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Anal. Chem. 1003, 65, 2563-2567
Analytical Applications of Catalytic Properties of Modified Cyclodextrins Ellen Tuanying Chen and Harry L. Pardue. Department of Chemistry, 1393 BR WN Building, Purdue University, West Lafayette, Indiana 47907-1393
This paper describes the evaluation of the catalytic properties of modified cyclodextrins for analytical applications. The 8-dimethylcyclodextrin was modified by adding one and two imidazolyl groups at carbon three positions. The modifications produced enhancements of catalytic activity for the hydrolysis of pnitrophenyl acetate at neutral pH by factors of 1000 or more relative to the unmodified cyclodextrins. The catalytic properties of the monosubstituted cyclodextrin were evaluated for the quantification of pnitrophenyl acetate in the concentration range of 10-90 pmol/ L. Results obtained by equilibrium, initial-rate, and error-compensatingpredictive kinetic methods were compared. The equilibrium and predictive kinetic options yielded virtually identical results, with linear changes with concentration throughout the range studied and severalfold larger than the initial-rate option and dependencies on temperature, pH, and catalyst concentration that are 5-10-fold smaller than the initialrate option. Cyclodextrins are macrocyclic compounds consisting of 6-12 D-glucose units joined at the a-1,4 positions. The most common forms consist of 6, 7, and 8 glucose units and are identified as the a-,8-, and y-cyclodextrins, respectively.' The cyclodextrins mimic enzymes in the sense that they catalyze certain types of chemical reactions such as hydrolyses of esters and phosphates; moreover, the catalytic activities can be enhanced by modifying the cyclodextrins to contain functional groups involved in the catalytic action of enzymes.'-S Although there have been extensive studies of the catalytic behavior of both unmodified and modified cyclodextrins (CD and M-CD),3-8there have been few if any studies of possible analytical applications of the catalytic properties of these compounds. This paper describes a study of the use of the catalytic behavior of cyclodextrins for the kinetic determination of selected organic compounds. We chose p-nitrophenyl acetate @-NPA) as a model substrate because the hydrolysis product, p-nitrophenolate ion @-NP-) is easily monitored by its absorbance near 400 nm. Because preliminary studies indicated that 8-cyclodex(1) Bender, M. L.; Komiyami, M. Cyclodextrin Chemistry; Springer-Verlag: Berlin, 1978. (2) Breslow, R.;Bovy, P.; Hersh, C. L. J. Am. Chem. SOC.1980,102, 2115-2117. - - - -- - . .
(3) Tabushi, I. Acc. Chem. Res. 1982,15, 1566-1572. (4) Szejtli,J.Cyclodextrin Technology;Kluwer Academic Publishere: Boston, 1988. (6)Stoddart, F. Cyclodextrins; Royal Society of Chemistry: London,
trin was the more active of the three most common CDs, most of the study was done with unmodified and modified forms of this compound. Two modified forma of 8-CDwere prepared and studied. The two modifications involved addition of one and two imidazole groups to 8-dimethylcyclodextrin (8DMCD). The two modified CDs are identified throughout as the mono- and bis-modified 8-dimethylcyclodextrine (mM8-DMCD and bM-8-DMCD). Some results are reported for unmodified a-cyclodextrin (a-CD) for comparison purposes. Results are reported and compared for data-processing methods without and with error-compensating capabi1ities.B The latter method is shown to reduce effects of experimental variables such as temperature and the concentration of catalyst.
