Geometric and computational aspects of polymer reconfiguration

Michael Soss, Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    We examine a few computational geometric problems concerning the structures of polymers. We use a standard model of a polymer, a polygonal chain (path of line segments) in three dimensions. The chain can be reconfigured in any manner as long as the edge lengths and the angles between consecutive edges remain fixed, and no two edges cross during the motion. We discuss preliminary results on the following problems. Given a chain, select some interior edge uv, defining two subchains which are adjacent to uv. We keep the two subchains individually rigid and rotate one around uv while leaving the other fixed in space, while maintaining the vertex-angles at uv. We call this motion an edge spin at uv. An O(n2) algorithm for this problem is given as well s an Ω (n log n) lower bound on the time complexity. In determining whether a chain can be reconfigured from one conformation to another, it is useful to consider reconfiguring through some canonical conformation. In our three-dimensional case, the most obvious choice is to flatten a chain into the plane. However, we demonstrate that determining if a given chain can be reconfigured into the plane without self-intersecting is NP-hard, even if the restriction that it must lie monotonically is added. We then provide an O(n) algorithm to decide if a chain has a non-crossing convex coil conformation (where all angles turn in the same direction), although we cannot yet decide if a sequence of motions to reconfigure a chain into a convex coil conformation exists.

    Original languageEnglish (US)
    Pages (from-to)303-318
    Number of pages16
    JournalJournal of Mathematical Chemistry
    Volume27
    Issue number4
    DOIs
    StatePublished - Jan 1 2000

    Fingerprint

    Reconfiguration
    Conformations
    Polymers
    Conformation
    Coil
    Angle
    Motion
    Flatten
    Line segment
    Time Complexity
    Three-dimension
    Standard Model
    Consecutive
    Interior
    Adjacent
    NP-complete problem
    Lower bound
    Restriction
    Three-dimensional
    Path

    Keywords

    • Edge spin
    • Flattening
    • Macromolecule conformations
    • Polymer conformations
    • Polymer motions

    ASJC Scopus subject areas

    • Chemistry(all)
    • Applied Mathematics

    Cite this

    Geometric and computational aspects of polymer reconfiguration. / Soss, Michael; Toussaint, Godfried.

    In: Journal of Mathematical Chemistry, Vol. 27, No. 4, 01.01.2000, p. 303-318.

    Research output: Contribution to journalArticle

    Soss, Michael ; Toussaint, Godfried. / Geometric and computational aspects of polymer reconfiguration. In: Journal of Mathematical Chemistry. 2000 ; Vol. 27, No. 4. pp. 303-318.
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