Anal. Chem. 1900, 62, 1523-1526
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CORRESPONDENCE Exchange of Comments on Fluorescence Quenching Measurements of Copper-Fulvic Acid Binding Sir: Recent work reported by Cabaniss and Shuman (I) on the measurement of copper-fulvic acid binding concluded that the methodologies for fluorescence quenching (FQ) titrations set forth by Ryan and Weber (2) rely on incorrect assumptions and are subject to large errors. Cabaniss and Shuman (I) proposed an alternate approach involving ion selective electrode (ISE) calibration of FQ and, on the basis of their measurements, evaluated the usefulness of the FQ technique. Their evaluation listed several “problems” with FQ including: (i) a large indeterminate error in calculating free copper ion concentrations ( [Cu2+]);(ii) the assumption that the amount of fluorescence quenched (Q)is directly proportional to the concentrations of copper-ligand complex by a proportionality factor A and that A is constant over the range of the FQ titration; (iii) difficulties encountered in obtaining reasonable binding parameter estimates for FQ data presumably caused by use of a “simplistic two-parameter model”. Other minor criticisms of the FQ methodology are also mentioned by Cabaniss and Shuman (I)as being potential problems, inconsistencies, or sources of error. The use of combined ISE and FQ measurements, as demonstrated by Cabaniss and Shuman (I),is no doubt a good approach which adds to our understanding of the copper-fulvic acid system. The complementary nature of the two techniques was shown by Fish and Morel (3) and a comparison of data was given in our original publication (2). However, we respectfully contend that Cabaniss and Shuman (1) have made certain invalid assumptions concerning FQ and ISE measurements and their interpretation of the data is seriously flawed. It is our opinion that these issues need to be presented to ensure that the full benefits of the FQ technique can be evaluated by others and that any future work will not be impeded by erroneous conclusions. Error Properties of FQ and ISE Data. Cabaniss and Shuman (I) have chosen to calculate the error of FQ titrations based on their quenching variable (8). Q is equal to the difference between the starting or maximum fluorescence intensity (Imax) and the fluorescence intensity a t any point in the titration (I)
Q=I,,-I
(1) Since Q is calculated by difference, the indeterminate error in Q (EQ) is relatively high at low values of total copper concentration (CUT)where very little quenching has taken place and I is similar in magnitude to Zm=. The error is high because Q is a small difference between two large numbers. However, calculating Q is obviously a poor way to represent FQ data and has no bearing on the procedure reported by Ryan and Weber (2, 4). An alternative transformation of FQ data to relative fluorescence (FREL), where F R E L = I/Ima,*lOO (2) as described by Ryan and Weber (2,4),gives more favorable error properties for the entire titration, especially at low CuT values. Since the FREL variable is defined as a ratio, the relative error (5)is calculated by using a different equation than that given by Cabaniss and Shuman (1)
Using the example, given by Cabaniss and Shuman (I),of a 2% error in the FQ titration and the fluorescence values a t 1pM CuT from their Figure 2, eq 3 gives a relative error of 2.8% in FREL. This is obviously superior to the 63% relative error in Q calculated in the manner described by Cabaniss and Shuman (I) for the identical conditions. It should be noted that the error in FREL increases slightly at higher values of CUTas I (eq 2) gets smaller. This relative error in FREL remains fairly small (i.e. < 5 % ) because I does not approach zero in FQ titrations of humic materials. The fluorescence intensity generally levels off a t minimum fluorescence values (I-) that are greater than or equal to 20% of ,I (1-4,6). Using fluorescence data in the form of FREL gives far better error properties than the transformation to Q. In addition, the error in FREL is lowest at low values of CUT, which are environmentally more significant than high copper concentrations. A discussion of error properties is also pertinent to data generated with the ISE. Cabaniss and Shuman (I, 7)transformed their ISE data to bound metal concentrations by a subtraction involving CuT and the free copper concentration ([Cuz+])determined by ISE. Propagation of error for ISE as described by Fish and Morel (3) clearly showed very high error at high copper concentrations where CUTand [Cu2+]are both large and their difference is small. This is the same area of the titration curve where ISE and FQ showed poor agreement. Cabaniss and Shuman (I)had an additional source of error in most of their experiments because they used p H buffers that are known to complex copper. In order to account for this complexation, they calculated a quantity, CUI, which included free copper and copper bound in inorganic complexes. There are many potential sources of error in determining the value of CUI. It is calculated from literature values of hydrolysis and stability constants which we (4) and others (8, 9) have determined will vary depending on their source. In addition, Cabaniss and Shuman (1)have completely ignored tenorite (CuO) formation which could dominate the copper equilibria in their pH 8.44 experiments with carbonate present (10).
