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Kinetic spectrophotometric method for the simultaneous quantitation of amino acids in two- and three-component mixtures
Analytica Chimica Acta, 173 (1985) 43-49 Elsevier Science Publishers B.V., Amsterdam -Printed
KINETIC SPECTROPHOTOMETRIC SIMULTANEOUS QUANTITATION THREECOMPONENT MIXTURES
YAHYA R. TAHBOUBa and HARRY Department
of Chemistry,
Purdue
in The Netherlands
METHOD FOR THE OF AMINO ACIDS IN TWO- AND
L. PARDUB*
University,
West Lafayette,
IN 47907
(US A.)
(Received 22nd January 1985)
SUMMARY The development and evaluation of a kinetic method for the simultaneous quantitation of two- and three-component mixtures of amino acids are described. The method is based on reaction with ninhydrin. Multipoint kinetic data collected during one or more halflives of the slower-reacting component are processed with a nonlinear regression program to resolve the data into the concentrations of the individual components in the mixture. Results demonstrate good linearity between prepared and calculated concentrations of each component and total amino acid in the mixture (lo-50 PM). Slopes of least-squares fits of calculated vs. prepared concentrations vary from 0.98 to 1.13 and intercepts vary from -0.1 to 2.9 PM with standard errors of the estimate (S,,) between 0.67 and 1.7 MM.
Differences in the kinetic behavior of components that undergo the same or similar reactions have been used to resolve quantitatively the individual
components in mixtures for several years. Earlier methods were based on graphical or simple computational procedures [l-4]. More recent papers have described multipoint curve-fitting methods to resolve mixtures with kinetic data [5-81. Some of the curve-fitting methods were based on nonlinear regression methods [5,7] while others were based on so-called multiplelinear regression methods [6, 81. Also, all the curve-fitting methods have involved the use of data collected during 7-8 half-lives of the slowest reacting component. Although this latter approach is satisfactory for the fast reactions used as models in the earlier studies, it is less satisfactory for slow reactions for which measurement time can present a problem. The primary objective of this study was to evaluate the utility of the curvefitting methods to resolve mixtures of amino acids based on reactions with ninhydrin. Secondary objectives were to compare the two curve-fitting approaches and to evaluate the feasibility of utilizing data ranges shorter than 7-8 half-lives to resolve mixtures. Conclusions are that the curvefitting methods can be used to resolve selected two- and three-component ‘Present address: Department of Chemistry, Oklahoma State University, Stillwater,
OK 74078,
U.S.A.
0003-2670/85/$03.30
0 1985 Elsevier Science Publishers B.V.
44
mixtures of amino acids, that the two curve-fitting methods yield virtually identical results, and that satisfactory results can be obtained with data processed over as little as two half-lives of the more slowly reacting component. EXPERIMENTAL
Principles and procedures involved in the curve-fitting methods were described earlier [5, 6, 81. Briefly, signal vs. time data collected for a fixed period of time are fitted to a mathematical model that describes the kinetic behavior of the mixture. In the present study, the model involved two or three simultaneous pseudo-first-order reactions monitored by absorbance changes. The computed value of the absorbance change, AA,, for each component that gave the best fit to the experimental model was used to compute the concentration of the component. Experimental conditions required for first-order behavior for amino acids were described earlier [ 91. Briefly they involve a reaction medium consisting of 4.8 X 10m2 M ninhydrin, 4.3 X low3 M hydrindantin, 0.5 M acetate buffer at pH 5.5, and a temperature of 80°C. The acetate buffer was prepared by dissolving 54.4 g of sodium acetate trihydrate in water, adding 9.0 ml of glacial acetic acid, and diluting to 100 ml with water. A composite reagent was prepared daily by dissolving 500 mg of ninhydrin and 80 mg of hydrindantin in 20 ml of methylcellosolve (all from Sigma Chemical Co.) and adding 6.7 ml of acetate buffer. For each sample, 0.50 ml of the composite reagent and 0.40 ml of water were mixed in a cuvet and 0.1 ml of sample containing amino acids was added after the solution in the cuvet had reached 80°C. Absorbance was monitored at 10-s intervals at 570 nm with a distilled-water blank. Absorbance/time data were processed with regression programs described earlier [5,6,81RESULTS
AND DISCUSSION
Uncertainties for all quantitative results are quoted as one standard-deviation unit. Unless stated otherwise, reported results were obtained with the nonlinear least-squares curve-fitting method [ 51. Response curves Figure 1A shows response curves for three amino acids (histidine, isoleucine, and leucine). Figure 1B is a response curve for an equimolar mixture of these three components. The pseudo-first-order rate constant and absorptivity of the product for each component are computed from data such as those in Fig. 1A. Then, the experimental values of rate constants are used in the curve-fitting programs to compute values of A, and values of ff, for each acid that give the “best” (least-squares) fit of A vs. t data to the model for three simultaneous first-order reactions with known rate constants.
