Average structures of a single knotted ring polymer

Shinya Saka, Hiroshi Takano

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Two types of average structure of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N-dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of average structure. The other type of average structure uses all the conformation vectors generated from those sampled in a simulation. In the case of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N increases. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.

Original languageEnglish
Article number124802
JournalJournal of the Physical Society of Japan
Issue number12
Publication statusPublished - 2008 Dec


  • Average structure
  • Brownian dynamics simulations
  • Knot
  • Knot localization
  • Ring polymer
  • Single polymer

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'Average structures of a single knotted ring polymer'. Together they form a unique fingerprint.

Cite this