EXPERIMENTAL SECTION Instrumentation. Data for absorbancevs time were obtained with a diode-array-based spectrophotometer (Model 845OA, Hewlett Packard Co., Palo Alto, CA). Data were transferred to and processed by a supermicrocomputer (Model5500 workstation, Masscomp, Westford, MA) as described earlier.'O Reagents. All reagents except the substrate were prepared in doubly distilled (Megapure distillation apparatus, Coming Inc., Corning, NY) deionized water. Substrate. The p-nitrophenyl acetate (AldrichChemicalCo., St. Louis, MO) was purified by recrystallization from hexane and tested for purity by using gas chromatography. Serial dilutionsof p-NPA were prepared in freshly distilled acetonitrile (Fisher Scientific, Chicago, L)and stored at 4 "C until used. Modified Cyclodextrins. The mono- and bis-modified dimethyl cyclodextrinswere synthesized by using a slightly modified procedure described earliere6 Briefly, 0.80 g of 80% sodium hydride (Aldrich)was washed three times with degassed n-hexane to obtain 0.6 g (0.026 mol) of purified sodium hydride. The purified sodium hydride was added to 5 g of 8-DMCD (Aldrich) in 0.040 L of dry tetrahydrofuran under nitrogen at 0 O C . The solution was heated and maintained at 35-38 "C for 10 h. After the solution was again cooled to 0 "C, 1.0 g of 2-(4-imidazolyl)ethyl bromide (synthesized as described previously'') in 10 mL of degassed tetrahydrofuran was added and the solution was maintained at 25 "C for 10 h to obtain the monosubstituted cyclodextrin(mM-P-DMCD)or 20 h to obtain the bis-substituted product (bM-fl-DMCD). Products were isolated by column chromatography on silica gel ((2-60, 200-240 mesh) by elution with a ternary mixture of n-butanol, dimethyl formamide, and water in volume ratios of 2:1:1, respectively. The product of the 10-hreaction is a yellowish solid;the product of the 20-h reaction is a green solid. The products were characterizedby using elemental (C, H,N) determinations, fast-atom-bombardment mass spectrometry (FAB-MS),two-dimensional nuclear magnetic resonance spectrometry (in DzO), and ultraviolet absorption. The yellow precipitate from the 10-h reaction was expected to be c-3-[2(4-imidazoly1)ethylldimethyl-P-cyclodextrin;the green precipitate from the 20-h reaction was expected to be c-3,31-[bis[2-
1989.
~~
(6) Ikeda, H.;Kojin, R.; Yoon, C.-I.; Ikeda, T.;Toda, F. J. Znclwion Phenom. 1989, 7, 117-124. (7)Bredow, R. Acc. Chem. Res. 1991,24, 317-324. (8)Schneider, H.-J.; Dtkr,H. Frontiers in Supramolecular Organic Chemistry and Photochemistry; V C H New York, 1991. 0003-2700/93/0365-2563$04.00/0
(9) Pardue, H. L. Anal. Chim. Acta
~~
1989,216,69-107. (10)Skoug,J.W.; Weber, W.E.;Cyliax,I.;Pardue, H.L. Trends Anal. Chem. 1986,5, 32-34. (11) Stensilb, K.-E.; Wahlberg, K.; Wahren, R. Acta Chim. S c a d . 1973,27,2179-2183. 0 1993 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 19, OCTOBER 1, 1993
(4-imidazolyl)ethyl]]dimethyl-~-cyclodextrin.The elemental Table I. Kinetic Parameters for the Hydrolysis of results (percent found) for the yellow precipitate were C (48.65), pNitropheny1 Acetate with and without Different H (7.341,and N (1.971, Corresponding to CalHl~OsaNr4H20,MW Catalysts = 1425 + 4H20. Results for the green precipitate were C (42.8), kc KUI ~O, H (7.271, and N (3.571, corresponding to C M H ~ I O O ~ ~ N ~ - ~ ~ Hcatalyst pH8 (OC) (10-26-1) (16ks-1) (10"M) ( k d k d MW = 1519.6 + 18H20. Molecularweights determined by FABbM-P-DMCD 7.2 30 6.06* 0.4b 1.26 1.45 0.2* 4810 MS were 1425.0 and 1519.6 for the yellow and green solids, mM-8-DMCD 7.2 30 1.57 1.26 7.24 1246 respectively. Two NMR peaks for each compound, corresponding mM-&DMCD 7.2 25 1.45 O.Olb 1.31 2.82 0.04 1106 to chemical shifts of 6 = 7.7 and 8.25, are consistent with peaks mM-O-DMCD 7.2 25 1.44 1.31 2.60 1100 found for the starting imidazole compound. Areas of these peaks ~IU-&DMCD 8.2 25 3.12 0.4b 2.85 1.97 0.6b 1095 for the yellow compound correspond to one hydrogen per peak mM-O-DMDDe 8.2 25 2.67 2.9 2.90 921 while areas for the green compound corresponded to two hydrogens per peak. a Phoephata buffer (0.067 M).