45 l.O(
E f 8
s ’
03
TIME (s)
808
0.3c
TIME (5)
808
Fig. 1. Response curves for selected amino acids: (A) 30 PM histidine (a), leucine (b), and isoleucine (c); (B) mixture containing 10 PM each histidine, leucine, and isoleucine.
The concentration of each component is computed from the absorbance change, AA, = A, - a,, by using a known value of absorptivity for the reaction product. The fitting process involves assumptions that there are no synergic effects among the amino acids and that all acids produce products with the same absorptivities. A bsorp tivitieshate constants Molar absorptivities for all amino acids examined except lysine are 2.24 X lo4 1 mol-’ cm-‘; the value for lysine is slightly larger at 2.37 X lo4 1 mol-’ cm-l. Pseudo-first-order rate constants for the five amino acids included in this study were 16.0, 12.5, 8.2, 6.8, and 3.9 X 10” s-l for histidine, glycine, leucine, lysine and isoleucine, respectively. It is of course important that these rate constants be independent of amino-acid concentration. For aminoacid concentrations between 10 and 50 PM, least-squares slopes of experimental values of rate constants vs. concentration (PM) were 2.6, 2.9 and 5.8 X 10” for glycine, leucine, and isoleucine, respectively, confirming the required low dependence on concentration. For isoleucine, the complete least-squares equation was h = 5.8 X 10” C? + 3.9 X 10-j For the lowest and highest concentrations (10 and 50 PM), computed values of le were 3.958 X 10” and 4.19 X 10” s-l, corresponding to a maximum difference of 0.23 X 10” s-l or 6%. This is the worst-case value; all other slopes and relative “errors” were smaller and well within the random uncertainty in experimental value of rate constants. Concentration data Results are reported here for two- and three-component samples processed with different data ranges and with the different curve-fitting approaches [5,6,81. Two-component samples. Samples contained lo-50 PM total amino acid and 5-45 PM of each component so that concentration ratios varied between 9:l and 1:9. The two different sets of mixtures evaluated were glycine with
46 50 0
40.0
0.0 0.0
10.0
20.0
PREPARED
40. 0
30.0
CONC.
50.0
(10.=M*1)
Fig. 2. Comparison of computed vs. prepared concentrations for two-component mixtures: (A) glycine with a fitting range of 7.4 half-lives; (B) isoleucine with a fitting range of 1.15 half-lives.
