Anal. Chem. 1999, 71, 4629-4636
Multivariate Curve Resolution of Cyclic Voltammetric Data: Application to the Study of the Cadmium-Binding Properties of Glutathione M. S. Dı´az-Cruz, J. Mendieta, R. Tauler, and M. Esteban*
Departament de Quı´mica Analı´tica, Facultat de Quı´mica, Universitat de Barcelona, Av. Diagonal 647, 08028-Barcelona, Spain
Linear sweep voltammetry (LSV) and cyclic voltammetry (CV) are considered the most effective and versatile electroanalytical techniques available for the study of redox systems.1 Although their mathematical treatment is not easy, both techniques are based on well-established theoretical foundations, and diagnostic criteria are available2 for different reaction schemes. Moreover, simulators for CV have been developed.3 One drawback of LSV and CV is the poor resolution of overlapping signals. LSV and CV have been widely used in the study of a variety of electrode reaction mechanisms of (bio)inorganic complexes. They have also been used, although not so extensively, in complexation equilibrium research, including, in some cases, the determination of stability constants. For well-characterized electrochemical processes, the relationship between the peak potentials (Ep) obtained from LSV or CV and the half-wave potentials (E1/2) from direct current polarography (DCP) is well-known. This suggests that LSV and CV could be used for the identification of the model of complexation and the determination of formation
constants of labile successive complexes through the Lingane or DeFord-Hume methods.4 This approach has been applied to a variety of systems, normally using graphical methods based on Leden functions. Secondary effects such as the influence of low ligand concentration on the shapes and potentials of LSV and CV signals have been addressed.5 Both LSV and CV are also used in the determination of complex stoichiometry through the (linear) dependence of the peak current (Ip) on concentration of the electroactive substance.6 More sophisticated treatments have also been applied. Thus, for instance, Barnard et al.7 used a transformation based on the classical semi-integral of the current8 for the calculation of E1/2, and those values have been used, through Lingane or DeFordHume equations, for the determination of the formation constants of Cd(II) with glycine, alanine, valine, and aspartic acid. All these cases are representative of the use of LSV and CV; only the two characteristic single parameters (Ep , Ip) of the recorded signals were used. This approach, which is called hard modeling, is well-established in electroanalytical chemistry. In addition to this traditional approach, the whole set of multivariate experimental data obtained using several electroanalytical techniques can be analyzed by factor analysis (FA).9 In this case, all the recorded experimental data points, of any single voltammogram in a series of experiments, are simultaneously analyzed without the a priori postulation of a particular chemical model. In this approach, the choice of the model is based on the comparison between the experimental and the reproduced data obtained with a reduced number of components estimated by the same method. This approach is known as soft modeling because it is based only on weak assumptions about the linearity of the signal. Isolation of sources of variation in one or more data matrix(es) is achieved using linear matrix algebra. Brown and Bear Jr.10 have critically reviewed the use of chemometric techniques in electrochemistry. They conclude that ‘the portion of papers in electroanalytical chemistry reporting the use of chemometrics
* Corresponding author. Tel: 34-93-4021277. Fax: 34-93-4021233. Email:
[email protected]. (1) Kissinger, P. T.; Heineman, W. R., Eds. Laboratory Techniques in Electroanalytical Chemistry, 2nd ed.; Marcel Dekker Inc.: New York, 1996. (2) Brown, E. R.; Large, R. F. Cyclic voltammetry, AC polarography and related techniques. In Physical Methods of Chemistry Part IIA Electrochemical Methods; Weissberger, A.; Rossiter, B. W., Eds.; Wiley-Interscience: New York, 1971; pp 423-530. (3) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A600A.
(4) Killa, H. M. J. Chem. Soc., Faraday Trans. 1 1985, 81, 2659-2666. (5) Killa, H. M.; Philp R. H., Jr. J. Electroanal. Chem. 1984, 175, 223-228. (6) Piszcek, L.; Ignatowicz, A.; Kielbasa, J.J. Chem. Educ., 1988, 65, 171-173. (7) Barnard, G. M.; Boddington, T.; Gregor, J. E.;. Petit L.; Taylor, D. N. Talanta, 1990, 37, 219-228. (8) Rieger, P. H. Electrochemistry, 2nd ed.; Chapman & Hall: New York, 1994; p 192. (9) Malinowski, E.R. Factor Analysis in Chemistry, 2nd ed.; Wiley: New York, 1991. (10) Brown, S. D.; Bear, R. S., Jr. Crit. Rev. Anal. Chem. 1993, 24, 99-131.
Multivariate curve resolution is applied to cyclic voltammetry (CV) data obtained in the study of Cd(II) complexation by glutathione (GSH). The relatively poor resolution of CV hinders the direct interpretation of raw data. The use of CV is improved by the combination of several chemometric techniques based on factor analysis: singularvalue decomposition, evolving factor analysis, and multivariate curve resolution with constrained alternating least squares optimization including a new peak-shape constraint. This multivariate analysis data treatment simultaneously reveals the formation of Cd(GSH)2 and Cd2(GSH)2 complexes, through the calculated concentration profiles, and allows the assignment of numerically obtained pure individual CV signals for the different Cd(II) ions present in solution (free and bound) and involved in the electrochemical process.
