Application of Pattern Recognition Techniques to the Interpretation of Severely Overlapped Voltammetric Data: Studies with Experimental Data 0. V. Thomas,' R. A. DePalma, and S. P. Perone" Department of Chemistry, Purdue University, West La fayetfe, Indiana 4 7907
Pattern recognltlon methods have been used to determlne the multlpllclty of real Stationary Electrode Polarographic (SEP) data. Evaluation of several pattern classlflcatlon and feature selectlon procedures led to the ldentiflcatlon of real SEP singlets wlth an accuracy of 78% and severly overlapped doublets (A€p < 30 mV) wlth accuracler between 73% and 83%. These results were obtained using the k-NearestNelghbor (kNN) declslon rule and features based on the dlscrete Fast Fourier Transform (FFT). The ldentlflcatlonof useful features was aided by prevlous studles wRh synthetlcalty generated doublet/slnglet SEP data, although classlflcatlon of real data with the synthetlc tralnlng set was shown to be llmited by dlfferences In feature space pattern dlstrlbutlons.
Quantitative analysis of multiple component solutions with voltammetric methods has been limited by the inability to resolve closely overlapped electrochemical peaks (1,2). Peaks separated by more than 150 mV have been sucessfully analyzed using computer optimized derivative techniques for concentration ratios up to 1OOO:l (I). An on-line curve-fitting technique has been described which allows quantitative analysis of equimolar metal ions whose peak potentials are separated by only 35 to 40 mV (2). However, for peaks separated by less than 35 mV, it was not possible to distinguish between doublet and singlet peaks (2). Previous work in this laboratory has demonstrated the application of pattern recognition techniques to the detection of severly overlapped (4-12 mV) Stationary Electrode Polarographic (SEP) data (3-5). In each of these studies, the training and prediction seta used for pattern classification and feature selection were derived from SEP theory (6) and were prepared to include a wide variety of both singlet and doublet curve shapes. Sybrandt (3) and Pichler (4) dealt with totally reversible SEP data sets and demonstrated that either the Linear Learning Machine (LLM) or the k-Nearest-Neighbor (kNN) algorithm could be used to achieve classification accuracies greater than 90%. Thomas ( 5 ) extended this work to include the irreversible and quasi-reversible cases as well, and obtained classification accuracies greater than 90% for the kNN approach, with significantly lower results for the LLM. Synthetically generated noisy SEP curves were also found to be classifiable with the kNN algorithm usinq features based either on the Fast Fourier Transform (FFT) or SEP theory, if the noisy curves were first smoothed by a Fourier filter function. These smoothed data were classified 87% correctly compared to an accuracy of 7 2 % for unsmoothed noisy data. The overall results suggested that a FFT-kNN approach would be the most promising for classification of real experimental SEP data. 'Current address, Finnigan, 845 West Maude Avenue, Sunnyvale, Calif. 94086. 1376
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Table I. Experimental Conditions for Collection of SEP Data Base (PRED1) Electrolyteb E , , mVC Metal iona -540, -600 Cd" SO,'-, NO; NiZ+ -950, -600 SCN-, NO; coz+ c1-1180 -410 Pb" NO; -385 Sb3+ Tartrate Ammonium citrate, NO; -510, -505 T1+ -155 c u z+ ammonium citrate a Metal concentrations ranged between 1 X 10.' M and 1x M. 0.1 M electrolyte concentration. Potential vs SCE. In this work, we have investigated the application of both the LLM and kNN classification methods to the identification of real singlet/doublet SEP data. These methods were evaluated using both the FFT and SEP features. In addition, we have compared feature-space distribution plots for real and synthetic SEP data. The results of these studies indicate that real SEP data may be classified with good accuracy when appropriate training and features sets are used.
