Significance of Knotted Structures for Function of Proteins and Nucleic Acids - September 17-21, 2014

Significance of Knotted Structures for Function of Proteins and Nucleic Acids

Poster Session II

45 – POS Board 17 Knotted Defect Tangles in Three-dimensional Random Waves Alexander Taylor , Mark R. Dennis. University of Bristol, Bristol, Bristol, United Kingdom.

Many physical 3D space filling processes can be understood in terms of complex filamentary tangles. These include polymer strands in a dense melt, as well as disclinations in liquid crystals, and the topological defects in quantum condensed matter systems and optical fields. On large scales these systems appear statistically random, but certain properties appear universal despite the physically different origins of complexity. We track the tangle of topological defects in numerical simulations of a random wave model [1]. These are the lines of zero intensity in the wavefield, and despite the linear input conditions form a dense filamentary tangle with nonlinear features that encompass the complexity of the field. As with other systems, the small scale conformations of the lines are described with a simple local model, but on global scales the tangling becomes random. We observe that while many standard quantities reveal only a common statistical scaling on the large scale [2], the topology – particularly the occurrence of knots in vortex loops - discriminates between tangles with different origins. In fact, knotting is somewhat less common than in standard random walk models, though highly complex knots do occur. [1] M V Berry and M R Dennis . Proc R Soc A 456, 2059-79 (2000) [2] A J Taylor and M R Dennis. Geometry and scaling of tangled vortex lines in three- dimensional random wave fields, in preparation.

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