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Keywords
(6)
Field Theory
Matrix Theory
Partition Function
Recursion Relation
Rna Folding
Secondary Structure
Related Publications
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RNA folding and large N matrix theory
RNA folding and large N matrix theory,10.1016/S05503213(01)005223,Nuclear Physics B,Henri Orland,A. Zee
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RNA folding and large N matrix theory
(
Citations: 9
)
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Henri Orland
,
A. Zee
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 socalled
secondary structure
(Hartree theory). Tertiary structure and pseudoknots 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. 456476, 2002
DOI:
10.1016/S05503213(01)005223
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Citation Context
(3)
...[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 nonzero genus g 6 0 can be drawn without any crossing on a surface with g handles...
Michael Bon
,
et 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 nonplanar corrections), which is what we will suppose from now on. At high temperatures, in the socalled “molten phase”, energetic considerations only play a minor role, and the probability Pij of two RNAbases to pair, is [6]...
François David
,
et 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. Dima
,
et al.
Extracting Stacking Interaction Parameters for RNA from the Data Set o...
References
(3)
Protein folding and heteropolymers
(
Citations: 16
)
T. Garel
,
H. Orland
,
E. Pitard
Published in 1997.
Quantum Field Theory and Critical Phenomena
(
Citations: 1737
)
J. Zinnjustin
Published in 1996.
Quantum Field Theory and Critical Phenomena
(
Citations: 1405
)
J. Zinn Justin
Published in 1996.
Sort by:
Citations
(9)
Enumeration of linear chord diagrams
(
Citations: 2
)
J. E. Andersen
,
R. C. Penner
,
C. M. Reidys
,
M. S. Waterman
Published in 2010.
TT2NE: A novel algorithm to predict RNA secondary structures with pseudoknots
Michael Bon
,
Henri Orland
Published in 2010.
Field theory of the RNA freezing transition
François David
,
Kay Jörg Wiese
Journal:
Journal of Statistical Mechanicstheory and Experiment  J STAT MECHTHEORY EXP
, vol. 10, no. 10, 2009
Topological Classification of RNA Structures
(
Citations: 8
)
Michael Bon
,
Graziano Vernizzi
,
Henri Orland
,
A. Zee
Journal:
Journal of Molecular Biology  J MOL BIOL
, vol. 379, no. 4, pp. 900911, 2008
A growth model for RNA secondary structures
(
Citations: 5
)
François David
,
Christian Hagendorf
,
Kay Jörg Wiese
Journal:
Journal of Statistical Mechanicstheory and Experiment  J STAT MECHTHEORY EXP
, vol. 4, no. 04, 2008