Overlapping deconvolution

Most EDS systems are controlled by minicomputers or microcomputers and are easy to use for the basic operations of spectrum collection and peak identification, even for the computer illiterate. However, the use of advanced analysis techniques, including deconvolution of overlapped peaks, background subtraction, and quantitative analysis will require some extra training, which usually is provided at installation or available at special schools. 

This present chapter will not focus on the statistical theory of overlapping peaks and the deconvolution of complex mixtures, as this is treated in more detail in Chapter 1. It is worth remembering, however, that of all the separation techniques, it is gas chromatography which is generally applied to the analysis of the most complex mixtures that are encountered. Individual columns in gas chromatography can, of course, have extremely high individual peak capacities, for example, over 1000 with a 10 theoretical plates column (3), but even when columns such as these are... 

Quantitative accuracy and precision (see Section 2.5 below) often depend upon the selectivity of the detector because of the presence of background and/or co-eluted materials. The most widely used detector for HPLC, the UV detector, does not have such selectivity as it normally gives rise to relatively broad signals, and if more than one component is present, these overlap and deconvolution is difficult. The related technique of fluorescence has more selectivity, since both absorption and emission wavelengths are utilized, but is only applicable to a limited number of analytes, even when derivatization procedures are used. 

Fig. 40.33. Restoration of two overlapping peaks by deconvolution. Dashed line measured data. Solid line after restoration. Dotted line difference between true and restored signals.

Nelson, T. J., Deconvolution method for accurate determination of overlapping peak areas in chromatograms, /. Chromatogr., 587, 129, 1991. 

Economou, A., Fielden, P. R., and Packham, A. J., Deconvolution of overlapping chromatographic peaks by means of fast Fourier and Hartley transforms, Analyst, 121, 97, 1996. 

Multidimensional GC with time of flight MS (ToF-MS) is increasingly being employed to examine complex mixtures. In this technique non-polar and polar GC stationary phases connected by a thermal modulator enable increased resolution of GC peaks. The fast scanning made possible by the ToF measuring system leads to many data points across peaks and the possibility of deconvolution of complex overlapping peaks. 

There may, however, be specific reasons to study a signal over an extended temperature range. For one, a linear increase in EPR amplitude with the inverse of the temperature (Curie s law) is proof that a spin system is a two-level system, i.e., an S = 1/2 or an effective S = 1/2 system. More importantly, in complex multicenter metalloproteins, overlapping spectra may be deconvoluted by virtue of their Tu value being different if two centers, a and b, have rMa < TMb then at TMb the spectrum of center a is broadened and that of center b is not. It is once more emphasized that these types of studies require determination of (anisotropic) saturation behavior at all relevant temperatures. 

Both methods are also limited in accuracy of secondary structure determinations because spectral peaks must be deconvolved estimates are made of the overlapping contributions of different structural regions. These estimates may introduce error based on the reference spectra used and because deconvolution methods equate crystallographic secondary structure with the secondary structure of the protein in solution (Pelton and McLean, 2000). As amyloid fibrils are neither crystalline nor soluble, there may be even greater error in estimates of secondary structure. To compound the problem, estimates of /f-sheet content are less reliable than those of a-helix, because of the flexibility and variable twist of / -structure (Pelton and McLean, 2000). In addition, / -sheet and turn bands overlap in FTIR spectroscopy (Jackson and Mantsch, 1995 Pelton and McLean, 2000). Side chains also contribute to spectral peaks in both methods, and they can skew estimates of secondary structure if not properly accounted for. In FTIR spectra, up to 10-15% of the amide I band may arise from side chain contributions (Jackson and Mantsch, 1995). 

We will not concern ourselves here with problems associated with line broadening, overlapping peaks, and background subtraction. There are, however, examples discussed later where both deconvolution and curve fitting procedures are shown to be essential in unraveling the contributions of differently bonded species of the same molecule to the total photoelectron yield. Carley and Joyner (14) have discussed recently deconvolution procedures for photoelectron spectra. 

It is important to point out that D. vulgaris hydrogenase contains three multinuclear iron clusters and each cluster may exist in equilibrium between two different oxidation states in each sample. Consequently, the raw Mossbauer spectra are complex, consisting of overlapping spectra originating from different iron sites of these various clusters. For clarity, we present only the deconvoluted spectra of the H cluster. These spectra were prepared by removing the contributions of other iron species from the raw spectra. Details of the analysis are available (Pereira et al. 2001). 

A third problem with simulation of high resolution diffraction data is that there is no unique instrament function. In the analysis of powder diffraction data, the instalment function can be defined, giving a characteristic shape to all diffraction peaks. Deconvolution of these peaks is therefore possible and fitting techniques such as that of Rietveld can be used to fit overlapping diffraction peaks. No such procedure is possible in high resolution diffraction as the shape of the rocking curve profile depends dramatically on specimen thickness and perfection. Unless you know the answer first, you cannot know the peak shape. 

Table 3.1 A portion of the membership of the ALIS screening library, composed of NG LI 27A443 (library 3 in this table) and four other libraries, which yields DHFR ligand 1 (NCD-157, entry 11). Compounds of similar exact molecular weight (EMW) are distributed among the five pooled libraries to minimize mass overlap and simplify hit deconvolution. Reprinted from [40] with permission from Elsevier.

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