The presence of inorganic copper species may affect the response of the copper ISE, especially if those species have a significantly high response factor (8). This interference would cause an erroneously high reading for [Cu2+]. Since this is the basis for the calculation of CUI,ultimately the bound copper concentration would be erroneously low. The calculation method used by Cabaniss and Shuman (I) may also have been in error. They used the program RATO OR (11) which we have found incorrectly calculates activity coefficients at 0.1 M ionic strength, the level used in their study (I). This error is potentially large compared to those mentioned above when calculating bound copper concentrations. However, any of the errors discussed so far are easily avoided or minimized by careful choice of data transformation methods and by avoiding the use of buffers (12) or using
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buffers that exhibit negligible Cu2+binding (13, 14). A final comment on FQ titration error is warranted by additional calculations made by Cabaniss and Shuman (1). In their paper, Cabaniss and Shuman (1)used or defined the proportionality constant A a t least six times. In their eqs 1 and 2, A was first defined; later in the Glossary A was again twice equated with certain variables, but its definition was changed. In the text, two additional hints were given as to the identity of A , but they do not agree. The most reasonable definition of A , and what we believe Cabaniss and Shuman ( I ) used in their calculation, is given in their eq 1 and can be rewritten
A = Q/[CuL]
(4)
This definition of A is confirmed by the units assigned to A by Cabaniss and Shuman (1) of mFl/pM CuL. Based on this definition for A , it is clear that CUIcannot be calculated from FQ measurements by CuT - AQ as stated by Cabaniss and Shuman (1) in their discussion of indeterminate errors. Determination of CuL by FQ and ISE. In comparing the FQ and ISE determination of copper complexation by fulvic acid, Cabaniss and Shuman (1, 7) clearly demonstrated an important difference between the two measurement techniques that has only been touched upon by others (2,3). This difference was manifested as a discrepancy between the copper binding measured by the two techniques under certain conditions. However, Cabaniss and Shuman ( I ) erroneously assumed that FQ and ISE should measure exactly the same binding and attempted to assign the discrepancy to inadequacies in the FQ methodology. Furthermore, they proposed to calibrate FQ with ISE measurements (1, 7), a procedure that would be highly inappropriate causing bias in the FQ data and loss of valuable information. The discussion below will hopefully clarify the relationship between FQ and ISE and give a better perspective on the measured quantities of these two techniques. It is our opinion that the most important issue to consider when comparing FQ and ISE is the recognition of which species are actually being measured by each technique. For ISE, free copper ion concentration, [Cu2+],is determined and either directly subtracted from CuT or used to calculate CUI, which is subtracted from CuT to give bound copper. We will refer to bound copper determined in this manner as [CUL]ISE. This designation is not meant to imply any stoichiometry, but rather refers to the copper concentration that is somehow associated with ligands in the system under study. An analogous definition can be made for binding as determined by FQ and will be designated here as [CuL],. For the sake of this argument, eq 4 can be rewritten
(5) The quantity [cuL]F$ is a molar concentration of ligand binding sites expressed in terms of copper that is bound. Again, no stoichiometry is implied by this definition. Cabaniss and Shuman (1)base their criticism of FQ on the fact that [cuL]FQ is not equal to [CUL]ISE under certain conditions. From this they concluded that A is not constant. Their evidence for this was given, in part, in their Figure 3 which showed reasonable linearity between [CUL]ISE and Q at low values of [c&]sE but deviated from linearity at higher copper loadings. We contend that Cabaniss and Shuman ( I ) interpreted this result incorrectly and that [cuL]FQshould not be equal to [CUL]ISE at higher copper loadings. Our reasoning is based on a fundamental understanding of how FQ and ISE work and what each is actually measuring. FQ measures a property of the humic material that changes with metal complexation. This process has recently been identified as static quenching (15). This means that the
