Jeffrey C. Hoch

Resolution and sensitivity of high field nuclear magnetic resonance spectroscopy.

The arrival of very high field magnets and cryogenic circuitries, and the development of relaxation-optimized pulse sequences have added powerful tools for increasing sensitivity and resolution in NMR studies of biomacromolecules. The potential of these advances is not fully realized in practice, however, since current experimental protocols do not permit sufficient data sampling for optimal resolution in the indirect dimensions. Here we analyze quantitatively how increasing resolution in indirect dimensions affects the S/N ratio and compare this with currently used sampling routines. Optimal resolution would require sampling up to ∼3R2−1, and the S/N reaches a maximum at ∼1.2R2−1. Currently used data acquisition protocols rarely sample beyond 0.4R2−1, and extending evolution times would result in prohibitively long experiments. We show that a general solution to this problem is to use non-uniform sampling, where only a small subset of data points in the indirect sampling space are measured, and possibly different numbers of transients are collected for different evolution times. Coupled with modern methods of spectrum analysis, this strategy delivers substantially improved resolution and/or reduced measuring times compared to uniform sampling, without compromising sensitivity. Higher resolution in the indirect dimensions will facilitate the use of automated assignment programs.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR.

Application of nonlinear sampling schemes to COSY-type spectra

SummaryNonlinear sampling along the t1 dimension is applied to COSY-type spectra. The sine dependence of the time domain signals for the cross peaks is matched by a nonlinear sampling scheme that samples most densely around the maximum of the sine function. Data are processed by maximum entropy reconstruction, using a modified implementation of the ‘Cambridge’ algorithm of Skilling and Bryan. The procedure is demonstrated for P.E.COSY spectra recorded on a cyclic hexapeptide and on a 126-residue domain of the protein villin. The number of t1 values in the nonlinearly sampled experiments was reduced by a factor of four compared to linear sampling. The sensitivity and resolution of the resulting spectra are comparable to those achieved by conventional methods. The method described can thus significantly reduce the measuring time for COSY-type spectra.

Improved resolution in triple-resonance spectra by nonlinear sampling in the constant-time domain

SummaryNonlinear sampling along the constant-time dimension is applied to the constant-time HNCO spectrum of the dimerization domain of Ga14. Nonlinear sampling was used for the nitrogen dimension, while the carbon and proton dimensions were sampled linearly. A conventional ct-HNCO spectrum is compared with a nonlinearly sampled spectrum, where the gain in experiment time obtained from nonlinear sampling is used to increase the resolution in the carbonyl dimension. Nonlinearly sampled data are processed by maximum entropy reconstruction. It is shown that the nonlinearly sampled spectrum has a higher resolution, although it was recorded in less time. The constant intensity of the signal in the constant-time dimension allows for a variety of sampling schedules. A schedule of randomly distributed sampling points yields the best results. This general method can be used to significantly increase the quality of heteronuclear constant-time spectra.

Maximum entropy signal processing of two-dimensional NMR data

The maximum entropy method (MEM) has been shown to yield one-dimensional NMR spectra with sensitivity and resolution superior to those obtained using the discrete Fourier transform (DFT) (S. Sibisi, J. Skilling, R. G. Brereton, E. D. Laue, and J. Staunton, Nature (London) 311, 446 (1984)). A property of MEM which has not been exploited in previous applications of the method to NMR is its ability to produce spectral estimates from short data records, free of the truncation artifacts which typify DFT spectra of zero-extended data records. This property holds significance for two-dimensional NMR spectroscopy, allowing reduction of the time necessary to acquire a two-dimensional data set. In this paper the application of MEM to two-dimensional NMR data is described. It is concluded that use of MEM in two-dimensional NMR studies can lead to sensitivity improvements, reduction of instrumental artifacts, and shortened data acquisition times. It is pointed out, however, that the nonlinear nature of MEM may render it unsuitable for certain applications in NMR spectroscopy.

