Session U1: RNA Folding at the Crossroads Between Molecular Biology and Statistical Physics

Aggregation and folding phase transitions of RNA molecules

RNA is a biomolecule that is involved in nearly all aspects of cellular functions. In order to perform many of these functions, RNA molecules have to fold into specific secondary structures. This folding is driven by the tendency of the bases to form Watson-Crick base pairs. Beyond the biological importance of RNA, the relatively simple rules for structure formation of RNA make it a very interesting system from the statistical physics point of view. We will present examples of phase transitions in RNA secondary structure formation that are amenable to analytical descriptions. A special focus will be on aggregation between several RNA molecules which is important for some regulatory circuits based on RNA structure, triplet repeat diseases like Huntington's, and as a model for prion diseases. We show that depending on the relative strength of the intramolecular and the intermolecular base pairing, RNA molecules undergo a transition into an aggregated phase and quantitatively characterize this transition.   

Ground state and glass transition of the RNA secondary structure

RNA molecules form a sequence-specific self-pairing pattern at low temperatures. Understanding the relevant energy scales that govern sequence specificity is important for thermal and mutational stability studies of functional RNAs. This problem has been analyzed using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix propagation [1]. The free energy cost for separating a chain into two equal halves offers a quantitative measure of sequence specific pairing [2]. In the low temperature glass phase, this quantity is shown to grow quadratically with the logarithm of the chain length, but it switches to a linear behavior of entropic origin in the high temperature molten phase. Numerical studies of the melting transition suggest similarities to the thermal depinning of a two-dimensional elastic manifold in a disordered medium, though details of the analogy need to be further explored. 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 specific assumptions for the base pairing energies. \newline \newline [1] Sheng Hui and Lei-Han Tang, Eur. Phys. J. B \textbf{53}, 77 (2006). \newline [2] R. Bundschuh and T. Hwa, Phys. Rev. Lett. \textbf{83}, 1479 (1999); Phys. Rev. E \textbf{65}, 031903 (2002).   

Glassiness in RNA folding

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. Based on an exact inequality, we argue that RNA conformations in the glass phase are similar to those at the transition. \\ $[1]$ M. Laessig and K.J. Wiese, The freezing of random RNA, Phys. Rev. Lett. 96 (2006), 228101. \\ $[2]$ F. David and K.J. Wiese, Systematic field theory of the RNA glass transition, q-bio.BM/0607044 (2006); accepted for publication in Phys. Rev. Lett.