New alphabet-dependent morphological transition in a random RNA alignment

Abstract

We study the fraction $f$ of nucleotides involved in the formation of a cactus--like secondary structure of random heteropolymer RNA--like molecules. In the low--temperature limit we study this fraction as a function of the number $c$ of different nucleotide species. We show, that with changing $c$, the secondary structures of random RNAs undergo a morphological transition: $f(c)\to 1$ for $c\le c_{\mathrm{cr}}$ as the chain length $n$ goes to infinity, signaling the formation of a virtually "perfect" gapless secondary structure; while $f(c)<1$ for $c>c_{\mathrm{cr}}$, what means that a non-perfect structure with gaps is formed. The strict upper and lower bounds $2\le c_{\mathrm{cr}}\le 4$ are proven, and the numerical evidence for $c_{\mathrm{cr}}$ is presented. The relevance of the transition from the evolutional point of view is discussed.

4 pages, 3 figures (title is changed, text is essentially reworked), accepted in PRL

References in corpus (1)

• Necklace-Cloverleaf Transition in Associating RNA-like Diblock Copolymers

Cited by in corpus (3)

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• New phase transition in random planar diagrams and RNA-type matching
• Topological transition in disordered planar matching: combinatorial arcs expansion