%0 Journal Article
%T Planar diagrams from optimization
%A S. K. Nechaev
%A A. N. Sobolevski
%A O. V. Valba
%J Quantitative Biology
%D 2012
%I arXiv
%R 10.1103/PhysRevE.87.012102
%X We propose a new toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model the sequential intervals between neighboring monomers along a chain are considered as quenched random variables. Using the optimization procedure for a special class of concave--type potentials, borrowed from optimal transport analysis, we derive the local difference equation for the ground state free energy of the chain with the planar (RNA--like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale--free) and demonstrate the existence of a topological crossover from sequential to essentially embedded (nested) configurations of paired links.
%U http://arxiv.org/abs/1203.3248v2