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Application of an evolving factor analysis-based procedure to speciation analysis in the copper(II)-polyuridylic acid system
538
Analytica Chimicp Acta, 283 (1993) 538-547 Elsevier Science Publishers B.V., Amsterdam
Application of an evolving factor analysis-based procedure to speciation analysis in the copped II) -polyuridylic acid system E. Casassas, R. Gargallo, I. Gimenez, A. Izquierdo-Ridorsa Lkpartament de Quihica Anal&a,
and R. Tauler
Uniuersitat de Barcelona, Au&a. Diagonal 64708028 Barcelona (Spain)
(Received 10th September 1992; revised manuscript received 14th December 1992)
Abstract
The acid-base. properties and the copper(II)_complexing behaviour of the polynucleotide polyuridylic acid were studied by means of potentiometric, spectrophotometric and electron spin resonance titrations in a working aqueous medium of 0.15 M ionic strength and at 37°C. Spectrophotometric data were treated with an evolving factor analysis-based procedure that allows different sets of speetrometric titrations of the same multi-equilibria system to be analysed simultaneously. A dimeric macromokcular complex species between copper ions and polyuridylic acid was detected in the system and its formation constant was evaluated. K&words: Electron spin resonance spectrometry; Potentiometry; Titrimetry; UV-Visible spectrophotometry; Copper complexes; Evolving factor analysis; Polynucleotides; Polyuridylic acid; Speciation
This work is part of a wider study concerning the interpretation of metal ions and proton interactions with nucleic acids and their constituents in aqueous solution under physiological conditions [l-3]. In this work, the acid-base properties and the copper@-complexing behaviour of the polynucleotide polyuridylic acid [polyW], where all the nitrogen bases are uracil molecules (see Scheme l), are presented. This study was carried out by means of potentiometric, spectrophotometric and electron spin resonance (ESR) titrations in a working aqueous medium of 0.15 M ionic strength and at 37°C which can be considered physiological conditions. Because the information obtained by the different tecniques is in certain respects compleCorrespondence lo: A. Izquierdo-Ridorsa, Departament de Quimica Analitica, Universitat de Barcelona, Avda. Diagonal 647, 08028 Barcelona (Spain). 0003-2670/93/$06.00
mentary, it is worth using them simultaneously in the study of complicated systems, such as that investigated here, which contains a macromolecular ligand. Complex formation by macromolecular ligands is influenced by some secondary effects [41, viz., polyfunctional effects, conformational changes and polyelectrolyte effects, which affect the stability of the species formed and vary with the degree of site occupation (complexation) and/or site deprotonation. Thus, the interpretation of experimental data using traditional least-squares curve fitting approaches, which are based on the postulation of a chemical model and on compliance with the mass action law, is difficult or even impossible for multi-equilibria systems involving macromolecular ligands. In this work, an approach which is an improvement of a previously developed SPFAC procedure [5-81 was applied to the spectrophotometric
Q 1993 - Elsevier Science Publishers B.V. All rights reserved
E. Casassas et al. /And
Chim. Acta 283 (1993) 538-547
539 EXPERIMENTAL
'H k Scheme 1. R = ribose-5’-monophosphate in polyW).
titrations. SPFAC is an evolving factor analysisbased procedure, which can be advantageously used for the study of multi-equilibria systems, in order to define the number of species present and to evaluate their concentrations, their individual spectra and their stability constants, without the requirement of postulating a chemical model and without making any use of the mass action law. Whereas in the previously described SPFAC procedure evolving factor analysis techniques were applied to the treatment of individual spectrometric titrations, in the modified SPFAC program [81 the simultaneous analysis can be performed on different sets of spectrometric titrations for the same multi equilibria system under different experimental conditions if the spectra in all the analysed titrations are measured at the same set of wavelengths. Some of the ambiguities that may appear when a single titration is analysed are removed when several spectrometric titrations under different starting conditions (different initial concentrations of the constituents) are analysed simultaneously and the individual spectra of the common species in the different spectrometric titrations are forced to be equal. In the macromolecular system studied here, the results obtained from SPFAC analysis may be a good starting point for chemical modelling and application of the traditional least-squares procedures, which cannot ensure by themselves the validity of the postulated model. The copper(B) complexation results obtained with poly(U) were compared with those obtained previously with the mononucleotide uridine-3,5’cyclic monophosphate (cyclic UMP) [3], which can be considered as a model compound as it contains the same coordinating centres as poly(U).
Reagents and solutions Nitric acid, copper(I1) oxide, sodium nitrate (Merck, analytical-reagent grade) and polyuridylic acid sodium salt (Sigma) were used without further purification. All the solutions were prepared using CO,-free deionized water. Stock solutions of copper(B) ion were standardized by iodimetric titration. Stock solutions of poly(U) were prepared form a known amount of the solid reagent and dissolution in water. The concentration of these solutions was referred to the concentration of the nucleotide uridine3’,5’cyclic monophosphate, which is the monomeric unity in the polynucleotide chain. CO,-free sodium hydroxide (Merck, analytical reagent grade) solutions were prepared by Kolthoff’s procedure 191 and standardized with potassium hydrogenphthalate. The ionic strength of the measured solutions was kept at 0.15 mol dme3 by adding, when necessary, the appropriate amount of sodium nitrate. Apparatus Visible absorption spectra at 37°C were recorded on a Beckman DU-7 spectrophotometer interfaced (RS232) to an IBM personal computer. Spectra acquisition was controlled through Beckman data capture software. ESR spectra were recorded on a Varian E-109 spectrometer in capillary glass tubes of diameter 1 mm (Wilmad, Cat. No. 800) ‘. pH measurements were performed with a Radiometer PHM-64 pH meter (with a precision of fO.l mV) and a combined Ross pH electrode (Orion 81-02). Titrant was added with a Metrohm Dosimat 655 autoburette equipped with an exchange unit of 5 cm3 (with a precision of f0.005 cm3). Sample solutions were titrated in a doublewalled vessel maintained at 37.0 f O.l”C by circulating water and stirred magnetically under a continuous flow of nitrogen.
a Belonging to the Inst. of Development and Investigation, CSIC, Barcelona, whose cooperation is acknowledged.
