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Partial least squares regression for determining the dissociation constants from the UV-Vis spectra without calibration

Overlapping of the spectral bands, variations caused by the aggregation of the colloidal system and inaccessibility of the pure species spectra, all present common problems in the determination of experimental dissociation constants (Ka) of weak acid or base species on surfaces of colloidal particles. Chemometric methods for reduction of spectral information measured via UV-Vis spectrophotometry, such as the principal component analysis (PCA), were proposed as solution of this problem, and enable capturing the relevant protonation model parameters [1–3]. In the present poster, an improved method for Ka determination from the UV-Vis spectra, based on partial least squares regression (PLS), is proposed and compared with PCA. By means of PLS, an optimal protonation model is determined from the dependence of the experimental spectra (X) and the protonation species concentration (Y) matrices, both defined for a set of varied pH values. This is achieved through maximization of the covariance between the X- and Y-scores [4], performed within the PLS-regression routine for testing the dependency of X on trial Yi. The latter are calculated from the Henderson-Hasselbalch equation (model) for varied discrete values of Ka, i. The expected <Yi> is given by the model which results with the least predictive error, which is in the present work defined as the mean squared error (MSE) of the leave-one-out cross validation. The number of the PLS components is also determined from the global minimum of MSE, while the property of MSE that it follows a χ2 distribution, enables calculating the 95 % confidence interval (CI) of Ka. The accuracy and precision of the PLS-based method was compared with the results obtained by means of a PCA-based method [3]. For this, the analyzed X data were computed as superpositions of model spectra of the pure components in the pKa and pH ranges of 2-9 and 4-7, respectively, to which random noise in spectral intensity and a random constant baseline were added. The results of the test presented in Fig. 1 clearly indicate that the PLS-based method outperforms the PCA-based method both in accuracy as well as precision of the determined pKa value. This is particularly true if the expected pKa lies outside of the probed pH range. Figure 1. "Fitted" vs. the exact pKa for the PLS-based method (a) and the PCA-based method (b). The dashed lines represent the 95% CI. Acknowledgements: This work was supported by the European Fund for Regional Development and the Ministry of Science, Education and Sports of the Republic of Croatia under the project Research Infrastructure for Campus-based Laboratories at the University of Rijeka (grant numberRC.2.2.06-0001) [1] K. Varmuza and P. Filzmoser, Introduction to multivariate statistical analysis in chemometrics, 2009, 1-3, 1-102, Boca Raton: CRC Press, Boca Raton, FL [2] M. Kubista, R. Sjoeback, and B. Albinsson, Anal. Chem., 1993, 65 (8), 994. [3] M. Kubista, R. Sjöback, and J. Nygren, Anal. Chim. Acta, 1995, 302 (1), 121. [4] S. Wold, M. Sjöström, and L. Eriksson, Chemom. Intell. Lab. Syst., 2001, 58 (2), 109.

multivariate ; principal component ; regression ; pK, model ; spectrophotometry ; UV/VIS ; scattering

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