10.1021/ac990467w CCC: $18.00 Published on Web 09/14/1999
© 1999 American Chemical Society
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appears to be lower than that observed in analytical chemistry as a whole’ and that ‘much progress has been made in applying chemometrics to electroanalytical problems, but there remains a tremendous potential for advancement’. Because both CV and LSV are highly versatile but poorly resolute techniques with relatively high detection limits, uses of chemometric techniques have been mainly applied to overcome these limitations. Thus, the improved resolution afforded by semidifferentiation allowed the detection of two redox couples as well as a good estimate of their formal potential values. The study of iron alkenyl compounds in dichloromethane illustrates this case.11 Brown and co-workers12,13 demonstrated the improvement in resolution made possible by semidifferentiation in LSV for both reversible and irreversible systems. Data from synthetic mixtures of Cd, Pb, and In were totally resolved with peak separations as small as 25 mV, while real systems were deconvoluted with separations as small as 40 mV. Brown and Brown14 demonstrated the use of the Kalman filter for multicomponent analysis of LSV. Besides separating overlapped peaks, the method also filters the noise from the signal and can be used to separate the capacitivecurrent component from the faradaic-current component. The method was validated further by using the Cd/In and Cd/In/Pb systems, which show peak separations of 40-200 mV. Brown et al.15 were the first to couple a simulation for LSV to an extended Kalman filter to perform the optimization recursively. The authors used the method to estimate the standard rate constant and charge-transfer coefficient for simple heterogeneous electrontransfer reactions. Later, the extended Kalman filter was used to estimate by CV the E°′ values for the reversible EE mechanism.16 Rusling and Connors17 applied nonlinear regression analysis to study pseudo-first-order rate constants for electrocatalytic reactions using LSV. Previous studies of the application of FA to LSV and CV are rare.10 Kankare et al.18 studied the spectroelectrochemical data produced from CV of poly(3-methylthiophene) in organic solvent. The experimental data analyzed were the spectra recorded during the anodic sweep of the CV measurement. With the aid of FA, the authors identified transient species produced during the CV run. Then, CV was used as the exciting signal, but the data analyzed were spectroscopic. In addition, the application of FA for determining the number of species in solution for the case of polarographic data was studied by Baumgartner et al.19 They used calculated data sets for the Cd-Cl, Bi-Cl and Cd-SCN systems, and experimental data sets, for Cd-Cl and Cu-morpholine systems, obtained by differential pulse polarography (DPP) and sampled DCP. (11) Philp, R. H. Jr.; Reger, D. L.; Bond, A. M. Organometallics 1989, 8, 17141718. (12) Toman, J. J.; Brown, S. D. Anal. Chem. 1981, 53, 1497-1504. (13) Caster, D. M.; Toman, J. J.; Brown, S. D. Anal. Chem. 1983, 55, 21432147. (14) Brown, T. F.; Brown, S. D. Anal. Chem. 1981, 53, 1410-1417. (15) Brown, T. F; Caster, D. M.; Brown, S. D. Anal. Chem. 1984, 56, 12141221. (16) Lavagnini, Y.; Pastore, P.; Magno, F. Anal. Chim. Acta 1989, 223, 193204. (17) Rusling, J. F.; Connors, T. F. Anal. Chem. 1983, 55, 776-781. (18) Kankare, J.; Lukkari, J.; Pajunen, T.; Ahonen, J.; Visy, C. J. Electroanal. Chem. 1990, 294, 59-72. (19) Baumgartner, E.; Gettar, R. T.; Mingorance, F. D.; Magallanes, J. F. Talanta 1989, 36, 1111-1115.
