Persistence Length Changes Dramatically as RNA Folds

We determine the persistence length $l_p$ for a bacterial group $I$ ribozyme as a function of concentration of monovalent and divalent cations by fitting the distance distribution functions $P(r)$ obtained from small angle x-ray scattering intensity data to the asymptotic form of the calculated $P_{\mathrm{WLC}}(r)$ for a wormlike chain. The $l_p$ values change dramatically over a narrow range of ${\mathrm{Mg}}^{2+}$ concentration from $\sim 21\AA$ in the unfolded state ($U$) to $\sim 10\AA$ in the compact ($I_C$) and native states. Variations in $l_p$ with increasing ${\mathrm{Na}}^{+}$ concentration are more gradual. In accord with the predictions of polyelectrolyte theory we find $l_p\propto 1/{\kappa }^2$ where $\kappa$ is the inverse Debye-screening length.

Figure 1

(a) Scattering intensity $I(Q)$ (taken from [12b]) as a function of $Q$ for 195 nucleotide Azoarcus ribozyme at different values of ${\mathrm{Mg}}^{2+}$ concentration in 20 mM Tris buffer, $\mathrm{pH}=7.5$ at 32 °C. The values of ${\mathrm{Mg}}^{2+}$ concentrations are given in the inset. (b) The dependance of $R_g^2$ on ${\mathrm{Mg}}^{2+}$ (squares) and ${\mathrm{Na}}^{+}$ (triangles) concentration. Solid line is the fit using Hill equation in the form $A\{1-[{\mathrm{Mg}}^{2+}{]}^n/(C_m^n+[{\mathrm{Mg}}^{2+}{]}^n)\}+y_0$, where $A$, $n$, and $y_0$ are adjustable parameters. We find $n$ is 3.33 and 1.20 for ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Na}}^{+}$, respectively.

Figure 2

Distance distribution functions. (a) $P(r)$ functions at various ${\mathrm{Mg}}^{2+}$ concentrations at 32 °C are obtained by inverting $I(q)$ by a Fourier transform with $Q_{\min }=0.07\AA$ and $Q_{\max }=0.01\AA$. The solid lines are fits of $P(r)$ to Eq. (1). (b) Same as (a) except the counterion is ${\mathrm{Na}}^{+}$. The concentrations of counterions are given in the insets.

Figure 3

(a) Calculation of $P(r)$ using the coordinates of the heavy atoms from the chain $B$ of the crystal structure (1U6B), the Westhof model [13], and SAXS data. The symbols are given in the inset. The solid lines show the fits using $P_{\mathrm{WLC}}(r)$ in the range 30 Å to 70 Å. In this range the root mean square deviation of the $P(r)$ for the 1U6B from $P_{\mathrm{WLC}}(r)$ is $0.13{\AA }^{-1}$ and for the Westhof model [13] it is $0.10{\AA }^{-1}$. The correlation coefficient of the fits of $P(r)$ to $P_{\mathrm{WLC}}(r)$ is 0.98. (b) Dependence of $l_p$ on $1/{\kappa }^2$ in ${\mathrm{Mg}}^{2+}$ (solid circles) and in ${\mathrm{Na}}^{+}$ (solid squares). Lines represent fits to the data. Note that the $1/{\kappa }^2$ scale for ${\mathrm{Mg}}^{2+}$ is given on top.

Figure 4

$P(r)$ for RNase $P$ from Ref. 9. The distance distribution function was calculated by inverting $I(q)$ with a different numerical Fourier Transform method [27]. The $\mathbf{U}$, $\mathbf{I}$, and $\mathbf{N}$ states are for ${\mathrm{Mg}}^{2+}$ concentrations 0, 0.1, and 10 mM, respectively. The lines are fits using Eq. (1).