Imbrie's Q-Mode Factor Analysis Applied to Simultaneous Determination of Individual Amino Acid in Binary and Ternary Mixtures

Ieda S. SCARMINIO, Wagner J. BARRETO, Dilson N. ISHIKAWA, Edio L. PACZKOWSKI, Iara C. ARRUDA
2000 Analytical Sciences  
One of the most important problems in analytical chemistry is determining the number and concentration of chemical species in mixtures by means of spectroscopy and chromatography. A series of statistical techniques has been utilized to develop multivariate methods which extract information from spectra and chromatograms in order to identify the species present and to determine the concentrations of some or all of them. The applicability of each method depends on the data set submitted for
more » ... is. From an analytical point of view, 1 the multivariate methods can be classified into three categories: I) spectral information is available for each individual species in the samples, II) spectral information about these species is incomplete or only partially known and, III) no information about the chemical compositions of the samples exists. This article proposes a multivariate calibration method to determine the chemical compositions of complex mixtures based on Imbrie's Q-mode factor analysis followed by varimax 2,3 and Imbrie's oblique rotations. 2 This method can be classified as one of category I as well as of category III, depending on the information available about the chemical system to be analyzed. For category I applications, this method does not require an extensive calibration set, as do the PCR, PLS, K-matrix and MLR methods. Only spectra of the pure absorbing species or standard spectra are necessary. In category III applications, the method is capable of identifying the number of absorbing species and their relative concentrations from only the set of spectra for the mixture being analyzed. An important requirement for applying all of the methods cited above is that the mixture spectra must be a linear combination of the individual spectra of the species involved, weighted by their respective concentrations. In other words, Beer's or an analogous law must be obeyed. Although quantitative analysis for amino acids is commonly used in clinical investigations, the food industry and research, there is no routine spectrophotometric method for their simultaneous determination in mixtures. In previous papers, 4 we proposed a method for the simultaneous determination of total amino acids and proteins using p-benzoquinone (PBQ). The reaction of PBQ and the amino acids was carried out at 100˚C for 20 min, since this reaction is very slow at ambient temperature. The products of the reaction have bands between 390 and 440 nm that follow Beer's law. Since this band is the resultant of a mixture of products, their individual simultaneous determinations are impossible by traditional methods, thus justifying the application of a multivariate analysis. In this report, individual amino acid determinations are discussed based on the application of Q-mode factor analysis to alanine-glutamine, threonine-glutamine and alanine-threonine binary mixtures and alanine-glutamine-threonine ternary mixtures. Methodology The objective of this analysis is to factor an nxp A matrix, formed by n objects (samples or mixtures) and p variables (absorbances at different wavelengths, retention times, etc.) into a product of two matrices, 5 where T is a score matrix, P a loading matrix and E a matrix of residuals. The number of factors describing the major part of the data variance is represented by q, and P t is the transpose of P. Each factor corresponds to a row or column of the T and P matrices, respectively. Imbrie's Q-mode factor analysis defines the similarity of objects by considering the component proportions. The method searches elements in the A matrix for the most divergent objects, represented by the pure component spectra or those constituted by a significant proportion of these components, which can be represented as vertices of a concentration simplex. The other data set objects are linear combinations of the divergent ones. The contribution of each object is obtained by an eigen-analysis of a real symmetric matrix obtained from the data matrix. Imbrie and Purdy 2 define an index of proportional similarity, called cos θ. For two objects, n and m, cos θ is calculated by (3) cos nm = θ . q j=1 ∑anjamj q j=1 ∑anj 2 q j=1 ∑amj 2
doi:10.2116/analsci.16.1337 fatcat:igyunyhuubfm3ggsq2hboxtphu