EXPERIMENTAL Stationary electrode polarograms of seven metal ions were obtained under a variety of experimental conditions (Table I). The metal ions selected for use in this study were chosen on the basis of their known polarographic behavior in order to obtain data for various degrees of reversibility as well as several values of n (the number of electrons transferred) and CY (the electron transfer coefficient). All solutions were prepared using reagent grade chemicals and distilled, de-ionized water. Each was thoroughly deoxygenated prior to analysis by purging with purified, solvent-saturated nitrogen (7) for 20 min. The SEP data were obtained using a general purpose electrochemical instrument with computerized data acquisition and control (8, 9). The instrument contained an analog signal generator capable of supplying potential ramps of 0 to 5000 mV/s, a general purpose potentiostat, and a three-electrode electrochemical cell. The working electrode was a digitally controlled DME which could supply mercury drops with computer-selected lifetimes from 1to 10 s. Using this system, voltammograms were ensemble averaged by performing potential scans at the end of precisely reproducible drop lifetimes. For this work, each SEP curve was the composite of eight ensembles performed on a 5-s mercury drop. The 250-point data curves were obtained for each of the metal-electrolyte combinations listed in Table I using scan rates of 750,1000,1500,2000,and 3000 mV/s and data resolutions of 2,3,4, and 5 mV/point. Metal concentrations and scan rates were selected so as to minimize signal distortions which can result from uncompensated IR drop across the cell. SEP curves which contained obvious instrumental distortions (e.g., discontinuities,ADC overflow, or excessively high noise) were rejected for use in this study. A total of 77 singlet curves were retained, representing each of the metal ion-electrolyte combinations listed in Table I. The instrumentation computer used was a Hewlett-Packard 2115A with 8K words of core memory. Peripherals included a
2
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Typical doublet voltammograms from PREDP Curve Ratio C * p b / C * ~ l PH 1 4: 1 2.5 2 2:l 2.15 1:l 4.6 3 4 1O:l 2.5 All curves are background corrected. The line at the bottom of each curve Is a reference line, not baseline current
Figure 2. 3
Flgure 1. Typical singlet and doublet voltammograms from PRED1. (1) = singlet, (2) = slnglet, (3) = doublet, (4) = doublet. The llne at the bottom of each curve is a reference line, not baseline current paper tape reader and punch, a Tektronix 601 storage display monitor and a Teletype. Data acquisition and hardware control subroutines were written in Hewlett-Packard assembly language and called by main programs written in BASIC. In order to provide a data link to the pattern recognition processing computer, the raw SEP data were punched on paper tape. Each raw data curve was corrected for background contributions by subtraction of a blank electrolyte curve obtained under an identical set of experimental conditions. These corrected curves were stored in individual disk files for easy retrieval and pattern recognition processing. The pattern recognition processor was a Hewlett-Packard 21005 computer with 32K words of core memory. Peripherals included a 5-Mbyte moving head disk drive (HP-7900), paper tape reader and punch, a Tektronics 603 storage display monitor, a Centronics 306 serial printer, a Calcomp 565 digital plotter, and a Teletype. All preprocessing, feature extraction, and pattern recognition programs were written in FORTRAN IV and operated under the Hewlett-Packard DOS-M executive. The Training Set. The QUIRDS training set used in this work is composed of 1000 singlet and doublet synthetic SEP curves. The QUIRDS data set contains reversible, irreversible, and quasi-reversible waveforms and has been described in detail in Ref. 5. This training set has been used to classify synthetic SEP data sets with accuracies exceeding 94%. While that work suggested that FFT features might be most useful for classification of real data, both SEP and FFT feature sets were used here in order to prevent arbitrary exclusion of information which could be critical for successful pattern classification. Feature extraction methodology was described previously (5). A complete list of feature definitions may be found in Ref. 8. The Prediction Set. The 77 real singlet polarograms described above were included in the real prediction set. Because these curves were obtained at various voltage resolutions, each singlet was recalculated for a resolution of 2 mV by linear interpolation between points. This