reduction in fluorescence is due to a complexation reaction that leads to a nonfluorescent complex or a complex of lower quantum yield than the free ligand (16). As metal is added in an FQ titration, quenching occurs until all the quenchable sites are filled with metal ions. At this point the curve of I or Q vs CUT should reach a plateau, and no further static quenching can occur. However, complexation is not necessarily complete even though FQ can no longer measure binding. At least two possible scenarios can be postulated for the solution chemistry as the titration is continued. First, it is possible that very weak, nonfluorescent ligands continue to bind as CUTbecomes very high. Second, the very large excess of copper may result in a shift in stoichiometry from primarily 1:l type complexes (Le. CuL) toward 2:l complexes (Le. Cu,L). As more copper is added, it becomes more likely that bidentate copper complexes may give way to monodentate complexes. In this example, the ligand, L, can be thought of either as discrete ligand molecules or as ligand sites which may have a distribution of more than one per molecule. Cabaniss and Shuman (1) mentioned the first possibility given above and interpret it to mean that A is changing. We feel, however, it is a demonstration that FQ has reached the limit of its useful measurement range for the sample. FQ cannot be further utilized to measure binding in molecules that either are nonfluorescent or do not undergo a change in fluorescence upon metal complexation. Indeed some evidence has been reported indicating fluorescence in some humic materials seems to be associated with smaller molecules (17). This situation is not changed by using an “empirical model” with several different A values (I). Use of this type of model in the high CuT range, where CuL is formed with no change in fluorescence, requires a value for A equal to zero. It is difficult to see how this will increase our understanding of FQ binding relationships or how a model with parameters that “should not be assigned chemical meaning ...” (1)can enhance the study of metal complexation by humic materials. ISE, as utilized by Cabaniss and Shuman ( I ) , measures any process occurring in solution that consumes free metal ion. This would include hydrolysis, complexation, adsorption, or ion exchange. Once FQ has stopped responding to complexation, the ISE would still measure very weak binding by nonfluorescent ligands or increased loading of metal onto sites that had shifted their stoichiometry. It would also measure the loss of free metal due to adsorption onto metal-humic material aggregates that often form a t high metal concentrations. These aggregates would induce increased binding upon their formation (2, 17, 18). It should be noted also that the comparison of ISE and FQ data given by Cabaniss and Shuman (1)in their Figure 3 shows the greatest deviation when [CUL]ISE is above approximately 8 pM. This can be readily visualized by superimposing a line with their reported slope (7 mFl/pM) on the data. Fish and Morel (3)have reported error propagation data for the copper ISE that shows errors ranging from approximately 13 to 50% as [CUL]wE varies from 8 to 12 pM. The situation is of course much worse when the data extend to 27 pM [CUL]ISE as reported by Cabaniss and Shuman (1). Although a large number of papers have reported reasonable data for copper ISE titrations of humic materials, a few studies have demonstrated a possible problem. The copper ISE responds (i.e. changes potential) to changes in free ligand concentration in the abscence of metal ion for a variety of complexing agents including humic material (19,20). It is not clear as yet how this response may affect ISE measurements of copper-fulvic acid; however, it remains a possible interference. Difficulties Obtaining FQ Parameters. It has been observed by several groups that, in certain instances, the
ANALYTICAL CHEMISTRY, VOL. 62, NO. 14, JULY 15, 1990
nonlinear regression data treatment proposed by Ryan and Weber (2) for fluorescence quenching gives unreasonable values for the binding parameters (2,4,2I-23). Cabaniss and Shuman ( I ) claimed to investigate the reasons for these difficulties and they give three possibilities. Unfortunately, they offered little or no evidence to support their statements. First, Cabaniss and Shuman ( I ) have suggested that the “assumption of a simplistic two-parameter model” can cause problems with obtaining reasonable binding parameters. The two paramekrs in question are K and LT. The model actually contains a third parameter that is fit, Imin, but this is not a binding parameter per se and will not be considered. In defense of using a simplistic model, we must point out that neither the binding characteristics nor the fluorescence properties of humic materials are very completely understood. It is therefore unwarranted to use more complex models when they have “no chemical meaning” ( I , 2 4 )and are merely exercises in curve fitting and in generating meaningless curve fitting parameters (25). In the discussion above we have presented our ideas on the binding and quenching relationships for humic materials. These ideas can be formulated into a model in which a paramagnetic metal ion such as copper binds to humic material and its fluorescence either is quenched completely or is reduced (Le. a change in fluorescence efficiency takes place) and the quenched fluorophore is no longer affected by binding of additional metal ions via a static quenching mechanism. At higher loadings of metal ion additional binding may take place to nonfluorescent sites or complexed sites that have already undergone fluorescence quenching. In this model a 1:l type of stoichiometry best describes the binding as measured by fluorescence quenching. Throughout most of the titration experiment