De novo Backbone and Sequence Design of an Idealized α/β-barrel Protein: Evidence of Stable Tertiary Structure

We have designed, synthesized, and characterized a 216 amino acid residue sequence encoding a putative idealized α/β-barrel protein. The design was elaborated in two steps. First, the idealized backbone was defined with geometric parameters representing our target fold: a central eight parallel-stranded β-sheet surrounded by eight parallel α-helices, connected together with short structural turns on both sides of the barrel. An automated sequence selection algorithm, based on the dead-end elimination theorem, was used to find the optimal amino acid sequence fitting the target structure. A synthetic gene coding for the designed sequence was constructed and the recombinant artificial protein was expressed in bacteria, purified and characterized. Far-UV CD spectra with prominent bands at 222 nm and 208 nm revealed the presence of α-helix secondary structures (50%) in fairly good agreement with the model. A pronounced absorption band in the near-UV CD region, arising from immobilized aromatic side-chains, showed that the artificial protein is folded in solution. Chemical unfolding monitored by tryptophan fluorescence revealed a conformational stability (ΔGH_2O) of 35 kJ/mol. Thermal unfolding monitored by near-UV CD revealed a cooperative transition with an apparent T_m of 65 °C. Moreover, the artificial protein did not exhibit any affinity for the hydrophobic fluorescent probe 1-anilinonaphthalene-8-sulfonic acid (ANS), providing additional evidence that the artificial barrel is not in the molten globule state, contrary to previously designed artificial a/ b-barrels. Finally, ^1H NMR spectra of the folded and unfolded proteins provided evidence for specific interactions in the folded protein. Taken together, the results indicate that the de novo designed α/β-barrel protein adopts a stable three-dimensional structure in solution. These encouraging results show that de novo design of an idealized protein structure of more than 200 amino acid residues is now possible, from construction of a particular backbone conformation to determination of an amino acid sequence with an automated sequence selection algorithm.

Enhanced Sensitivity by Nonuniform Sampling Enables Multidimensional MAS NMR Spectroscopy of Protein Assemblies

We report dramatic sensitivity enhancements in multidimensional MAS NMR spectra by the use of nonuniform sampling (NUS) and introduce maximum entropy interpolation (MINT) processing that assures the linearity between the time and frequency domains of the NUS acquired data sets. A systematic analysis of sensitivity and resolution in 2D and 3D NUS spectra reveals that with NUS, at least 1.5- to 2-fold sensitivity enhancement can be attained in each indirect dimension without compromising the spectral resolution. These enhancements are similar to or higher than those attained by the newest-generation commercial cryogenic probes. We explore the benefits of this NUS/MaxEnt approach in proteins and protein assemblies using 1-73-(U-(13)C,(15)N)/74-108-(U-(15)N) Escherichia coli thioredoxin reassembly. We demonstrate that in thioredoxin reassembly, NUS permits acquisition of high-quality 3D-NCACX spectra, which are inaccessible with conventional sampling due to prohibitively long experiment times. Of critical importance, issues that hinder NUS-based SNR enhancement in 3D-NMR of liquids are mitigated in the study of solid samples in which theoretical enhancements on the order of 3-4 fold are accessible by compounding the NUS-based SNR enhancement of each indirect dimension. NUS/MINT is anticipated to be widely applicable and advantageous for multidimensional heteronuclear MAS NMR spectroscopy of proteins, protein assemblies, and other biological systems.

Maximum entropy reconstruction of complex (phase-sensitive) spectra

Abstract There is no general agreement on the definition of the entropy of a complex spectrum. We consider a number of possible definitions for use in maximum entropy reconstruction, comparing their analytical properties and the quality of spectrum reconstructions computed for synthetic and experimental NMR data. On the basis of this comparison, we conclude that the entropy of the power spectrum is not well suited for spectrum reconstruction in NMR; conversely, there is one definition which appears to be better suited in every respect than the others considered.

