NMR, one-dimensional

The NMR data X(t) can be treated in terms of the response theory, which is well-known in electrical engineering. The theory deals with the time domain (data collection) and the frequency domain (data exhibition). 

Both time and frequency domains can carry the same information, although in different forms. This is accomplished by the Fourier transformation. Let s(t) be the functions in the time domain and S((d) or (v) be functions in the frequency 

The FID obtained from the pulse method contains all the NMR data of a sample. Fourier transformation not only enables the transformation from the time domain, s t), to the frequency domain, 5(o)) or 5(v) but can also pretreat the time domain. The unnecessary data in the time sequence, such as noise, can be eliminated or trimmed before the transformation process. This would provide greater clarity of presentation and economy in labor. The pretransformation is carried out mathematically by the convolution theorem as follows Let r(t) be the function to pretreat the data function s(t). The convolution integral of the two functions is defined by 

Any pretreatment and filtering process in the NMR (such as apodization) can be expressed as 

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The typical chemical shift values and CH coupling constants in the one-dimensional NMR spectra reveal three functional groups ... 

In the one-dimensional NMR experiments discussed earlier, the FID was recorded immediately after the pulse, and the only time domain involved (ij) was the one in which the FID was obtained. If, however, the signal is not recorded immediately after the pulse but a certain time interval (time interval (the evolution period) the nuclei can be made to interact with each other in various ways, depending on the pulse sequences applied. Introduction of this second dimension in NMR spectroscopy, triggered byjeener s original experiment, has resulted in tremendous advances in NMR spectroscopy and in the development of a multitude of powerful NMR techniques for structure elucidation of complex organic molecules. 

Figure 7.21 One-dimensional NMR imaging. When a magnetic field gradient is applied across a sample, it gives a spectrum that is a profile of the sample in the direction of the gradient.

Unlike the one dimensional NMR techniques to which this book is largely devoted, those 2D 19F NMR techniques to be briefly discussed below will not generally be required for day to day structure elucidation by the working organic chemist. However, there will inevitably be situations where these techniques will be indispensible in determining the detailed 3-dimensional structure of compounds that contain fluorine, and at such times it may be necessary for the synthetic chemist to turn to an NMR specialist for assistance. 

NOESY NMR spectroscopy is a homonuclear two-dimensional experiment that identifies proton nuclei that are close to each other in space. If one has already identified proton resonances in one-dimensional NMR spectroscopy or by other methods, it is then possible to determine three dimensional structure through NOESY. For instance, it is possible to determine how large molecules such as proteins fold themselves in three-dimensional space using the NOESY technique. The solution structures thus determined can be compared with solid-state information on the same protein obtained from X-ray crystallographic studies. The pulse sequence for a simple NOESY experiment is shown in Figure 3.23 as adapted from Figure 8.12 of reference 19. 

Multidimensional NMR was pioneered by Richard Ernst (Nobel Prize for Chemistry, 1991) and its application to structure determination of biological macromolecules, already heroically undertaken with all the limitations of one-dimensional NMR, was further developed and refined by Klaus Wtithrich (Nobel Prize for Chemistry, 2002). 

Finally, the last step of the procedure for optimizing experimental conditions is to identify the denaturation temperature of the protein. This step is important because the rotational tumbling rate of a protein increases with temperature, and faster tumbling results in sharper resonance lines. Therefore, the temperature during the NMR experiments should be as high as possible without denaturating the protein. The denaturation temperature can best be determined by either CD-spectroscopy or one-dimensional NMR. 

Standard onedimensional NMR One-dimensional NMR — simple one-pulse experiment, typically with presaturation of solvent during the recycle delay with a weak RF field To quantify small molecules To identify some simple small molecules... 

In many cases, the analytical tasks are simply to detect and quantify a specific known analyte. Examples include the detection and quantification of commonly used buffer components (e.g., Tris, acetate, citrate, MES, propylene glycol, etc.). These simple tasks can readily be accomplished by using a standard one-dimensional NMR method. In other situations, the analytical tasks may involve identifying unknown compounds. This type of task usually requires homonuclear and heteronuclear two-dimensional NMR experiments, such as COSY, TOCSY, NOESY, HSQC, HMBC, etc. The identification of unknown molecules may also require additional information from other analytical methods, such as mass spectrometry, UV-Vis spectroscopy, and IR spectroscopy.14... 

NMR is a remarkably flexible technique that can be effectively used to address many analytical issues in the development of biopharmaceutical products. Although it is already more than 50 years old, NMR is still underutilized in the biopharmaceutical industry for solving process-related analytical problems. In this chapter, we have described many simple and useful NMR applications for biopharmaceutical process development and validation. In particular, quantitative NMR analysis is perhaps the most important application. It is suitable for quantitating small organic molecules with a detection limit of 1 to 10 p.g/ml. In general, only simple one-dimensional NMR experiments are required for quantitative analysis. The other important application of NMR in biopharmaceutical development is the structural characterization of molecules that are product related (e.g., carbohydrates and peptide fragments) or process related (e.g., impurities and buffer components). However, structural studies typically require sophisticated multidimensional NMR experiments. 

Figure 10 shows the NMR spectrum of sonicated POPC-TTC vesicles at room temperature and selected pressures. Already the one-dimensional NMR spectra exhibit some interesting features. With increasing pressure, the signal intensity of the acyl-chain protons at 0.85 and 1.24 ppm decrease due to the pressure-induced rigidization of the acyl-chains, as it is also observed for pure phospholipid samples. At pressures above the fluid-gel main transition, which is detected at a pressure of about 1200 bar at 20 °C in pure POPC dispersions, the acyl-chain signals of pure lipid samples disappear completely, whereas in the spectra of the POPC-TTC system considerable signal intensities remain even up to pressures of 2800 bar. Furthermore, we observe for the... 