the metal ion concentration greatly exceeds the ligand concentration which precludes the formation of 1:2 (i.e. ML2) type complexes. As metal ion concentrations become very high, it is quite possible that 2:l (i.e. M2L) type complexes will form, but these are not measured by FQ since the fluorescence of L is quenched upon binding the first metal ion. A more appropriate criticism of the FQ data treatment might be that the model is inadequate to describe the measured behavior in certain instances. We have studied the performance of the two-parameter model for FQ, modified it, and derived other forms of data treatment. This work inolved adding more parameters to the model, testing the models with calculated data containing varying numbers of data points, developing a linear data treatment, and testing new models based on Stern-Volmer theory and modifications thereof. Several methods of treating FQ data that are different from the model originally proposed (2)have resulted from the work and will be summarized elsewhere. However, for those few data sets that we have found to give unreasonable fitting parameters, no improvement has been realized with new data treatments involving more complex models or additional fitting parameters. The second point mentioned by Cabaniss and Shuman ( I ) is that “large errors in calculated [Cu2+]”may be the cause of data analysis problems. This could not possibly be the case since the model in question (2)does not involve a calculation of [Cu2+];a t no point in the analysis is [Cu2+]used. In addition, as discussed above, the Ryan and Weber (2) data treatment uses FQ data in a form that gives rise to very favorable error properties. It is quite possible, as reasoned by Cabaniss and Shuman (I),that the high correlation between fitting parameters could cause problems in the nonlinear regression analysis. Bates and Watts (26) have demonstrated that highly correlated parameters can be an indication that the model is too com-
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plicated for the data set. This does not necessarily indicate that the model is inadequate or should be simplified, but that there may not be enough data to correctly drive the model. Convergence can be hindered if there is not enough data in all areas of the “design space” to provide for valid parameter estimates (26). For a well-defined titration curve, there should be no problem utilizing nonlinear regression analysis with the model described by Ryan and Weber (2) to obtain valid equilibrium parameters. This is indicated by the favorable results obtained in the majority of experiments (2, 4). There are two very likely explanations for why the nonlinear regression analysis did not converge to reasonable parameters in certain experiments: (I) There is not enough data to correctly define the equilibrium under study. (2) Large variances in the data or a changing variance over the course of the titration curve is affecting the ability of the model to fit the data. We recommend that fluorescence quenching titrations be conducted over the widest range of metal concentrations possible and that a large number of data points be collected to completely define the full modeling space. Care must be taken to avoid data collection where humic material aggregation takes place since neither the fluorescence nor the metal complexation behavior can be adequately modeled under these conditions as yet. This can be determined by performing light scattering experiments along with fluorescence ( 2 ) . In conclusion, it is evident from the many studies on humic material fluorescence referenced here (1-4,6,7,15,17,21-23) that FQ is of considerable interest and usefulness even in kinetic studies (27,28). Fluorescence quenching can be used to measure the binding process of humic materials. Ion selective electrodes can be used to measure free metal concentration and its change with binding. There is nothing fundamentally wrong with either approach to metal speciation; however, they are very different. ISEs show binding of the metal while FQ is unique in that it gives a perspective on the ligand during the binding. Comparing ISE and FQ by using variables generated by each technique is not a productive exercise ( I ) . A much better test of the two techniques would be to compare a common parameter or parameters derived from each. This was done by using ligand concentrations for FQ, ISE, and other techniques in the original paper by Ryan and Weber (2)and could also be done by comparing stability constants ( K ) . In the present context a comparison based on K would be much more suitable than attempts to reconcile variables which have different error properties dependent on the extent of the titration experiment. Cabaniss and Shuman ( I , 7) have presented interesting data comparing FQ and ISE measurements of copper-fulvic acid complexation. However, their interpretation of these data are superficial and flawed in many respects ( I ) . Every technique for metal speciation has certain advantages as well as certain disadvantages. It is our intent that the preceding discussion more accurately presents the strengths and weaknesses of FQ as compared to ISE.
