Significance of Knotted Structures for Function of Proteins and Nucleic Acids
Friday Abstracts
Defining and Identifying Knots in Linear Polymers
Stuart Whittington
.
University of Toronto, Toronto, Canada.
Identifying topological entanglements in ring polymers is straightforward since knotting is well-
defined. For linear polymers this is not so simple and a variety of schemes have been proposed to
identify entanglements in linear polymers. These schemes all have advantages and disadvantages
and several schemes will be described and compared. The difficulty of finding an unambiguous
definition of knotting in linear polymers will be illustrated by examples that correspond to an
entanglement by one definition but not by another. For very long polymers it will be shown that
all the schemes being considered detect knotting even though they may disagree about the
particular knot type.
The Knot Complexity of Compressed Polygons in a Lattice Tube
Christine Soteros
, Jeremy Eng.
University of Saskatchewan, Saskatoon, Canada.
Towards characterizing the likelihood and the nature of knotted structures in proteins and nucleic
acids, a polygon model of ring polymers confined to a lattice tube and under the influence of a
tensile force has been developed. This simplified model has the advantage that results about
entanglement complexity can be proved and generation of all conformations for small tube sizes
is possible. One objective of this work is to obtain exact results about the entanglement
complexity of compressed polygons in lattice tubes. The methods used include both theoretical
and numerical approaches based on the transfer-matrix method. We prove a pattern theorem for
compressed polygons and obtain exact results about the probability of knotting for small tube
sizes. A comparison is made to the results for stretched polygons. We conclude that all but
exponentially few sufficiently long compressed polygons in an L x M x infinity lattice tube are
highly knotted. We also observe from the numerical data that, as expected, polygon
entanglement complexity decreases as the stretching force strength is increased.
- 26 -
