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.
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.
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have proposed
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a cactus-like hierarchical secondary structure
planar secondary structures
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The specific feature of this model consists in the fact, that the
In this model the
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monomers
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monomers
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concave-type
concave--type
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have derived the stochastic differential
derive the local difference
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. We have considered
with the planar (RNA--like) architecture of paired links. We consider
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scale-free) and have demonstrated
scale--free) and demonstrate
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transition
crossover