3 research outputs found
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
Mesoscopic models for DNA stretching under force: new results and comparison to experiments
Single molecule experiments on B-DNA stretching have revealed one or two
structural transitions, when increasing the external force. They are
characterized by a sudden increase of DNA contour length and a decrease of the
bending rigidity. It has been proposed that the first transition, at forces of
60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA,
while the second one, at stronger forces, is a strand peeling resulting in
single stranded DNAs (ssDNA), similar to thermal denaturation. But due to
experimental conditions these two transitions can overlap, for instance for
poly(dA-dT). We derive analytical formula using a coupled discrete worm like
chain-Ising model. Our model takes into account bending rigidity, discreteness
of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit
of zero force, this model simplifies into a coupled model already developed by
us for studying thermal DNA melting, establishing a connexion with previous
fitting parameter values for denaturation profiles. We find that: (i) ssDNA is
fitted, using an analytical formula, over a nanoNewton range with only three
free parameters, the contour length, the bending modulus and the monomer size;
(ii) a surprisingly good fit on this force range is possible only by choosing a
monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase
length; (iii) mesoscopic models are not able to fit B to ssDNA (or S to ss)
transitions; (iv) an analytical formula for fitting B to S transitions is
derived in the strong force approximation and for long DNAs, which is in
excellent agreement with exact transfer matrix calculations; (v) this formula
fits perfectly well poly(dG-dC) and -DNA force-extension curves with
consistent parameter values; (vi) a coherent picture, where S to ssDNA
transitions are much more sensitive to base-pair sequence than the B to S one,
emerges.Comment: 14 pages, 9 figure