RNA Denaturation: Excluded Volume, Pseudoknots, and Transition Scenarios

A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous transition. Otherwise a smooth crossover occurs from the swollen linear polymer behavior to highly ramified, almost compact conformations with secondary structures. In the latter scenario, which is appropriate when these structures are much more stable than pseudoknot links, probability distributions for the lengths of both loops and main branches obey scaling with nonclassical exponents.

Figure 1

RNA configurations and corresponding contact maps. Overlapped steps (contacts) are slightly split. In (a) a pseudoknot is present (crossing of bridge “1” with bridge “2”). In (b) a loop of length $\ell =5$ is marked by a thicker line, both on the chain and in the contact map. Here, “1” and “4” are main bridges.

Figure 2

$⟨R_e{⟩}^2/⟨R_g{⟩}^2$ as a function of $ϵ/T$ for three different values of $N$. Inset: detail of the crossings of four curves for model II. The circles enclose intersections between the curve pairs $(300,400)$, $(400,600)$, and $(600,800)$.

Figure 3

Log-log plots for $P_{\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{p}}(\ell )$ (thick lines, shifted down by 0.5 for clarity) and $P_{\mathrm{r}\mathrm{e}\mathrm{t}}(n)$ (thin lines), both for $N=800$ and for different $T$ values. The dot-dashed lines have slope $-1.1$.