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ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
Enzyme-Catalyzed Reaction-Rate Method for Determination of Arsenic in Water Scott R. Goode” and Ray J. Matthews’ Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208
A new, unique enzymatic method for the determination of arsenic is discussed. The enzyme glyceraldehyde-3phosphate dehydrogenase is used to perform an oxidative arsenolysis of ~-glyceraldehyde-3-phosphate. The rate of reaction, as measured by fluorescence, is first order in arsenic(V). The method has a linear calibration plot for the range 0.02 to 2.0 kg/mL arsenic. Samples of public drinking water and river water are analyzed by the enzymatic technique. The nearquantitative recovery of spiked samples indicates that these matrices do not contain sufficient quantities of interferents to require any sample preconcentration or chemical treatment prior to analysis.
The detection of arsenic in natural waters is one of the most difficult tasks facing the analytical chemist. Arsenic is not desirable in concentrations greater than 0.01 Fg/mL, and water containing more than 0.05 Fg/mL is not suitable for drinking (I). The ideal analytical technique will offer sufficient accuracy and precision a t these concentration levels to afford analysis without lengthy preconcentration steps. Two procedures are recommended for the determination of arsenic in water (2). Either flame atomic absorption spectrometry (AAS) or complex formation with silver diethyldithiocarbamate (SDDC) followed by a spectrophotometric determination of the chloroform extract is acceptable. The limit of detection for the AAS determination is 1 kg/mL (3)and for the SDDC method it is 0.5 pg/mL ( 4 ) . Obviously, both methods lack the sensitivity necessary for the direct determination of arsenic in drinking water, and must be coupled to a preconcentration step. If arsenic is present as As(III), it can be extracted into methyl isobutyl ketone following complexation with ammonium pyrrolidine dithiocarbamate ( 3 ) , or may be distilled as AsC13 ( 5 ) . The recommended ( 2 ) preconcentration method is the reduction of arsenic to arsine, AsH3, which is a gas a t room temperature. The gas is either trapped and coupled with the SDDC spectrophotometric analysis or passed into a nitrogen-hydrogen-entrained air flame to produce a transient atomicabsorption signal. The reported limits of detection are 0.03 pg/mL with the SDDC method ( 2 ) and 0.002 pg/mL in a 20-mL sample with atomic absorption (3). Preconcentration by arsine generation has several disadvantages. First, the analyses are relatively lengthy, as samples must be processed individually, rather than in a batch. Automated arsine generation has been demonstrated by several wqrkers (6-8) but the instrumentation is relatively complex and requires skilled operators. Second, arsine generation is subject to several interferences. The presence of chromium, cobalt, copper, mercury, molybdenum, platinum, and silver all interfere in the generation of arsine ( 2 ) . These interferences become significant when the total heavy metal concentrations exceed 5-7 Fg/mL (9, I O ) . Also, arsine generation can be relatively imprecise. The relative standard ‘Present address; Brockway Glass Co., Engineering and Research, Brockway, Pa. 0003-2700/78/0350-1608$0 1.OO/O
deviation of replicate analyses of synthetic samples, containing none of the interferences, is 14% with non-automated arsine generation and detection by SDDC ( 2 ) . This article presents a new analytical method, based on an enzyme-catalyzed reaction. The reaction conditions are adjusted to achieve a system which is pseudo-first-order in arsenate. The utility of the enzymatic method is demonstrated by analysis of drinking water and river water to which arsenic has been added. The limit of detection is 0.02 kg/mL without any preconcentration.
