RNA matrix models with external interactions and their asymptotic behavior

Garg, I.; Deo, Nivedita

doi:10.1103/physreve.79.061903

Cited by 6 publications

(6 citation statements)

References 38 publications

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“…The leading order term in this expansion ω (0) 1 (x) is often referred to simply as the resolvent. It is simply related to the density of eigenvalues ρ(x) which becomes continuous in large N limit and has the following asymptotics for large x (23) ω…”

Section: Matrix Models and Spectral Curves: Generalitiesmentioning

confidence: 99%

“…where the contour C encircles the cut. Moreover, expanding the resulting expression around infinity and imposing the condition (23) provides a relation between 't Hooft coupling T and the cut endpoints. This one-cut resolvent will be sufficient for our computations in this paper, however, it is not hard to generalize the above formula to the case with many cuts having endpoints a i and b i ; in this case, one only needs to replace the radicals in numerator and denominator of the integrand respectively by i (x…”

Section: Matrix Models and Spectral Curves: Generalitiesmentioning

confidence: 99%

“…and from the first line, it is clear that ( 26) is satisfied. The expansion in the second line together with the condition (23)…”

Section: Matrix Models and Spectral Curves: Generalitiesmentioning

confidence: 99%

“…The genus of the diagram determines the topological complexity of the interaction. This genus filtration has been profitably employed in a number of studies [34,38,42,7,23,18] as well as in folding algorithms [41,39] in the special case of a single RNA molecule (i.e., b = 1), which will be further discussed in section 1.2. Likewise, a folding algorithm for two interacting RNA molecules (i.e., b = 2) pertinent to antisense RNA for instance has been studied in [4].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

et al. 2013

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We introduce and study the Hermitian matrix model with potential Vs,t(x) = x 2 /2 − stx/(1 − tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st = 0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given topology as well as the number of cells in Riemann's moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly for genera less than four.

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Section: Matrix Models and Spectral Curves: Generalitiesmentioning

confidence: 99%

Section: Matrix Models and Spectral Curves: Generalitiesmentioning

confidence: 99%

“…and from the first line, it is clear that ( 26) is satisfied. The expansion in the second line together with the condition (23)…”

Section: Matrix Models and Spectral Curves: Generalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

et al. 2013

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“…This algorithm gfold is different in kind from the work in [108] which only generates RNA structures of genus one without any loop-based energy model, cf. also [47]. Further combinatorics of γ-structures are studied in [54,80].…”

Section: Chemistry and Topologymentioning

confidence: 99%

Moduli spaces and macromolecules

Penner

2016

Bull. Amer. Math. Soc.

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Abstract. Techniques from moduli spaces are applied to biological macromolecules. The first main result provides new a priori constraints on protein geometry discovered empirically and confirmed computationally. The second main result identifies up to homotopy the natural moduli space of several interacting RNA molecules with the Riemann moduli space of a surface with several boundary components in each fixed genus. Applications to RNA folding prediction are discussed. The mathematical and biological frameworks are surveyed and presented from first principles.

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Topological classification and enumeration of RNA structures by genus

et al. 2012

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To an RNA pseudoknot structure is naturally associated a topological surface, which has its associated genus, and structures can thus be classified by the genus. Based on earlier work of Harer-Zagier, we compute the generating function Dg,σ (z) = ∑n dg,σ (n)zn for the number dg,σ (n) of those structures of fixed genus g and minimum stack size σ with n nucleotides so that no two consecutive nucleotides are basepaired and show that Dg,σ (z) is algebraic. In particular, we prove that dg,2(n) ∼ kg n3(g−1/2 )γ n2, where γ2 ≈ 1.9685. Thus, for stack size at least two, the genus only enters through the sub-exponential factor, and the slow growth rate compared to the number of RNA molecules implies the existence of neutral networks of distinct molecules with the same structure of any genus. Certain RNA structures called shapes are shown to be in natural one-to-one correspondence with the cells in the Penner-Strebel decomposition of Riemann's moduli space of a surface of genus g with one boundary component, thus providing a link between RNA enumerative problems and the geometry of Riemann's moduli space.

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RNA matrix models with external interactions and their asymptotic behavior

Cited by 6 publications

References 38 publications

Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

Moduli spaces and macromolecules

Topological classification and enumeration of RNA structures by genus

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