E. Casassaset al. /Anal. Chim.Acta 283 (1993) 538-547
540
Procedure Potentiometric titrations were carried out automatically. The potentiometric assembly was controlled by an HP 9816 microcomputer via an HP 3421 A data acquisition control unit (for details, see [lo]). Solutions for ESR and visible spectrometric studies were obtained during the potentiometric titration, with a standardized sodium hydroxide solution, of slightly acidic solutions containing different copper(B) ion concentrations and different ligand-to-metal ion concentration ratios. With the aid of a peristaltic pump the solution being titrated was introduced continuously into the flow cell in the spectrophotometer. After each titrant addition the pH of the solution was measured, the visible spectrum obtained (the absorbance was measured every 10 nm between 520 and 820 nm) and a sample of 100 ~1 withdrawn for ESR spectrum determination. For every titration, a previous calibration of the potentiometric cell was carried out by Gran’s method [ll]. In aqueous medium of 0.15 M ionic strength and at 37°C the value of the ionic product of the medium is -log K, = 13.30 f 0.03, and in the working pH range the pH dependence of the liquid junction potential is negligible. The experimental conditions of the titrations performed are given in Table 1. All the titrations can be performed up to basic pH values without the formation of any precipitate in the solutions.
Data treatment Data treatment of the experimental potentiometric data was carried out with the SUPERQUAD program [12], which uses traditional least-squares curve-fitting approaches, and is based on the postulation of a chemical model and on compliance with the mass action law. The accuracy of the results obtained is indicated by the value of the parameter SIGMA, which is the ratio of the root mean square of the weighted residuals to the estimated error under our working conditions (0.005 ml for the autoburette volume readings and 0.1 mV for the e.m.f. readings), and by the value of the statistical parameter x2, which is based on weighted residuals of e.m.f. readings [ 121. The interpretation of the experimental spectrophotometric data was carried out with the new version of the SPFAC program [8] and also, whenever possible, using the computer program SQUAD [131, which is a traditional least-squares curve-fitting approach based on the postulation of a chemical model and on compliance with the mass action law. The SPFAC program is written in FORTRAN 77 and runs either on an IBM 3090 mainframe (large sets of data) or in an IBM PC environment (for smalls sets of data). Essentially, the data treatment consists of the following tasks: (1) Building up of the data matrix D(NSOLN, NWAVE). When an individual titration is analysed, the matrix D contains the spectra at
TABLE 1 Experimental conditionsof the titrations performed Titration Potentiometric
Spectrophotometric and ESR
Titration number 1 2 3 4 5 6 7 8 9 10
l&a& (mM)
2.173 2.911 3.861 2.135 3.015 3.178 2.575 10.51 12.63 8.24
lcul,
(mM)
Ligand-to-metal ratio
2.013 2.329 2.145 1.161
1.0: 1 1.3 : 1 1S:l 2.2: 1
10.91 4.849 4.872
O.%:l 2.6 : 1 1.7 : 1
541
E. Casassas et al. /Anal. Chim. Acta 283 (1993) 538-547
NWAVE wavelengths of the NSOLN mixtures obtained at the successive titration points of the spectrometric titration. When more than one titration is analysed simultaneously, the augmented data matrix D contains the same number of columns (NWAVE), as the spectra in all the titrations are measured at the same set of wavelengths, and a number of rows (NSOLN) equal to the total number of solutions in all the titrations. Matrix D is treated in the same way whether augmented or not. (2) Factor analysis of the experimental data matrix D: calculation of the eigenvalues and eigenvectors of the matrix DDT and estimation of the number of absorbing species in the system. This number is estimated using different independent methods: (a> from the changes in magnitude of the eigenvalues and from the plot of the RSD function (residual standard deviation function) obtained using the principles of the theory of error in factor analysis as proposed by Malinowski [14-161; (b) from the plot of the SEP function (standard error of prediction function) obtained from cross-validation of the complete spectral matrix data as proposed by Wold 1171; and (c) from the abstract distribution plot ob-
tained in evolving factor analysis [18,19] (see below). (3) Evolving factor analysis (EFA). This is based on the evolution with pH of the magnitudes of the eigenvalues during the spectrometric titration. From the results obtained in the EFA, and considering the previously deduced number of species present in the system, an abstract representation of the concentration profiles is obtained. (4) From the initial estimation of the concentration profiles obtained using EFA, the generalized Beer’s law equation in matrix form is solved iteratively by least-squares (alternating leastsquares procedure) to obtain the matrices of individual spectra A and of concentration profiles C which best fit the data. The concentration profiles in matrix C should be unimodal and positive; only a certain amount (given in the input data) of departure from the unimodal condition is allowed at any instant. The total amount of absorbing material at each titration point is experimentally known and used in the iterations as a constraint. Negative values of absorbance obtained in the iterative least-squares estimation of A are set equal to zero. To these general con-
11
PK, lo.8 10
8.B
9
a.6
I
7.6
7
I 0.1
0.s
0.0
a7
degree of deprotonadon
Fig. 1. Plot of pK, versus the degree of dissociationfor poly(U). + = Titration 1;
A =
titration 2; o = titration 3.
542
straints present in both SPFAC versions, a new constraint is added in the new one: the unitary spectrum (i.e., the variation of molar absorptivity with wavelength) of any individual species is equal in any one of the different titrations. In SPFAC and SQUAD programs the goodness of the fit is measured by the standard deviation of the residuals.
RESULTS AND DISCUSSION
Potentiometric study of the H-poly(U) system The polynucleotide poly(U) presents no polyfunctional effect as it contains the same monomeric unit repeated along its structure: the nucleotide cyclic UMP. This nucleotide has only one protonation site to be taken into account under the working conditions, which is the nitrogen atom in position 3 (N-3) in the nitrogen base moiety. The first acidic group in the phosphate residue has a pK value of acid dissociation lower than 1, and hence it is always deprotonated in the working pH range. In the polynucleotide the protonation site is repeated along the molecule, conferring to poly(U) a polyelectrolytic character, which must be taken into account in the study of its acid-base properties. As deprotonation takes place, there is an increase in the negative charge on the molecule surface, which could affect the acid-base characteristics of the next dissociation site and could lead to a dependence of the dissodlldl
Fig. i. Experimental ESR spectra for the copper(polyW) system, obtained in one of the titrations performed (titration 8). pH = (A) 1.82, (B) 5.10, (C) 5.39 (D) 5.48 and (E) 5.54.
