Distribution of graph-distances in Boltzmann ensembles of RNA secondary structures

Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium therefore provides useful information on the overall shape of the molecule can provide insights into the interplay of its functional domains. Spatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between arbitrary nucleotides can be computed in polynomial time by means of dynamic programming. A naive implementation would yield recursions with a very high time complexity of O(n^11). Although we were able to reduce this to O(n^6) for many practical applications a further reduction seems difficult. We conclude, therefore, that sampling approaches, which are much easier to implement, are also theoretically favorable for most real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Isothermal folding of G-quadruplexes

Thermodynamic studies of G-quadruplex stability are an essential complement to structures obtained by NMR or x-ray crystallography. An understanding of the energetics of quadruplex folding provides a necessary foundation for the physical interpretation of quadruplex formation and reactivity. While thermal denaturation methods are most commonly used to evaluate quadruplex stability, it is also possible to study folding using isothermal titration methods. G-quadruplex folding is tightly coupled to specific cation binding. We describe here protocols for monitoring the cation-driven quadruplex folding transition using circular dichroism or absorbance, and for determination of the distribution of free and bound cation using a fluorescence indicator. Together these approaches provide insight into quadruplex folding at constant temperature, and characterize the linkage between cation binding and folding