangles are removed at each reduction (e.g., 345 and 567 at the first reduction). Among all the possible surfaces by different routines of reduction, we can find the minimal surface [ 25 , 41 ] and the corresponding final triangle (e.g., the case of Figure 2 b) to define the threading. With the definition of threading produced by a pair of rings, we call them one passive ring (A) and one active ring (B) respectively.…”

“…al surface [25,41] and the corresponding final triangle (e.g., the case of Figure 2b) to defin ding. With the definition of threading produced by a pair of rings, we call them one passive nd one active ring (B) respectively.…”

Persistence homology of entangled rings

“…Ring polymers are the simplest class of topologically nontrivial polymers that manifestly depart from the predictions of theoretical cornerstones such as the reptation and tube models [1]. Over the last three decades there have been several theoretical and experimental attempts at understanding the statics and dynamics of rings [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and yet their behavior in entangled solutions is still poorly understood. Individual ring polymers in the melt or entangled solutions assume compact non-Gaussian conformations, which are distinct from the ones assumed by linear polymers.…”

“…Unlike previous definitions of threadings, an H-threading is defined by the homological property of the system, and its identification is unique. Persistent homology provides us with a powerful tool to extract useful information hidden in the big data obtained from, e.g., large-scale MD simulations of polymer melts [6,40] or x-ray tomography of elastic bands [18]. Additionally, it has several advantages over other methods: (i) the ability to detect and quantify so-far elusive hierarchical loops in the folding of rings, (ii) very efficient and stable numerical (open-source) implementation, (iii) uniqueness of the analysis result (no free parameters), and (iv) it can be readily generalized to detect higher-dimensional structures in data sets.…”