On exclusivity of alphabets with four nucleotide types

Details On exclusivity of alphabets with four nucleotide types On exclusivity of alphabets with four nucleotide types

2011-09-25

arxiv.org/abs/1109.5410v2

Biology

Quantitative Biology

Genomics

9 pages, 3 figures (text has been essentially rewritten, figure 3 was changed)

Scientific paper

The free energy of random heteropolymers which can form hierarchical cactus-like secondary structure, typical for RNA molecules, is analyzed. In particular, the fraction $f$ of nucleotides involved in the formation of the secondary structure as a function of the number $c$ of different monomer species is investigated. It is shown, that with changing $c$ the secondary structures of random heteropolymers undergo a phase transition. Namely, for $c \le c_{\rm cr} = 4$ the fraction of "active" nucleotides $f$ tends to 1 as the chain length $n$ goes to infinity, signaling the formation of a virtually "perfect" gapless secondary structure. In turn, for $c>4$ the value of $f$ tends to some self-averaged value $\bar{f}(c)<1$, meaning that a non-perfect structure with gaps is formed. The value $c_{cr}=4$ is critical: $f$ approaches 1 logarithmically for $n\to\infty$. Such a critical behavior allows one to speculate about exclusivity of a four-letter alphabet used in natural RNAs with complex cactus-like secondary structures.

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