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

Abstract

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.