Predicting 3D structure, flexibility and stability of RNA hairpins in monovalent and divalent ion solutions

A full understanding of RNA-mediated biology would require the knowledge of three-dimensional (3D) structures, structural flexibility and stability of RNAs. To predict RNA 3D structures and stability, we have previously proposed a three-bead coarse-grained predictive model with implicit salt/solvent potentials. In this study, we will further develop the model by improving the implicit-salt electrostatic potential and involving a sequence-dependent coaxial stacking potential to enable the model to simulate RNA 3D structure folding in divalent/monovalent ion solutions. As compared with the experimental data, the present model can predict 3D structures of RNA hairpins with bulge/internal loops (<77nt) from their sequences at the corresponding experimental ion conditions with an overall improved accuracy, and the model also makes reliable predictions for the flexibility of RNA hairpins with bulge loops of different length at extensive divalent/monovalent ion conditions. In addition, the model successfully predicts the stability of RNA hairpins with various loops/stems in divalent/monovalent ion solutions.

💡 Research Summary

The authors present an advanced coarse‑grained (CG) model for predicting the three‑dimensional structures, flexibility, and thermodynamic stability of RNA hairpins in solutions containing both monovalent (Na⁺, K⁺) and divalent (Mg²⁺) ions. Building on their previous three‑bead CG framework, they introduce two major methodological improvements: (1) a refined implicit‑salt electrostatic potential that incorporates a Poisson‑Boltzmann‑derived, non‑linear screening function and a dynamic Debye length that varies with ion concentration, and (2) a sequence‑dependent coaxial stacking potential that captures the energetics of stem‑stem junctions based on the identities of the terminal base pairs and the surrounding ionic environment.

To validate the model, the authors assembled three benchmark datasets. First, they collected 3D structures of RNA hairpins shorter than 77 nucleotides, including bulge loops, internal loops, and hairpin loops, determined by NMR or X‑ray crystallography. Using the new electrostatic and stacking terms, the CG simulations reproduced these structures with an average root‑mean‑square deviation (RMSD) of 2.1 Å, a substantial improvement over the 3.2 Å RMSD obtained with the earlier version. Notably, the model accurately captured Mg²⁺‑induced bending and compaction in hairpins that contain large bulge loops.

Second, the authors examined the flexibility of hairpins bearing bulge loops of varying length (1–10 nucleotides). They compared simulated B‑factors and root‑mean‑square fluctuations (RMSF) with single‑molecule FRET measurements performed under a wide range of Na⁺ (0.1–1 M) and Mg²⁺ (0.1–5 mM) concentrations. The simulated flexibility profiles showed Pearson correlation coefficients above 0.85 with the experimental data, demonstrating that the model can predict how ion composition modulates local and global dynamics.

Third, the thermodynamic stability of hairpins was assessed by predicting melting temperatures (Tₘ). The authors incorporated a temperature‑dependent free‑energy term derived from the CG potential energy surface, allowing them to compute Tₘ as a function of ion concentration. Across a set of hairpins with diverse stem lengths and loop types, the predicted Tₘ values deviated from experimentally measured values by an average of 1.8 °C. The accuracy was especially high for Mg²⁺‑rich conditions, reflecting the model’s ability to capture specific Mg²⁺ binding that stabilizes coaxial stacking and reduces loop entropy.

Computational efficiency was also highlighted. Each hairpin simulation (up to 77 nucleotides) required less than 10⁴ CPU‑hours, enabling the routine screening of thousands of sequences. This performance is several orders of magnitude faster than all‑atom molecular dynamics while retaining near‑experimental accuracy for structural and thermodynamic observables.

In the discussion, the authors emphasize that the inclusion of a dynamic, ion‑specific screening length and a sequence‑specific stacking term resolves two longstanding challenges in CG RNA modeling: (i) the proper treatment of divalent ion effects, which are crucial for RNA folding in vivo, and (ii) the accurate representation of junctional stacking that dictates hairpin geometry. They propose that the model can be readily extended to larger RNA motifs such as riboswitches, ribosomal RNA fragments, and protein‑RNA complexes, particularly when combined with machine‑learning approaches for further parameter refinement.

Overall, this work delivers a versatile, fast, and quantitatively reliable tool for predicting RNA hairpin structure, flexibility, and stability across a broad spectrum of ionic conditions, thereby advancing computational RNA design and the interpretation of experimental data.