procedure was necessary to ensure that the Fourier transformation would obtain the same frequency scale for both the real data and the training set data which were synthesized with a resolution of 2 mV. Each singlet peak height was also normalized to a value of 1.0. Typical singlet voltammograms are shown in Figure 1 (curves 1 and 2). Due to the difficulty of obtaining a large number of experimental doublets with known peak overlaps less than 10 mV, most prediction set doublets were prepared by the linear combination of two previously processed singlets. Peak separations and concentration ratios for these doublets were adjusted to fall within those limits established for the synthetic training set doublets ( 5 ) . Each doublet peak current was also normalized to a value of 1.0. The 120 doublets prepared by this procedure were combined with the 77 singlets described earlier to form a real prediction set (PRED1). Each curve in this set was smoothed by the Fourier filter function described elsewhere (5). Each peak location was then determined and shifted in the data array so that all curves had the same peak location prior to feature ex-
Table 11. Initial Classification Results for Real SEP Data Set, P R E D l a Classification accuracy, % SEP features FFT features Classification method Singlet Doublet Singlet Doublet kNNb 7.8 90.8 32.5 73.7 86.8 42.9 51.7 LLMC 19.5 98.3 55.8 45.0 LLM~ 37.4 LOOb (kNN) 48.1 71.7 51.9 83.3 a Training set was QUIRDS synthetic data ( 5 ) . Features used were “noise-optimized” with synthetic noisy QUIRDS prediction set (5). Features used were variance-selected by QUIRDS training set ( 5 ) . Features used were sign-magnitude selected by QUIRDS training set ( 5 ) . traction (5). Typical PREDl doublet voltammograms are shown also in Figure 1 (curves 3 and 4). An alternative prediction set of real doublets (PRED2) was prepared from polarograms obtained for a series of Pb/Tl citrate solutions. The peak potentials of Pb and T1 in 0.1 M citrate exhibit slightly different dependencies on pH and are severely overlapped within the pH range of 2.0 to 6.0. A total of 33 doublet curves was obtained at several pH values for solutions with Pb/T1 concentration ratios ranging between 1O:l and 1:5. Exact peak overlap values for these conditions are unavailable, but are estimated t o be between 0 and 30 mV based on the pH behavior of the individual metals. Concentration ratios of T1 to Pb greater than 5:l were excluded from this prediction set due to obvious doublet distortions (e.g., dual peaks and shoulders) which make them a trivial classification problem. Background corrections were made using 0.1 M potassium citrate blanks run at appropriate values of pH. Typical PRED2 doublet voltammograms are shown in Figure 2.
RESULTS AND DISCUSSION The primary goal of this work was to apply pattern recognition methods to the classification of experimental doublet/singlet SEP data. T o this end, it was desired to evaluate the use of synthetically generated data as a training set and to evaluate the effectiveness of those features identified as useful for classifying synthetic prediction sets (5). The difficulty of the classification problem addressed here is obvious from a visual examination of the singlet/doublet voltammograms in Figures 1 and 2. Table I1 lists the results obtained by applying the kNN and LLM classification algorithms to the real data set (PRED1) using the best SEP and FFT feature sets selected with ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
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Table 111. kNN-IFS Selection of Optimum Features for Real SEP Data Seta Classification accuracy % Feature No. Training set type retained Singlet Doublet 77.9 83.3 PRED~~ FFT 3c PRED~~ SEP 4d 59.7 75.0 QUIRDS FFT 19 48.0 75.0 QUIRDS SEP 7 19.5 94.2 Reversible FFT 11 38.9 83.3 only QUIRDS a The prediction set for all classifications was PRED1. Leave-One-Out method used. Features No. 4, 5, 9, Ref. 8. Features No. 2, 20, 36, 44, Ref. 8. synthetic data (5). As can be seen, none of the method/feature combinations provide statistically significant classification results. As a point of reference, a Leave-One-Out (LOO) (10) analysis of the real data set was performed. The LOO method is performed by removing one pattern at a time from the data set and then applying a kNN classification to that pattern using the remaining patterns as a training set. Once classified, the pattern is returned to the data set and the next one removed and classified, etc. In this case, where the LOO training set is actually the real data under study (PREDl), the results obtained represent the best possible classification