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Conjugacy invariant pseudo-norms, representability and RNA secondary structures

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  • Siddhartha Gadgil

    (Indian Institute of Science)

Abstract

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.

Suggested Citation

  • Siddhartha Gadgil, 2011. "Conjugacy invariant pseudo-norms, representability and RNA secondary structures," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(4), pages 225-237, August.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:4:d:10.1007_s13226-011-0015-7
    DOI: 10.1007/s13226-011-0015-7
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    Cited by:

    1. Siddhartha Gadgil & Manjunath Krishnapur, 2023. "Random words in free groups, non-crossing matchings and RNA secondary structures," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(1), pages 146-158, March.

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