E. Casassas et al. /Anal. Chim. Acta 283 (1993) 538-547
ciation constant on the degree of site deprotonation. Actually, the plot (Fig. 1) of the pK value of acid dissociation for the N-3 site in poly(U) as a function of the degree of deprotonation indicates the absence of appreciable polyelectrolytic effects as the pK value is hardly dependent on the number of deprotonated positions. Thus, to determine with the required precision the protonation constant of the N-3 site in polyW), this macromolecular ligand can be assimilated to a group of individual monomeric units, and the numerical treatment of the experimental e.m.f. data can be performed with a traditional program for the determination of stability constants, such as the program SUPERQUAD. The value of the protonation constant for the N-3 site in the polynucleotide, obtained in aqueous solution of 0.15 M ionic strength and at 37°C is log K = 9.363 f 0.004. ESR study of the copper(poiy(U) system Figure 2 shows some of the ESR spectra obtained for one of the titrations performed. At pH < 5 no copper(B) complexation is observed as the experimental ESR spectra coincide with that of free copper(B) (Fig. 2, spectrum A). Copper@) complexation takes place between ca. pH 5 and 6, as indicated by the decrease in the intensity of the band due to free copper(B) (Fig. 2, spectra B-E). The disappearance of the band at pH 6 indicates that at this pH copper(B) is already quantitatively complexed. In the pH range of complexation there is no appearance of new bands at higher magnetic field owing to the hyperfine interaction between the unpaired electron and the complexed copper(B) nucleus, which is consistent with the formation of diamagnetic copper(B) species, that is, with the formation of dimeric species that contain two copper(B) ions close enough to each other to allow interaction between their unpaired electrons. A probable dimeric species would be that formed by two copper(B) ions each bonded to a nitrogen atom in polyW and with two hydroxo bridges between them, as the complex is formed in a pH region where the formation of the binary hydroxo complexes Cu(OH)+ and Cu,(OH)i+ [2O] must be taken into account.
E. Casassas et al./AnaL Chins. Acta 283 (1993) 538-547
Fig. 3. Plot of the proportion of complexed copper at every pH value for the copperOI)-polyW ( 0 1 and copper(cyclic Uh4P (continuous line) systems.
From the ESR signal obtained for the free copper(R) present at every point of the titration, it is possible to determine the proportion of complexed copper(R) ion at every pH value. The results obtained are presented in Fig. 3, together with those obtained when the ligand is the monomeric nucleotide cyclic UMP, the copper(H) complexation of which has been studied previously [3]. While the nucleotide cyclic UMP at pH values around 6 always yields a precipitate from the copper(R) solutions under the working conditions, which is attributed to a basic salt of copper(R), the polynucleotide poly(U1 yields much stronger complexes and copper(R) remains in solution over the whole pH range studied and for all the studied copper(R)-to-ligand ratios.
Potentiometric study of the copper(poly(U) system The experimental formation curves obtained for the titrations performed in the potentiometric study of the copper(R)-poly(U) system are shown in Fig. 4. They suggest the presence of hydroxo and polynuclear species in the system. Thus, in order to avoid additional difficulties, the study of this system was only performed up to pH values around 6.5, where complexation is already almost quantitative. The experimental e.m.f. data were treated with the SUPERQUAD program, and the best fit of the experimental data was found with the model that contains as a major species the dimeric
-log v-1 Fig. 4. Experimental formation curves for the copper( poly(U) system. n = Titration 4; o = titration 5; 0 = titration 6; l = titration 7. Continuous lines are the theoretical curves obtained with the calculated set of constants.
species already proposed from the ESR results. This species is usually denoted by its stoichiometric coefficients, 2 : 2 : - 2 for C&I) : L : proton stoichiometry, where L represents the deprotonated N-3 sites in the ligand that are bound to copper(H) ions and the negative sign indicates hydroxide ions. When the ligand-to-metal ion ratio is around 1: 1, additional hydroxo ligands enter into the
Fig. 5. Three-dimensional plot of the spectrometric data for titration 8.
544
E. Casassas et al. /Anal.
complex. Thus, a 2 : 2 : - 4 species is also detected in the system. The values obtained for the logarithm of the formation constants show a great lack of precision, probably because complexation causes conformational changes in the polymer, the extent which may depend on the ligand-to-metal ion ratio and on the concentration of the different reagents. For the 2 : 2 : - 2 species log p = 3.1 f 0.2 and for the 2:2: -4 species log p = -9.1 f 0.4. In Fig. 4 the calculated formation curves are also shown. It can be concluded that they show good agreement with the experimental data, taking into account that the studied system is very complicated as it contains a macromolecular ligand whose complexing behaviour may be greatly affected by possible conformational changes and
polyelectrolytic metal ion.
Chim. Acta 283 (1993) 538-547
effects due to the presence of the
Spectrophotometric
study of the copper
-
pob 03 system Figure 5 shows a three-dimensional plot of the experimental visible spectra obtained in a titration of a solution containing copper011 ions and poly(U). There is no variation of the absorption band due to the copper ion until a pH value of ca. 5, which is indicative of the beginning of complexation. In the pH range where complexation takes place, ca. 5-6, the absorption band moves towards lower wavelengths and there is an increase in intensity. The numerical treatment of the experimental absorption data was carried out with the SPFAC program [8]. First, each of the spectrophotomet-
SEP
2
3
1
5
Number of factora
Numbar of factors
5
Number of factors
1
2
1
.
5
Number of factors
Fig. 6. Determination of the number of components: (A) and (B) are plots of the SEP and RSD functions versus the number of factors for titration 8; (C) and (D) are plots of the SEP and RSD functions versus the number of factors for titration 9.
