Planar diagrams from optimization for concave potentials

S. K. Nechaev 12, A. N. Sobolevski 34, O. V. Valba 15

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