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To the best of our knowledge, multivariate factor analysis techniques have not yet been applied to the study of electrochemical systems with species which are interacting with each other, such as metal complexation equilibria systems, to obtain both concentration profiles and unitary voltammograms. In previous papers from this laboratory, soft modeling was applied to the electroanalytical study of metal ion interactions with (i) macromolecular ligands, such as polycarboxylates, yielding slow mobile complexes,20 (ii) cysteine-containing peptides yielding very strong complexes with heavy metals,21 (iii) monomeric weak complexing agents, such as carboxylates, yielding consecutive labile complexes with low formation constants,22 and (iv) strong complexing ligands, such as nitrilotriacetic acid (NTA), which yield 1:1 metal complexes showing either labile or inert characteristics depending on the different time window of the technique used.23 Most of these studies were performed by DPP, because of its high resolution, although differential pulse anodic stripping voltammetry and normal and reverse pulse polarographic techniques were also used. In all cases, Multivariate curve resolution with alternating least squares (MCR-ALS) was used. The method was originally proposed and applied to the analysis of spectrometric data.24,25 Recently the MCR-ALS method was adapted for use with voltammetric data. In particular, during the ALS optimization, the shape of the resolved voltammetric profiles is optionally constrained to have the signal shape expected for certain electrochemical techniques and processes.21 This is achieved by the implementation of a parametric equation during the ALS optimization (see Data Treatment section). The goal of these studies is the development of soft-modeling methods complementary to the classical hard-modeling ones, especially for those involved cases with highly overlapping electrochemical signals. A general conclusion is that MCR-ALS yields reliable results where inert strong metal complexes are formed, with low dissociation constants.21,23 In contrast, FA limitations and ambiguities in the application of MCR-ALS to successive labile weak complexes should be taken into account.22 In this paper, MCR-ALS is extended to the study of highly complex electrochemical signals, such as current data matrixes obtained by CV. The development of soft-modeling approaches in addition to simulators for CV responses could be interesting for the understanding of involved experimental signals. The Cd(II)-glutathione system has been chosen because of the previous knowledge attained by a variety of techniques. The reduced glutathione (γ-L-glutamyl-L-cysteinylglycine, GSH) is widely present in living systems, where it has key physiological roles. Because of the affinity of the thiol group for heavy metals, their complexation by GSH is important in toxicology.26 This is (20) Dı´az-Cruz, J. M.; Tauler, R.; Grabaric, B. S.; Esteban, M.; Casassas, E. J. Electroanal. Chem. 1995, 393, 7-16. (21) Dı´az-Cruz, M. S.; Mendieta, J.; Tauler, R.; Esteban, M. J. Inorg. Biochem. 1997, 66, 29-36. (22) Grabaric, B. S.; Grabaric, Z.; Tauler, R.; Esteban, M.; Casassas, E. Anal. Chim. Acta 1997, 341, 105-120. (23) Torres, M.; Dı´az-Cruz, J. M.; Arin ˜o, C.; Grabaric, B. S.; Tauler, R.; Esteban, M. Anal. Chim. Acta 1998, 371, 23-37. (24) Tauler, R.; Casassas, E.; Izquierdo-Ridorsa, A. Anal. Chim. Acta 1991, 248, 447-458. (25) Tauler, R.; Smilde, A. K.; Kowalski, B. R. J. Chemom. 1995, 9, 31-58. (26) Dolphin, D.; Avramovic, O.; Poulson, R., Eds. Glutathione. Chemical, Biochemical, and Medical Aspects, Part A; John Wiley & Sons: New York, 1989; pp 147-186.
the case, for instance, for Cd2+-GSH complexes in red blood cells.27 Moreover, GSH is of interest as a model system for the binding of metal ions by larger thiol-containing peptides and proteins. GSH presents eight potential binding sites, but because they cannot be simultaneously coordinated to a single metal ion, the coordination chemistry of GSH is characterized by the formation of protonated and polynuclear complexes.26 Coordination chemistry of Cd2+ and GSH has been extensively studied, mainly by potentiometry,28,29 proton NMR,30,31 and 13C NMR.32 In potentiometric studies, the species distribution diagrams in a wide pH range were obtained and the stability constants determined. However, controversy has arisen about some of the postulated species.28,29 The behavior of GSH was studied by DCP,33 and the complexation of GSH by Zn2+ and Cd2+ was studied by DPP in Tris buffer at pH 9.1.34 Through the titration of Cd2+ with GSH it was observed that equimolar concentrations of GSH were not sufficient for the completion of the reaction, and the reaction only seemed to be terminated at 1:2 Cd2+/GSH molar ratio, suggesting the formation of the 1:2 Cd2+/GSH complex without formation of a stable 1:1 intermediate. From titrations of GSH with Cd2+, the formation of the less stable 1:1 complex was suggested. However, the complexity of the polarographic responses hindered the measurement of the peaks and further interpretation. In contrast, the results obtained by DPP and analyzed by MCR-ALS, together with structural data from the literature, allowed