545
E. Casassas et al. /Anal. Chim. Acta 283 (1993) 538-547
ric titrations performed was studied individually in order to ascertain if the results obtained by the SPFAC treatment are dependent or not on the ligand-to-metal ion ratio present in the solutions. Figure 6 includes plots of SEP and RSD functions for titrations 8 and 9. These plots show the presence of only two main factors and, perhaps, of a third whose contribution is very much lower. As the instrumental random error is ca. 0.002
absorbance units, the variation in the experimental data is completely explained when only the two first main factors are considered. Figure 7 displays the results obtained in the evolving factor analysis of the two titrations mentioned before, and the abstract distribution plot resulting from the evolving factor analysis results and considering the presence of only two absorbing species in the system. The first factor, which
A
log A
2 -1
2
-3
-4
3
PH
PH Fig. 7. Evolving factor analysis plots for (A) titration 8 and (B) titration 9. Continuous lines give the abstract estimated concentration profiles of the hvo detected species. Symbols refer to the upsurging and decreasing factors in the evolving factor analysis. Each factor is numbered to the left for the backward eigenanalysis and to the right for the forward eigenanalysis.
546
E. Casassas et al. /Anal. Chim. Acta 283 (1993) 538-547
1
04
so0
5alsoo
650
7ca
750
WI 8.x vd.bel."pth ,nm,
Fig. 8. Spectra of the individual species obtained in the individual treatment of the spectrometric titrations with the SPFAC program. Solid line, titration 8; short dashed line, titration 9; long dashed line, titration 10.
is not represented in the forward evolving factor analysis, as it is present from the beginning of the titration, can be related to free copper(I1) ions. From the reverse evolving factor analysis it can be concluded that at pH > 6.5 the concentration of free copper ions is already negligible, which shows that complexation is quantitative. The second factor appears at a pH = 5 and can be attributed to the complex formed between copper@) ions and poly(U). The next step is the estimation of the concentration profiles and the spectra of the individual
species which best explain the data matrix for every titration. Figure 8 shows the individual spectra obtained in the individual analysis of each titration. It is observed that, depending on the ratio of the ligand site to copper ion concentration in’the titrated solution, the spectra of the individual species have the same shape and spectral features but a different intensity. This was observed whenever several titrations at different concentrations of the metal ion and of the macromolecule were analysed independently [21], and can be interpreted as if the intensity of the individual spectra and the concentration of the related species are exchangable to a certain extent for a similar fit of the experimental data. In order to remove this ambiguity, the different experimental data matrices of spectra obtained in the three titrations were analysed together with the improved SPFAC version. The results obtained for the unitary spectra of the two species are presented in Fig. 9. It is found that the standard deviation of the residuals between the factor analysis reduced data matrix and the calculated data matrix using the best set of species spectra and of species concentration is around 0.01 absorbance units, which falls well within the error in the experimental conditions.
mol” I cm”
“J!
Fii. 9. Comparison of SQUAD and SPFAC procedures
in the study of the copper(poly(U) system. Continuous lines refer to SQUAD results and symbols to SPFAC results obtained in the simultaneous analysis of the titrations. Numbers refer to the following species: 1 = free copper ions; 2 = 2: 2 : - 2 species. 0 = SPFAC spectrum for free copper ions; o = spectrum directly obtained from SPFAC analysis for the copper(poly(U) complex; A = spectrum of this complex if it is dimeric (its molar absorptivities being twice those given by SPFAC; see text).
E. Casassas et al. /And.
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Chitn Acta 283 (1993) 538-547
From the results obtained in the ESR study of the copper(B)-poly(U) system, the complex found in the SPFAC treatment of the spectrophotometric data could be attributed to the dimeric 2 : 2 : - 2 species. The experimental spectrophotometric data were also treated with the computer program SQUAD [13]. The value obtained for the formation constant of the 2 : 2 : - 2 species is log K = 3.0 f 0.3. Figure 9 shows the visible spectra of free copper(B) ions and of the dimeric species calculated with the SQUAD program. For the studied system the SPFAC program applies, in the alternating least-squares step, the mass balance equation for copper(B) ions, and hence the concentration of every individual species detected is given in relation to the concentration of copper(B) ions that it contains. As the dimeric complex contains two copper(B) ions per molecule, the concentration of dimeric species given by the SPFAC program is the double of that found with the SQUAD program and, therefore, for compliance with Beer’s law, the absorbances for this species evaluated with SPFAC program are approximately half those found with SQUAD program. There is a’ very close agreement between the results obtained with both programs (see Fig. 9) when the visible spectrum found with the SPFAC program is multiplied by two. Conclusions Evolving factor analysis-based techniques, such as SPFAC, are powerful tools for the study of systems involving macromolecular ligands, when difficulties are encountered with traditional least-squares fitting approaches owing to polyelectrolyte, polyfunctional or conformational effects. In the copper(B)-poly(U) system, only one complexed copper(B) species was clearly detected with the SPFAC program. Whereas in the absence of copper(B) ions poly(U) is known to have a random coil conformation, the dimeric copper(B) complex formed must lead to conformational changes in the polynucleotide, as each of the two complexed copper(B) ions is assumed to be bonded to a nitrogen atom in poly(U) and with two hydroxo bridges between them. These
conformational changes, whose relative importance may vary with the ligand-to-metal ion ratio and with the copper011 and poly&J) concentrations present in the solutions, contribute to the stability of the species found and, thus, the application of traditional least-squares procedures to this system gives results that show a great lack of precision and which do not by themselves allow the model to be validated. The results obtained with SPFAC give real proof of the validity of the model assumed. This research was supported by a CICYT grant, No. PB90-0821.
