Conjugacy invariant pseudo-norms, representability and RNA secondary structures

  • Siddhartha GadgilEmail author


To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases. We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms.

We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

Key words

RNA secondary structure stem-loop free groups Milnor invariants lower central series 

6. References

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    D. Burago, S. Ivanov and L. Polterovich, Conjugation-invariant norms on groups of geometric origin. (English summary) Groups of diffeomorphisms, 221–250, Adv. Stud. Pure Math., 52, Math. Soc., Japan, Tokyo, 2008.Google Scholar
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    S. Gadgil, Watson-Crick pairing, the Heisenberg group and Milnor invariants, J. Math. Biol., 59 (2009), 123–142.MathSciNetzbMATHCrossRefGoogle Scholar
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    R. F. Gesteland and J. F. Atkins, The RNA world: the nature of modern RNA suggests a prebiotic RNA world Cold Spring Harbor Laboratory Press, 1993.Google Scholar

Copyright information

© The Indian National Science Academy 2011

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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