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Inferring Global Topology from Local Juxtaposition Geometry: Interlinking Polymer Rings and Ramifications for Topoisomerase Action

Zhirong Liu ^*, E. Lynn Zechiedrich  and Hue Sun Chan ^*

^* Department of Biochemistry, and Department of Medical Genetics and Microbiology, Faculty of Medicine, University of Toronto, Toronto, Ontario M5S 1A8, Canada; and Department of Molecular Virology and Microbiology, Baylor College of Medicine, Houston, Texas 77030 USA

Correspondence: Address reprint requests to Hue Sun Chan, Tel.: 416-978-2697; Fax: 416-978-8548; E-mail: chan{at}arrhenius.med.toronto.edu; or E. Lynn Zechiedrich, Tel.: 713-798-5126; Fax: 713-798-7375; E-mail: elz{at}bcm.edu.

Lattice modeling is applied to investigate how the configurations of local chain juxtapositions may provide information about whether two ring polymers (loops) are topologically linked globally. Given a particular juxtaposition, the conditional probability that the loops are linked is determined by exact enumeration and extensive Monte Carlo sampling of conformations satisfying excluded volume constraints. A discrimination factor f_L, defined as the ratio of linked to unlinked probabilities, varies widely depending on which juxtaposition is presumed. |log f_L|s that are large for small loop size n tend to decrease, signaling diminishing topological information content of the juxtapositions, with increasing n. However, some juxtaposition geometries can impose sufficient overall conformational biases such that |log f_L| remains significant for large n. Notably, for two loops as large as n = 200 in the model, the probability that passing the segments of a hooked juxtaposition would unlink an originally linked configuration is remarkably high, 85%. In contrast, segment-passage of a free juxtaposition would link the loops from an originally unlinked configuration more than 90% of the time. The statistical mechanical principles emerging from these findings suggest that it is physically possible for DNA topoisomerases to decatenate effectively by acting selectively on juxtapositions with specific "hooked" geometries.

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