Sven G. Hyberts, Scott A. Robson, Gerhard Wagner*

SUPPLEMENT TOInterpolating and extrapolating with hmsIST -seeking a tmax for optimal sensitivity, resolution and frequency accuracy.

Sven G. Hyberts, Scott A. Robson, Gerhard Wagner*

Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA 02115

*
phone 617-432-3213

fax 617-432-4383

Keywords: non-uniform sampling; NUS; protein backbone chemical shift assignments; maximum entropy reconstruction; iterative soft threshold reconstruction; reduced time multidimensional NMR spectroscopy.

Figure S1

Figure S1: Kurtosis (the fourth statistical measure) and SNrmsR vs. SNmaxR ratio calculated form the data in figure 2. Both show a nearly straight line over the range, indicating further and further deviation from a Gaussian white distribution when the number of non-obtained data points increases.

Figure S2

Figure S2. Comparison of SNR metrics over two time ranges.To test whether the findingsin Figure 2are not dependent on the range of time, the findings are evaluated in the range t = 0.125*T2 to 1.0*T2 (left) and t = 0.25*T2 to 2.0*T2 (right). The SNrmsR values in large still follow those of the theoretical iSNR. A maximum of around 0.5T2 is still found for the SNmaxR values. Added to this figures are the values of SNtopR calculated as the average signal height over the standard deviation of the signal height. Note the factor of 3 difference between the left and right vertical axes.

Figure S3

Figure S3: Comparison of graphs of reconstructed NUS data without explicit apodization (left) and withexplicit apodization applied. As the test case is reconstruction to t*max = tmax and then applied zero filling, the apodization length varies. It is observed that the difference between the measured SNR values without apodization vs. with apodization is more pronounced at low values of t/T2. By applying the test to reconstruction of uniformly weighted random NUS data, the effective difference of sampling strategy is suppressed.

Figure S4

Figure S4: The figure verifies that the distinction between the three measures of noise, SNrmsR, SNmaxR and SNtopR, disappears when the NUS simulated data are just processed using DFT without reconstruction. There is no sensitivity maximum and any extrapolation leads to decreased SNR in this case. Both the kurtosis and the SNrmsR /SNmaxR values remains closely at 3.0, indicating that Fourier transformation of intermittent Gaussian noise is of Gaussian nature. NUS was scheduled exponentially weighted random.

Figure S5

Figure S5: Comparison of SNR metrics for data obtained with a very steep exponentially weighted random schedule. At first glance, the figure contradicts our finding with a maximum sensitivity (SNmaxR) at tmax at approximately ½*T2. However, by closer analysis, in this case no sampling schedule had the actual tmax later than 0.56*T2. The range of initial weights are distributed from 1 to e-30, or 1 to 1*10-13, indicating that the sampling points are drastically skewed towards earlier sampling times.

Figure S6

Figure S6:Representative cross peak shape obtained for different values of t1max. This provides a visual example verification of the variation of the effects due to sampling strategy of a HSQC spectrum of GB1: A) Sampling contiguously 64 points to a tmax of 35 msec (0.25*T2) and then reconstruction to 512 points. B) Sampling 64 of the first 128 points to tmax of 70 msec (0.5*T2) by NUS and then reconstruction of all missing data points to 512 points. C) Sampling 64 of the first 256 points to tmax of 140 msec (1*T2) by NUS and processed as in B. D) Sampling 64 of the total 512 points to tmax of 280 msec (2*T2) by NUS and processed as in B. The line broadening and intensity attenuation are visible in A), C) and especially D). The position variation is hard to see in this particular visualization. Still it seems as the most compact signal is achieved by sampling to about ½*T2 (B).

Figure S7

Figure S7: Comparison of reconstructed line widths from alternativesignal simulations, using Lorentzian and Gaussian line shapes as well as placing signals on and off the Nyquist grid. The simulations here are done on a 512 complex data point FID with varying 25% acquisition to conform to the situation at the HSQC experimental analysis. No essential variation is found between the three line assumptions, and the figure conforms with figure 6c in the manuscript with showing no variation in the result depending on acquisition parameters.

Figure S8

Figure S8: Frequency variation between inter- and intra-residue signals in the nitrogen dimension of the HNCA of Fig. 1. The absolute frequency variations measured between inter- and intra-residue signals in GB1.“Short sampling”(blue bars) is measured in the spectrum indicated in the middle panel of figure 1a, i.e. uniformly sampled to 1/10th of T2 and extended by hmsIST to ½ of T2. “Long sampling” (red bars) is measured on the time equivalent 20% NUS spectrum and reconstructed by hmsIST represented to the left in figure 1b.The frequency variations are purely random and in a few cases with small variations the valuesareworse for “long sampling” than for “short sampling”. Large variations are only seen with short sampling. Expectation wise, the accuracy of the signal position in the NUSspectrumis 4 to 5 times better in than in the spectrum that was uniformly sampled and then extended.

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