REFERENCES 1 R. Tamer, J.F. Cid and E. Casassas, J. Inorg. B&hem., 39 (1990) 277. 2 E. Casassas, A. Izquierdo-Ridorsa and R. Tamer, J. Inorg. Biochem., 39 (1990) 327. 3 E. Casassas, I. GimCnez, A. Izquierdo-Ridoma and R. Tauler, J. Inorg. B&hem., submitted for publication. 4 J. But%, Complezation in Aquatic Systems: an Analytical Approach, Honvood, Chichester, 1988. 5 R. Tamer and E. Casassas, J. Chemometr., 3 (1988) 151. 6 R. Tauler and E. Casassas, Anal. Chim. Acta, 223 (1989) 257. 7 R. Tauler, E. Casassas and A. Izquierdo-Ridorsa, Anal. Chim. Acta, 248 (1991) 447. 8 R. Tauler, A. Izquierdo-Ridorsa and E. Casassas, Chemometr. Inteli. Lab. Syst., (1992) in press. 9 I.M. Kolthoff, E.B. Sandell, E.J. Meehan and S. Bruckenstein, Quantitative Chemical Analysis, Collier-Macmillan Canada, Toronto, 1969, p. 781. 10 E. Casassas, G. Fonrodona and R. Tarrier, Polyhedron, 6 (1987) 1517. 11 G. Gran, Analyst, 77 (1952) 661. 12 P. Gans, A. Sabatini and A. Vacca, J. Chem. Sot., Dalton Trans., (1985) 1195. 13 D.J. Leggett, S.L. Kelly, L.R. Shiue, Y.T. Wu, D. Chang and KM. Radish, Talanta, 30 (1983) 579. 14 E.R. Malinowski and D.E. Howery, Factor Analysis in Chemistry, Wiley, New York, 1980. 15 E.R. Malinowski, J. Chemometr., 1 (1987133. 16 E.R. Malinowski, J. Chemometr., 3 (1988) 39. 17 S. Wold, Technometrics, 20 (1978) 397. 18 H. Gampp, M. Maeder, C.J. Meyer and A.D. Zuberbiihler, Talanta, 32 (1985) 1133. 19 H. Gampp, M. Maeder, C.J. Meyer and A.D. Zuberbiihler, Talanta, 33 (1986) 943. 20 C.W. Childs, Inorg. Chem., 9 (1970) 2465. 21 R. Tamer and E. Casassas, Chemometr. Intell. Lab Syst., 14 (1992) 305.
Analytica Chimicp Acta, 283 (1993) 538-547 Elsevier Science Publishers B.V., Amsterdam
Application of an evolving factor analysis-based procedure to speciation analysis in the copped II) -polyuridylic acid system E. Casassas, R. Gargallo, I. Gimenez, A. Izquierdo-Ridorsa Lkpartament de Quihica Anal&a,
and R. Tauler
Uniuersitat de Barcelona, Au&a. Diagonal 64708028 Barcelona (Spain)
(Received 10th September 1992; revised manuscript received 14th December 1992)
Abstract
The acid-base. properties and the copper(II)_complexing behaviour of the polynucleotide polyuridylic acid were studied by means of potentiometric, spectrophotometric and electron spin resonance titrations in a working aqueous medium of 0.15 M ionic strength and at 37°C. Spectrophotometric data were treated with an evolving factor analysis-based procedure that allows different sets of speetrometric titrations of the same multi-equilibria system to be analysed simultaneously. A dimeric macromokcular complex species between copper ions and polyuridylic acid was detected in the system and its formation constant was evaluated. K&words: Electron spin resonance spectrometry; Potentiometry; Titrimetry; UV-Visible spectrophotometry; Copper complexes; Evolving factor analysis; Polynucleotides; Polyuridylic acid; Speciation
This work is part of a wider study concerning the interpretation of metal ions and proton interactions with nucleic acids and their constituents in aqueous solution under physiological conditions [l-3]. In this work, the acid-base properties and the copper@-complexing behaviour of the polynucleotide polyuridylic acid [polyW], where all the nitrogen bases are uracil molecules (see Scheme l), are presented. This study was carried out by means of potentiometric, spectrophotometric and electron spin resonance (ESR) titrations in a working aqueous medium of 0.15 M ionic strength and at 37°C which can be considered physiological conditions. Because the information obtained by the different tecniques is in certain respects compleCorrespondence lo: A. Izquierdo-Ridorsa, Departament de Quimica Analitica, Universitat de Barcelona, Avda. Diagonal 647, 08028 Barcelona (Spain). 0003-2670/93/$06.00
mentary, it is worth using them simultaneously in the study of complicated systems, such as that investigated here, which contains a macromolecular ligand. Complex formation by macromolecular ligands is influenced by some secondary effects [41, viz., polyfunctional effects, conformational changes and polyelectrolyte effects, which affect the stability of the species formed and vary with the degree of site occupation (complexation) and/or site deprotonation. Thus, the interpretation of experimental data using traditional least-squares curve fitting approaches, which are based on the postulation of a chemical model and on compliance with the mass action law, is difficult or even impossible for multi-equilibria systems involving macromolecular ligands. In this work, an approach which is an improvement of a previously developed SPFAC procedure [5-81 was applied to the spectrophotometric
Q 1993 - Elsevier Science Publishers B.V. All rights reserved
E. Casassas et al. /And
Chim. Acta 283 (1993) 538-547
539 EXPERIMENTAL
'H k Scheme 1. R = ribose-5’-monophosphate in polyW).
titrations. SPFAC is an evolving factor analysisbased procedure, which can be advantageously used for the study of multi-equilibria systems, in order to define the number of species present and to evaluate their concentrations, their individual spectra and their stability constants, without the requirement of postulating a chemical model and without making any use of the mass action law. Whereas in the previously described SPFAC procedure evolving factor analysis techniques were applied to the treatment of individual spectrometric titrations, in the modified SPFAC program [81 the simultaneous analysis can be performed on different sets of spectrometric titrations for the same multi equilibria system under different experimental conditions if the spectra in all the analysed titrations are measured at the same set of wavelengths. Some of the ambiguities that may appear when a single titration is analysed are removed when several spectrometric titrations under different starting conditions (different initial concentrations of the constituents) are analysed simultaneously and the individual spectra of the common species in the different spectrometric titrations are forced to be equal. In the macromolecular system studied here, the results obtained from SPFAC analysis may be a good starting point for chemical modelling and application of the traditional least-squares procedures, which cannot ensure by themselves the validity of the postulated model. The copper(B) complexation results obtained with poly(U) were compared with those obtained previously with the mononucleotide uridine-3,5’cyclic monophosphate (cyclic UMP) [3], which can be considered as a model compound as it contains the same coordinating centres as poly(U).
