A Random Loop Model for Long Polymers

Details A Random Loop Model for Long Polymers A Random Loop Model for Long Polymers

2007-05-10

arxiv.org/abs/0705.1470v3

Phys. Ref. E (76) 051805, 2007

Physics

Condensed Matter

Soft Condensed Matter

8 pages, 7 figures; major changes: added paragraph with calculation of the annealed ensemble

Scientific paper

10.1103/PhysRevE.76.051805

While the structure of chromatin has been studied in great detail on length scales below 30 nm, amazingly little is known about the higher-order folding motifs of chromatin in interphase. Recent experiments give evidence that the folding may depend locally on gene density and transcriptional activity and show a leveling-off at long distances where approximately $ \sim O(1)$. We propose a new model that can explain this leveling-off by the formation of random loops. We derive an analytical expression for the mean square displacement between two beads where the average is taken over the thermal ensemble with a fixed but random loop configuration, while quenched averaging over the ensemble of different loop configurations -- which turns out to be equivalent to averaging over an ensemble of random matrices -- is performed numerically. A detailed investigation of this model shows that loops on all scales are necessary to fit experimental data.

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