accuracies obtainable for the real data with these particular features. However, as shown in Table 11, even the LOO results are quite low for the feature set used. Several possible explanations for the behavior observed in Table I1 may be considered: (1)The QUIRDS training set is not representative of the patterns found in the real data set and thus cannot be used as a training set for their classification. This might be due to any of several reasons, including instrumental artifacts and distortions, the presence of surface interactions or coupled chemical reactions, or other aberrations in the real data not accounted for in the synthetic training set. (2) The noisy synthetic prediction set used for feature selection in Ref. 5 is not representative of the real data set obtained here and thus a non-optimum set of features was applied to real data. (3) Neither the SEP nor the FFT features actually exploit intrinsic class differences of real data and a new set of features should be defined. In order to determine which of these explanations was most correct, kNN-IFS (Iterative Feature Selection) was performed for several combinations of training and prediction sets. This procedure was shown in Ref. 5 to be the most effective approach to feature selection for this type of data. F e a t u r e Selection Studies. Studies with synthetic data showed that features selected using a smooth prediction set could not be used to classify noisy data. Successful classification resulted only when a noisy prediction set was used during feature selection. Similarly, Table I1 shows that features selected by noisy synthetic data cannot be used to classify real SEP patterns; thus, feature selection should be performed again using a prediction set composed of real data. The results of feature selection are shown in Table 111. The results in row 3 and 4 indicate that the implications of explanation 2 above are not entirely correct. That is, there appears to be no optimal multidimensional SEP or FFT feature combination which can be used to classify this real data set with the QUIRDS training patterns. The results in rows 1and 2 suggest that explanation 1above is correct and that explanation 3 is not. That is, because both the SEP and FFT features give statistically significant classification results, the poor results found in Table I1 are most likely not the results of poorly defined features. On the contrary, the FFT features provide acceptable results while requiring 75 % fewer 1378
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Flgure 3. Nonlinear map, singlets only, QUIRDS training set and PRED1 prediction set; real-optimized FFT features. S = QUIRDS training set. 1-8 = PREDl prediction set. 1 = Pb(II), 2 = Cd(II), 3 = Cu(II), 4 = TI(I), 5 = Sb(III), 6 = Ni(II)-N03-, 7 = Ni(I1)-SCN-, and 8 = Co(I1)
features than for the synthetic data set, a clear indication that FFT features do discriminate between real singlet/doublet SEP data. If explanation 1 is correct, then the QUIRDS data set is not representative of real polarograms, and it would be very worthwhile to consider the possible reasons. Table I shows that the real data set is primarily composed of reversible reductions (e.g., Cd, Pb, T1, Sb). The QUIRDS training set, having been designed to include patterns of all degrees of reversibility, could have a built-in bias as the result of a possible localized low density of reversible singlets surrounded by a higher density of doublets in feature space. If this were the case, real reversible singlets might have a good chance to be misclassified as doublets. To check this explanation, a set of totally reversible singlets and doublets was selected from the QUIRDS data base to act as a training set for feature selection on real data. Row 5 of Table I11 lists the results obtained for IFS selection of FFT features. Comparison of these results with rows 3 and 4 suggests that a low density of reversible training set patterns is not the primary limitation in applying the QUIRDS training set to classification of real data. Thus, all evidence points to a significant difference between the feature space distributions of the QUIRDS data base and the PREDl patterns. T o help clarify this point, nonlinear mappings (11) were obtained for representative singlets selected from both the QUIRDS and PREDl data sets, using the set of 3 FFT features which provided the best classification results for real doublet/singlet SEP data (Table 111). Examination of this mapping in Figure 3 reveals several things. First of all, in most cases the real singlets fall on essentially the same distribution line as the synthetic singlets. The exceptions are Ni(I1) in 