The abundance of unknots in various models of polymer loops

N. T. Moore, A. Y. Grosberg

    Research output: Contribution to journalArticle

    Abstract

    A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼exp(-N/N 0), where N 0 marks the crossover from a mostly unknotted (i.e., topologically simple) to a mostly knotted (i.e., topologically complex) ensemble. In the present work, we use computational simulation to look closer into the variation of N 0 for a variety of polymer models. Among models examined, N 0 is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian-distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power-law tail.

    Original languageEnglish (US)
    Article number005
    Pages (from-to)9081-9092
    Number of pages12
    JournalJournal of Physics A: Mathematical and General
    Volume39
    Issue number29
    DOIs
    StatePublished - Jul 21 2006

    Fingerprint

    Unknot
    Polymers
    Knot
    Ensemble
    polymers
    Oils and fats
    Computational Simulation
    Conformations
    fats
    Conformation
    Model
    Crossover
    Tail
    crossovers
    Power Law
    Trivial
    Fractional
    simulation

    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    The abundance of unknots in various models of polymer loops. / Moore, N. T.; Grosberg, A. Y.

    In: Journal of Physics A: Mathematical and General, Vol. 39, No. 29, 005, 21.07.2006, p. 9081-9092.

    Research output: Contribution to journalArticle

    Moore, N. T. ; Grosberg, A. Y. / The abundance of unknots in various models of polymer loops. In: Journal of Physics A: Mathematical and General. 2006 ; Vol. 39, No. 29. pp. 9081-9092.
    @article{b6862760c69b4dd7b11dba080167ba6b,
    title = "The abundance of unknots in various models of polymer loops",
    abstract = "A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼exp(-N/N 0), where N 0 marks the crossover from a mostly unknotted (i.e., topologically simple) to a mostly knotted (i.e., topologically complex) ensemble. In the present work, we use computational simulation to look closer into the variation of N 0 for a variety of polymer models. Among models examined, N 0 is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian-distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power-law tail.",
    author = "Moore, {N. T.} and Grosberg, {A. Y.}",
    year = "2006",
    month = "7",
    day = "21",
    doi = "10.1088/0305-4470/39/29/005",
    language = "English (US)",
    volume = "39",
    pages = "9081--9092",
    journal = "Journal of Physics A: Mathematical and Theoretical",
    issn = "1751-8113",
    publisher = "IOP Publishing Ltd.",
    number = "29",

    }

    TY - JOUR

    T1 - The abundance of unknots in various models of polymer loops

    AU - Moore, N. T.

    AU - Grosberg, A. Y.

    PY - 2006/7/21

    Y1 - 2006/7/21

    N2 - A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼exp(-N/N 0), where N 0 marks the crossover from a mostly unknotted (i.e., topologically simple) to a mostly knotted (i.e., topologically complex) ensemble. In the present work, we use computational simulation to look closer into the variation of N 0 for a variety of polymer models. Among models examined, N 0 is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian-distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power-law tail.

    AB - A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼exp(-N/N 0), where N 0 marks the crossover from a mostly unknotted (i.e., topologically simple) to a mostly knotted (i.e., topologically complex) ensemble. In the present work, we use computational simulation to look closer into the variation of N 0 for a variety of polymer models. Among models examined, N 0 is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian-distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power-law tail.

    UR - http://www.scopus.com/inward/record.url?scp=33745826696&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=33745826696&partnerID=8YFLogxK

    U2 - 10.1088/0305-4470/39/29/005

    DO - 10.1088/0305-4470/39/29/005

    M3 - Article

    VL - 39

    SP - 9081

    EP - 9092

    JO - Journal of Physics A: Mathematical and Theoretical

    JF - Journal of Physics A: Mathematical and Theoretical

    SN - 1751-8113

    IS - 29

    M1 - 005

    ER -