Asynchronous correlation map

The asynchronous correlation map allows the elementary components of overlapping bands or spectra measured in sitn to be distinguished, showing the uncorrelated or independent changes of IR signals at two different wavenumbers. Strong correlation peaks at B, C) and (C, B) in the asynchronous correlation map (Fig. 3.52) show that the changes at the wavenumbers B and C are out of phase or occur at different rates with respect to one another. Only cross peaks located... 

In comparison to other spectroscopic techniques, where generahzed covariance was performed to obtain synchronous and asynchronous correlation maps and where both correlation maps were interpreted, the asynchronous map was rarely exploited if considered at aU for NMR purposes. Yet, the synchronous map as an equivalent to the direct covariance spectrum served to correlate species in different samples for a few studies. In contrast, analysis of the sample variation by statistical total correlation NMR, STOCSY, has become a comer stone of metabolomics investigations this field was considered beyond the scope of this chapter, hence only the current variants of STOCSY and their purposes were briefly presented. 

Figire 7.13 The asynchronous correlation map for low and high density polyethylenes. Diagram due to Gregoriou Noda et aL [29]... 

Figure 10.3 Bidimensional correlation maps corresponding to changes in position (band shifting) of a band composed of one (bottom) or two peaks (top). Synchronous maps are located on the left and asynchronous on the right. Axes are as in Figure 10.2...

To increase interpretability, the dynamic IR spectra are snbjected to mathematical cross-correlation to prodnce two different types of 2D1R correlation spectra, or two-dimensional correlation maps. These maps, in which the. r- and y- axes are independent wavenumber axes (vi, V2), show the relative proportions of in-phase (synchronous) and ont-of-phase (asynchronons) response (Figs. 3.51 and 3.52). Initially, the mathematical formalism was based on the complex Fourier transformation of dynamic spectra [277]. To simplify the computational difficulties, the Hilbert pansform approach was developed [280], which produces two-dimensional correlation maps from a set of dynamic spectra as follows. First, the average spectrum y(v) is subtracted from each spectrum in the set, y(v, Pj) = y v, Pj) — y(v), where Pj is the dynamic parameter. Then, the synchronous spectrum, 5 (vi,V2), and the asynchronous spectrum, A(vi,V2), are calculated as... 

The asynchronous contour map was described as helpful for enhancing resolution in the same way 2D correlation spectroscopy does [12] Assuming that the cause of the variations of two coincidentally overlapping peaks are sufficiendy different, asynchronous correlation peaks will be obtained at the corresponding spectral positions, thus spreading the spectral crowding into two dimensions. 

Flu et al. [39] used both synchronous and asynchronous maps to investigate silk spider thread by solid-state NMR techniques. They constructed C— C correlation maps from a spin diffusion experiment that was not fur-... 

Figure 20.29 (a) Synchronous 2D-FTIR correlation map of poly DRl M-co-BEM. with a DRl M mole fraction of 0.23 during the photo-induced orientation process. In this figure, the negative peaks are indicated by a minus sign and the one-dimensional (ID) spectra are the dichroic difference spectra recorded after 5 min (dashed line) and 60 min (solid line) of irradiation (b) Asynchronous 2D-FTIR... 

In principle, there is no difference in the information content of a pair of synchronous and asynchronous correlation spectra and the corresponding power and phase spectra. Some spectroscopists find it easier to interpret the former pair of spectra and some the latter. However, the use of two-dimensional correlation maps to assist in the interpretation of spectral data is becoming extremely common. 

Figure 21.22. (a) Synchronous and (b) asynchronous two-dimensional correlation maps of ac-field induced homogeneous/homeotiopic transition in the nematic Uquid crystal SPCH. (Reproduced from [18], hy permission of the Society for Applied Spectroscopy copyright 1993.)... 

The functions, and ij/, are called the synchronous and asynchronous 2D intensity correlation functions, respectively. These functions represent the overall similarity and dissimilarity, respectively, between two intensity variations at vi and V2 caused by changing the magnitude of the perturbation. The results are plotted on two orthogonal axes (vi and V2) with the spectral intensity plotted on the third axis normal to the 2D spectral plane. Figures 3-31A and 3-3 IB illustrate schematic contour maps of a synchronous and an asynchronous 2D correlation spectrum, respectively, where + and - signs indicate the directions of the contour peaks relative to the 2D spectral plane. 

Figure 3-31 Schematic contour maps of a synchronous (A) and an asynchronous (B) 2D correlation spectra. (Reproduced with permission from Ref. 98.)...

Figure 3.52. Schematic contour map of asynchronous 2DIR correlation spectrum. Shaded areas represent negative-intensity regions. Reprinted, by permission, from I. Noda, A. E. Dowrey, and C. Marcott, Appl. Spectrosc. 47, 1317 (1993), p. 1318, Fig. 3. Copyright 1993 Society for Appiied Spectroscopy.

D IR analysis of the protein component of human skin has been attempted in the past [3, 21], Asynchronous 2D IR spectra suggest IR bands assignable to different protein conformations can be readily differentiated by the development of asynchronous cross peaks. Synchronous 2D IR spectra, on the other hand, can correlate different IR bands belonging to similar protein conformations. Thus, 2D IR spectroscopy may be used systematically to map out the IR band assignments of complex protein molecules. 

Figure 3.12A and B, depicts schematic contour maps of synchronous and asynchronous 2D correlation spectra, respectively (the terms synchronous and asynchronous are always used even when the spectral variation is measured as a function of not time but another physical variable) (13). A one-dimensional refernce spectrum is provided at the top and left side of the contour map to show the basic feature of spectra of the system during experiment. A synchronous spectrum is symmetric with respect to a diagonal line corresponding to spectral coordinates = V2. Peaks... 

Figure 21.1 Schematic illustrations of (a) synchronous and (b) asynchronous 2D correlation spectra. White and gray areas in the contour maps represent positive and negative correlation intensities, respectively.

---