Reagents and solutions Nitric acid, copper(I1) oxide, sodium nitrate (Merck, analytical-reagent grade) and polyuridylic acid sodium salt (Sigma) were used without further purification. All the solutions were prepared using CO,-free deionized water. Stock solutions of copper(B) ion were standardized by iodimetric titration. Stock solutions of poly(U) were prepared form a known amount of the solid reagent and dissolution in water. The concentration of these solutions was referred to the concentration of the nucleotide uridine3’,5’cyclic monophosphate, which is the monomeric unity in the polynucleotide chain. CO,-free sodium hydroxide (Merck, analytical reagent grade) solutions were prepared by Kolthoff’s procedure 191 and standardized with potassium hydrogenphthalate. The ionic strength of the measured solutions was kept at 0.15 mol dme3 by adding, when necessary, the appropriate amount of sodium nitrate. Apparatus Visible absorption spectra at 37°C were recorded on a Beckman DU-7 spectrophotometer interfaced (RS232) to an IBM personal computer. Spectra acquisition was controlled through Beckman data capture software. ESR spectra were recorded on a Varian E-109 spectrometer in capillary glass tubes of diameter 1 mm (Wilmad, Cat. No. 800) ‘. pH measurements were performed with a Radiometer PHM-64 pH meter (with a precision of fO.l mV) and a combined Ross pH electrode (Orion 81-02). Titrant was added with a Metrohm Dosimat 655 autoburette equipped with an exchange unit of 5 cm3 (with a precision of f0.005 cm3). Sample solutions were titrated in a doublewalled vessel maintained at 37.0 f O.l”C by circulating water and stirred magnetically under a continuous flow of nitrogen.
a Belonging to the Inst. of Development and Investigation, CSIC, Barcelona, whose cooperation is acknowledged.
E. Casassaset al. /Anal. Chim.Acta 283 (1993) 538-547
540
Procedure Potentiometric titrations were carried out automatically. The potentiometric assembly was controlled by an HP 9816 microcomputer via an HP 3421 A data acquisition control unit (for details, see [lo]). Solutions for ESR and visible spectrometric studies were obtained during the potentiometric titration, with a standardized sodium hydroxide solution, of slightly acidic solutions containing different copper(B) ion concentrations and different ligand-to-metal ion concentration ratios. With the aid of a peristaltic pump the solution being titrated was introduced continuously into the flow cell in the spectrophotometer. After each titrant addition the pH of the solution was measured, the visible spectrum obtained (the absorbance was measured every 10 nm between 520 and 820 nm) and a sample of 100 ~1 withdrawn for ESR spectrum determination. For every titration, a previous calibration of the potentiometric cell was carried out by Gran’s method [ll]. In aqueous medium of 0.15 M ionic strength and at 37°C the value of the ionic product of the medium is -log K, = 13.30 f 0.03, and in the working pH range the pH dependence of the liquid junction potential is negligible. The experimental conditions of the titrations performed are given in Table 1. All the titrations can be performed up to basic pH values without the formation of any precipitate in the solutions.
Data treatment Data treatment of the experimental potentiometric data was carried out with the SUPERQUAD program [12], which uses traditional least-squares curve-fitting approaches, and is based on the postulation of a chemical model and on compliance with the mass action law. The accuracy of the results obtained is indicated by the value of the parameter SIGMA, which is the ratio of the root mean square of the weighted residuals to the estimated error under our working conditions (0.005 ml for the autoburette volume readings and 0.1 mV for the e.m.f. readings), and by the value of the statistical parameter x2, which is based on weighted residuals of e.m.f. readings [ 121. The interpretation of the experimental spectrophotometric data was carried out with the new version of the SPFAC program [8] and also, whenever possible, using the computer program SQUAD [131, which is a traditional least-squares curve-fitting approach based on the postulation of a chemical model and on compliance with the mass action law. The SPFAC program is written in FORTRAN 77 and runs either on an IBM 3090 mainframe (large sets of data) or in an IBM PC environment (for smalls sets of data). Essentially, the data treatment consists of the following tasks: (1) Building up of the data matrix D(NSOLN, NWAVE). When an individual titration is analysed, the matrix D contains the spectra at
TABLE 1 Experimental conditionsof the titrations performed Titration Potentiometric
Spectrophotometric and ESR
Titration number 1 2 3 4 5 6 7 8 9 10
l&a& (mM)
2.173 2.911 3.861 2.135 3.015 3.178 2.575 10.51 12.63 8.24
lcul,
(mM)
Ligand-to-metal ratio
2.013 2.329 2.145 1.161
1.0: 1 1.3 : 1 1S:l 2.2: 1
10.91 4.849 4.872
O.%:l 2.6 : 1 1.7 : 1
541
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NWAVE wavelengths of the NSOLN mixtures obtained at the successive titration points of the spectrometric titration. When more than one titration is analysed simultaneously, the augmented data matrix D contains the same number of columns (NWAVE), as the spectra in all the titrations are measured at the same set of wavelengths, and a number of rows (NSOLN) equal to the total number of solutions in all the titrations. Matrix D is treated in the same way whether augmented or not. (2) Factor analysis of the experimental data matrix D: calculation of the eigenvalues and eigenvectors of the matrix DDT and estimation of the number of absorbing species in the system. This number is estimated using different independent methods: (a> from the changes in magnitude of the eigenvalues and from the plot of the RSD function (residual standard deviation function) obtained using the principles of the theory of error in factor analysis as proposed by Malinowski [14-161; (b) from the plot of the SEP function (standard error of prediction function) obtained from cross-validation of the complete spectral matrix data as proposed by Wold 1171; and (c) from the abstract distribution plot ob-
tained in evolving factor analysis [18,19] (see below). (3) Evolving factor analysis (EFA). This is based on the evolution with pH of the magnitudes of the eigenvalues during the spectrometric titration. From the results obtained in the EFA, and considering the previously deduced number of species present in the system, an abstract representation of the concentration profiles is obtained. (4) From the initial estimation of the concentration profiles obtained using EFA, the generalized Beer’s law equation in matrix form is solved iteratively by least-squares (alternating leastsquares procedure) to obtain the matrices of individual spectra A and of concentration profiles C which best fit the data. The concentration profiles in matrix C should be unimodal and positive; only a certain amount (given in the input data) of departure from the unimodal condition is allowed at any instant. The total amount of absorbing material at each titration point is experimentally known and used in the iterations as a constraint. Negative values of absorbance obtained in the iterative least-squares estimation of A are set equal to zero. To these general con-
11
PK, lo.8 10
8.B
9
a.6
I
7.6
7
I 0.1
0.s
0.0
a7
degree of deprotonadon
Fig. 1. Plot of pK, versus the degree of dissociationfor poly(U). + = Titration 1;
A =
titration 2; o = titration 3.
