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Simulations of Action of DNA Topoisomerases to Investigate Boundaries and Shapes of Spaces of Knots

Alessandro Flammini ^*  , Amos Maritan  and Andrzej Stasiak 

^* International School for Advanced Studies, Trieste, Italy; Department of Physics "G. Galilei" of the University of Padua, Padua, Italy; and Laboratory of Ultrastructural Analysis, Department of Biology and Medicine, University of Lausanne, 1015 Lausanne-Dorigny, Switzerland

Correspondence: Address reprint requests to Andrzej Stasiak, Tel.: 41-21-692-42-82; Fax: 41-21-692-41-05; E-mail: andrzej.stasiak{at}lau.unil.ch.

The configuration space available to randomly cyclized polymers is divided into subspaces accessible to individual knot types. A phantom chain utilized in numerical simulations of polymers can explore all subspaces, whereas a real closed chain forming a figure-of-eight knot, for example, is confined to a subspace corresponding to this knot type only. One can conceptually compare the assembly of configuration spaces of various knot types to a complex foam where individual cells delimit the configuration space available to a given knot type. Neighboring cells in the foam harbor knots that can be converted into each other by just one intersegmental passage. Such a segment-segment passage occurring at the level of knotted configurations corresponds to a passage through the interface between neighboring cells in the foamy knot space. Using a DNA topoisomerase-inspired simulation approach we characterize here the effective interface area between neighboring knot spaces as well as the surface–to-volume ratio of individual knot spaces. These results provide a reference system required for better understanding mechanisms of action of various DNA topoisomerases.

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