BASIS FOR ANALYSIS The enzyme glyceraldehyde-3-phosphate dehydrogenase (GAPDH), in conjunction with the coenzyme nicotinamide adenine dinucleotide (NAD), catalyzes the oxidative phosphorylation of ~-glyceraldehyde-3-phosphate (G3P) to 1,3diphosphoglycerate: HCO I HCOH + N A D I CH,OPO 2 -
+
GAPDH HP0,2- =====
OCOP0,Z1 HCOH + NADH i CH,OPO 2-
+
H’
Glyceraldehyde-3-phosphate dehydrogenase is one of the key enzymes in the glycolytic conversion of glucose to pyruvic acid, one of the pathways of carbohydrate metabolism. In the presence of arsenate, 1-arseno-3-phosphoglycerate (APG) is produced: HCO OCOASO,~‘ I GAPDH 1 HCOH + N A D + HA SO,^‘ F=== HCOH + NADH + H i I C H 2 0 P 0, 2 CH,OPO,’(APG)
The APG hydrolyzes to release arsenate and form 3phosphoglycerate. OCOAsO *cooI I HCOH HCOH + HASO,*- t H’ I H O I CH,OPO,*- .-L CH,OPO,*Under physiological conditions, the hydrolysis is “dead-end,” and robs the metabolic pathway of energy. Glyceraldehyde-3-phosphate dehydrogenase has been used by several workers to determine inorganic phosphate (11-13). Each used GAPDH as part of a system to form 1,3-diphosphoglycerate, which is then removed by other enzymes to force the equilibrium toward completion. Detection of the reduced NAD is by absorbance ( I I ) , fluorescence (121, or voltammetry (13). The enzyme has been studied extensively ( 1 4 ) and a mechanism for oxidative phosphorylation has been proposed (15,16). With reagent concentrations near the physiological levels, and the pH in excess of 7.5, the rate of reaction is limited by release of NADH from the enzyme-product -NADH complex (16). The concentrations of the reagents must be adjusted to achieve pseudo-first-order kinetics in arsenate if the reaction is to be used for chemical analysis. The experimental measurement is the initial rate of production of NADH, as measured by the NADH fluorescence B 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
Table I. Results of Sequential Simplex Optimization optimum volume of reagent used in solution analysis, mL 0.5 pg/mL As 2.00 1.13 0.2 M Tris (pH 8 . 5 ) 0.25 M BME 0.21 0.27 M NaF 0.28 0.001 M D - G ~ P 0.026 0.02 M NAD 0.065 750 pg/mL GAPDH 0.039 as a function of time. Chemical analysis by rate measurement can be more accurate than equilibrium-based measurements, because species which influence the position of equilibrium are not interferences in a rate method unless they react during the same time scale as does the analyte (I 7,181. An enzymatic procedure contributes additional accuracy from the specificity inherent in enzyme-catalyzed reactions, but experimental conditions such as temperature and pH must be carefully controlled to maintain precision. EXPERIMENTAL Reagents. Solutions are prepared fresh daily, other than 0.2 M Tris buffer (pH 8.5) and 0.27 M NaF, which are stable for at least 1 month. The arsenic solutions are prepared by serial dilution of a 1000 kg/mL stock made from As205. The preparations described below are sufficient for approximately 20 analyses. The working solutions of the organic reagents are all kept in an ice bath. The stock materials are stored in accordance with the supplier’s instructions. Glyceraldehyde-3-phosphateDehydrogenase. The enzyme, GAPDH, is obtained as the crystalline suspension which is isolated from rabbit muscle (Sigma Chemical Co, St. Louis, Mo). The working solution is made by dilution of 50 pL of the suspension to 1.00 mL, corresponding to a concentration of 750 pg protein/mL. ~-Glyceraldeyde-3-phosphate. The substrate, G3P, is in the form of the diethyl acetal monobarium salt, as the free acid is unstable over long periods of time. The salt (Sigma Chemical Co.) is converted t o the free acid by the ion-exchange procedure recommended by the manufacturer. The resulting solution is approximately 0.001 M in D - G ~ P The . solution is kept frozen and thawed just before use. @-NicotinamideAdenine Dinucleotide. A solution which is approximately 0.02 M in NAD is made by dissolving 28.8 mg of NAD (Grade 111, Sigma Chemical Co) in 2.0 mL of HzO. P-Mercaptoethanol. A 0.25 M BME solution is made by dissolving 70 pL of BME (Eastman Organic Chemicals) in 4.0 mL of water. Instrumentation. The fluorescence of NADH is measured by a spectrofluorometer (Model 430, Turner Associates, Palo Alto, Calif.) and recorded on a strip-chart recorder (EU-205-11,Heath Co, Benton Harbor, Mich.). Excitation is at 360 nm and emission is observed at 460 nm. Procedure. Two milliliters of the sample to be analyzed is pipetted into a 12 X 75 mm test tube. Next, Tris buffer, BME, G3P, NaF, and NAD are added and mixed. Optimal concentrations of all reagents are shown in Table I. Finally, the enzyme is added, the test tube is inverted twice, and then placed in the spectrofluorometer. The signal, which steadily increases, is recorded for 1-2 min. O P T I M I Z A T I O N O F REAGENT CONCENTRATIONS The reaction rate must be optimized to obtain the sensitivity inherent in the method. The concentrations of five factors (GAPDH, G3P, NAD, BME, and NaF) are varied in a systematic manner to determine the optimum conditions for analysis. S e q u e n t i a l Simplex Optimization. The sequential simplex algorithm (19, 20) has been applied successfully to many chemical systems (21, 22). The algorithm has been
