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BP: Fachverband Biologische Physik

BP 4: Protein Structure and Folding

BP 4.2: Talk

Monday, March 26, 2007, 17:45–18:00, H43

Exact Solution of the RNA Folding Problem with Loop Entropy — •Thomas R. Einert, Paul Näger, and Roland Netz — Physikdepartment (T37), Technische Universität München, 85748 Garching, Deutschland

We discuss the equilibrium statistical mechanics of the secondary structure of an RNA molecule taking into account the loop entropy. We derive a recursion relation for the restricted partition Z(N,M) function of an RNA of length N with M free backbone segments, M being a measure for the spatial extension of the molecule. The additional index M enables us to include loop entropy costs (characterized by the loop exponent c) and allows us to study stretching of the RNA. As an advantage over previous iterative formulations, our iteration equation can be solved in polynomial time. In the homopolymeric case, the recursion relation is solved analytically with generating functions methods. A phase transition is present only in the range 2<c<2.47... and is characterized by non-universal critical exponents . Explicit results for the force-extension curve are obtained.