RNA Multi-Structure Landscapes

Sebastian Bonhoeffer, John S. McCaskill, Peter F. Stadler, and Peter Schuster

Statistical properties of RNA folding landscapes obtained by the partition function algorithm (McCaskill, 1990) are investigated in detail. The pair correlation of free energies as a function of the Hamming distance is used as a measure for the ruggedness of the landscape. The caluculation of the partition function contains information about the entire ensemble of secondary structures as a function of temperature and opens the door to all quantities of thermodynamic interest in contrast with the conventional minimal free energy approach. A metric distance of structure ensembles is introduced and pair coorelations at the level of the structures themselves are computed. Just as with landscapes based on most stable secondary structure prediction, the landscapes defined on the full biophysical {\bf GCAU} alphabet are much smoother then the landscapes restricted to pure {\bf GC} sequences and the correlation lengths are almost constant fractions of the chain lengths. Correlation functions for multi-structure landscapes exhibit an increased correlation length, especially near the melting temperature. However, the main effect on evolution is rather an effective increase in sampling for finite populations where each sequence explores multiple structures.

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