Real 2D NMR data

In our definition, real 2D NMR data are either homo- or hetero-nuclear data, where Fourier transformation is performed in both directions and a chemical shift map is created, as seen in COSY, TOCSY, NOESY, J-RES, HSQC, etc. In the case of HSQC, a short delay is being incremented during which the signals in the ID spectrum are being coded with the frequency of the corresponding hetero-nucleus and 2D Fourier transformation is employed to create the frequency map. An example of a real 2D NMR spectrum can be seen in Fig. 3A. With homo-nuclear data a similar picture is obtained, but the plot is symmetrical on the diagonal axis. 

Fig. 3. (A) An example of real 2D NMR data being a part of a H- N] HSQC spectrum of a peptide and (B) pseudo 2D NMR data in the form of diffusion-weighted data.

With pseudo 2D NMR data consisting of a series of ID profiles, analysis by multivariate techniques is obvious, since the large number of potentially overlapping variables makes visual analysis very difficult and improved methods of analysis are already called for. Analysis of real 2D NMR data by multivariate techniques is less obvious, since a lot of information can already be extracted from the 2D Fourier-transformed data. However, if real 2D NMR data from a series of samples needs to be compared, the application of multivariate techniques is an obvious possibility. 

Although all 2D NMR experiments are acquired as a collection of ID spectra, there are still fundamental differences in the resulting data and the way in which they are traditionally pre-processed and analysed. In this paper, we therefore choose to divide 2D NMR data into two different groups which we call real 2D and pseudo 2D NMR data in order to be able in a simple way to highlight and keep track of this difference. 

With 2D experiments the situation is a little more complicated as the size of the overall digitised matrix depends on the number of time increments in tl as well as parameters specific to the 2D acquisition mode. Nevertheless, a digitised matrix of TD(2) X TD(1) complex data points is acquired and stored. Similar to ID the effective number o measured data points used for calculation TD(used) and the total number of data points SI to be transformed in t2 and tl may be defined prior to Fourier transformation. These parameters may be inspected and defined in the General parameter setup dialog box accessible via the Process pull-down menu. With 2D WIN-NMR the definitions for TD(2) and TD(1) are the same as for TD with ID WIN-NMR. However, unlike ID WIN-NMR, with 2D WIN-NMR SI(2) and SI(1) define the number of pairs of complex data points, instead of the sum of the number of real and imaginary data points. Therefore the 2D FT command (see below) transforms the acquired data of the current data set into a spectrum consisting of SI data points in both the real and the imaginary part. 

A 2D NMR experiment can lead to a data set that is either phase modulated or amplitude modulated as a function of fj, depending on the particular experiment and coherence pathways selected. A regular ID spectrum consists of absorption A(p) and dispersion peaks corresponding to the real and imaginary parts of the spectral lines, respectively. In 2D experiments, phase modulation in fj results in twisted 2D real lineshapes as a result of the Fourier transformation of bi-exponential time domain... 

For the purpose of image filtering, a smoothing function is often applied to the 2D FID data set Shown in Fig. 7.18 is the smoothed 2D FID data array (real component). This surface plot shows both the oscillation set by G,. and the variable phase of that oscillation set by Gy This last point, the phase encoding by a pulse or gradient, is a key feature of multidimensional NMR experiments. 

The FIDs and interferograms can be multiplied by appropriate mathematical functions before Fourier transformation in order to improve sensitivity, resolution, or line shape exactly as in ID NMR. The NMR data are usually obtained as two separate components 90° out of phase from each other in a mode called quadrature detection to yield two spectral components denoted real and imaginary. A suitable linear combination of these two components allows the generation of a spectrum with a pure absorption phase. In 2D NMR, this phase-sensitive detection sometimes results in line shapes and phases that do not allow a pure absorption spectrum to be obtained and then the compromise of a magnitude mode presentation is used. This comprises the square root of the sum of the squares of the real and imaginary components and is wholly positive. Usually, 2D NMR spectra are plotted as contour maps as though the 2D spectral peaks are a series of mountains viewed from above relative to the orthogonal ffli and 0)2 axes. 

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