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shown to converge rapidly to an optimum, using strategy based on the results of previous experiments. The optimization is a function of seven variables, two of which are kept constant. The volume of the arsenic standard, 0.5 pg/mL, is held a t 2.0 mL. The amount of Tris buffer is calculated to keep the total volume of the analysis at 3.75 mL. The other five factors are adjusted, and an optimum was reached within 30 experiments. The final values, assumed to be optimum, are shown in Table I. Interaction of Factors. The only information available from the simplex method are the conditions under which the rate of reaction is maximum. The dependence of the rate on variations in the concentrations of the reagents must also be determined. This information gives the analytical chemist the knowledge of which reagents must be measured with high precision, and which are not so critical. A 46-experiment Box-Behnken partial factorial design (231, followed by regression analysis, produces this information. These studies indicate that the rate of reaction is influenced most by the concentration of enzyme, which must be measured with care. The NaF concentration is not a t all critical, but some NaF is necessary. Additionally, the rate of reaction is greatest when NAD of G3P is high, but not when both are high. This phenomenon, known as negative cooperativity, is documented in GAPDH which has been crystallized from rabbit muscle (24).
RESULTS The optimum conditions (Table I) are used to obtain the calibration plot, limit of detection, and the information on interferences, all presented in the following sections. Calibration Plot. The calibration plot is linear over the range 0.02 to 2.0 kg/mL arsenic, a concentration range of two decades. The detection limit, defined as the concentration at which the signal is twice the standard deviation of the blank (signal-to-noise ratio of 2 ) is 0.02 pg/mL of arsenic. This corresponds to 40 ng of arsenic in the 2.0-mL analysis solution. The minimum detectable quantity is ultimately limited by the uncertainty in the rate observed from the reagent blank. The reaction is known to proceed by an alternative mechanism in the absence of arsenate or phosphate (25). The relative standard deviation of replicate analyses of a 0.5 pg/mL standard is 4.6%. The largest source of imprecision is the delivery of the reagents to the curvette. Precision would be improved if a composite reagent mixture or automated procedure were used (26). Dependence on Oxidation State. The enzymatic analysis requires that arsenic be present as As(V), in the form of the hydrogen arsenate ion, HASO:-. This is the predominant form present in aqueous samples as there is no evidence for the existence of cationic As3+(27),and the As(II1) oxo acids and anions are all air-oxidized to arsenate. The arsenate is partitioned among H3As04,H2As04-,HA SO,^-, and As043-, but a t the pH used in the analysis, 85% of the arsenic is present as HAs04*-. Samples of anaerobic industrial wastes and sludges may contain reduced forms of arsenic. Arsenic(II1) can be oxidized to As(V) by alkaline Hz02and iodide. The oxidation is near quantitative even a t the sub pg/mL level. Matrix Interferences. The immunity from matrix effects is tested by analysis of solutions containing species which are potential interferences in addition to 0.5 pg/mL arsenic. The results are shown in Table 11. Phosphate is not a serious interference, even a t concentrations of 50 pg/mL, which is greatly in excess of that found in natural waters. This is not too surprising as the analysis conditions (Table I) often differ by several orders of magnitude from those used in the determination of phosphate (11, 12). Silicate also poses no interference problems. Two metals known to poison enzymes,
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
Table 11. Influence of M a t r i x and Concomitant on Sample Recovery
recovery, species ~0,s-
PO,+ ~
0
~
3
-
Si0,'drinking water river water seawater
concn, Ug/mL 0.5 5 50
5
... *.. ...
100 95 116 98 90 85 10
Compared to 0.5 pg/mL As in distilled water. Corrected for blank. mercury(I1) and iron(III), interfere when present a t the 5 pg/mL level, by decreasing the rate of reaction by 50 to 75%. This is approximately the same concentration at which arsine generation is also affected (IO), so the enzymatic method does not offer major improvement for the determination of arsenic in industrial wastes or heavily polluted water samples. The high salt content of seawater also causes interferences. The major advantage of the enzymatic method is its simplicity and ease of operation. The method of standard additions was used to analyze river water and drinking water. The recoveries were 85-90%, indicating that these commonly analyzed matrices do not contain enough interfering species to contribute significant error. The enzymatic technique affords sufficient sensitivity, accuracy, and precision to analyze these samples without major preconcentration or treatment.