ACKNOWLEDGMENT We wish to thank R. B. Smart (West Virginia University) and P. Sullivan (New England Aquarium) for comments on the manuscript. Special thanks go to M. Flynn for word processing. LITERATURE CITED (1) Cabaniss, S. E.; Shuman, M. S. Anal. Chem. 1988, 60, 2418-2421. (2) Ryan, D. K.; Weber, J. H. Anal. Chern. 1982, 5 4 , 986-990. (3) Fish, W.; Morel, F. M. M. Can. J . Chem. 1985, 63, 1185-1193. (4) Ryan, D. K.; Weber, J. H. Envlron. Sci. Techno/. 1982, 16, 866-872. (5) West, C. D. Essentials of Quantitative Analysis: McGraw-Hili, Inc.: New York, 1987; Chapter 2. (6) Ryan, D. K.; Thompson, C. P.; Weber, J. H. Can. J . Chern. 1983, 61, 1505- 1509. (7) Cabaniss, S. E.; Shuman, M. S. Anal. Chern. 1986, 58, 398-401.
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Anal. Chem. 1990, 62, 1526-1528 Nelson, H.; Bend. D.; Erickson, R.; Mattson, V.; Lindberg, J. U S . EPA Report EPA/600/3-86/023, U.S. EPA: Duluth, MN, 1986. Gulens, U.; Leeson, P. K.; Segutn, L. Anal. Chim. Acta 1984, 756, 19-31. Stumm, W.; Morgan, J. J. Aquatic Chemistry: An Introduction Emphaslzing Chemical €quillbria in Natural Waters ; Wiley-Interscience: New York, 1970; p 268. Cabaniss, S. E. Envlron. Sci. Technol. 1987, 27, 209-210. Skogerboe, R. K.;Wilson, S. A.; Osteryoung, J. G.; Florence, T. M.; Batiey, G. E. Anal. Chem. 1980, 52, 1980-1962. Perrin, D. D.; Dempsey, B. Buffers for pH and Metal Ion Control; John Wiley 8 Sons: New York, 1974; 176 pages. Good, N. E.; Winget, G. D.; Winter, W.; Connolly, T. N.; Izawa, S.; Singh, K. M. M. 6iochemstry 1968, 3 , 467-477. Power, J. F.; LeSage, R.; Sharma, D. K.; Langford, C. H. Environ. Technol. Lett. 1988, 7 , 425-430. Patonay, 0.; Shapho, A.; Diamond, P.; Warner, I.M. J . fhys. Chem. 1988, 9 0 , 1963-1966. Underdown, A. W.; Langford, C. H.; Gamble, D. S. Environ. Sci. Techno/. 1985, 79, 132-136. Teasdale, R. D. J . Soil Sci. 1987, 3 8 , 433-442. Sekerka, I.; Lechner, J. F. Anal. Lett. 1978, A l l , 415-427. Fltch, A.; Stevenson, F. J.; Chen, Y. Org. Geochem. 1988, 9 , 109-1 16. Berger, P.: EwaM, M.; Liu, D.; Weber, J. H. Mar. Chem. 1984, 74, 289-295. Holm, T. R.; Barcelona, M. J. I n froceedlngs of the eound Water OeOChemktty Conference 7988; Water Well Journal Publlcation Co.: Dublin, OH, 1988; pp 245-287. Newell, A. D. An investNtbn of copper-organic complexes in the fatuxent Rlver. Matyknd; UNC, Department of Environmental Science 8 Engineerlng: Chapel HIII, NC, 1983. Cabaniss. S. E.; Shuman. M. S. Geochim. Cosmochim. Acta 1988, 52, 195-200.
