Cofolding and DNA Parameters

Folding of a single RNA molecule can be readily extended to simultaneous folding of two or more RNA molecules (Hofacker et al., 1994; Andronescu et al., 2003). Algorithms for cofolding make use of dynamic programming and are fast and efficient. It is important also to compute suboptimal conformations for cofolded ensembles in order to be able to distinguish stable complexes from associations of marginal stability (for review see, e.g., Schuster, 2005).

DNA resembles RNA in many aspects and the algorithms used for the prediction of RNA secondary structures can be applied successfully to DNA too. The differences are: DNA as a molecule in solution is more stable than RNA and less easily degraded. DNA secondary structures, however, are less stable because of weaker stacking energies. In detail the empirical parameters for DNA folding differ in many aspects from their RNA counterparts (SantaLucia, 1998; SantaLucia and Hicks, 2004). Recent interest in DNA folding as well as RNA-DNA cofolding is caused by the need to design molecules that are suitable primers for PCR as well as candidates for forming stable RNA-DNA hybrids. The discovery of small interfering RNA molecules (McManus and Sharp, 2002) turned the study of RNA-DNA interactions into a topic of high actuality and importance.

The digression into RNA structures is completed through mentioning other approaches of secondary structure prediction. Homology modeling is based on the comparison of sequences from different organisms (Brimacombe, 1984; Michel and Westhof, 1990; Schnare et al., 1996; for reviews see Woese and Pace, 1993, Westhof and Michel, 1994), which form the same structure. It is highly successful but appears unsuitable for designing RNA structure and studying RNA evolution (Section 2.3) because it is restricted to natural RNA molecules. An interactive prediction algorithm for secondary structures (Gaspin and Westhof, 1995) applies folding constraints dynamically and allows for intervention by the researcher. By not elaborating on full three-dimensional structures of RNA and DNA molecules here we do not intend to belittle their role in structural biology and nucleic acid catalysis. On the contrary, it is the spatial structure that determines the molecular properties. The forthcoming discussion of RNA in vitro evolution requires, however, some insight into sequence-structure relations that can currently be achieved only for secondary structures and therefore we shall not further discuss tertiary structures of nucleic acids here.

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