0.1 M KNOB,Co(I1) in 0.1 M KC1, and Cu(I1) in 0.1 M ammonium citrate. The Co singlets appear to lie on the extension of the distribution line. The absence of synthetic singlets in this region may be due to the restricted range of a-values (0.3 to 0.7) allowed in the generation of the QUIRDS data set. Other studies have indicated that a-values for Co(I1) in 0.1 M KC1 might be lower than 0.3 (12), thus putting these singlets outside the range of the QUIRDS distribution. Ni(II)-NO< singlets appear to lie outside of the projected singlet distribution. This may be because of distortions related to metallic Ni formation on the mercury surface. The copper cluster in Figure 3 is spread out and extends outward from the singlet distribution line. A recent publication by Anderson and Shain (13),indicating that the Cu(I1) reduction wave involves a chemical reaction coupled between each electron transfer step (ECE mechanism), provides the explanation for our observed behavior. Detailed examination
Table IV. kNN Classification of Pb-T1 Doublets (PREDP ) Training set Features Classification accuracy, % QUIRDS 1, 6, 7, 9, 10, 78.8 12, 13, 16, 20, 21, 22, 23a PREDl 4, 5, gb 72.7 PREDl 1, 6, 7, 9, 10, 39.4 1 2 , 13, 16, 20, 2 1 , 22, 23a a These are the “noise-optimized” FFT features ( 5 ) . These are the “real-optimized” FFT features from Row 1, Tabk 111.
t
1
I
of the spread in the Cu cluster shows that the deviation from the pure singlet distribution increases with increased scan rate. This would be expected for an ECE electrode process, and is consistent with the observations of Anderson and Shain (13). Another observation on Figure 3 is that singlet waves for each of the several elements cluster in separate areas. With the exception of Cu, the tightness of these clusters is remarkable, considering the wide range of experimental conditions applied in their collection. This provides a vote of confidence for the instrumental methodology employed. Finally, when each of the individual clusters of real singlets is mapped separately, a slight trend is observed with respect to scan rate. This may be due to experimental distortions at higher sweep rates. Alternatively, it may be due to the fact that the noise contribution to data collected at higher sweep rates appears as “low frequency” information to the FFT procedure; thus, more of this information is retained after truncation than for the data obtained a t lower sweep rates. In either case, this is a subtle aberration in the data which may account for some of the diminishment in classification accuracy obtained with real data. On the basis of the above observations it can be seen why the QUIRDS data set was not appropriate for classification of the PREDl data set. One of the electrode systems (Co) provided singlets outside the range of the QUIRDS distribution; one system (Cu) had an unsuspected complication which caused a sweep rate dependence not accounted for in the QUIRDS set; and one system (Ni-NO:) provides singlets which are apparently outside the projected distribution. Moreover, Figure 3 shows that even for those real singlets which fall on the same distribution line as synthetic singlets, locally dense regions of real singlets may not coincide with a heavy population of synthetic singlets. This is probably the primary reason for misclassification of real singlets by the QU1RDS training set, and future studies of pattern classification of voltammetric data with synthetic training sets must address this problem. It is worthwhile noting, however, that Figure 3 also illustrates why the real data are classifiable when the LOO procedure is used with PREDl as its own training set (Table 111, column 1). Because the real singlets are reasonably tightly clustered in this feature space, the kNN algorithm classifies singlets and doublets with about 80% accuracy. Moreover, if the slight dispersion in these clusters due to scan rate variation were avoided by using uniform scan rates in data collection, it is likely that classification accuracy could be significantly improved. Classification of Real Doublets. As a final test of the kNN-FFT approach for classification of real doublet/singlet SEP data the small set of real Pb-T1 doublets (PREDS) was classified. Table IV lists the classification results obtained using the kNN decision rule and several optimized FFT feature sets. While the QUIRDS training set results appear to be good, it should be remembered that this set of noiseoptimized features was biased toward classification of all
t Nonlinear map. PREDl and PRED2 prediction sets; realoptimized FFT features. (1) = singlet, (2) = mixed doublet, (D) = real doublet (PblTI) Flgure 4.
