On topological transition in a Random Interval Model of RNA-like chains

Details On topological transition in a Random Interval Model of RNA-like chains On topological transition in a Random Interval Model of RNA-like chains

2012-03-15

arxiv.org/abs/1203.3248v1

Physics

Condensed Matter

Soft Condensed Matter

8 pages, 8 figures

Scientific paper

We have proposed a new toy model of a heteropolymer chain capable of forming a cactus-like hierarchical secondary structure typical for RNA molecules. The specific feature of this model consists in the fact, that the sequential intervals between neighboring along a chain monomers are considered as quenched random variables. Using the optimization procedure for a special class of concave-type potentials, borrowed from optimal transport analysis, we have derived the stochastic differential equation for the ground state free energy of the chain. We have considered various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale-free) and have demonstrated the existence of a topological transition from sequential to essentially embedded (nested) configurations of paired links.

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