Significance of Knotted Structures for Function of Proteins and Nucleic Acids - September 17-21, 2014

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.

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