Fourier deconvolution

Several peaks of interest (ideally higher order reflections of the same type hkl, 2h, 2k, 21, 3h, 3k, 31,. .., nh, nk, nl) are fitted by Fourier series the same procedure is applied to the diffraction lines of a reference sample, in which size and strain effects are negligible, in order to determine the instrumental line broadening. Such information is used in order to deconvolute instrumental broadening from sample effects (Stokes-Fourier deconvolution [36]). 

HP IR measurements have recently been reported by workers at Sasol for cobalt-catalysed 1-dodecene hydroformylation reactions using bicyclic phosphines (4) derived from (R)-(+)-limonene [68]. Using Fourier deconvolution to separate absorptions due to [HCo(CO)4] and [Co2(CO)7(phosphine)], it was possible to estimate the ratio of modified [HCo(CO)3(phosphine)] to un-modified [HCo(CO)4] in the catalytic mixture, using peak areas. Values of this ratio ranged from ca. 2-20, depend-... 

Fourier Deconvolution. A synthetic 30-residue polypeptide was synthesized as an electron-transfer protein.42 A spin label was attached at position 21 and the distance between the two labels in a dimer was determined by Fourier deconvolution of the CW line-shape in frozen solution. Based on the known geometry of the label, it was calculated that the interspin distance of 22.5 A corresponded to 13.5 + 0.9 A between the Ca carbons on the two polypeptide chains. 

Applications to Biological Samples. - Methods of distance measurements were compared for four doubly spin-labelled derivatives of human carbonic anhydrase.53 The distances between the spin labels were obtained from continuous wave spectra by analysis of the relative intensity of the half-field transition, Fourier deconvolution of the line-shape broadening, and computer simulation of line-shape changes. For variants with interspin distances greater than 18 A, the DEER method also was used. For each variant, at least two methods were applicable and reasonable agreement between distances obtained by different methods was obtained. The useful distance ranges for the techniques employed at X-band with natural isotope abundance spin labels were estimated to be half-field transition (5-10 A), line-shape simulation (up to 15 A), Fourier deconvolution (8 - 20 A), and four-pulse DEER (> 18 A).53... 

Fourier Deconvolution. Pairs of spin labels were introduced in the N-terminus of a-spectrin.66 Distances in the range of 8.3 to 11.7 A were determined by Fourier deconvolution of the dipolar broadening. The trends in distances for positions i to i+2, i + 3, i+4, and i + 5 were consistent with an a-helix. 

Pairs of spin labels were introduced in human prostaglandin endoperoxide H2 synthase-2 (PGHS-2) at locations where significant structural changes had been observed in X-ray crystal structures of holoenzyme and protein bound to NSAID s.75 Interspin distances were obtained by Fourier deconvolution of spectra recorded at 183 K for 10 doubly spin-labelled mutants. Interspin distances for complexes with arachidonic acid, flurbiprofen, and SC-58125 agree well with values predicted from X-ray crystal structures, but do not agree well for the holoenzyme. It is proposed that the predominant conformation of the holoenzyme in solution is different from the structure in the crystal. 

If the molecular tumbling rate is slow enough that larger electron-electron dipolar couplings are not motionally averaged, Fourier deconvolution can be used to analyze dipolar interactions in fluid solution.18 Distances in doubly spin-labelled rhodopsin were measured by Fourier deconvolution of CW line-shape changes in room temperature solution.78 The broadening function was modelled as the sum of Pake patterns from a distribution of distances. As a reference point for the distance measurements one label was attached at the cytoplasmic termination of transmembrane helix 1. The second label was attached near the cytoplasmic termination of transmembrane helix 7 or in the short helix 8. The distances and conformational flexibility in the dark state are... 

A widely used approach to extract information on protein secondary structure from infrared spectra is linked to computational techniques of Fourier deconvolution. These methods decrease the widths of infrared bands, allowing for increased separation and thus better identification of overlapping component bands present under the composite wide contour in the measured spectra [705]. Increased separation can also be achieved by calculating the nth derivative of the absorption spectrum, either in the frequency domain or though mathematical manipulations in the Fourier domain [114], An example is the method of Susi [775] which uses second derivative FT-IR spectra recorded in D20 for comparison with similar spectra derived from proteins with known structure. These methods have not yielded quantitative results that are more accurate than those obtained with methods that do not use deconvolution. 