us to propose the formation of the Cd(GSH)2 and Cd2(GSH)2 complexes.21 Although the use of Hg electrodes is now less popular and Hg may introduce additional complications into the measurements (anodic processes, adsorption), modern Hg electrode stands permit greater reproducibility than solid electrodes. EXPERIMENTAL SECTION Chemicals and Instrumentation. Reduced glutathione (GSH) (>99% iodometric purity) and cadmium nitrate (analytical-grade) were purchased from Merck. All other chemicals were of analytical-grade. Ultrapure water from a Milli-Q plus 185 system was used. CV measurements were carried out with an Autolab System (EcoChemie, The Netherlands) attached to a Metrohm 663 VA Stand (Metrohm, Switzerland) and a personal computer using a GPES3 software package (EcoChemie). The system was also connected to a Metrohm 665 Dosimat for the addition of the standard Cd2+solution. In all experiments, the working, reference, and auxiliary electrodes were the Hanging Mercury Drop Electrode (HMDE), with a drop area of 0.40 mm2, Ag/AgCl, KCl (3 M), and glassy carbon, respectively. A scan rate of 200 mV s-1 was used. Measurements were performed at thermostated room temperature of ca. 22 °C in a glass cell. Purified nitrogen was used for deaeration. Manual additions of reagents were made with a Socorex Swiss Micropipet. (27) Rabenstein, D. L.; Isab, A. A.; Kadima, W.; Mohanakrishnan, P. Biochim. Biophys. Acta 1983, 762, 531-541. (28) Perrin, D. D.; Watt, A. E. Biochim. Biophys. Acta 1971, 230, 96-104. (29) Corrie, A. M.; Walker, M. D.; Williams, D. R. J. Chem. Soc., Dalton Trans. 1976, 1012-1015. (30) Rabenstein, D. L. J. Am. Chem. Soc. 1973, 95, 2797-2803. (31) Kadima, W.; Rabenstein, D. L. J. Inorg. Biochem. 1990, 38, 277-288. (32) Fuhr, B. J.; Rabenstein, D. L. J. Am. Chem. Soc. 1990, 95, 6944-6950. (33) Stricks, W.; Kolthoff, I. M. J. Am. Chem. Soc. 1952, 74, 4646-4653. (34) Wagner-Roos, L.; Zahn, H.; Se´quaris, J. M.; Valenta, P. Toxicol. Environ. Chem. 1989, 22, 77-90.
Procedures. Ten milliliters of 0.13 mol L-1 borate buffer at pH 7.0 or 8.5 is placed into the voltammetric cell and deareated with pure nitrogen for 20 min, and a cyclic voltammogram is recorded. An aliquot of the standard GSH solution (oxygen-free, fresh, and containing the same borate buffer solution) is added, with a micropipet, to the cell. After deareating for 1 min, with mechanical stirring, a new CV curve is recorded. Then, aliquots of a standard Cd2+ solution are automatically added, through the Dosimat, to the cell, to change the Cd2+ to GSH concentration ratio, and the respective CV curves are recorded. All these solutions are deaerated, after the Cd2+ addition, for 1 min. During the measurements, nitrogen is passed over the surface of the solutions. DATA TREATMENT Experiments are carefully planned in order to fulfill the necessary conditions using FA. Experimental data obtained from various voltammetric runs at different Cd/GSH concentration ratios are equally spaced in the potential scale, i.e., voltammograms are recorded with current measured at equally spaced identical potentials. In all cases the background current (measured for supporting electrolyte) is subtracted from the currents obtained in the presence of the electroactive substances. A point-by-point subtraction of the background current from the total current with analyte is applied. Experimental voltammograms recorded at different Cd/GSH ratios are carefully smoothed by Fast Fourier Transform Filtering (FFTF), through the FFTF option in the Table Curve 2D software.35 After carefully checking several smoothing levels, 20% has been chosen to avoid distortion of the original data and introduction of artifacts. This zeroes the upper 3/4 of the frequency channels. For each experiment, the individual voltammograms are arranged in a data matrix of currents I (nR, nE), with as many nR rows as number of recorded voltammograms at each Cd/GSH ratio and as many nE columns as potentials scanned during the current measurements. In the case of a CV experiment, at each potential two currents are measured, one in the forward run and the other in the backward run, thus, giving a data matrix I with dimensions (nR, 2× nE). This data matrix I consisted of two data subsets: the first corresponding to the forward run Iforw(nR, nE) and the second to the backward run Iback(nR, nE). Therefore, for CV the whole data matrix is a row-wise augmented data matrix I ) [Iforw , Iback]. If negative currents are obtained in the backward scan (as is the case for the present data set), the backward signal is unfolded and inverted at the switching potential (see conversion from Figure 1 to Figure 4). Thus, both scans have the same sign. After that, smoothing and background correction is applied. In either case, LSV or CV, the I matrix is mathematically decomposed into the product of two factor matrices
I ) C VT + X
(1)
where matrix C(nR, N) is the concentration matrix describing the evolution of the N chemical components during the experiment, matrix VT(N, nE) is the voltammetric matrix describing the pure individual voltammetric responses of these components, and matrix X(nR, nE) is the error or residual data matrix giving the (35) Table Curve 2D User’s Manual; Jandel Scientific: San Rafael, CA, 1994.
