Indirect time domain

Fig. 18 (continued) cross-section was obtained by fixing frequencies in CO3, CO4, and CO5 dimensions to the values of chemical shifts of of 1157, of 1158, and Hn of 1158, respectively. Peaks corresponding to the sequential and intraresidual correlations are displayed in black and red, respectively. Experiment was acquired within 20 h on 700 MHz spectrometer using RT-probe. Only a fraction of 0.00034% points was collected in indirect time domains. See [92] for further details... 

Every NMR experiment must have a preparation sequence (inducing the nuclei to resonate) and detection capability (finding out what happened). Two-dimensional NMR spectroscopy adds two more domains between preparation and detection. These are an indirect evolution time, q, and a mixing sequence (see Figure 3.15). The two dimensions of two-dimensional NMR spectroscopy are those of time. In one time domain, FIDs containing frequency and intensity information about the observed nuclei is collected. The second time dimension refers to the time that elapses between some perturbation of the system and the onset of data collection in the time domain. The second time period is varied, and a series of FID responses are collected for each of the variations. 

To make this into a 3D experiment we need to create a third time domain, in this case a time domain that encodes the chemical shift of the Hn proton. We simply stop for a moment on our journey from 15N SQC to Hn SQC to Ha and side-chain H coherence, at the point where we have an Hn coherence, and insert an evolution delay to indirectly record the chemical shift of the Hn- The pulse sequence is shown in Figure 12.46 (center) and the coherence pathway is diagramed in Figure 12.47. The new evolution delay is called f2 because it is the second independent time domain, forcing us to rename the direct time domain of the FID as 3. In the center of the t2 evolution delay there is a 15N 180° pulse to reverse the 1Jnh coupling evolution so that the Hn will not be split by 15N in the F2 dimension, just as the t evolution delay includes a 180° pulse in the center to decouple ... 

Three techniques are actually available for measuring the fluorescence lifetime Strobe, Time Correlated Single Photon Counting (TCSPC), and multifrequency and crosscorrelation spectroscopy. Strobe and TCSPC are based on measurement in the time domain, while multifrequency and cross-correlation spectroscopy measure fluorescence lifetimes in the frequency domain. The time domain allows direct observation of fluorescence decay, while the frequency domain is a more indirect approach in which the information regarding the fluorescence decay is implicit. 

The 2D experiments are time consuming due to the necessity of acquiring many t increments in the indirect time dimension. It was realized that time-domain experiments , in which only a limited number of U increments (or even a single delay... 

The technique employs a specially designed 2D NMR pulse sequence [ 100], which forces nuclear spins to act collectively via their dipolar couplings, thereby creating unobservable multiple-quantum (MQ) coherences. The MQ coherences then evolve in the /, time domain and, after conversion into observable singlequantum coherences, are indirectly detected over the acquisition time t2- The multiple-quantum information is contained in the F dimension of the 2D spectrum (Fig. 13). The modified phase-incremented experiment [ 105] proceeds with the evolution held fixed and offers ease of operation and more accurate intensity distributions in return for loss of information contained in the fine structure and shapes of the MQ peaks. 

Fig. 1 Illustration of the projection-cross-section theorem [17-19] for a 2D frequency space with two indirect dimensions k and j. ID data cf (t) on a straight line in the 2D time domain (ty, tj) (left) is related to a ID orthogonal projection (of) of the spectrum in the 2D frequency domain (

Fig. 10 Two-dimensional /1//2 cross-sections from four-dimensional N.C-NOESY data for the DHl domain of Kalirin. One dimensional cross sections parallel to the/i axis at the f2 frequencies indicated by the colored lines are shown above each panel. Panel A is the real/real component of the two dimensional DPT spectrum using quadrature detection in all dimensions. Panel B is the DPT spectrum obtained using only the real/real/real component from the three indirect time dimensions of the time domain data. Panel C is the maximum entropy spectrum obtained using random phase detection. Panels B and C employ l/8th the number of samples used in panel A...

Backbone scalar couplings are widely used in NMR studies of structure and dynamics of biomolecules [93]. Additionally, there is a substantial interest in precise determination of residual dipolar couplings for structural studies of weakly oriented biomolecules. Most of the relevant coupling constants in proteins are rather small - of the magnitude from a few to a hundred hertz. Therefore, in order to achieve the sufficient resolution in indirectly measured dimensions, the majority of traditional methods devoted to coupling constants determination in biomolecules are limited to two-dimensional techniques, which frequently suffer from peak overlap. However, the random sampling of evolution time domain allows one to obtain spectra of resolution limited only by transverse relaxation... 

Fig. 7 Comparison of alternative processing on a 3D N-NOESY-HSQC spectrum of human translation initiation factor eIF4e. (a) Uniformly sampled reference. The time domain data were acquired as 6,400 hyper-complex points sampled in the two indirect dimensions [128 (Hjndir) x 50 ( N)]. The spectra were measured on a 700-MHz spectrometer with sweep widths of 9765 Hz and 2270 Hz, respectively. The t ,ax hence were 0.013 and 0.022 s each for the indirect proton and nitrogen dimensions, respectively, representing nearly an optimal situation for the nitrogen dimension, but not for the indirect proton dimension. Data were transformed with the standard KFT procedure after cosine apodization and doubling the time domain by zero filling, (b) Reducing the number of complex points to 42 (32%) (bl) and 13 (10%) (b2) in the indirect proton dimension, cosine apodization, and zero filling result in low resolution spectra in the indirect...

---