ACKNOWLEDGMENT The authors thank Suzanne Thorpe and John Baynes for valuable information on enzymology and for the loan of a spectrofluorometer, and S. L. Morgan for many valuable comments and suggestions.
LITERATURE CITED Public Health Service, "Drinking Water Standards", U S . Department of Health, Educatlon, and Welfare, Washington, D.C. 1962. American Public Health Association, "Standard Methods for Water and Wastewater". C. R. Parker, "Water Analysis by Atomic Absorption Spectroscopy", Variin Techtron, Palo Alto, Calif., 1976 p. 32. H. Bode and K. Hachman, Fresenius 2.Anal. Chem., 229, 261 (1967). P. H. Davis, G. R. Dulude, R . M. Griffin, W. R. Matson, and E. W. Zink, Anal. Chem., 50, 137 (1978). P. D. Goulden and P. Brooksbank, Anal. Chem., 46, 1431 (1974). F. D. Pierce, T. C. Lamoreaux, H. R. Brown, and R. S. Fraser, Appl. Spectrosc., 30, 38 (1976). M. Fishman and Robert Spencer, Anal. Chem., 49, 1599 (1977). S. S. Sandhu and P. Nelson, Anal. Chem., 50, 322 (1978). F. D. Pierce and H. R . Brown, Anal. Chem.. 49, 1412 (1977). R. Gaynn, D. Veloso, and R . Veech, Anal. Biochem., 45, 277 (1972). R. Scopes, Anal. Biochem., 49, 88 (1972). G. G. Guilbalt and T. Cserfalvi, Anal. Lett.. 277 (1976). J. I.Harris and Michael Waters, Glyceraldehyde-3-phosphate Dehvdroaenase in "The Enzvmes". P. D. Bover, Ed., VoI. XIII. Dart C. 3rd eb., A-cademic Press, New York, N.Y.. y976. (15) H. S. Segal and P. D. Boyer, J. Biol. Chem., 204, 265 (1953). (16) P. J. Harrigan and D. R. Trentham, Biochem. J.. 135, 695 (1973). (17) H. V. Malmstadt, E. A. Cordes, and C. J. Delaney. Anal. Chem., 44(12). 26A (1972). (18) H. B. Mark, Jr. and G. A. Rechnitz, "Kinetics in Analytical Chemistry", Wley-Interscience, New York. N.Y., 1968. (19) W. Spendley, G. R. Hext, and F. R. Himsworth, Technometrics, 4, 441 (1962). (20) J. A. Nelder and R. Mead, Comput. J., 7, 308 (1965). (21) S. N. Deming, S. L. Morgan, and M. R. Willcott, Am. Lab., 8 (IO), 13 (1976). (22) S. N. Deming and S. L. Morgan, Anal. Chem., 45, 278A (1973). (23) G. E. P. Box and D. W. Behnken, Technometrics. 2, 455 (1960). (24) J. J. M. De V i p , W. Boers, A. G. Hikers, B. J. Harmsen, and E. C. Shter in "Pyridine Nucleotide Dependent Dehydrogenases", H. Sund, Ed., Springer-Verlag, New York, N.Y., 1970 p 233. (25) S. F. Velick and J. E. Hays. Jr., J . Blol. Chem., 203, 545 (1953). (26) L. P. Leon, M. Sansu, L. R. Snyder, and C. Horvath, Clin. Chem. ( Winston-Salem, N . C . ) , 23, 1556 (1977). (27) J. F. Kcpp and R. C. Kroner, "Trace Metals in Waters of the Untted States", US. Department of Interior, Division of Pollution Surveillance, Cincinnati, Ohio. 1967.
RECEIVED for review May 30, 1978. Accepted July 17, 1978.
ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
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Kinetic Method That Is Insensitive to Variables Affecting Rate Constants Glen E. Mieling and Harry L. Pardue”
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907
This paper describes a new approach to first-order kinetic analyses that is insensitive to variables such as pH and temperature that influence rate constants. The method uses a multiple-linear-regressionprogram to compute values of the rate constant, k,initial absorbance, A,, and final absorbance, A,, that fit experimental data to a first-order model. Analyte A,. The Feconcentration Is computed from AA = A , (III)/SCN- system is used as a model reaction and dependencies of the method upon pH, temperature, ionic strength, Fe(II1) concentration, data range, number of data points, and initial estimates of k , A,, and A m are evaluated. When 248 A, vs. f points collected over four half-lives are used In the computation, within-run lmpreclslon Is less than 0.1 % for thiocyanate concentrations between 25 and 250 pmoi/L. When results for 278 pairs of results determined by the kinetic and a nearequlllbrlum method for different temperatures, pH, Ionic strengths, and Fe( 111) concentrations are compared, the least-squares equation for kinetic ( y ) vs. equilibrium ( x ) results is y = (1.006 f 0 . 0 0 0 6 ) ~ -0.0002 f 0.0001 with standard error of estimate of 0.001 and correlation coefficient of 0.9 9994.
-
Recent advances in instrumentation, data processing methods, and operating procedures have made kinetic methods of analysis competitive with the more common equilibrium methods in terms of simplicity, speed, and precision ( I , 2). However, it is generally recognized that kinetic methods tend to be more dependent upon experimental variables such as pH and temperature than most equilibrium methods. Variations in experimental variables among standards and samples are often translated into uncertainties in experimental results via variations in rate constants that are used explicitly or implicitly in computational steps. Procedures that could reduce the dependency of the analytical result upon variations in the rate constant could likely reduce the dependency of kinetic methods upon experimental variables. First-order reactions have the unique property that the first-order rate constant can be determined independent of any knowledge of the concentration of the rate-limiting species. It has already been noted that this property can be exploited by using the first-order rate constant as a diagnostic tool in the detection of errors in kinetic analyses based on first-order reactions ( 3 , 4 ) . Perhaps more importantly, this property should permit the independently determined rate constant for each sample to be used in a computational step for that sample. Such a procedure should minimize effects on analytical results of differences in experimental variables that influence the rate constant. This paper describes and evaluates a new approach to first-order kinetic analyses that takes advantage of this property of first-order reactions to reduce the dependency upon experimental variables. The method retains the advantages of selectivity and inherent blank correction normally associated with kinetic methods, 0003-2700/78/0350-1611$01 .OO/O
but it involves a sacrifice in speed compared to initial-rate methods. Simply stated, the new method uses a multiple-linearregression program to compute initial and equilibrium values of the signal and the first-order rate constant that represent the “best fit” of signal vs. time data to a first-order model. Analyte concentration is computed from the difference between initial and equilibrium signal values. The method derives its reduced dependency upon experimental variables from the facts that the total change in signal at equilibrium is less dependent upon the variables than are the kinetic data, and that the rate constant used to define the first-order process is determined independently for each sample while the analysis is in progress. A kinetic procedure for thiocyanate based on the Fe(III)/thiocyanate reaction was used as a model to evaluate important characteristics of the new approach. Data presented for temperature, pH, ionic strength, and Fe(II1) dependencies show that the characteristics of the method are more nearly those of an equilibrium approach than of a more conventional kinetic approach.
GENERAL CONSIDERATIONS The Fe(III)/SCN- reaction was monitored by measuring the absorbance of the product at 450 nm. Therefore, the treatment presented here is in terms of absorbance; however the treatment can be generalized to any signal system that changes linearly with concentration. Concept of t h e Method. Concepts involved in the new method are illustrat,ed in Figure 1. The open diamonds represent selected data points measured during a part of the reaction, and the solid diamonds represent near-equilibrium results that are used for comparison with kinetic results. The solid line represents a fit of the data, represented by open diamonds, to a linearized first-order model with a multiple-linear-regression method (5,6). The regression values pf the initial absorbance, A,, and equilibrium absorbaqce, a r t used to compute the total absorbance change, AA = A , - A,; and analyte concentration is evaluated from this absorbance change. Because the method computes the absorbance change that would be measured if the reactions were monitored to completion, the method should have characteristics more closely related to the equilibrium methods than to conventional kinetic methods provided the first-order rate constant used to fit the model is the correct one for the conditions existing for each individual sample. The multiple regression method satisfies this criterio? by detFrmining the value of the rate constant (as well as A. and A , ) that represents the “best fit” to the data for each individual sample. Mathematical Description. For a first-order reaction monitored via absorbance changes, the absorbance vs. time relationship is given by
4,
At = A , - ( A , - A,) e-kt
(1)
where Ao, A,, and A , are initial, intermediate, and final absorbances, and k and t are the first-oTdef rate coptant and time. The simultaneous estimation of A,, A,, and k is simpler 0 1978 American Chemical Society