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data variation not explained by the proposed N contributions. Equation 1 assumes a linear model similar to that usually assumed in spectrochemical analysis.24,25 For the CV signals, VT matrix is the row-wise augmented matrix consisting of two subsets, one corresponding to the forward scan VTforw and the other corresponding to the backward run VTback, i.e., VT)[VTforw, VTback]. Therefore, in the CV experiments, the dimensions of the VT matrix are (nR, 2xnE). Equation 1 assumes that data matrix I is bilinear, i.e., that the electrochemical signal can be decomposed into the sum of individual contributions, each described by a concentration profile in matrix C and by a pure voltammogram in matrix VT. This assumption is only strictly valid for electrochemically inert systems.20,21 Matrices C and VT in eq 1 are the keys for the interpretation of the complexation model and for the interpretation of the electrochemical signals. The number of components or contributions to be considered in the mathematical decomposition of eq 1 can be initially estimated by singular value decomposition (SVD) analysis.9 In the present work, a visual inspection of the magnitude of the different eigenvalues or singular values provided a good estimation of the number of significant components. Once a number of components is being selected, the data lack of fit (lof) may be calculated for this number of components as
x
∑(d
lof )
ij
-k d ij )2
i,j
∑d
(2) 2 ij
i,j
where dij are the experimental values and k dij are the corresponding calculated values using the SVD decomposition. Equation 1 is solved iteratively using an Alternating Least Squares (ALS) procedure based on the two following matrix equations
C ) I (VT)+
(3)
VT ) C+ I
(4)
and
where (VT)+ and C+ are the pseudo-inverse matrixes of VT and C,25 respectively. Initial estimates are needed to start the ALS procedure described by these two equations. Initial estimates of VT can be obtained by evolving factor analysis (EFA)36 applied to the transposed data matrix obtained in the LSV experiments IT. Since the individual voltammograms of the components are expected to have an evolving peak shape, for which EFA is suitable, starting the iterative procedure with initial estimates of pure voltammograms reaches faster and easier ALS optimizations than with initial estimates of concentration profiles. CV whole signals are analyzed when the forward LSV scan had been studied. Therefore, for the ALS analysis of CV data, the matrix C obtained in the resolution of the LSV scan is assumed to be a good initial estimate of the concentration matrix C. (36) Gampp, H.; Maeder, M.; Meyer, Ch.; Zuberbuhler, A. D. Talanta 1985, 32, 1133-1139.
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At each iterative cycle, the solutions of eqs 3 and 4 were further constrained to be nonnegative and unimodal.37 In the present work, the MCR-ALS method used in previous studies 20-22 was extended, with an additional constraint of taking into account the expected peak-shaped LSV and CV signals, the main features of which depend on the characteristics of the electrode process. After a preliminary study in which a set of possible peak equations were tested to fit the LSV response of a Cd2+ solution, the logistic power peak equation was chosen.35 This equation yields, on one hand, a good fit of the experimental LSV voltammograms and, on the other, a set of parameters easily related with the morphological features of the peaks. The parametric form of this equation is given by the expression:
(
(
y ) a 1 + exp -
))
x + c ln(d) - b c
-d-1
(
exp -
d-d(d + 1)d+1 ×
)
x + c ln(d) - b (5) c
where a corresponds to peak amplitude and b corresponds to the peak potential value at the peak maximum. Parameters c and d are related with the width at half peak and the degree of asymmetry of the peak, respectively. During the iterative optimization, the resolved pure individual signals in VT estimated at every ALS iterative cycle are fitted to eq 5. The optimal values of a, b, c, and d are found by application of Marquardt’s nonlinear leastsquares method,38 implemented, like the rest of the procedure, through MATLAB high-performance numeric computation and visualization software.39 Initial estimates of these parameters are obtained from the current resolved ALS signals (peak position, peak height, width at half peak height, and asymmetry degree). In the case of CV signals, eq 5 takes into account that every component for a diffusion-controlled reversible process has two peaks, one peak in the forward scan and the other peak in the backward scan. So pairs of peaks must be resolved together for each individual component. Accordingly, during the constrained ALS optimization, the resolved pure CV voltammograms are simultaneously fitted to a function that is the sum of two nonoverlapping logistic power peak functions. When eq 5 is applied to experimental data corresponding to fully reversible diffusion-controlled processes, adsorption and/or other possible phenomena will be consigned to the residuals. Data fitting finally achieved using ALS is also evaluated applying eq 2 where now k dij are the corresponding calculated data values using ALS optimal estimations of concentration profiles and pure individual voltammetric responses. Some points of the method should be critically discussed to check its validity and applicability and to understand its limitations. First, there is the assumption that, in the experimental conditions, the measured currents are linearly dependent on the concentration of the electroactive species present in the system. In contrast to what happens with spectroscopic data, this assumption is not necessarily valid for all the electrochemical measurements, because of their nature. This assumption is strictly not valid for labile complex systems because the responses (currents) of free (37) Tauler, R.; Casassas, E. Analusis 1992, 20, 255-268. (38) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431-441. (39) The Matlab, version 4.2; MathWorks Inc.: Cochituate Place, MA, 1994.