* Average of three runs, Reference 6. The two-dimensionalNMFt results indicated that the imidazole groups are attached through the ethyl group to carbon 3 on one of the glucose units in the cyclodextrin. Both compounds gave an ultraviolet absorption maximum at 250nm when diesolved in water. With the exceptionof the carbon content for the green solid, all these results are consistent with mono- and bis-substituted /3-dimethylcyclodextrinand the products are identified below as mM-B-DMCD and bM-b-DMCD, respectively. Procedures. Catalyst (in buffer) and substrate (in acetonitrile) solutions were prepared fresh each day and equilibrated to the desired temperature by immersion in a temperaturecontrolledwater bath. For each run, 1.00 mL of catalyst solution and 5.0 p L of substrate solution were added to the temperaturecontrolled cuvette in the spectrophotometer and the resulting solution was stirred briefly with a small stirring rod. Data acquisition was initiated 6 s after addition of sample, and absorbance values at 400 nm were recorded at 2-8 intervals. Equilibrium results were computed as the average of 10 data points collected between 786 and 806 s (-23 tip). Predicted equilibrium absorbance changes were computed by fitting firstorder12and Mi~haelis-Menten'~models to time-dependent data during the first 75-80% of each reaction. Initial rates were Time (s) computed by applying a moving-window derivative method" to time-dependent data during the first 10% of the reaction. ~~
* *
1
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RESULTS AND DISCUSSION Imprecision is reported at the level of one standard deviation (& 1 SD) throughout. Kinetic Behavior. To facilitate comparisons with earlier reports,- some studies were done initially at pH 7.2 and 8.2 in phosphate buffer (0.067 M) at 30 "C. Plots of reciprocal velocityvs reciprocal concentration (Lineweaver-Burke plots) were linear. Michaelis constants, Km, and maximum velocities, V-, were evaluated in the usual way from the slopes and intercepts, respectively, of these plots. Catalytic rate constants, k,, were computed, as the maximum velocity divided by the catalyst concentration k, = V,JCat. Values of selected constants obtained for the mono- and bis-substituted 8-dimethylcyclodextrin are included in Table I along with the rate constants for the uncatalyzed reaction and results obtained in an earlier study.6 There is reasonable agreement among constants determined in this study and those reported earlier. The largest discrepancy (32%) is between Michaelis constants determined at pH 8.2 and 25 OC in the two studies. Even here, similar orders of magnitude were obtained. Response Curves. Because reactions were quite slow for pH values described in the previous section, the remainder of these studies were done at pH 10.6 where reactions were faster. Figure 1A compares responses for the hydrolysis of p-nitrophenyl acetate under conditions that are the same except for the catalysts used. Plots a and b represent responses for the bis- and monosubstituted 8-DMCD whereas (12)Mieling, G.E.;Pardue, H. L.; Thompson,J. E.; Smith, R. A. Clin. Chem. 1979,25,1581-1590. (13)Hamilton,S.D.; Pardue, H.L. Clin. Chem. 1982,28,2359-2365. (14)Savitzky, A.;Golay, J. E. A d . Chem. 1978,50,1611-1618.
o.6
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.................................
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I
I
1
I
200
400
600
800
Time (s) Fig&. 1. Response cwves for hydrolysisof pnkrophenyl acetate. (A) Catalysts: (a) bM-BDMCD, (b) mM-B-DMCD, (c) and none, and (d) 8-DMCD. Condltkns: Cda,b,d) 54 pmol/L; , ,C = 0.411 "ol/ L; temp, 30.0 O C ; pH 7.2 (phosphete buffer). (B) Effects of substrate concentration: (a)9.95, (b) 27.2, (c) 45.3, (d) 84.7, and (e) 84.6 pmol/ L. Catalyst, mM&OMCD; C, = 4.2 mmol/L; temp, 25.OoC pH 10.8 (carbonate buffer): lonlc strength, 63.2 "ol/L. Experimental data (-); firstorder fit (-).