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straints present in both SPFAC versions, a new constraint is added in the new one: the unitary spectrum (i.e., the variation of molar absorptivity with wavelength) of any individual species is equal in any one of the different titrations. In SPFAC and SQUAD programs the goodness of the fit is measured by the standard deviation of the residuals.
RESULTS AND DISCUSSION
Potentiometric study of the H-poly(U) system The polynucleotide poly(U) presents no polyfunctional effect as it contains the same monomeric unit repeated along its structure: the nucleotide cyclic UMP. This nucleotide has only one protonation site to be taken into account under the working conditions, which is the nitrogen atom in position 3 (N-3) in the nitrogen base moiety. The first acidic group in the phosphate residue has a pK value of acid dissociation lower than 1, and hence it is always deprotonated in the working pH range. In the polynucleotide the protonation site is repeated along the molecule, conferring to poly(U) a polyelectrolytic character, which must be taken into account in the study of its acid-base properties. As deprotonation takes place, there is an increase in the negative charge on the molecule surface, which could affect the acid-base characteristics of the next dissociation site and could lead to a dependence of the dissodlldl
Fig. i. Experimental ESR spectra for the copper(polyW) system, obtained in one of the titrations performed (titration 8). pH = (A) 1.82, (B) 5.10, (C) 5.39 (D) 5.48 and (E) 5.54.
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ciation constant on the degree of site deprotonation. Actually, the plot (Fig. 1) of the pK value of acid dissociation for the N-3 site in poly(U) as a function of the degree of deprotonation indicates the absence of appreciable polyelectrolytic effects as the pK value is hardly dependent on the number of deprotonated positions. Thus, to determine with the required precision the protonation constant of the N-3 site in polyW), this macromolecular ligand can be assimilated to a group of individual monomeric units, and the numerical treatment of the experimental e.m.f. data can be performed with a traditional program for the determination of stability constants, such as the program SUPERQUAD. The value of the protonation constant for the N-3 site in the polynucleotide, obtained in aqueous solution of 0.15 M ionic strength and at 37°C is log K = 9.363 f 0.004. ESR study of the copper(poiy(U) system Figure 2 shows some of the ESR spectra obtained for one of the titrations performed. At pH < 5 no copper(B) complexation is observed as the experimental ESR spectra coincide with that of free copper(B) (Fig. 2, spectrum A). Copper@) complexation takes place between ca. pH 5 and 6, as indicated by the decrease in the intensity of the band due to free copper(B) (Fig. 2, spectra B-E). The disappearance of the band at pH 6 indicates that at this pH copper(B) is already quantitatively complexed. In the pH range of complexation there is no appearance of new bands at higher magnetic field owing to the hyperfine interaction between the unpaired electron and the complexed copper(B) nucleus, which is consistent with the formation of diamagnetic copper(B) species, that is, with the formation of dimeric species that contain two copper(B) ions close enough to each other to allow interaction between their unpaired electrons. A probable dimeric species would be that formed by two copper(B) ions each bonded to a nitrogen atom in polyW and with two hydroxo bridges between them, as the complex is formed in a pH region where the formation of the binary hydroxo complexes Cu(OH)+ and Cu,(OH)i+ [2O] must be taken into account.
E. Casassas et al./AnaL Chins. Acta 283 (1993) 538-547
Fig. 3. Plot of the proportion of complexed copper at every pH value for the copperOI)-polyW ( 0 1 and copper(cyclic Uh4P (continuous line) systems.
From the ESR signal obtained for the free copper(R) present at every point of the titration, it is possible to determine the proportion of complexed copper(R) ion at every pH value. The results obtained are presented in Fig. 3, together with those obtained when the ligand is the monomeric nucleotide cyclic UMP, the copper(H) complexation of which has been studied previously [3]. While the nucleotide cyclic UMP at pH values around 6 always yields a precipitate from the copper(R) solutions under the working conditions, which is attributed to a basic salt of copper(R), the polynucleotide poly(U1 yields much stronger complexes and copper(R) remains in solution over the whole pH range studied and for all the studied copper(R)-to-ligand ratios.
Potentiometric study of the copper(poly(U) system The experimental formation curves obtained for the titrations performed in the potentiometric study of the copper(R)-poly(U) system are shown in Fig. 4. They suggest the presence of hydroxo and polynuclear species in the system. Thus, in order to avoid additional difficulties, the study of this system was only performed up to pH values around 6.5, where complexation is already almost quantitative. The experimental e.m.f. data were treated with the SUPERQUAD program, and the best fit of the experimental data was found with the model that contains as a major species the dimeric
-log v-1 Fig. 4. Experimental formation curves for the copper( poly(U) system. n = Titration 4; o = titration 5; 0 = titration 6; l = titration 7. Continuous lines are the theoretical curves obtained with the calculated set of constants.
species already proposed from the ESR results. This species is usually denoted by its stoichiometric coefficients, 2 : 2 : - 2 for C&I) : L : proton stoichiometry, where L represents the deprotonated N-3 sites in the ligand that are bound to copper(H) ions and the negative sign indicates hydroxide ions. When the ligand-to-metal ion ratio is around 1: 1, additional hydroxo ligands enter into the
Fig. 5. Three-dimensional plot of the spectrometric data for titration 8.
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E. Casassas et al. /Anal.
complex. Thus, a 2 : 2 : - 4 species is also detected in the system. The values obtained for the logarithm of the formation constants show a great lack of precision, probably because complexation causes conformational changes in the polymer, the extent which may depend on the ligand-to-metal ion ratio and on the concentration of the different reagents. For the 2 : 2 : - 2 species log p = 3.1 f 0.2 and for the 2:2: -4 species log p = -9.1 f 0.4. In Fig. 4 the calculated formation curves are also shown. It can be concluded that they show good agreement with the experimental data, taking into account that the studied system is very complicated as it contains a macromolecular ligand whose complexing behaviour may be greatly affected by possible conformational changes and
polyelectrolytic metal ion.
