Titre
Geometry and physics of knots
Type
article
Institution
UNIL/CHUV/Unisanté + institutions partenaires
Périodique
Auteur(s)
Katritch, V.
Auteure/Auteur
Bedna, J.
Auteure/Auteur
Michoud, D.
Auteure/Auteur
Scharein, G. S.
Auteure/Auteur
Dubochet, J.
Auteure/Auteur
Stasiak, A.
Auteure/Auteur
Liens vers les personnes
Liens vers les unités
ISSN
0028-0836
Statut éditorial
Publié
Date de publication
1996
Volume
384
Numéro
6605
Première page
142
Dernière page/numéro d’article
145
Peer-reviewed
Oui
Langue
anglais
Résumé
KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).
PID Serval
serval:BIB_0E7B92EC5132
Date de création
2008-01-24T09:25:54.019Z
Date de création dans IRIS
2025-05-20T20:27:52Z