curve c is for the hydrolysis without a catalyst and curve d is for hydrolysis in the presence of unmodified 8-DMCD. Clearly both the mono- and bis-substituted cyclodextrinsyield enhanced reaction rates. Either catalyst could have been used in this study. However, because larger amounts of monosubstituted product (mM 8-DMCD) were synthesized, it was used in the remainder of this study.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 19, OCTOBER 1, 1993
- 157
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Concentration (1 O 5 moi/L) Flgure 2. Callbratlon plots for predictive and inltlal-rate methods. Conditionsas In Figure 18. Linear least-squares flts through first three points: predictive method (0, -): rate method (A, -).
--
Figure 1B represents time-dependent response curves for the catalyzed hydrolysis of different concentrations of p-nitrophenyl acetate in the presence of equal concentrations of mM-8-DMCD. Individual points represent experimental data, and the solid lines represent fits of a first-order model to the data. The first-order model fits the data quite well and waa used for all subsequent studies. Calibration Results. Calibration results for the initialrate and predictive methods are given in Figure 2. The ordinate values for the predictive method are multiplied by a constant factor (30) to adjust the numerical values of the two data seta to be about the same for the three lowest concentrations where both plots are linear. The linear plots in the figure represent linear-least squares fits through the first three points in each case. The least-squares statistics for these fits are included as the first two rows in Table 11. The relative standard deviations for the slopes are about thesame, 7.2% fortheratemethodand6.7% forthepredictive method. In each case, the standard error of the estimate is 5.9% of the midpoint value and the correlation coefficients are essentially the same. The primary difference between the two data sets is the curvature of the rate data toward the concentration axis at higher concentrations. The larger intercept for the rate method probably results from the fact that the plot is already beginning to curve toward the concentration axis at the highest concentration value included in the least-squares fit. Although there is some scatter at higher concentrations for the predictive method, both points at higher concentrations are much closer to the least-squares line than for the rate data. Clearly, the predictive method is linear to much higher concentrationsthan the rate method. Other data in Table I1 represent least-squares statistics for equilibrium results and predictive results with different fitting ranges. There are only small differences between results by the equilibrium and predictive methods for fitting ranges of two half-lives or more. It is noted that the relative standard deviations of the slopes for the predictive method (-2.6% ) are better than those for the equilibrium (9.6%) and initial-rate (7.2%) methods. The same is true for the standard errors of the estimate relative to midpoint values (2.6% for the predictive method relative to 11%and 5.9% for the equilibrium and rate methods, respectively). Variable Dependencies. One goal of this study was to evaluate the effects of changes in selected experimental variables on results obtained by the different data-processing options. Variable studied were temperature, pH,and catalyst
2505
concentration. Relative error coefficients (rec) were used to quantify and summarize effects of these variables on the initial-rate,equilibrium, and predictive data-processing methods. Relative Error Coefficients. The relative error coefficient for any variable, V, is equal to the change in concentration, AC, produced by a change, AV, in the variable of interest divided by the concentration [rec (%) = lOO(AC/AW/C]. There are different ways to quantify relative error coefficients.16.16 In this study, we obtained signals for a single anal@ concentration at each of severalvaluesof each variable. The error coefficients were evaluated in linear regions of calibration plots for each data-processing option. Assuming a linear calibration plot with intercept, a, two measured signals, Siand SI, at a single anal@ concentration, and two values, Vi and V,, of the variable of interest, one can compute a ratio
Ri = (Si- al)/(S1 - Or)
(1)
