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The effect of confinement on knotting and geometry of random polygons

Banff International Research Station for Mathematical Innovation and Discovery

It is well known that genomic materials (long DNA chains) of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. In this talk we introduce and study a model of equilateral random polygons confined in a sphere. This model is not meant to generate polygons that model DNA packed in a virus head directly. Instead, the average topological characteristics of this model may serve as benchmark data for totally randomly packed circular DNAs. The difference between the biologically observed topological characteristics and our benchmark data might reveal the bias of DNA packed in the viral capsids and possibly lead to a better understanding of the DNA packing mechanism, at least for the bacteriophage DNA. In more detail we consider equilateral random polygons of length n in a confinement sphere of radius R>1. In this talk we discuss how knotting probabilities and geometric properties of the random polygons change as a function of both n and R. Even for relatively small length (in our study we use polygons of a length up to 90 steps) such random polygons are knotted with very high probability - and the knots obtained are very complex (i.e. the knots have more than 16 crossings and cannot be identified). Work in collaboration with Y. Diao, E Rawdon, U. Ziegler.

Mathematics; Biology and other natural sciences; Manifolds and cell complexes; Mathematical biology

video/mp4

Author affiliation: Western Kentucky University

2014-08-07

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49727

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/