and bound metal are coupled through the mean diffusion coefficient, leading to a nonlinear relation between individual fluxes (and, as a consequence, currents) and species concentrations. However, the extent of nonlinearity can vary with both the experimental technique and the conditions. Thus, for instance, although a system like Zn-polymethacrylate yielding a labile complex should behave as a nonlinear system, this nonlinearity was negligible under the experimental conditions, which allowed us to study this system using MCR-ALS.20 In the case of the Cd-GSH system studied here, linearity can be assumed in the experimental conditions used. Thus, there is evidence that the electrochemical system behaves as a mixture of free Cd(II) ions and different complexes with low dissociation constants. This is demonstrated by the fact that the signal due to free Cd(II) always appears at the same potential, independent of the metal-to-ligand ratio. When labile complexes are formed (and linearity cannot be assumed a priori) the signal due to the reduction of the metal ion is systematically shifted toward more negative potentials by the addition of the ligand.20,22 This behavior was not observed for the Cd-GSH system. Second, during the MCR-ALS analysis of experimental data, few components are resolved, and it is assumed that they are associated with the chemical sources of data variation, usually loosely interpreted as chemical species. This basic assumption has been widely tested and confirmed in many systems by spectrometric techniques.24,25,37 However, the nature of the electrochemical measurements is quite different, the signal measured being a picture of what happens at the electrode interface. Thus, in the interpretation of previous MCR-ALS results,20-23 the concept of component was not related to a chemical species but to an electroactive site yielding an electrochemical signal. As mentioned in the above paragraph, whether this signal is linear or not with respect to the concentration of the electroactive site depends on thermodynamic and kinetic aspects.20-23 RESULTS AND DISCUSSION Electrochemical Behavior of the Cd(II)-GSH System at pH 7.0. The CV curves (without smoothing or background-current correction) corresponding to the solutions obtained after successive additions of Cd(II) to a 2 × 10-5 M GSH solution are shown in Figure 1. From previous studies by polarographic techniques,21,33 it is known that the peak at -0.54 V corresponds to the electrochemical oxidation of the mercury from the electrode in the presence of the free thiol group from GSH, giving the mercuric complex, and the peak at -0.35 V corresponds to the oxidation of mercury in the presence of the Cd-GSH complex in solution. Only the more cathodic peak will be considered because it is close to the signals directly related with the complexation process of Cd(II) by GSH. Apart from the above-mentioned peaks, two signals can be clearly distinguished in both forward and backward scans. In the cathodic scan the signal appearing at ∼-0.73 V is related to the reduction of some Cd-GSH complex, while that at ∼-0.67 V only appears when free Cd2+ is in the system. In the anodic scan the difference between the two signals is much higher, ∼100 mV, and the signal at ∼-0.67 V is poorly defined. In the following, attention will be focused in the region of potentials between -0.45 and -0.85 V.
Figure 1. Cyclic voltammograms of the Cd-GSH system for different concentration ratios at 2 × 10-5 M GSH and pH ) 7.0.
Figure 2. Singular values of the experimental data matrix corresponding to the forward scan obtained for the Cd-GSH system at 2 × 10-5 M GSH and pH ) 7.0.
Multivariate Curve Resolution of Data at pH 7.0. Before analyzing the whole CV current data matrix (Figure 1), only the cathodic forward run, that is the LSV experiment, was studied. The experimental data were ordered in a matrix of currents. SVD was applied to this data matrix to calculate the number of linearly independent components necessary to explain satisfactorily the variation observed in the data. Figure 2 shows the singular values of the matrix of the cathodic scan for an increasing number of considered components. From these results it was considered that only three independent components were necessary to explain the data variance. This conclusion was also supported by a SVD lack of fit of 5.41%, for three components, while the lacks of fit for two and four components were 11.54 and 3.77%, respectively. Following the procedure previously described (see Data Treatment), an initial estimation of the individual voltammograms associated with three components was obtained using EFA. Figure 3 shows the MCR-ALS resolved profiles using these estimates and the constraints of nonnegativity and unimodality. Although the lack of fit was low (11.45%), the shape of the resolved profiles was not satisfactory from an electrochemical point of view. Thus, for instance, the resolved voltammogram associated with the reduction of free Cd2+ (curve II in Figure 3a) showed an unrealistic peak shape. These results were improved by application of the logistic power peak shape constraint (eq 5). Figure 3b,c shows the results obtained after ALS optimization was applied using the Analytical Chemistry, Vol. 71, No. 20, October 15, 1999
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Figure 4. Splitting of a portion of the cyclic voltammograms (after the background correction) of the Cd-GSH system for different concentration ratios at 2 × 10-5 M GSH and pH ) 7.0 before the MCR-ALS analysis.