in which the subscripts, i and r, refer to test and reference values, respectively, of the variable. For several such ratios obtained in this way, it is easily ~hown15that the slope of a plot of the ratios, Ri,as ordinate vs different values, Vi, of the variable is equal to the relative error coefficient at the value of the variable at which the slope is measured. In this study, all the intercepts in eq 1were very small and relative error coefficients were determined from plots of ratios computed with intercepts assumed to be zero, i.e., Ri = SJS,. Results for temperature, pH, and catalyst concentration are given below. Temperature. Effects of temperature change are illustrated in Figure 3 for the three data-processingoptions. The ordinate is the ratio of signals at 29,33, and 35 OC to that at 31 O C . Whereas plots for the equilibrium and predictive methods are virtually flat, the plot for the initial-rate method has a significant positive slope indicating a positive error coefficient. Numerical values of the error Coefficients computed from the slopes of these plots are summarized in the first data column of Table I11 for the equilibrium, predictive, and initial-rate methods. The equilibrium and predictive methods have essentially the same temperature coefficients, and both options are -15-20-fold less dependent on temperature than the initial-rate option used in the concentration range for which initial-rate varies linearly with concentration. For higher substrate concentrations for which the rate changes less rapidly with change in concentration, the temperature coefficient for the rate option would be significantly larger than that computed above whereas the error coefficients for the equilibrium and predictive methods would be essentially the same. Correlation coefficients,r, for least-squares fits of signalratios vs variable values are also included in parentheses in the table. Results for the equilibrium and predictive methods are much less correlated with temperature than are results by the rate option. The temperature coefficients for the equilibrium and predictive options are somewhat larger than we had expected relative to the value for the rate option. In an attempt to identify the source of this larger temperature dependency for these two options, we evaluated the effect of temperature on the absorbance after the reaction had been permitted to react to equilibrium. At 31 OC, the molar absorptivity of the reaction product (at 400 nm) was determined to be 11.7 X 109 L/mol-cm and varied linearly with temperature between 25 and 35 "C with a slope of 160 L/mol.cm°C. This slope corresponds to a relative temperature coefficient of 1.4%/ (15)Lim,K. B.; Pardue, H. L. Anal. Chem., in press. (16) Li, J.; Pardue, H. L. Anal. Chem., in press.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 19, OCTOBER 1 , 1993
Table 11. Least-Squares Results for Different Data-Processing Options. slope (SD)(le L/pmobb intercept (SD)(absorbance)b method (10-4 L/pmol.s)c (10-4s-1)C rated predictive (4tl/# equilibriume predictivee (range, t l p ) f 8 6 4 3 2
SE (absorbance)b (10-4
correl coeff
2.36(0.17) 7.45(0.5) 7.79(0.75)
3.8(5.3) O.Ol(0.015) 0.0092(0.04)
4.2 0.012 0.044
0.997 0.998 0.997
7.69(0.2) 7.74(0.2) 7.65(0.2) 7.66(0.2) 7.75(0.2)
0.0022(0.01) 0.0041(0.01) 0.0051(0.01) 0.0053(0.01) 0.010(0.02)
0.011 0.012 0.010 0.012 0.017
0.9993 0.9992 0.9996 0.9992 0.9984
a Conditions as in Figure 1B. b Equilibrium, predictive methods. Rate method. Lowest three concentrations. e All concentrations. f Fitting range.
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Flgure 4. Effectsof pH on resultsobtained by different data-processing = 50 pmol/L and options. Conditions as in Figure 1B except &A C, = 27 pmol/L. Symbols as In Figure 3. Reference signals at pH 10.6: (0)0.52 X lo4; (0)0.59 X lo3; (A) 3.04 X lo4 s-'.
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~~~
Table 111. Relative Error Coefficients for Three Variables and Three Data-Processing Options re1 error coeff (corr coeffp temp PH catayst option (%/"C) ( % /pH unit) ( % /mmol.L) 14.3 (0.99)b 0.7 (0.73) 1.0 (0.78)
316 (0.997)c -3.8 (-0.68) 3.0 (0.50)
13
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Flgure 9. Effects of temperature on results obtained by differentdataprocessing options. Conditions as In Figure 18 except CFA = 50 pmol/L and C,, = 60 pmol/L. Equilibrium (0); predictive (0); Initial rate (A). Reference signals at T = 31.0 OC: (O), 0.599 X lo3; (0) (A) 4.43 X lo3 s i . 0.611 X
rate equilibrium predictive
12
84 (0.98) 1.4 (0.22) 1.6 (0.15)
a Correlation coefficients for least-squares fits of signal ratio vs variable of interest over full range in Figures 3-5 except as noted below. 29-35 OC. pH 10.6-12.0.
