Predicting ion binding properties for RNA tertiary structures

Abstract

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg(2+) ions in RNA folding. In this study, we develop an all-atom model to predict the ion electrostatics in RNA folding. The model can treat ion correlation effects explicitly by considering an ensemble of discrete ion distributions. In contrast to the previous coarse-grained models that can treat ion correlation, this new model is based on all-atom nucleic acid structures. Thus, unlike the previous coarse-grained models, this new model allows us to treat complex tertiary structures such as HIV-1 DIS type RNA kissing complexes. Theory-experiment comparisons for a variety of tertiary structures indicate that the model gives improved predictions over the Poisson-Boltzmann theory, which underestimates the Mg(2+) binding in the competition with Na(+). Further systematic theory-experiment comparisons for a series of tertiary structures lead to a set of analytical formulas for Mg(2+)/Na(+) ion-binding to various RNA and DNA structures over a wide range of Mg(2+) and Na(+) concentrations.

Figure 1

(A–F) The tightly bound regions in 0.1 M Mg²⁺ solution: (A) A 24-bp DNA duplex (structure produced from X3DNA (51)). (B) A 24-bp RNA duplex (structure produced from X3DNA (51)). (C) HIV-1 DIS kissing complex (PDB code: 2B8S) (55). (D) Beet Western yellow virus (BWYV) pseudoknot fragment (PDB code: 437D) (52). (E) A 58-nt ribosomal RNA (rRNA) fragment (PDB code: 1HC8) (66). (F) Yeast tRNA^Phe (PDB code: 1TRA) (54). The figure for the three-dimensional structures is generated by the software PyMol (http://pymol.sourceforge.net/). (Green dots) Boundary of the tightly bound regions defined in the TBI model (37–40). (G) Illustration of the HIV-1 DIS type RNA loop-loop kissing complexes (KC-1 and KC-2) used in the calculations. The thermodynamic parameters for KC-1 and KC-2 at 1 M NaCl are taken from the experimental measurements (49,50). (Shaded lines) Basepairs at the kissing interface.

Figure 2

The Mg²⁺ and Na⁺ binding fractions per nucleotide for oligomeric DNA and RNA helices as functions of [Mg²⁺] or [Na⁺]. (Symbols) Experimental data. (Solid lines) Atomistic TBI predictions. (Dotted lines) PB predictions. (Dashed lines) PB predictions with a smaller Mg²⁺ radius (≃3.5 Å). (Shaded lines) TBI predictions on a coarse-grained DNA duplex. (A) A 24-bp B-DNA duplex in 20 mM Na⁺ (28,63). (B) A 24-bp B-DNA duplex in 5 mM Mg²⁺ (28,63). (C and D) A 40-bp RNA duplex in 10 mM [Na⁺] and 100 mM [Na⁺], respectively. The experimental data are for poly(A.U) (64). (E and F) A 40-bp DNA duplex in 1 mM [Na⁺] and 5 mM [Na⁺], respectively. The experimental data are for calf thymus DNA (65).

Figure 3

The Mg²⁺ and Na⁺ (or K⁺) binding fractions per nucleotide for various RNA tertiary structures. (Symbols) Experimental data. (Solid lines) Atomic TBI predictions. (Dotted lines) PB predictions. (Dashed lines) PB predictions with a smaller Mg²⁺ radius (≃3.5 Å). (A and B) BWYV pseudoknot fragment at different Na⁺ concentrations: 54 mM Na⁺ and 79 mM Na⁺, respectively. The experimental data are adopted from Soto et al. (12). (C and D) A 58-nt rRNA fragment at different K⁺ concentrations: 20 mM K⁺ and 150 mM K⁺, respectively. The experimental data are from Grilley et al. (66). (E and F) Yeast tRNA^Phe at different Na⁺ concentrations: 10 mM Na⁺ and 32 mM Na⁺, respectively. The experimental data was taken from Rialdi et al. (67) and Römer and Hach (68) for panels A for panels B, respectively.

Figure 4

The free energies ΔG₃₇ (A and B) and melting temperature T_m (C and D) as functions of the Na⁺ concentration (A and C) and the Mg²⁺ concentration (B and D). (C) The experimental data for KC-1 and KC-2 are from Weixlbaumer et al. (49) and Lorenz et al. (50), respectively. (D) The experimental data are from Weixlbaumer et al. (49). (Solid lines) TBI predictions. (Dotted lines) PB predictions.