Ground state and glass transition of the RNA secondary structure
- 58 Downloads
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
Unable to display preview. Download preview PDF.
- B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter, Molecular Biology of the Cell (Garland Science, New York, 2002) Google Scholar
- For a review, see T. Garel, H. Orland, E. Pitard, in Spin Glasses and Random Fields, edited by A.P. Young (World Scientific, 1998), p. 387 Google Scholar
- RNA Structure and Function, edited by R.W. Simons, M. Grunberg-Manago (Cold-Spring, Harbor, 1998) Google Scholar
- Nucleic Acids in Chemistry and Biology, edited by G.M. Blackburn, M.J. Gait (IRL Press, Oxford, 1990) Google Scholar
- M.L.M. Anderson, Nucleic Acid Hybridization (Springer, New York, 1998) Google Scholar
- R. Durbin, S.R. Eddy, A. Krogh, G. Mitchison, Biological Sequence Analysis (Cambridge University Press, Cambridge, UK, 1998) Google Scholar
- M. Mézard, J. Phys. 51, 1831 (1990) Google Scholar
- J. Krug, P. Meakin, J. Phys. A 23, L987 (1990) Google Scholar
- F. David, K. J. Wiese, e-print arXiv:q-bio.BM/0607044 Google Scholar