Planar diagrams from optimization for concave potentials

S. K. Nechaev ¹, ², A. N. Sobolevski ³, ⁴, O. V. Valba ¹, ⁵

Physical Review E 87 (2013) 012102

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.

1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
2 : P. N. Lebedev Physical Institute
Russian Academy of Science
3 : Higher School of Economics
National Research University
4 : Kharkevich Institute for Information Transmission Problems
Russian Academy of Sciences
5 : Moscow Institute of Physics and Technology (MIPT)
Moscow Institute of Physics and Technology