Figure 3. Results obtained after the alternating least squares (ALS) optimization of the forward scan experimental data for the Cd-GSH system at 2 × 10-5 M GSH and pH ) 7.0. (a) Normalized voltammograms obtained by applying nonnegativity and unimodality constraints in the ALS optimization. (b) Normalized voltammograms obtained by applying nonnegativity, unimodality and peak shape constraints in the ALS optimization. (c) Concentration profiles obtained by applying nonnegativity, unimodality, and peak shape constraints in the ALS optimization. (Empty and full dots represent the individual calculated values after MCR-ALS process, while the lines denote one of the best fits, obtained by Table Curve 2D, to the individual values.)
nonnegativity, unimodality, and voltammogram peak shape constraints. In this case the lack of fit increased (13.52%), as a consequence of the higher restrictions in the ALS optimization process, but the global results were more satisfactory from the electrochemical point of view. The normalized resolved voltammograms (Figure 3b) showed three peaks: peak I, corresponding to GSH; peak II, corresponding to the reduction of free Cd2+; and peak III, at more negative potentials, due to the reduction of complexed Cd2+. From the species distribution plot (Figure 3c), it can be deduced that only one complex, labeled as III in Figure 3, was formed. This complex appears immediately after the first Cd2+ addition, and its concentration clearly increases until the [Cd2+]/ [GSH] ratio is within the region 0.5-1, just when free Cd2+ begins to appear (labeled as II in Figure 3). After that, signal III remains approximately constant, and the free Cd2+ signal increases until 4634 Analytical Chemistry, Vol. 71, No. 20, October 15, 1999
the end of the experiment. The signal due to GSH disappears completely in the 0.5-1 ratio region. In our previous study using DPP,21 the concentration profile due to free GSH disappeared and that for free Cd2+ appeared when the Cd/GSH concentration ratio reached a value of ∼0.5. Although the concentration profiles obtained from LSV data were not so conclusive as those from DPP data, all these results seem to confirm the formation of a Cd(GSH)2 complex, signals II and III corresponding to the reduction of free and complexed Cd2+, respectively. The next step was the analysis of the data matrix corresponding to the whole CV experiment. As mentioned in the Data Treatment, in this case a new row-wise augmented data matrix was built (Figure 4). SVD of this matrix revealed that only three components were necessary to explain the data variance, with a lack of fit of only 3.92% respective to the experimental data. Figure 5a shows the resolved voltammograms obtained for the complete CV data matrix after the constrained ALS optimization assuming, first, only the nonnegativity and unimodality constraints. The resolved voltammograms are not satisfactory because some of the peaks were split, especially that of free Cd(II) either in the forward scan or in the backward scan (Figure 5a). When the peak shape constraint was applied, the shape of the resolved voltammograms improved (Figure 5b), although the lack of fit value increased (12.94%). In the forward scan, signals II and III correspond to the reduction of free and complexed Cd(II), respectively, while in the backward scan, signal II and signal III are due to the reoxidation of the Cd(Hg) amalgam to form the free Cd(II) and the complex, respectively. Signal I is due to GSH, and it is consistent with the experimental results obtained for GSH, alone, in the present study (see the less negative region in Figures 1 and 6) and with those reported by other authors.40 The resolved concentration profiles given in Figure 5c are practically identical to those found in the analysis of the forward scan (Figure 3c), and they confirm the formation of a single Cd(GSH)2 complex. Electrochemical Behavior and MCR Analysis of the Cd(II)-GSH System at pH 8.5. Figure 6 shows the set of CV curves (40) Le Gall, A. C.; van den Berg, C. M. G. Analyst (Cambridge, U.K.) 1983, 118, 1411-1415.
Figure 6. Cyclic voltammograms of the Cd-GSH system for different concentration ratios at 2 × 10-5 M GSH and pH ) 8.5.
Figure 5. Results obtained after the alternating least squares (ALS) optimization, by applying nonnegativity, unimodality, and peak shape constraints, of the whole CV experimental data for the Cd-GSH system at 2 × 10-5 M GSH and pH ) 7. (a) Normalized voltammograms obtained by applying nonnegativity and unimodality constraints in the ALS optimization. (b) Normalized voltammograms obtained by applying nonnegativity, unimodality, and peak shape constraints in the ALS optimization. (c) Concentration profiles obtained by applying nonnegativity, unimodality, and peak shape constraints in the ALS optimization. (Empty and full dots and triangles represent the individual calculated values after MCR-ALS process, while the lines denote one of the best fits, obtained by Table Curve 2D, to the individual values.)
corresponding to the solutions obtained after successive additions of Cd(II) to a 2 × 10-5 M GSH solution at pH 8.5. The experimental voltammograms obtained in this case are more complex than those obtained previously at pH 7.0 (Figure 1). Whereas the peaks in the anodic run are nearly identical to those obtained at pH 7.0, the overlap of the signals obtained at more negative potentials during the cathodic run increased dramatically. A shift toward more negative potentials was observed for all the peaks, and an additional peak was detected in the same interval of potentials. The interval of potentials between -0.5 and -0.95 V was selected for analysis. SVD of the whole row-wise augmented matrix CV signal suggested that only four components were necessary to explain the whole data variation (lack of fit of 2.35%). In Figure 7 the resolved concentration profiles and individual voltammograms for
Figure 7. Results obtained after the alternating least squares (ALS) optimization, by applying nonnegativity, unimodality, and peak shape constraints, of the whole CV experimental data for the Cd-GSH system at 2 × 10-5 M GSH and pH ) 8.5. (a) Concentration profiles. (Empty and full dots and triangles represent the individual calculated values after MCR-ALS process, while the lines denote one of the best fits to the individual values.) (b) Normalized CV curves (normalization has been performed for the forward scan peaks).