DeRose and coworkers have explored conformational changes of TAR RNA upon binding of divalent metal ions (Ca " ) by measuring the dipolar coupling between two attached spin labels 20 using CW EPR (Fig. 2). The U25-U40 distances obtained from Fourier deconvolution methods are 11.9 0.3 A for TAR RNA in the absence of divalent metal cations and 14.2 0.3 A when 50 mM Ca " was added [45]. These results are in accordance with the proposed coaxial stacking of the two TAR helices upon addition of metal ions based on the X-ray crystal structure [80]. 

Susi, H. Byler, D.M. Fourier deconvolution of the Amide I Raman band of proteins as related to conformation. Appl Spectrosc. 1988a, 42, 819-826. 

The first detailed X-ray diffraction (XRD) studies on PEMFC electrodes were performed by Wilson et al. [43] using a Warren-Averbach Fourier transformation method for determining the weighted crystallite sizes. Warren and Averbach s method takes into account not only the peak width but also the shape of the peak. This method is based on a Fourier deconvolution of the measured peaks and the instrument broadening to obtain the true diffraction profile. This method is capable of yielding both crystallite size distribution and lattice microstrain. The particle-size distributions can be determined from the actual shape of the difliaction peaks, with the use of Warren-Averbach analysis. 

More complex means of attacking the particle size question have also been attempted. These include experiments using mathematical modeling for simultaneous removal of particle size and water [29], the use of Fourier deconvolution [30], multiplicative scatter corrections [31 ], and principal components elimination [32]. Barnes et al. [33] introduced a procedure termed detrending that uses standard normal variate (SNV) with polynomial baseline correction [34]. These corrections for particle size may not always improve accuracy of NIRS analysis for two reasons. First, none of these procedures does a perfect job of removing particle size effects independent of absorption information. Second, particle size may be useful information in the calibration even though linear mathematics is used to derive the analytical equation. 

Fourier deconvolution and component fitting. When the salt concentration increases, the practical disappearance of the component located in the spectrum of the mixed solvent at 3635 cm assigned to nearly free (non-hydrogen-bonded) OH oscillators, is observed. This effect is more evident in alcohol-rich samples (CH3OH mole fraction = 0.35). As in other systems [37,163,164], the component located at 3225 cm generally attributed to... 

This work, bprom Ref. 17. Assignments from Ref. 17. H-bond donor candidates from Ref. 18. Estimated from Fourier deconvolution. 

Figure 3. (Bottom) Fourier transfonn Raman spectrum of the RC from Rc. gelatinosus in the presence of ascorbate (reductjd RC) this spectrum is dominated by the preresonance Raman contributions of the primary donor in its reduced state, P. (Top) Fourier transform resonance Raman spectrum of tlie RC in the presence of ferricyanide this spectrum is dominated by the resonance Raman contributions of the primary donor in its oxidized state, P+-. Obvious new bands in this spectrum include those at 1602, 1641, and 1720 cm which are all atributable to (see text for discussion). Spectral resolution is 4 cm. Conditions room temperature, 200 mW of 1064 nm excitation, coaddition of 2000 scans. Inset Fourier deconvolution of the complex band at ca. 1610 cm-1 in the reduced P spectrum showing components at 1607 and 1616 cm" ... 

The use of Fourier deconvolution requires knowledge of the half-widths of the peaks to be examined, but in practice the half-widths of the component peaks of overlapping band systems are not known. Underestimation of the bandwidth results in a deconvoluted band that has a shape close to Lorentzian, but that has a lower resolution enhancement than would be achieved with the correct bandwidth. When overestimation occurs, negative lobes flank the deconvoluted band, and the degree of sharpening achieved is greater than expected. Overconvolution also results in serious distortions of the intensities. 

Fourier deconvolution is a valuable means for finding peaks in spectra of polymers with extensive overlapping of bands. The Fourier self-deconvoluted IR spectrum of... 

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