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
