Comparing atomistic simulation data with the NMR experiment: how much can NOEs actually tell us?

Simulated molecular dynamics trajectories of proteins and nucleic acids are often compared with nuclear magnetic resonance (NMR) data for the purposes of assessing the quality of the force field used or, equally important, trying to interpret ambiguous experimental data. In particular, nuclear Overhauser enhancement (NOE) intensities or atom-atom distances derived from them are frequently calculated from the simulated ensembles because the distance restraints derived from NOEs are the key ingredient in NMR-based protein structure determination. In this study, we ask how diverse and nonnative-like an ensemble of structures can be and still match the experimental NOE distance upper bounds well. We present two examples in which simulated ensembles of highly nonnative polypeptide structures (an unfolded state ensemble of the villin headpiece and a high-temperature denatured ensemble of lysozyme) are shown to match fairly well the experimental NOE distance upper bounds from which the corresponding native structures were derived. For example, the unfolded ensemble of villin headpiece, which is on average 0.90 +/- 0.13 nm root-mean-square deviation away from the native NMR structure, deviates from the experimental restraints by only 0.027 nm on average. However, this artificially good agreement is largely a consequence of 1) the highly nonlinear effects of r(-6) (or r(-3)) averaging and 2) focusing only on the experimentally observed set of NOE bounds. Namely, in addition to the experimentally observed NOEs, both simulated ensembles (especially the villin ensemble) also predict a large number of NOEs, which are not seen in the experiment. If these are taken into account, the agreement between simulation and experiment gets markedly worse, as it should, given the nonnative nature of the underlying simulated ensembles. In light of the examples given, we conclude that comparing experimental NOE distance restraints with large simulated ensembles provides just by itself only limited information about the quality of simulation.