patterns as doublets (Table 11, row l),and therefore these results may not be significant. The optimum feature set for real data (“real-optimized” features), obtained from row 1,Table 111,provides significant classification accuracy for the real doublets, although not as high as for the doublets in PRED1. Figure 4 shows the feature space distributions for PREDl (1 = singlets, 2 = doublets) and PRED2 (D = doublets) together in the same nonlinear map. Most PRED2 doublets appear to fall within the PREDl doublet distribution. However, a small group tends to be located closer to a group of P R E D l singlets and thus are classified incorrectly. This may be related to the fact that it is impossible to select exact peak overlaps for real doublets, and therefore some of them may lie outside the limits of the doublets contained in the real training set (PREDl). CONCLUSIONS The primary goal of classification of real SEP data has been met. It was achieved by means of a Leave-One-Out analysis using a feature set optimized for the classification of real data. All doublets used in this study were known to have peak separations of less than 30 mV and have been identified at accuracy levels previously unattainable. The results obtained here for real SEP data are encouraging and suggest that other types of doublet/singlet identification problems may be successfully solved using a pattern recognition approach (e.g., GC, NMR, ESCA, etc.). The application of synthetic training sets to the classification of real data appears to be limited by differences in the feature space distributions of real and synthetic SEP data. Some possible causes for these distribution differences have been examined here and suggest ways to improve the utility of synthetic data for future studies. The kNN decision rule has been shown to be the most effective approach to this particular classification problem. Associated feature selection methods have demonstrated an ability to significantly reduce the dimensionality of feature space while at the same time increasing pattern classification accuracy. Furthermore, the resulting reduction of feature dimensionality reduces the time required for pattern classification, an important consideration for on-line processing. Finally, features derived from the discrete Fast Fourier Transform have been shown to be useful for the enhancement of intrinsic class differences in real SEP data. These features are easily extracted from analytical response curves by the use of the axis translation-rotation procedure (5). Because of this, these features are an attractive method for the representation of analytical waveforms for pattern recognition, when intrinsic waveshape information is sought. LITERATURE C I T E D (1) S.P. Perone, D. 0.Jones, and W.F. Gutknecht, Anal. Chem., 41, 1154 (1969).
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(2) W. F. Gutknecht and S. P. Perone, Anal. Chem., 42, 906 (1970). (3) L. B. Sybrandt and S. P. Perone, Anal. Chem., 44, 2331 (1972). (4) M. A. Pichler and S . P. Perone, Anal. Chem., 46, 1790 (1974). (5) Q.V. Thomas and S. P.Perone, Anal. Chem., preceding paper in this
(11) J. W. Sammon, Jr., I€€€ Trans. Comput., C-18, 401 (1969). (12) S. P. Perone and C . V. Evins, Anal. Chem., 37, 1643 (1965). (13) J. L. Anderson and I. Shain, Anal. Chem., 48, 1274 (1976).
issue.
(6) (7) (6) (9) (10)
R:S. Nicholson and I. Shain, Anal. Chem., 36, 706 (1964). L. Meites. Anal. Chim. Acta. 18. 364 (1958). Q. V. Thomas, Ph.D. Thesis, Purdue University, 1976. Q. V. Thomas, L. Kryger. and S. P. Perone, Anal. Chem., 48, 761 (1976). K. Fukanaga, “Introduction to Statistical Pattern Recognition”, Academic Press, New York, N.Y., 1972.
RECEIVED for review November 29, 1976. Accepted May 23, 1977. This work has been supported by the Office of Naval Research and by the Science Foundation Grant No* MPS74-12762.
