Decoding complex multicomponent chromatograms by fourier analysis

Abstract

SummaryThe present work discusses the many attributes -classified as observable, intrinsic or hidden -which can be conceived for any complex multicomponent chromatogram. Discussion ensues on how to decode such chromatograms, i.e. determining the intrinsic and/or hidden attributes from those which can be observed. There are two main steps. The first is based on Fourier Analysis (FA) and determines the intrinsic attributes: i.e., the number of single components which can be detected; their distribution over the available chromatographic space and peak capacity. The second evaluates the hidden attributes: i.e., the effects of incomplete separation, the number of peaks created by one or more single components as well as their degree of purity. The hidden attributes can be obtained by applying the theory of Statistical Degree of peak Overlapping (SDO) and the paper goes into the extent to which the SDO step depends on the FA results. In addition, the role Exponential distribution plays as a point of reference for the distribution of both single component peak position interdistances and peak heights is discussed. Finally, a simplified graphical FA procedure is presented and the main achievements in this field are reviewed.

Spot overlapping in two‐dimensional polyacrylamide gel electrophoresis maps: Relevance to proteomics

“…The situation is a consequence of the mixture complexity itself and results in a drop in the quality of analytical information contained in the map; this loss is proportional to the degree of randomness of the map itself [18][19][20]. As a consequence of spot overlapping [18][19][20][21][22][23][24][25][26][27][28][29][30] (i) the number of spots, p, detectable in the map is always lower than the number m of components present in the mixture. The number of spots, p, does not represent the real complexity of the mixture: the loss of analytical information is represented by the separation degree g = p/m and is proportional to the degree of overlapping present in the mixture [18][19] Therefore, the total number of detectable spots, p, is given by:…”

“…A statistical model of peak overlap allows a quantitative description of spot overlapping [18,19,[28][29][30][31][32][33]: it regards the separation as an ensemble whose average properties can be estimated using mathematical statistics. The fundamental basis is the separation model, i.e., the mathematical function describing the way by which the SCs arrange themselves over the available separation space.…”

“…Many statistic theories have been developed to describe spot overlapping in 2-D separations [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]: they all have been tested extensively by computer-simulated data [19][20][21][22][23][24]26] as well as by experimental data [25,30]. In the simplest and more general model, spots formed by only 1 SC are randomly distributed on all the separation space [19,20].…”

“…The procedure allows an accurate and precise estimation of the number of components, m. The reliability of the procedure was validated on computersimulated maps as well as on maps obtained from literature sources [28]. Theoretical and experimental evidences show that the whole complex separation can be regarded as the superimposition of several separations of groups of compounds (classes, homologues series) present in the multicomponent mixture: the statistical properties of each individual separation are additive, resulting in the properties of the whole separation [27,[29][30][31][32][33]. In this case, the 2-D map is regarded as superimposition of several 1-D strips into which the map is divided [28].…”

Spot overlapping in two-dimensional polyacrylamide gel electrophoresis separations: A statistical study of complex protein maps

“…Therefore, a mathematical approach is required to extract all the analytical information contained in the map and hidden therein by spot overlapping -m, protein pI and M r parameters, protein abundance distribution [5][6][7][8]. Among the several methods to deal with this problem [5][6][7][8][9][10][11][12], some of the authors, on the basis of the original SMO (statistical model of peak overlapping) [5][6][7][8], developed the quantitative theory of SMO [13][14][15].…”