these four components are given. These profiles were obtained by ALS using the nonnegativity, unimodality, and peak shape constraints. The lack of fit corresponding to this mathematical solution was 10.5%. The disappearance of GSH (signal I) and the appearance of free Cd2+ (signal II) take place at Cd/GSH concentration ratios of 0.5 and 1, respectively, practically identical to the values found in the study by DPP.21 The resolved shapes of the CV voltammograms (Figure 7b) were also satisfactory, although some discussion is necessary. Signals I and II, associated with the redox processes of free GSH and Cd2+, respectively, can be taken as tests for the accuracy of the resolution finally achieved. For signal II, the difference between the forward peak (reduction Analytical Chemistry, Vol. 71, No. 20, October 15, 1999
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of free Cd(II)) and the backward peak (reoxidation of Cd(Hg) amalgam to free Cd(II)) is ∼40 mV, somewhat higher than the theoretical value of ∼30 mV for a two-electron fully reversible process, but equal to the experimental value of 40 mV for the curves obtained in borate medium at pH 7.0 (eight independent replicates). For signal I, the anodic and cathodic peaks appear at practically the same potentials, the peak of the backward anodic scan being very poorly defined. This result is also consistent with previous results obtained in the determination of GSH by cathodic stripping voltammetry.40 However, resolution of peak I in the backward scan is rather difficult because it is weak and close to the end of the potential scan, where the background current contributes to the measured signal, even after the background current correction is applied. Peak III in the cathodic scan can be assigned to the reduction of Cd(II) contained in the Cd(GSH)2 complex, and it is related to peak III in the backward anodic scan, i.e., to reoxidation of Cd(Hg) to yield the Cd(GSH)2 complex. According to the resolved profiles, this redox process would not be fully reversible because there is a difference between the anodic and cathodic peaks of ∼75 mV. The voltammogram plot of Figure 7b showed that in the backward scan peaks II and IV were strongly overlapping and embedded. Signal IV in the forward scan was assigned to the reduction of a Cd(II) in the Cd2(GSH)2 complex, to give the Cd(GSH)2 complex, but in the backward scan it appeared approximately at the same potentials as peak II, where Cd(Hg) was reoxidized to give free Cd(II). This behavior could be explained in two waysson the basis of kinetics or on the metalto-ligand ratios. In the first case, the kinetics of the process involving the reoxidation of Cd(Hg) to give Cd(II) which is incorporated into the Cd(GSH)2 complex to yield the Cd2(GSH)2 complex could be too slow for the time window of the experiment. Then, this process would be equivalent to the reoxidation of Cd(Hg) to yield free Cd(II) (process II). The second alternative explanation could be the different metalto-ligand ratios in the forward and backward scans. As a result of the reduction of Cd-GSH complexes in the forward scan and the releasing of free GSH onto the diffusion layer, at the beginning
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of the backward scan the metal-to-ligand ratio in the diffusion layer is different from that in the bulk, and it could be lower than that necessary to form both the Cd(GSH)2 and Cd2(GSH)2 complexes. As a consequence, the observed global process in the backward scan is not necessarily the same as in the forward scan. But the resolution of this difference is beyond the present capabilities of the proposed method. CONCLUSIONS Multivariate curve resolution has been shown to be a powerful method for the resolution of LSV and CV data signals obtained in the study of Cd(II) complexation by the thiol-containing peptide glutathione. The use of an ALS optimization including a new peakshape constraint was necessary for improving the resolution of the strongly overlapping signals obtained by LSV and CV. The multivariate analysis data treatment allowed the simultaneous detection of the Cd(GSH)2 and Cd2(GSH)2 complexes and the numerical resolution and estimation of the pure individual electrochemical LSV and CV signals and of the concentration profiles of the different Cd(II) bound in the complexes. ACKNOWLEDGMENT The authors gratefully acknowledge financial support from the Ministerio de Educacio´n y Cultura (DGICYT, Projects PB96-379C03 and PB96-0377) and from the Direccio´ General de Universitats de la Generalitat de Catalunya (GRQ97-385). J. Mendieta and M.S. Dı´az-Cruz also acknowledge financial support from the Programa de Acciones para la Incorporacio´n de Doctores y Tecno´logos, from the Ministerio de Educacio´n y Cultura, and from a doctoral Grant from the Universitat de Barcelona, respectively. The authors thank Prof. A. Sorribas, from the Departament de Cie`ncies Me`diques Ba`siques of the Universitat de Lleida, for access to Table Curve 2D software (Jandel Scientific).
Received for review May 3, 1999. Accepted July 15, 1999. AC990467W
