Crowders perturb the entropy of RNA energy landscapes to favor folding

Abstract

Biological macromolecules have evolved to fold and operate in the crowded environment of the cell. We have shown previously that molecular crowding stabilizes folded RNA structures. Here we report SAXS measurements on a 64 kDa bacterial group I ribozyme in the presence of mono- and divalent ions and PEG crowders of different molecular weight. These experiments show that crowders always stabilize the folded RNA, but this stabilization is weaker in NaCl solutions than MgCl2 solutions. Additionally, we find that RNAs with the same global structure, parametrized by Rg, have different scattering functions depending upon the ratio of electrostatic and entropic stabilization by ions and crowders, respectively. We quantify this difference using the scattering length per scattering volume and find that this ratio is larger for RNAs that fold in lower ionic strength solutions due to the higher crowder content. We conclude that lower RNA flexibility, or reduced configurational entropy, widens the free energy gap between the unfolded and folded RNA in crowded MgCl2 solutions.

Figure 1. Crowders favor smaller RNA structures

Radius of gyration (R_g) of the Azoarcus ribozyme as a function of crowder (PEG) concentration. a) Unfolded RNA (0.4 mg/ml) in 20 mM Tris-HCl, pH 7.5. b) Folded RNA (0.4 mg/ml) in Tris buffer plus 2 mM MgCl₂. The crossover concentrations, C^#, mark the transition from dilute (C < C^#) to semi-dilute (C > C^#) PEG solutions. The error bars represent 1 s.d. Data above and below the crossover concentrations were fit to a line (least-squares), omitting the point at 18% PEG3350 which deviates from this trend. The fitted lines are extrapolated beyond the crossover concentrations to emphasize the different behavior above and below C^#. These fits are intended to guide the eye. This range of PEG concentrations is too narrow to discriminate among theoretical models of crowded solutions.

Figure 2. PEG stabilizes folded RNA at low cation concentrations

MgCl₂ and NaCl titrations showing the decrease in R_g of the Azoarcus ribozyme at 37 °C at a range of PEG 3350 concentrations. (a) Folding in MgCl₂. Solid lines are fits to an adjusted Hill equation (Eq 1) assuming a two-state collapse and a linear decrease in R_g of the unfolded RNA with increasing MgCl₂ concentration. Parameters of the fits are given in Table S1. Ionic strength is given by 2.5 × [MgCl₂]. (b) Folding in NaCl. Solid lines are fits to Eq 2, which assumes R_g of the unfolded RNA is proportional to the logarithm of salt concentration. Parameters of the fits are given in Table S2. Ionic strengths are equal to the molar concentrations. Typical values for 1 s.d. are ± 1 Å for unfolded RNA and ± 0.15 Å for folded RNA.

Figure 3

Folding free energy of Azoarcus ribozyme is decreased by crowding. ΔΔG is the change in ΔG of folding due to the presence of PEG as macromolecular crowders, with (a) MgCl₂ and (b) NaCl as the stabilizing counterion. Values were calculated using Eq 3 and parameters from the fits of the Hill equation to experimental data. The data and fits for the MgCl₂ titrations are shown in Fig 2a, PEG3350; Fig S1a, PEG1000; Fig S1c, PEG8000. The data and fits for the NaCl titrations are shown in Fig 2b, PEG3350; Fig S1b, PEG1000.

Figure 4. Correlation lengths of folding intermediates

Scattering functions of the Azoarcus ribozyme in intermediate folding conditions. Each pair of curves represents samples with the same R_g. The area under the curve yields the correlation length relative to the sample volume, l_c/V. a) RNA folded in MgCl₂ and 1% or 10% PEG8000. The sample of higher ionic strength (0.4 mM MgCl₂ black line) has lower scattering intensity above the Guinier region, resulting in a lower integral of QI(Q) and thus lower l_c/V (Eq 4). b) Samples with no crowders folded in MgCl₂ (red) or NaCl (black). These data have identical integrals of QI(Q) and thus l_c/V, but systematic differences are observed above the Guinier region. The correlation length is marked in blue for three selected Q-values: r = 2π/Q.

Figure 5. RNA distance distribution functions for RNA in crowded and uncrowded solutions

These probability distribution functions are calculated using GNOM and show how the unfolded RNA at 0 mM MgCl₂ is compressed in the crowded solution. These plots represent a selected number of scattering functions in the 0% and 18% PEG1000 titrations.

Figure 6. Molecular crowding increases local structure

The correlation length per scattering volume, l_c/V, of the Azoarcus ribozyme plotted as a function of R_g for RNA particles in solutions containing PEG8000 as a macromolecular crowder and MgCl₂ as the counterion. l_c/V is calculated according to Eq 4 by integrating QI(Q) over the scattering function (Q = 0 to ∞ Å⁻¹). The values shown here are calculated with integration limits of Q = 0.015 to 0.3 Å⁻¹. Outside this region the scattering functions are identical, see Fig 4 for examples. Thus the absolute values plotted are shifted by an undefined correction term, but the relative order of the values is correct.

Figure 7. Molecular crowding changes the RNA folding landscape

a) Schematic illustration of a central RNA double helix (blue cylinder) connected by single stranded sections (black/grey lines) to helical “arms” (ochre – low salt, high crowder; red – high salt, low crowder). The two arms make the same contributions to the RNA's radius of gyration, so that R_g (low salt, left) = R_g (high salt, right). Due to the higher flexibility of the arms in high salt, the number of conformations, Ω, is greater, raising the entropy of the unfolded state. b) Energy level diagram illustrating the change in folding energy differences ΔG_F due to changes to the unfolded state's flexibility. On the right is the base line folding free energy ΔG_F0. The unfolded RNA on the left (red) has greater flexibility, and therefore higher configurational entropy than the unfolded state on the right (ochre). G_U − G_U = ΔG_U,Rg = −RTln(Ω_Rg/Ω_Rg), where Ω_Rg > Ω_Rg so ΔG is positive, correctly identifying the higher entropy (red) state as the lower energy state. Thus, ΔG_F1 is smaller than ΔG_F0.