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)=x2/2−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.
Skip Nav Destination
Article navigation
April 2013
-
Cover Image
Cover Image
- PDF Icon PDF LinkFront Matter
- PDF Icon PDF LinkTable of Contents
Conference Article|
March 21 2013
Enumeration of RNA complexes via random matrix theory
Jørgen E. Andersen;
Jørgen E. Andersen
*Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 Århus C, Denmark
Search for other works by this author on:
Leonid O. Chekhov;
Leonid O. Chekhov
†Department of Theoretical Physics, Steklov Mathematical Institute, Moscow 119991, Russia
‡School of Mathematics, Loughborough University, Loughborough, Leicestershire LE11 3TU, U.K.
Search for other works by this author on:
Robert C. Penner;
Robert C. Penner
*Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 Århus C, Denmark
§Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, U.S.A.
Search for other works by this author on:
Christian M. Reidys;
Christian M. Reidys
∥Department of Mathematics and Computer Science, University of Southern Denmark, DK-5230 Odense M, Denmark
Search for other works by this author on:
Piotr Sułkowski
Piotr Sułkowski
1
§Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, U.S.A.
¶Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1090 GL, Amsterdam, The Netherlands
**Faculty of Physics, University of Warsaw, ul. Hoża 69, 00-681 Warsaw, Poland
1To whom correspondence should be addressed (emailpsulkows@theory.caltech.edu).
Search for other works by this author on:
Publisher: Portland Press Ltd
Received:
October 31 2012
Online ISSN: 1470-8752
Print ISSN: 0300-5127
© The Authors Journal compilation © 2013 Biochemical Society
2013
Biochem Soc Trans (2013) 41 (2): 652–655.
Article history
Received:
October 31 2012
Citation
Jørgen E. Andersen, Leonid O. Chekhov, Robert C. Penner, Christian M. Reidys, Piotr Sułkowski; Enumeration of RNA complexes via random matrix theory. Biochem Soc Trans 1 April 2013; 41 (2): 652–655. doi: https://doi.org/10.1042/BST20120270
Download citation file:
Sign in
Don't already have an account? Register
Sign in to your personal account
You could not be signed in. Please check your email address / username and password and try again.
Captcha Validation Error. Please try again.