Freezing transition of the random bond RNA model: statistical properties of the pairing weights

Details Freezing transition of the random bond RNA model: statistical properties of the pairing weights Freezing transition of the random bond RNA model: statistical properties of the pairing weights

2006-11-23

arxiv.org/abs/cond-mat/0611611v1

Phys. Rev. E 75, 031103 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages, 32 figures

Scientific paper

10.1103/PhysRevE.75.031103

To characterize the pairing-specificity of RNA secondary structures as a function of temperature, we analyse the statistics of the pairing weights as follows : for each base $(i)$ of the sequence of length N, we consider the $(N-1)$ pairing weights $w_i(j)$ with the other bases $(j \neq i)$ of the sequence. We numerically compute the probability distributions $P_1(w)$ of the maximal weight, the probability distribution $\Pi(Y_2)$ of the parameter $Y_2(i)= \sum_j w_i^2(j)$, as well as the average values of the moments $Y_k(i)= \sum_j w_i^k(j)$. We find that there are two important temperatures $T_cT_{gap}$, the distribution $P_1(w)$ vanishes at some value $w_0(T)<1$, and accordingly the moments $\bar{Y_k(i)}$ decay exponentially in $k$. For $T

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