The knot nomenclature in common use, summarized in Rolfsen's knot table [Rolfsen (1990) Knots and Links, American Mathematical Society], was not originally designed to distinguish between mirror images. This ambiguity is particularly inconvenient when studying knotted biopolymers such as DNA and proteins, since their chirality is often significant. In the present article, we propose a biologically meaningful knot table where a representative of a chiral pair is chosen on the basis of its mean writhe. There is numerical evidence that the sign of the mean writhe is invariant for each knot in a chiral pair. We review numerical evidence where, for each knot type K, the mean writhe is taken over a large ensemble of randomly chosen realizations of K. It has also been proposed that a chiral pair can be distinguished by assessing the writhe of a minimal or ideal conformation of the knot. In all cases examined to date, the two methods produce the same results.
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Conference Article|
March 21 2013
New biologically motivated knot table
Reuben Brasher;
Reuben Brasher
*Mathematics Department, San Francisco State University, San Francisco, CA 94132, U.S.A.
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Rob G. Scharein;
Rob G. Scharein
†Hypnagogic Software, Vancouver, BC, Canada, V6K 1V6
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Mariel Vazquez
Mariel Vazquez
1
*Mathematics Department, San Francisco State University, San Francisco, CA 94132, U.S.A.
1To whom correspondence should be addressed (emailmariel@sfsu.edu).
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Publisher: Portland Press Ltd
Received:
December 17 2012
Online ISSN: 1470-8752
Print ISSN: 0300-5127
© The Authors Journal compilation © 2013 Biochemical Society
2013
Biochem Soc Trans (2013) 41 (2): 606–611.
Article history
Received:
December 17 2012
Citation
Reuben Brasher, Rob G. Scharein, Mariel Vazquez; New biologically motivated knot table. Biochem Soc Trans 1 April 2013; 41 (2): 606–611. doi: https://doi.org/10.1042/BST20120278
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