Sir: While some of Ryan and Ventry’s criticisms ( I ) are correct, they have missed the principal point of OUT paper (2). They ignore the motivation for fluorescence quenching (FQ) measurements, which is to describe metal speciation in solutions containing humic and fulvic acids. The authors also incorrectly assert that FQ measurements alone can be used to calculate equilibrium K values for copper-fulvic acid binding withoug having to calculate free (or inorganic) copper concentration ( I ) . FQ titration data can be represented as FREL (relative fluorescence) which has a low relative standard deviation ( < 5 % ) for all data points. Ryan and Ventry argue that binding parameters CL (complexation capacity) and equilibrium K
can be determined from a model (3)that ”does not involve a calculation of [Cu2+]”( I ) . It would be indeed surprising if binding parameters determined without calculating [Cu2+] could accurately describe metal binding (predict [CuL] and [Cu2+]in solution). If this contention were true, the findings of the paper in question (2) and earlier papers ( 4 , 5) would be irrelevant. In fact, their argument is incorrect because (1)any method of determining K must include a term for [Cu2+],and the method used in ref 3 is no exception and (2) binding constants generated by the method used in ref 3 do not necessarily describe metal binding well. Although they correctly describe the fluorescence intensity as a function of added metal, this is not the purpose of the measurements. Determining KUsing FQ. Since the definition of K (eq 1) uses [Cu2+],either [Cu2+]or some mathematically equivalent term must be used to calculate or curve-fit K . [Cu2+] calculated by
(25) Perdue. E. M.; Lytle, C. R. Symposium on Terrestrlal and Aquatic Humic Materials, Chapel Hill, NC, 1981. (26) Bates. D. M.; Watts, D. 0. Nonlinear Regvesslon Anabsis and Its Applicatbns; John Wiley & Sons: New York, 1988; 365 pages. (27) Hering, J. G.; Morel, F. M. M. €nnvhon. Sci. Technol. 1988, 22, 1469-1478. (28) Plankey, B. J.; Patterson, H. H. Environ. Sci. Technol. 1988, 22, 1454- 1459.
’
Current address: Chemistry Department, University of Lowell, Lowell, MA 01854.
David K. Ryan*J Lisa S. Ventry Edgerton Research Laboratory New England Aquarium Boston, Massachusetts 02110 RECEIVED for review August 14, 1989. Accepted March 12, 1990. This work was supported in part by Grant R-812101 from the U.S. Environmental Protection Agency, Office of Research and Development, and by a Donner Research Fellowship to D. K. Ryan from the University of Massachusetts, Boston, Environmental Sciences Program. L. S. Ventry was at the New England Aquarium through the Doctoral Internship Program, Department of Chemistry, Northeastern University, Boston, MA.
[Cu2+1 = CUT - [CUL]
(2) has high relative error if most of the total copper is present in bound form ( 2 , 4 ) . In the approach developed by Ryan and Weber (3,6) and adopted by others (7-9),a solution of ligand is titrated with copper and [Cu2+] is calculated by mass balance from CUTand [CuL] using eq 2. K is defined as in 1above. Combining maw balance in total ligand concentration CL = [L] + [CUL] (3) with eq 1, the fraction of bound ligand, X (X = [CuL]/CL) is shown to be a function of K and [Cuz+] K[Cu2+]
X=
1
+ K[CU2+]
(4)
Equations 4 and 2 are combined to give X as a function of K , CL, CUT,and X K(CUT - XCL) X = 1 + K(CUT - XCL) (5) Equation 5, in which [Cu2+]has been replaced by CUT- XCL), is written as a quadratic in X and the values of K and CL are found by nonlinear regression. (See eqs 3-9 of ref 3.) This method clearly relies upon a calculation of [Cu2+], contrary to the claim of Ryan and Ventry (3) quoted above; this is obvious on comparing eqs 4 and 5. Rearranging eq 5 into a quadratic does not remove the dependence on calculated [Cu2+],and neither does using FREL (proportional to (1- X)) instead of X. Describing Metal Binding. It is important to recall the motivation for these experiments. We study the binding of metals like Cu(I1) to dissolved organic material like fulvic acid because “(t)he transport, toxicity, and removal of trace metal ions in aquatic systems is intimately related to their speciation” (7). Consequently, we wish to be able to predict metal speciation in natural waters as a function of total metal,
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