Chim. Acta 283 (1993) 538-547
effects due to the presence of the
Spectrophotometric
study of the copper
-
pob 03 system Figure 5 shows a three-dimensional plot of the experimental visible spectra obtained in a titration of a solution containing copper011 ions and poly(U). There is no variation of the absorption band due to the copper ion until a pH value of ca. 5, which is indicative of the beginning of complexation. In the pH range where complexation takes place, ca. 5-6, the absorption band moves towards lower wavelengths and there is an increase in intensity. The numerical treatment of the experimental absorption data was carried out with the SPFAC program [8]. First, each of the spectrophotomet-
SEP
2
3
1
5
Number of factora
Numbar of factors
5
Number of factors
1
2
1
.
5
Number of factors
Fig. 6. Determination of the number of components: (A) and (B) are plots of the SEP and RSD functions versus the number of factors for titration 8; (C) and (D) are plots of the SEP and RSD functions versus the number of factors for titration 9.
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ric titrations performed was studied individually in order to ascertain if the results obtained by the SPFAC treatment are dependent or not on the ligand-to-metal ion ratio present in the solutions. Figure 6 includes plots of SEP and RSD functions for titrations 8 and 9. These plots show the presence of only two main factors and, perhaps, of a third whose contribution is very much lower. As the instrumental random error is ca. 0.002
absorbance units, the variation in the experimental data is completely explained when only the two first main factors are considered. Figure 7 displays the results obtained in the evolving factor analysis of the two titrations mentioned before, and the abstract distribution plot resulting from the evolving factor analysis results and considering the presence of only two absorbing species in the system. The first factor, which
A
log A
2 -1
2
-3
-4
3
PH
PH Fig. 7. Evolving factor analysis plots for (A) titration 8 and (B) titration 9. Continuous lines give the abstract estimated concentration profiles of the hvo detected species. Symbols refer to the upsurging and decreasing factors in the evolving factor analysis. Each factor is numbered to the left for the backward eigenanalysis and to the right for the forward eigenanalysis.
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1
04
so0
5alsoo
650
7ca
750
WI 8.x vd.bel."pth ,nm,
Fig. 8. Spectra of the individual species obtained in the individual treatment of the spectrometric titrations with the SPFAC program. Solid line, titration 8; short dashed line, titration 9; long dashed line, titration 10.
is not represented in the forward evolving factor analysis, as it is present from the beginning of the titration, can be related to free copper(I1) ions. From the reverse evolving factor analysis it can be concluded that at pH > 6.5 the concentration of free copper ions is already negligible, which shows that complexation is quantitative. The second factor appears at a pH = 5 and can be attributed to the complex formed between copper@) ions and poly(U). The next step is the estimation of the concentration profiles and the spectra of the individual
species which best explain the data matrix for every titration. Figure 8 shows the individual spectra obtained in the individual analysis of each titration. It is observed that, depending on the ratio of the ligand site to copper ion concentration in’the titrated solution, the spectra of the individual species have the same shape and spectral features but a different intensity. This was observed whenever several titrations at different concentrations of the metal ion and of the macromolecule were analysed independently [21], and can be interpreted as if the intensity of the individual spectra and the concentration of the related species are exchangable to a certain extent for a similar fit of the experimental data. In order to remove this ambiguity, the different experimental data matrices of spectra obtained in the three titrations were analysed together with the improved SPFAC version. The results obtained for the unitary spectra of the two species are presented in Fig. 9. It is found that the standard deviation of the residuals between the factor analysis reduced data matrix and the calculated data matrix using the best set of species spectra and of species concentration is around 0.01 absorbance units, which falls well within the error in the experimental conditions.
mol” I cm”
“J!
Fii. 9. Comparison of SQUAD and SPFAC procedures
in the study of the copper(poly(U) system. Continuous lines refer to SQUAD results and symbols to SPFAC results obtained in the simultaneous analysis of the titrations. Numbers refer to the following species: 1 = free copper ions; 2 = 2: 2 : - 2 species. 0 = SPFAC spectrum for free copper ions; o = spectrum directly obtained from SPFAC analysis for the copper(poly(U) complex; A = spectrum of this complex if it is dimeric (its molar absorptivities being twice those given by SPFAC; see text).
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From the results obtained in the ESR study of the copper(B)-poly(U) system, the complex found in the SPFAC treatment of the spectrophotometric data could be attributed to the dimeric 2 : 2 : - 2 species. The experimental spectrophotometric data were also treated with the computer program SQUAD [13]. The value obtained for the formation constant of the 2 : 2 : - 2 species is log K = 3.0 f 0.3. Figure 9 shows the visible spectra of free copper(B) ions and of the dimeric species calculated with the SQUAD program. For the studied system the SPFAC program applies, in the alternating least-squares step, the mass balance equation for copper(B) ions, and hence the concentration of every individual species detected is given in relation to the concentration of copper(B) ions that it contains. As the dimeric complex contains two copper(B) ions per molecule, the concentration of dimeric species given by the SPFAC program is the double of that found with the SQUAD program and, therefore, for compliance with Beer’s law, the absorbances for this species evaluated with SPFAC program are approximately half those found with SQUAD program. There is a’ very close agreement between the results obtained with both programs (see Fig. 9) when the visible spectrum found with the SPFAC program is multiplied by two. Conclusions Evolving factor analysis-based techniques, such as SPFAC, are powerful tools for the study of systems involving macromolecular ligands, when difficulties are encountered with traditional least-squares fitting approaches owing to polyelectrolyte, polyfunctional or conformational effects. In the copper(B)-poly(U) system, only one complexed copper(B) species was clearly detected with the SPFAC program. Whereas in the absence of copper(B) ions poly(U) is known to have a random coil conformation, the dimeric copper(B) complex formed must lead to conformational changes in the polynucleotide, as each of the two complexed copper(B) ions is assumed to be bonded to a nitrogen atom in poly(U) and with two hydroxo bridges between them. These
conformational changes, whose relative importance may vary with the ligand-to-metal ion ratio and with the copper011 and poly&J) concentrations present in the solutions, contribute to the stability of the species found and, thus, the application of traditional least-squares procedures to this system gives results that show a great lack of precision and which do not by themselves allow the model to be validated. The results obtained with SPFAC give real proof of the validity of the model assumed. This research was supported by a CICYT grant, No. PB90-0821.
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