Gadgil, Siddhartha (2009) Watson-Crick pairing, the Heisenberg group and Milnor invariants. In: Journal of Mathematical Biology, 59 (1). pp. 123-142.
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We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Springer.|
|Keywords:||RNA secondary structure:Stem-loop; Free groups;Milnor invariants;Lower central series|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||14 Dec 2009 09:25|
|Last Modified:||19 Sep 2010 05:33|
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