Basis spectra

The major assumption in the fitting procedure was that the basis spectra (i.e., spectra for individual molecular components) are independent of flow tube temperature. This approximation was tested by running mass spectra of stable molecules such as toluene and st3Tene over the full range of flow tube temperatures, and the peak ratios in these spectra change by no more than l%-2%. Based on this result and the signal-noise ratio in the experiments, the fitting uncertainty was estimated at about 5%. 

A series of 14 linear and cyclic peptides have been studied 135 by CD, NMR, and MD simulations. Quantitative NOE measurements and MD were used to determine the fractions of type I and II (3-turns in each peptide. The CD spectra for these same peptides were analyzed by convex constraint analysis 136 to derive a set of CD curves for the two types of 13-turns (Figure 6). These basis spectra gave fractional (3-turn contents in good agreement with NMR measurements. Two basis spectra (components 1 and 4) were obtained for the type I... 

Another method is to produce EPR basis spectra by irradiating various nucleic acid bases. The EPR spectrum of DNA is simulated by taking various combinations of the... 

Sevilla et al. [49] have simulated the EPR spectrum of whole DNA equilibrated with D2O irradiated and observed at 77 K. The results were 77% Cyt and 23% Thy for the anions and >90% Gua for the cations. The analysis produced a small imbalance in the cations (44%) and anions (56%). It was suggested that some holes remain trapped in the solvation shell. It is also possible that this reflects small errors in the treatment of the basis spectra, or that some DNA radicals are not accounted for because their EPR signal is too broad and poorly resolved. 

To convert an optical signal into a concentration prediction, a linear relationship between the raw signal and the concentration is not necessary. Beer s law for absorption spectroscopy, for instance, models transmitted light as a decaying exponential function of concentration. In the case of Raman spectroscopy of biofluids, however, the measured signal often obeys two convenient linearity conditions without any need for preprocessing. The first condition is that any measured spectrum S of a sample from a certain population (say, of blood samples from a hospital) is a linear superposition of a finite number of pure basis spectra Pi that characterize that population. One of these basis spectra is presumably the pure spectrum Pa of the chemical of interest, A. The second linearity assumption is that the amount of Pa present in the net spectrum S is linearly proportional to the concentration ca of that chemical. In formulaic terms, the assumptions take the mathematical form... 

There has been some discussion as to whether CD can distinguish parallel from antiparallel p sheets. As stable, well-defined model compounds are lacking, the spectra available have been derived from secondary structure deconvolutions (see below). Overall, the ability of CD to provide adequate estimates of both parallel and antiparallel p sheet contents is still an ongoing question. Johnson and co-workers were the first to derive basis spectra which corresponded to both parallel and antiparallel p sheet structures in globular proteins using the singular value deconvolution method [11, 12, 51-53], However, the basis spectra were significantly different from spectra reported for model sleet structures. Recently, Perczel et al. [54] employed another approach, convex curve analysis, to obtain improved p sheet baas spectra. The major improvement was to include more p sheet proteins into the data base. 

Recently, attempts have been made to derive CD spectra of various p turns using deconvolution procedures (see below). Employing an approach termed convex constraint analysis, Perczel, Fasman, and others [58-61] have derived CD spectra for both types I and H turns. Three basis spectra were extracted for a data base of fourteen peptides which displayed either types I or II p turns. One basis spectrum for type I turns resembled a class C spectrum and the other a variation of a class B. The type II turn is said to display a classic class B spectrum [59-61],... 

