McSally, J. P. | bioRxiv Science

bioRxiv2026

Longer Is Not Always Better: Effects of Equilibration Length on Umbrella Sampling Estimations for RNA Hairpin Folding Stabilities

Umbrella sampling is widely used to estimate biomolecular free energy landscapes and relative folding stabilities. Although equilibration is a critical component of umbrella sampling workflows, the impact of equilibration length on thermodynamic predictions remains poorly understood. Here, we investigate the effect of equilibration length on relative folding free energy predictions for four RNA hairpins with loop sequences GUGAAA, CUGGGA, GUAAUA, and UUAAUU with helical stems of three base pairs. Umbrella sampling simulations were performed using an end-to-end distance reaction coordinate spanning 15-45 [A], where equilibrium simulations (windows) were spaced at roughly 1 [A] intervals. In these calculations, the hairpin stem-loops were allowed to equilibrate in an end-to-end distance window and then the coordinates were transferred to the next larger end-to-end distance window to equilibrate. Two equilibration lengths, 2 ns and 100 ns per window, were followed by 600 ns of production sampling. Potential of mean force (PMF) profiles were reconstructed using the Weighted Histogram Analysis Method (WHAM) and used to calculate pairwise free energy differences with thermodynamic cycles. Increasing the equilibration length produced substantial, sequence-dependent changes in the reconstructed free energy landscapes. The 100 ns protocol generated markedly flatter PMFs for GUGAAA and UUAAUU and pronounced reshaping of the free energy landscape for GUAAUA. These changes were accompanied by reductions in hydrogen-bonding and stacking interactions, particularly within the intermediate regions of the reaction coordinate. The resulting thermodynamic predictions, as free energy change differences, were therefore highly sensitive to equilibration length. Across nearly all hairpin pairs, the 100 ns equilibration yielded substantially larger magnitude free energy change difference values than the corresponding 2 ns equilibration, with differences that greatly exceeded replica-to-replica variability. Comparison with optical melting measurements and nearest-neighbor thermodynamic predictions revealed that 2 ns equilibration times more closely agreed with experimental values than those obtained using 100 ns equilibration. These findings demonstrate that longer equilibration can systematically alter the structural ensembles sampled during umbrella sampling and amplify predicted stability differences without improving agreement with experiment. More widely, our results highlighted equilibration length as a critical and nontrivial parameter in RNA free energy calculations and demonstrate that increased equilibration does not necessarily lead to more accurate thermodynamic predictions.

biophysics↗

bioRxiv2025

NMR and molecular dynamics demonstrate the RNA internal loop GAGU is dynamic and adjacent base pairs determine conformational preference

The conformational variability of RNA duplexes with the internal loop 5GAGU/3UGAG was investigated by a combination of nuclear magnetic resonance spectroscopy (NMR) and all-atom molecular dynamics (MD) simulations. A previous study showed that the CG-flanked internal loop in the sequence 5GACGAGUGUCA/3ACUGUGAGCAG existed in a major conformation (conformation I) characterized by Uridines U7 and U7* bulging into solution, A5 and A5* stacking, and with G4-G6* and G6-G4* base pairs closing the loop on either end. It was also determined that a minor conformation existed with a set of closing G-U pairs with a bifurcated hydrogen bond and A-G non-canonical pairs with a single hydrogen bond (conformation II). A maximum hydrogen bonding structure with wobble G-U pairs and A-G pairs with two hydrogen bonds (conformation III) was not observed by NMR or predicted by molecular dynamics. In this work, alternative flanking base pairs A-U, U-A and G-C were studied by substituting the C-G base pair adjacent to the GAGU internal loop. NMR spectra demonstrated changes in conformational preference depending on the identity of the flanking pair. Clustering analyses of structures from MD simulations of C-G- and U-A-flanked duplexes showed transitions between minor conformations II and III with a greater fraction of the structures in conformation II, in spite of the simulations starting in conformation III. In addition, U-A-flanked simulations contained a substantial amount (25%) of structures in an intermediate state between conformations II and III. A-U- and G-C-flanked structures were all in a single cluster whose centroid structure was in conformation II. MD simulations showed a dominance of structure II over structure III, in agreement with NMR data for C-G closure, but in contrast with the NMR data for other closures. Simulations starting in conformation I did not transition to either of II and III, with all structures being in a single cluster for all flanking base pairs except for G-C-closure where 22% of the structures were in a state defined by a C3endo sugar pucker for G4 and G4*. Bases G4 and G4* were also in syn orientation around the glycosidic bond for all flanking pairs while G6 and G6* transitioned between syn and anti orientations for C-G- and A-U-flanked simulations, consistent with NMR observations.

biophysics↗