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Accurate determination of rates from non-uniformly sampled relaxation data

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Abstract

The application of non-uniform sampling (NUS) to relaxation experiments traditionally used to characterize the fast internal motion of proteins is quantitatively examined. Experimentally acquired Poisson-gap sampled data reconstructed with iterative soft thresholding are compared to regular sequentially sampled (RSS) data. Using ubiquitin as a model system, it is shown that 25 % sampling is sufficient for the determination of quantitatively accurate relaxation rates. When the sampling density is fixed at 25 %, the accuracy of rates is shown to increase sharply with the total number of sampled points until eventually converging near the inherent reproducibility of the experiment. Perhaps contrary to some expectations, it is found that accurate peak height reconstruction is not required for the determination of accurate rates. Instead, inaccuracies in rates arise from inconsistencies in reconstruction across the relaxation series that primarily manifest as a non-linearity in the recovered peak height. This indicates that the performance of an NUS relaxation experiment cannot be predicted from comparison of peak heights using a single RSS reference spectrum. The generality of these findings was assessed using three alternative reconstruction algorithms, eight different relaxation measurements, and three additional proteins that exhibit varying degrees of spectral complexity. From these data, it is revealed that non-linearity in peak height reconstruction across the relaxation series is strongly correlated with errors in NUS-derived relaxation rates. Importantly, it is shown that this correlation can be exploited to reliably predict the performance of an NUS-relaxation experiment by using three or more RSS reference planes from the relaxation series. The RSS reference time points can also serve to provide estimates of the uncertainty of the sampled intensity, which for a typical relaxation times series incurs no penalty in total acquisition time.

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Acknowledgments

This work was supported by NIH GM102447 awarded to A.J.W. M.A.S. is an NIH predoctoral trainee (GM008275). We thank Prof. Gerhard Wagner and Dr. Scott Robson for providing the hmsIST software and early assistance with data processing. We also thank Dr. Sven Hyberts and Dr. Haribabu Arthanari for helpful discussion. We are grateful to Dr. Kathy Valentine for technical assistance and extensive discussion. We gratefully acknowledge Li Liang for providing the AK sample, Dr. Nathaniel Nucci for providing the ubiquitin sample in 30 % glycerol, and Bryan Marques for providing the MBP sample.

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  1. Johnson Research Foundation and Department of Biochemistry and Biophysics, University of Pennsylvania Perelman School of Medicine, 905 Stellar-Chance Laboratories, 422 Curie Blvd, Philadelphia, PA, 19104-6059, USA

    Matthew A. Stetz & A. Joshua Wand

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Correspondence to A. Joshua Wand.

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Stetz, M.A., Wand, A.J. Accurate determination of rates from non-uniformly sampled relaxation data. J Biomol NMR 65, 157–170 (2016). https://doi.org/10.1007/s10858-016-0046-9

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