An automated tool for maximum entropy reconstruction of biomolecular NMR spectra

calculations are computationally costly (that is, efficiency is low). Modern large-scale ∆∆G prediction methods use heuristic algorithms with effective force fields and empirical parameters to estimate the stability changes caused by mutations in agreement with experimental data2–5. There are, however, two considerable drawbacks pertinent to the heuristic methods. First, most of these prediction methods rely on parameter training using available experimental ∆∆G data. Such training is usually biased toward mutations that feature large-to-small residue substitutions, such as alanine-scanning experiments (that is, poor transferability). Second, protein backbone flexibility, which is crucial for resolving atomic clashes and backbone strains in mutant proteins, is not considered in these methods, thereby reducing accuracy and limiting the application of heuristic methods (that is, limited applicability). To address the issues of efficiency, transferability and applicability, we developed the Eris method, which uses a physical force field with atomic modeling as well as fast side-chain packing and backbone relaxation algorithms. The free energy is expressed as a weighted sum of van der Waals forces, solvation, hydrogen bonding and backbone-dependent statistical energies6 (Supplementary Methods online). The weighting parameters are independently trained to recapitulate the native amino acid sequences for 34 proteins using high-resolution X-ray structures6. Additionally, an integral step of Eris is backbone relaxation when severe atom clashes or backbone strains are detected during calculation. We tested Eris on 595 mutants from five proteins, for which the ∆∆G values were documented (Fig. 1a). We found significant agreement between the predicted and measured ∆∆G values with a correlation coefficient of 0.75 (P = 2 × 10−108). The correlation between the predictions and experiments is comparable to that reported using other methods2–5. Unlike previous methods, Eris also has high predictive power for small-to-large3 sidechain-size mutations (Fig. 1b,c), owing to its ability to effectively relax backbone structures and resolve clashes introduced by mutations. As a direct comparison with other methods, we computed the stability changes of the small-to-large mutations using Eris and other web-based stability prediction servers. We found that Eris outperformed other available servers (Supplementary Discussion and Supplementary Tables 1 and 2 online). Additionally, Eris features a protein structure pre-relaxation option, which remarkably improves the prediction accuracy when a highresolution protein structure is not available (Supplementary Discussion and Supplementary Fig. 1 online). Our test validates the unbiased force field, side-chain packing and backbone relaxation algorithms in Eris. We anticipate Eris will be applicable to examining a much larger variety of mutations during protein engineering. We built a web-based Eris server for ∆∆G estimation. The server is freely accessible online (http:// eris.dokhlab.org).

Nonuniform Sampling and Maximum Entropy Reconstruction in Multidimensional NMR

NMR spectroscopy is one of the most powerful and versatile analytic tools available to chemists. The discrete Fourier transform (DFT) played a seminal role in the development of modern NMR, including the multidimensional methods that are essential for characterizing complex biomolecules. However, it suffers from well-known limitations: chiefly the difficulty in obtaining high-resolution spectral estimates from short data records. Because the time required to perform an experiment is proportional to the number of data samples, this problem imposes a sampling burden for multidimensional NMR experiments. At high magnetic field, where spectral dispersion is greatest, the problem becomes particularly acute. Consequently multidimensional NMR experiments that rely on the DFT must either sacrifice resolution in order to be completed in reasonable time or use inordinate amounts of time to achieve the potential resolution afforded by high-field magnets. Maximum entropy (MaxEnt) reconstruction is a non-Fourier method of spectrum analysis that can provide high-resolution spectral estimates from short data records. It can also be used with nonuniformly sampled data sets. Since resolution is substantially determined by the largest evolution time sampled, nonuniform sampling enables high resolution while avoiding the need to uniformly sample at large numbers of evolution times. The Nyquist sampling theorem does not apply to nonuniformly sampled data, and artifacts that occur with the use of nonuniform sampling can be viewed as frequency-aliased signals. Strategies for suppressing nonuniform sampling artifacts include the careful design of the sampling scheme and special methods for computing the spectrum. Researchers now routinely report that they can complete an N-dimensional NMR experiment 3(N-1) times faster (a 3D experiment in one ninth of the time). As a result, high-resolution three- and four-dimensional experiments that were prohibitively time consuming are now practical. Conversely, tailored sampling in the indirect dimensions has led to improved sensitivity. Further advances in nonuniform sampling strategies could enable further reductions in sampling requirements for high resolution NMR spectra, and the combination of these strategies with robust non-Fourier methods of spectrum analysis (such as MaxEnt) represent a profound change in the way researchers conduct multidimensional experiments. The potential benefits will enable more advanced applications of multidimensional NMR spectroscopy to study biological macromolecules, metabolomics, natural products, dynamic systems, and other areas where resolution, sensitivity, or experiment time are limiting. Just as the development of multidimensional NMR methods presaged multidimensional methods in other areas of spectroscopy, we anticipate that nonuniform sampling approaches will find applications in other forms of spectroscopy.