"C. Thus, most of the temperature Coefficients for the equilibrium and predictive options probably result from the temperature coefficient of the absorptivity of the reaction product rather than the kinetic behavior of the reaction. pH. Figure 4 includes data for the effects of pH on results obtained by the three data-processingoptions. For pH values between 9 and 10, all three options have relatively small dependencieson pH. However, above pH 10,the dependency of the initial-rate method on pH increases sharply. The error coefficients in this pH range for the three data-processing options are summarized in the second data column in Table 111. The rate method is roughly 100-fold more dependent on pH above pH 10.6 than are the other two options. For higher analyte concentrations (see Figure 2) the difference would be larger.
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Concentration (pmol/L) Flgure 5. Effects of catalyst concentration on results obtained with different data-processing options. Conditions as In Figure 1B except C ~ = 50 A pml/L. Symbols as in Figure 3. Reference signals at Cat values: (0)0.450 X lo4 s-l at 336 pmol/L; (0)0.464 X lo4 s-l at 756 pmol/L; (A) 1.63 X lo4 s-l at 336 pmoi/L.
Catalyst Concentration. Figure 5 shows plots of signal ratios, SJS,, vs catalyst concentration. Plots for the equilibrium and predictive options are virtually flat whereas that for the initial-rate option has a positive slope. The error
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 19, OCTOBER 1, 1993
coefficients obtained from the slopes of these plots are summarized in the third data column in Table 111. The equilibrium and predictive options are -50-fold less dependent on catalyst concentration than the initial-rateoption. As with temperature and pH, correlation coefficients for R vs V show much less correlation between equilibrium and predictive results and catalysts concentration than for the rate option. Time Dependence. The effect of storage time on the modified cyclodextrin was evaluated by preparing a stock solution of catalyst (1.86 pmol/L) in carbonate buffer (pH 10.6) and storing a portion at room temperature (-25 "C) and at 4 "C. Measurements were made at six different times during a 16-day period by using 50 pmol/L substrate. The apparent first-order rate constant, initial rate, measured equilibrium absorbance, and predicted equilibrium absorbance were determined for each data set and regressed ( h e a r least-squares) against time. For catalyst stored at 25 "C and at 4 "C,the slopes for rate constants vs time were -1.9 X 106 and -3 X 1od 8-1 day1 with initial values of 4.7 X 10-9 and 4.9 X 10-98-1, respectively. These slopescorrespond to changes of about -0.4 and -0.6%/day. Slopes for initial rates and measured and predicted equilibrium absorbances vs time all corresponded to changes of about (2 f 1)5% /day for samples stored at both 25 and 4 O C . We had expected that any change in catalyticactivitywould have larger effeds on rate constants and initial rates than on measured or predicted absorbances. We are unable to explain why this is not the case. In any event, time-dependent changes were relatively small.
Reproducibility. We evaluated the within-run reproducibility for each of the three data-processing options by making 10 runs on a fixed concentration (50 pmol/L) of substrate at a fixed set of conditions (25 O C , pH 10.6, ionic strength of 0.0632, and catalyst concentration of 26.7 pmol/ L). Average values of rates and absorbance changes for the initial-rate equilibrium, and predictive options were 6.68 s-l, 0.740, and 0.86, respectively, and the relative standard deviations were 5.12, 3.10, and 1.74%, respectively.
CONCLUSIONS Addition of one or two imidazolylgroups to 8-cyclodextrins enhances the catalytic activity several thousandfold relative to unmodified cyclodextrins. The modified compounds can be used to quantify esters such as p-nitrophenyl acetate in the submillimolar range. The combination of the catalytic properties of the modified cyclodextrina with error-compensating data-processing methods can extend linear ranges and reduce variable dependencies by 10-fold or more relative to initial-rate options.
ACKNOWLEDGMENT This work was supported in part by Grant GMl3326-24 from the National Institutes of Health.
RECEIVED for review December 28,1992. Accepted July 2, 1993.' ~~
Abstract published in Advance ACS Abstract& August 16, 1993.
