Free energy profile of RNA hairpins: a molecular dynamics simulation study

Abstract

RNA hairpin loops are one of the most abundant secondary structure elements and participate in RNA folding and protein-RNA recognition. To characterize the free energy surface of RNA hairpin folding at an atomic level, we calculated the potential of mean force (PMF) as a function of the end-to-end distance, by using umbrella sampling simulations in explicit solvent. Two RNA hairpins containing tetraloop cUUCGg and cUUUUg are studied with AMBER ff99 and CHARMM27 force fields. Experimentally, the UUCG hairpin is known to be significantly more stable than UUUU. In this study, the calculations using AMBER force field give a qualitatively correct description for the folding of two RNA hairpins, as the calculated PMF confirms the global stability of the folded structures and the resulting relative folding free energy is in quantitative agreement with the experimental result. The hairpin stabilities are also correctly differentiated by the more rapid molecular mechanics-Poisson Boltzmann-surface area approach, but the relative free energy estimated from this method is overestimated. The free energy profile shows that the native state basin and the unfolded state plateau are separated by a wide shoulder region, which samples a variety of native-like structures with frayed terminal basepair. The calculated PMF lacks major barriers that are expected near the transition regions, and this is attributed to the limitation of the 1-D reaction coordinate. The PMF results are compared with other studies of small RNA hairpins using kinetics method and coarse grained models. The two RNA hairpins described by CHARMM27 are significantly more deformable than those represented by AMBER. Compared with the AMBER results, the CHARMM27 calculated DeltaG(fold) for the UUUU tetraloop is in better agreement with the experimental results. However, the CHARMM27 calculation does not confirm the global stability of the experimental UUCG structure; instead, the extended conformations are predicted to be thermodynamically stable in solution. This finding is further supported by separate unrestrained CHARMM27 simulations, in which the UUCG hairpin unfolds spontaneously within 10 ns. The instability of the UUCG hairpin originates from the loop region, and propagates to the stem. The results of this study provide a molecular picture of RNA hairpin unfolding and reveal problems in the force field descriptions for the conformational energy of certain RNA hairpin.

Figure 1

Native structures of (a) 5′-GCC(UUCG)GGC-3′ and (b) 5′-CGC(UUUU)GCG-3′ hairpin loops.

Figure 2

Potential of mean force (PMF) as a function of the end-to-end distance for UUCG, obtained with different initial velocities using AMBER ff99. Solid: set 1; dotted: set 2; dashed: set 3. The structures shown along with the PMF are snapshots of structures sampled by the umbrella sampling simulation. Note that because the hairpin becomes more disordered at large end-to-end distance, a significantly larger ensemble was sampled than is suggested by these snapshots at large r. The sampled conformations are better represented by these snapshots at short end-to-end extensions.

Figure 3

PMF of UUUU obtained with different initial velocities using AMBER ff99. Solid: set 1; dotted: set 2; dashed: set 3. The snapshots of representative structures sampled by the umbrella sampling simulation are also displayed.

Figure 4

PMF of UUCG calculated using CHARMM27 and the snapshots of representative structures sampled by the umbrella sampling simulations.

Figure 5

PMF of UUUU calculated using CHARMM27 and the snapshots of representative structures sampled by the umbrella sampling simulation.

Figure 6

Time series of the heavy atom RMS difference relative to the native structure of UUCG. The three unrestrained MD simulations were started from the experimental structure and lasted for 7 ns and 10 ns. Solid lines: two CHARMM27 trajectories (7 ns and 10 ns); dotted line: an AMBER ff99 trajectory (10 ns).

Figure 7

CHARMM27 simulation time series of RMS difference relative to the crystal structure of UUCG. (a) 7 ns trajectory; (b) 10 ns trajectory. Solid line: loop region; dotted line: stem.