Andersen, Jørgen E^{5}; Chekhov, Leonid O.^{2}; Penner, Robert C^{5}; Reidys, Christian^{3}; Sułkowski, Piotr^{4}

Affiliations:

^{1} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University^{2} Department of Theoretical Physics, Steklov Mathematical Institute, Moscow^{3} Department of Mathematics and Computer Science, University of Southern Denmark^{4} Institute for Theoretical Physics, University of Amsterdam^{5} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University

Subtitle:

Biochemical Society Transactions

DOI:

10.1042/BST20120270

Abstract:

In the present article, we review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the Hermitian matrix model with potential V(x)=x(2)/2 - stx/(1 - tx), where s and t are respective generating parameters for the number of RNA molecules and hydrogen bonds in a given complex. The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory. These numbers of RNA complexes also have profound meaning in mathematics: they provide the number of chord diagrams of fixed genus with specified numbers of backbones and chords as well as the number of cells in Riemann's moduli spaces for bordered surfaces of fixed topological type.

Type:

Journal article

Language:

English

Published in:

Biochemical Society Transactions, 2013, Vol 41, Issue 2, p. 652-655

Keywords:

free energy Hermitian matrix model random matrix theory RNA complex