Molecular crowding stabilizes folded RNA structure by the excluded volume effect

Abstract

Crowder molecules in solution alter the equilibrium between folded and unfolded states of biological macromolecules. It is therefore critical to account for the influence of these other molecules when describing the folding of RNA inside the cell. Small angle X-ray scattering experiments are reported on a 64 kDa bacterial group I ribozyme in the presence of polyethylene-glycol 1000 (PEG-1000), a molecular crowder with an average molecular weight of 1000 Da. In agreement with expected excluded volume effects, PEG favors more compact RNA structures. First, the transition from the unfolded to the folded (more compact) state occurs at lower MgCl(2) concentrations in PEG. Second, the radius of gyration of the unfolded RNA decreases from 76 to 64 A as the PEG concentration increases from 0 to 20% wt/vol. Changes to water and ion activities were measured experimentally, and theoretical models were used to evaluate the excluded volume. We conclude that the dominant influence of the PEG crowder on the folding process is the excluded volume effect.

Figure 1

Molecular crowding and RNA folding. The unfolded RNA (left side) is modeled as a random coil without internal excluded volume (a Brownian walk). The dashed line around the unfolded RNA represents the effective hard particle used in eq 1, defined as a convex hull surrounding the coil that excludes volume available to all other particles in the solution [36]. The folded RNA (black circle; right side) is modeled as a hard sphere. The dark blue circles represent crowder molecules; the lighter blue ‘halos’ represent the (RNA size-dependent) volume that is excluded to the center of gravity of the RNA molecules due to the crowders. The uppermost crowder on the unfolded side is as close to the RNA as possible, hence the center of the RNA is at the light blue halo’s edge. ΔG⁰ is the Gibbs free energy change for RNA folding at the standard state, defined as ΔG⁰ = G^F,0 − G^U,0 = −RTlnK⁰; ΔΔG^U = RTlnγ_U and ΔΔG^F = RTlnγ_F are the changes in free energies of the unfolded and folded RNA states due to the introduction of crowders, γ’s defined according to eq 1; ΔG^0,C = (G^F,0+ RTlnγ_F) − (G^U,0+ RTlnγ_U).

Figure 2

SAXS measurements of RNA folding. I(Q) from 0.4 mg/mL Azoarcus ribozyme in a) no PEG and b) 18% PEG, plus 20 mM Tris-HCl and 0–3.13 mM MgCl₂. The significant increase in I(Q) occurs between 0.5 and 0.81 mM MgCl₂ (0% PEG), and 0.14 and 0.51 mM MgCl₂ (18% PEG), as the RNA becomes more compact. Systematic variation at the extreme low and high Q values in (b) are due to slight beam drift during this titration, resulting in inaccurate background subtraction. This only affects the extreme Q-values, however, which were truncated in the analysis. We confirmed, using experiments where the beam had not drifted, that truncation of these data did not significantly affect the Fourier transform and the derived R_g values.

Figure 3

MgCl₂ titration curves of R_g values at a range of PEG concentrations. Solid lines are fits to an adjusted Hill equation (eq 2); this equation assumes a two-state model of RNA 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. These data come from individual titration measurements; for a demonstration of their reproducibility, see the supporting information.

Figure 4

Midpoints of Azoarcus ribozyme transitions. Red symbols: experimental transition midpoints (c_m) calculated using the modified Hill equation (eq 2). Error bars represent the difference in MgCl₂ concentration between the data points just above and below the midpoint of the fit. Blue curve: theoretical change in transition midpoint due to excluded volume effects, calculated from changes to the chemical potential assuming that both the unfolded and folded RNA are hard spheres. Green curve: same as blue curve but with unfolded particles modeled as a chain with Brownian walk statistics.

Figure 5

Water activity in PEG solutions. Measured water activity, a_W, from vapor pressure osmometry as a function of MgCl₂ molality in solutions containing 10 and 18% PEG. The arrows are equal length and are intended to illustrate the fact that PEG and MgCl₂ molality independently affect the water activity.

Figure 6

Change in water activity linked to RNA folding. Log of the transition midpoint MgCl₂ concentration (c_m) multiplied by n from eq 1, versus the log of water activity a_w obtained from vapor pressure osmometry measurements. The slope of the line represents the total number of waters Δn_w that would have to be released during folding in order to account for the measured perturbation to the folding free energy.