Early attempts used data obtained from homopolypeptides, such as poly(Lys), for their basis spectra [87, 88]. In the past fifteen years, approaches using data from globular proteins have emerged [18, 89-101]. Basically, a data base comprised of proteins with known secondary structure compositions is assembled and far UV CD spectra recorded. The choice of the proteins to be included is critical and various combinations have been examined. Mathematical matrix methods can be used to extract basis spectra which represent the contributions from the various secondary structures. Typically, four or five basis spectra can be obtained (corresponding to a helices, jj sheets, p turns, and random coil structures). In some approaches, such as those developed by Johnson and co-workers [11, 12, 51, 52, 102], separate basis spectra can be obtained for parallel and antiparallel p sheets. These basis spectra are then linearly combined to reconstruct the CD spectrum of the protein of interest The proportion of the basis spectra used to provide the best fit to the spectrum corresponds to the percentage of that secondary structure in the protein of interest Complete details of the mathematical algorithms that have been employed can be found elsewhere [10, 12, 17, 89, 103]. 

In Figure 6, the change in ellipticity, A0, is presented under different experimental conditions as a function of the calculated transmembrane potential. The experimental points obtained under the different conditions are a continuous curve. Table I shows the secondary structure calculated from the ellipticity at different potential differences across the membrane. The evaluation of the alamethicin conformation was performed similarly to that of bacteriorhodopsin under the influence of electric field, namely, by fitting the basis spectra for a helix, random coil, and P forms presented either by Chen et al. (33) or by Chang et al. (34). There is a trend toward P structure as the positive inside potential increases and toward helicity at opposite polarity. 

Another application of the Johnson and Gray method was to an RNA (PK5) that had been shown by NMR to contain a pseudoknot at low temperatures and a hairpin at higher temperatures. Fitting the basis spectra to the experimental CD and absorption spectra of the PK5 RNA gave base-pair, single-strand, and nearest-neighbor base-pair frequencies which agreed well with the pseudoknot structure at low temperatures... 

For proteins, it is the amide chromophore and the long-range order or lack of it that is responsible for the characteristic spectra of each of the secondary structural elements. A number of approaches have been employed to analyze the ORD or CD spectrum of a protein for the type and content of component secondary structures utilizing a set of basis spectra. The basis spectra are derived from the ORD/CD spectra of proteins from which the secondary structural content has been determined by X-ray crystallography. It is the solution of the linear combination of the basis spectra that gives the relative proportion for each of the secondary structural elements in the protein. 

The spatial and spectral engines are synchronised to produce a hyperspectral scene. Basis spectra are matched with image frames where the intensity of each pixel in the frame determines how much of that basis spectrum is present in the pixel. By cycling through a complete set of frames and their corresponding basis spectra in a period of time that is short compared to the WIIT s integration time, a hyperspectral scene is produced. 

The decomposition of the data set to determine pseudo (basis) spectra, singular values and time courses (SVD)... 

Luckily, the matrices E and arc ultimately related to U and V. from whence they can be obrained, as explained below. The matrix U has the same dimensions as A (m X n). whereas V and S are square (n x n, see Figure II. When plotted, the columns of U have features that are reminiscent of spectra and arc termed pseudo spectra or basis spectra, a linear combination of these can give any spcctmm captured during the course of the experiment. The columns of V are the time courses. In tact, the pairs of matrices (U, E) and (V. C ) arc related, because the entire matrices E and C can be generated by linear combination of the columns in U and V, respectively. 

The contributions that various secondary structural elements make to a protein of unknown structure can be estimated by fitting the observed CD spectrum with a sum of basis spectra like those shown in Fig. 9.9B, C [27-29, 41-44]. A web-server providing a variety of algorithms for this analysis is available [33,45]. 

Comonomer Concentrations An important innovation made by the addition of a full spectrum UV spectrophotometer into ACOMP detector train led to the determination of the instantaneous concentration of each comonomer during the reaction, in the case of the copolymerization of comonomers with similar spectral characteristics [19, 20], The working assumption was that a UV spectrum at any instant is a Unear combination of the normalized basis spectra of the comonomers, the copolymer, and any other UV absorbing species, and that the unknown comonomer concentrations can be foimd by minimizing the error between measured and computed spectra over many wavelengths, even when spectral diffaences are small at any iven wavelength. 

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