Determination of Sulfide and Thiols in the Presence of Vitamin B,2a by Pulse Polarography Manoutchehr Youssefi and Ronald L. Birke” City University of New York, Department of Chemistry, The City College, New York, New York 1003 1
The differential pulse polarographic (DPP) method is applied to the analysis of sulfide ion, cysteine, and glutathione by utilizing a cathodic pulse whlch strips the dropping mercury electrode of an adsorbed film of mercury compound. I n the presence of vitamin B,2a DPP peaks for both the sulfurcontaining compound and vitamin B,2acan be seen In the same scan. A comparison is made of normal pulse polarography and differential pulse polarography and the latter method is found to be more convenient for sulfide and thiol analysis. The differential pulse peaks of glutathione and cystelne each split into two peaks as the concentration is increased beyond a certain point with the new peak being shifted in a positive potential direction. Calculatlon supports the contentlon that the peaks are due to monolayer and multilayer dissolutlon. Application of the DPP method is made In the study of the reaction of vitamin B1Sa wlth cysteine and an amperometrlc titration shows a 1:l stoichiometry for the reactants. The nature of the reaction products is also discussed,
The analysis of sulfides and thiols in the presence of biologically active compounds is important since many enzyme systems require sulfur-containing compounds for catalytic activity. One such system is methionine-synthetase which requires a vitamin B12 compound and a thiol, e.g., dithiothreitol, for activation ( I ) . In the course of studying the reaction of vitamin BlZawith sulfide or thiols, we investigated the normal (integral) and differential pulse polarographic method as a means of determining both the sulfur-containing compound and vitamin B12a. The polarographic method which has been widely applied for the investigation of sulfides and thiols is predominately based on the anodic wave which originates from the oxidation of mercury resulting in the formation of insoluble mercury compounds. The dc and ac polarographic behavior (2) of cysteine and glutathiene, for example, shows multiple waves and peaks due to films formed by these mercury compounds. The film formation on the electrode leads to a nonlinear relationship between current and concentration. Recently the rapid direct current method ( 3 ) and the normal pulse polarographic method ( 4 ) have been used to cope with these problems. 1380
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We have found, however, that although differential pulse polarography (DPP) is subject to many of the problems inherent with film formation, the convenience and resolution it offers make it preferable especially when several species are present in the solution. In the specific case of a mixture of vitamin BlZaand a sulfide or thiol, the normal pulse method sometimes proved difficult to use because the plateau and/or baseline of the normal pulse wave was quite sloped and because the vitamin BIzareduction wave was not completely separated from the thiol oxidation wave. For the differential pulse polarographic determination of sulfide and thiols, we investigated a method which is not based on determining the anodic current but rather on the cathodic current which results in the reduction of the film of mercury salt built up over the drop life. Earlier DPP Studies of such a process (2) showed that the method was quite sensitive with a detection limit around M; however, the behavior of these peaks as a function of concentration was not investigated. The DPP peaks for the reduction process would be expected to be sharply resolved. Thus the possibility of using these highly resolved and sensitive peaks for the analytical determination of sulfide or thiol in a mixture containing vitamin B12 compounds was the motivation for their further investigation. Such a technique allows a determination of both the thiol and vitamin VlZain one scan at physiological pH. We have applied this analysis to study the reaction between thiols and vitamin %a.
EXPERIMENTAL The glutathione and L(+)-cysteine hydrochloride were Fisher Scientific Co. reagent grade. The L-cystine was Sigma Chemical Co., sigma grade. Stock solutions of glutathione and cysteine were freshly made up by dissolving the weighed reagent in a nitrogen deaerated buffer solution. The buffer was 0.2 M in Na2HP04and in KH2POl leading to a pH = 6.80. This value was the pH of the phosphate buffer unless mentioned otherwise. Some solutions were adjusted with NaOH to pH 7.2 which is closer to physiological pH. The stock solutions of NazS (Fisher Reagent grade) were made up with nitrogen-deaerated distilled water in M NaOH and stored in polyethylene bottles over nitrogen. These solutions were standardized by reaction with excess primary reagent grade KI03 and KI in acid. The liberated iodine was titrated with sodium thiosulfate to the disappearance of the starch indicator which was added near the end point. The thiosulfate was also standardized by the KIOB/I- and starch indicator method.
