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RNA folding and large N matrix theory

RNA folding and large N matrix theory,10.1016/S0550-3213(01)00522-3,Nuclear Physics B,Henri Orland,A. Zee

RNA folding and large N matrix theory   (Citations: 9)
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We formulate the RNA folding problem as an N×N matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit N→∞ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating the 1/N2 corrections to the partition function. We propose a generalization of the Hartree recursion relation to generate the tertiary structure.
Journal: Nuclear Physics B - NUCL PHYS B , vol. 620, no. 3, pp. 456-476, 2002
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    • ...[21, 22, 23, 24, 25, 26, 27, 28, 29]; the list is not exhaustive) . There exists however a novel approach: in order to include the pseudoknots, the RNA folding problem has been formulated in terms of a sophisticated mathematical theory, namely a quantum matrix field theory [30]...
    • ...These diagrams, which are the usual Feynman diagrams of quantum field theory, can be viewed as the set of all the possible pairings of the RNA, with the correct corresponding Boltzmann weights [30, 33]...
    • ...As was shown in a previous paper [30, 34], this expansion relies on a topological number called the genus which characterizes the pairing...
    • ...The matrix field theory representation of the problem suggests representing a pairing not by a single dotted line, but rather by a double line (which should never be twisted) [30, 31]...
    • ...More generally, it was shown in [30] that the secondary structure diagrams are all the planar diagrams with g = 0. Likewise, in fig.4 one sees also how diagrams with non-zero genus g 6 0 can be drawn without any crossing on a surface with g handles...

    Michael Bonet al. Topological Classification of RNA Structures

    • ...A given configuration is thus characterised by the set of base pairings, see figure 1. These pairings are mostly planar [2, 3, 4] (see [5] for non-planar corrections), which is what we will suppose from now on. At high temperatures, in the so-called “molten phase”, energetic considerations only play a minor role, and the probability Pij of two RNA-bases to pair, is [6]...

    François Davidet al. A growth model for RNA secondary structures

    • ...K3.33 K1.65 K0.63 K3.40 K3.40 CG (189) (156) (45) (13) (81) (82) K3.33 K3.25 K1.90 K0.68 K3.31 K3.37 GC (29) (33) (5) (5) (20) (3) K1.65 K1.91 0.29 0.75 K1.71 K0.21 GU (19) (17) (2) (12) (5) (8) K0.63 K0.68 0.75 K0.83 K1.10 K1.23 UG (72) (76) (12) (15) (19) (29) K3.40 K3.31 K1.71 K1.10 K2.44 K3.15 AU (88) (82) (7) (12) (20) (22) K3.40 K3.37 K0.21 K1.23 K3.15 K2.98 UA...

    Ruxandra I. Dimaet al. Extracting Stacking Interaction Parameters for RNA from the Data Set o...

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