Reducing the measurement time of exact NOEs by non-uniform sampling.

We have previously reported on the measurement of exact NOEs (eNOEs), which yield a wealth of additional information in comparison to conventional NOEs. We have used these eNOEs in a variety of applications, including calculating high-resolution structures of proteins and RNA molecules. The collection of eNOEs is challenging, however, due to the need to measure a NOESY buildup series consisting of typically four NOESY spectra with varying mixing times in a single measurement session. While the 2D version can be completed in a few days, a fully sampled 3D-NOESY buildup series can take 10 days or more to acquire. This can be both expensive as well as problematic in the case of samples that are not stable over such a long period of time. One potential method to significantly decrease the required measurement time of eNOEs is to use non-uniform sampling (NUS) to decrease the number of points measured in the indirect dimensions. The effect of NUS on the extremely tight distance restraints extracted from eNOEs may be very pronounced. Therefore, we investigated the fidelity of eNOEs measured from three test cases at decreasing NUS densities: the 18.4 kDa protein human Pin1, the 4.1 kDa WW domain of Pin1 (both in 3D), and a 4.6 kDa 14mer RNA UUCG tetraloop (2D). Our results show that NUS imparted negligible error on the eNOE distances derived from good quality data down to 10% sampling for all three cases, but there is a noticeable decrease in the eNOE yield that is dependent upon the underlying sparsity, and thus complexity, of the sample. For Pin1, this transition occurred at roughly 40% while for the WW domain and the UUCG tetraloop it occurred at lower NUS densities of 20% and 10%, respectively. We rationalized these numbers through reconstruction simulations under various conditions. The extent of this loss depends upon the number of scans taken as well as the number of peaks to be reconstructed. Based on these findings, we have created guidelines for choosing an optimal NUS density depending on the number of peaks needed to be reconstructed in the densest region of a 2D or 3D NOESY spectrum.