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
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