Enumeration of RNA complexes via random matrix theory
Abstract
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^2/2stx/(1tx), 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 socalled 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2013
 DOI:
 10.48550/arXiv.1303.1326
 arXiv:
 arXiv:1303.1326
 Bibcode:
 2013arXiv1303.1326A
 Keywords:

 Quantitative Biology  Quantitative Methods;
 Condensed Matter  Soft Condensed Matter;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Proceedings of the conference "Topological Aspects of DNA Function and Protein Folding", Isaac Newton Institute, Cambridge, 2012