Fig. 7. One-dimensional NMR spectra of the designed four-helix bundles SA-42 (lower trace) and GTD-43 (top two traces). The chemical shift dispersion of SA-42 in 90% H2O and 10% D2O at 323 K and pH 4.5 is poor and the resonances are severely broadened due to conformational exchange. The chemical shift dispersion of GTD-43 in the same solvent at 288 K and pH 3.0 is comparable to that of the naturally occurring four-helix bundle IL-4 and the resonances are not significantly affected by conformational exchange. Upon raising the temperature to 298 K line broadening is observed (top trace) which shows that GTD-43 is in slow exchange on the NMR time scale, unlike SA-42 where an increased temperature reduces the line width. These spectra are therefore diagnostic of structures with disordered (SA-42) and ordered (GTD-43) hydrophobic cores...

Due to extensive overlap within the region 5 3.0-4.5 ppm, H NMR spectra of oligosaccharides in many cases produce complex patterns. In one-dimensional NMR analysis, the solvent pyridine-ds improves signal dispersion better than methanol- /4 or acetone-dg. For structural analysis, the following steps are suggested ... 

Identification of constitutive monosaccharides two-dimensional homonuclear NMR techniques such as DQF-COSY and TOCSY are used to assign chemical-shift values for all C-bonded protons in each individual monosaccharide (96). One-dimensional NMR spectra provide useful information about the chemical shifts and scalar couplings of such well-resolved signals as methyl groups for 6-deoxy monosaccharides (fucose, quinovose, and rhamnose) at 6 1.1-1.3 ppm. 

It is usual to plot a normal (one-dimensional) NMR spectrum along each of the axes to give referenee speetra for the peaks that appear in the two-dimensional spectrum. 

The NOESY spectrum relies on the Nuclear Overhauser Effect and shows which pairs of nuclei in a molecule are close together in space. The NOESY spectrum is very similar in appearance to a COSY spectrum. It is a symmetrical spectmm that has the Iff NMR spectmm of the substance as both of the chemical shift axes (Fi and F2). A schematic representation of NOESY spectmm is given below. Again, it is usual to plot a normal (one-dimensional) NMR spectmm along each of the axes to give reference spectra for the peaks that appear in the two-dimensional spectmm. 

Apart from all of this, multi-dimensional NMR finds considerable and still growing applications in more traditional areas of chemistry. Even if most organometallic and coordination compounds are smaller in size and exhibit simpler spectra than biopolymers, they are composed of a large pool of building blocks whose spectroscopic characteristics are less well known or unknown at all, and the bond connectivity patterns are much more diverse and intricate. Consequently, NMR spectra of organometallic and coordination compounds are less predictable, and multi-dimensional techniques are in many cases indispensable as analytical tools when structural assignments derived from the analysis of one-dimensional NMR spectra remain ambiguous or even incomplete. 

H is particularly important in NMR experiments because of its high sensitivity and natural abundance. For macromolecules, 1H NMR spectra can become quite complicated. Even a small protein has hundreds of 1H atoms, typically resulting in a one-dimensional NMR spectrum too complex for analysis. Structural analysis of proteins became possible with the advent of two-dimensional NMR techniques (Fig. 3). These methods allow measurement of distance-dependent coupling of nuclear spins in nearby atoms through space (the nuclear Overhauser effect (NOE), in a method dubbed NOESY) or the coupling of nuclear spins in atoms connected by covalent bonds (total correlation spectroscopy, or TOCSY). 

FIGURE 2 A one-dimensional NMR spectrum of a globin from a marine blood worm. This protein and sperm whale myoglobin are very close structural analogs, belonging to the same protein structural family and sharing an oxygen-transport function. 

Figure 9.1 represents a one-dimensional NMR spectrum (the intensities of the peaks are not considered to be a second dimension). More sophisticated NMR studies, in two, three or four dimensions can be used to determine the position of ail the atoms present in a molecule. This chapter only deals with one-dimensional (1 -D) NMR. 

New techniques for data analysis and improvements in instrumentation have now made it possible to carry out stmctural and conformational studies of biopolymers including proteins, polysaccharides, and nucleic acids. NMR, which may be done on noncrystalline materials in solution, provides a technique complementary to X-ray diffraction, which requires crystals for analysis. One-dimensional NMR, as described to this point, can offer structural data for smaller molecules. But proteins and other biopolymers with large numbers of protons will yield a very crowded spectrum with many overlapping lines. In multidimensional NMR (2-D, 3-D, 4-D), peaks are spread out through two or more axes to improve resolution. The techniques of correlation spectroscopy (COSY), nuclear Overhausser effect spectroscopy (NOESY), and transverse relaxation-optimized spectroscopy (TROSY) depend on the observation that nonequivalent protons interact with each other. By using multiple-pulse techniques, it is possible to perturb one nucleus and observe the effect on the spin states of other nuclei. The availability of powerful computers and Fourier transform (FT) calculations makes it possible to elucidate structures of proteins up to 40,000 daltons in molecular mass and there is future promise for studies on proteins over 100,000... 

Foam characteristics in several commercial beers were evaluated using one-dimensional NMR image. Foam texture differences and regions of cling, head, and liquid beer can be clearly distinguished. Significant differences in rates of foam collapse were measured [22]. 

Figure 7.25 One-dimensional imaging with the NMR-MOUSE (a) Single-point imaging sequence for phase-encoding of space, (b) drawing of the NMR-MOUSE with coils for pulsed field gradients, (c) sample of an elastomer sheet with parallel textile fibres and one-dimensional NMR image with the space direction perpendicular to the fiber direction...

One-dimensional NMR Studies of Molecular Motions and Dynamic Order... 

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