Issue Eur. Phys. J. B Volume 53, Number 1, September I 2006 Page(s) 77 - 84 Section Statistical Physics and Biological Information DOI 10.1140/epjb/e2006-00347-x Published online 07 September 2006

Eur. Phys. J. B 53, 77-84 (2006)
DOI: 10.1140/epjb/e2006-00347-x

Ground state and glass transition of the RNA secondary structure

S. Hui and L.-H. Tang

Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, P.R. China

lhtang@hkbu.edu.hk

(Received 15 May 2006 / Received in final form 21 July 2006 / Published online 7 September 2006)

Abstract
RNA molecules form a sequence-specific self-pairing pattern at low temperatures. We analyze this problem using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix propagation. The free energy cost for separating a chain into two equal halves offers a quantitative measure of sequence specific pairing. In the low temperature glass phase, this quantity grows quadratically with the logarithm of the chain length, but it switches to a linear behavior of entropic origin in the high temperature molten phase. Transition between the two phases is continuous, with characteristics that resemble those of a disordered elastic manifold in two dimensions. For designed sequences, however, a power-law distribution of pairing energies on a coarse-grained level may be more appropriate. Extreme value statistics arguments then predict a power-law growth of the free energy cost to break a chain, in agreement with numerical simulations. Interestingly, the distribution of pairing distances in the ground state secondary structure follows a remarkable power-law with an exponent -4/3, independent of the specific assumptions for the base pairing energies.

PACS
87.14.Gg - DNA, RNA.
87.15.-v - Biomolecules: structure and physical properties.
64.70.Pf - Glass transitions.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2006

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