isoleucine, and leucine with isoleucine, involving ratios of rate constants of 3.2 : 1 and 2.1: 1, respectively. Best-case and worst-case results for the glycine/ isoleucine mixture are presented in Fig. 2. Reproducibility was evaluated for fixed amounts of each component in the presence of variable amounts of the other component(s). For 5, 20 and 35 PM each of the acids, standard deviations were 0.51, 0.39 and 0.41, respectively, for glycine and 0.84, 0.81 and 0.40, respectively, for isoleucine with data ranges of 8-408 s for glycine and 8-608 s for koleucine. More complete results are presented as pooled stanTABLE 1 Least-squares statistics for calculated vs. prepared concentration total amino acid in glycine/isoleucine mixturesa Date range
Glycine 8-408 8-248 8-208 Isoleucine S-608 8-248 8-208 Total amino 8-608 8-248 8-208
Synkc (0U
rd
0.12 f 0.21 -0.25 k 0.26 -0.26 + 0.35
0.64 0.78 1.05
0.999 0.997 0.995
1.00 + 0.01 1.02 * 0.02 1.03 * 0.02
0.32 f 0.21 -0.19 f 0.33 -0.01 * 0.49
0.67 1.09 1.61
0.999 0.995 0.990
1.00 f 0.01 0.99 + 0.01 0.99 It 0.01
0.14 f 0.21 0.36 + 0.41 0.43 f 0.45
0.45 0.64 0.95
0.999 0.999 0.996
Number of half-lives
Pooled s.d.b WI)
Slope + s.d.a
7.4 4.5 3.8
0.51 0.71 0.95
0.99 f 0.01 1.01 * 0.01 0.01 f 0.02
3.4 1.4 1.15 acid -
0.69 1.21 1.51 0.43 0.75 0.91
(s)
of glycine, isoleucine and
Intercept + s.d.a (PM)
a30 samples; 5-45 MM glycine, 5-45 PM isoleucine, and 10-50 MM total amino acid. bSeven groups with 5, 5, 4, 4, 4, 3, and 3 samples, respectively. CStandard error of estimate. dCorrelation coefficient.
47 TABLE 2 Least-squares statistics for calculated vs. prepared concentration total amino acid in leucine/isoleucine mixture@ Data range (s)
Half-lives (s)
Pooled s.d. (PM)
Slope * s.d.
7.05 4.75 3.60
0.76 1.26 0.94
1.03 f 0.02 1.00 f 0.03 0.95 f 0.04
-0.32 -0.10 -0.24
8-608 3.4 8-408 2.3 8-308 1.75 Total amino acid 8-608 8-408 8-308 -
0.69 1.68 2.24
1.07 f 0.02 1.05 f 0.03 0.98 i 0.05
-1.20 -0.36 -2.20
0.71 0.98 1.26
1.02 f 0.02 1.00 f 0.02 1.02 f 0.03
a30 samples; 5-45
PM leucine, 5-i5
Leucine 8-608 8-408 8-308
of leucine, isoleucine and
Intercept * s.d. (rM)
S &,
’
* 0.36 f 0.60 * 0.46
0.67 1.00 0.86
0.998 0.996 0.996
f 0.33 * 0.71 i 0.98
0.67 1.45 2.00
0.998 0.992 0.983
-0.43 f 0.55 0.32 f 0.81 0.39 * 0.98
0.69 1.00 1.25
0.999 0.998 0.997
Isoleucine
PM isoleucine, and lo-50
PM total amino acid,
dard deviations and least-squares statistics for fits of computed vs. prepared concentrations in Tables 1 and 2 for these two-component mixtures. In each case, best results were obtained for the faster-reacting component with data processed over longer times and worst results were obtained for the slowerreacting component with data processed over shorter times. To provide a basis for comparison, single-component samples were processed over similar data ranges by the predictive kinetic method described earlier [9]. The least-squares statistics for a fit of computed concentration (e) vs. prepared concentration (co) of glycine were C?’ = (1.007 + O.OOS)b - 0.16 f 0.21 with a standard error of the estimate (S,,) of 0.35 PM and correlation coefficient of 0.9996. All results for two-component samples are degraded relative to those for the single-component sample. However, when the standard error of the estimate is used as a measure of the scatter about the best fit to the data, results are degraded by little more than a factor of 2 as long as ratios of rate constants are 2:l or larger, and the data range includes three or more half-lives of the slower-reacting component. Shorter reaction times can be used with a corresponding increase in uncertainty. Three-component mixtures. Results obtained for two sets of three-component samples are summarized in Table 3. To obtain reasonably reliable results with these mixtures, it was necessary to process data over some 4.5 half-lives of the slower-reacting component. Results are substantially degraded relative to results for single-component samples and the best results for two-components mixtures but are similar to those for two-component
48 TABLE 3 Least-squares statistics for calculated vs. prepared concentration amino acid in three-component mixturesa Amino acid
Pooled s.d.b (fiM)
Hi&dine/lysine/isoleucine Histidine 1.12 Lysine 1.66 Isoleucine 1.25 Total amino acid 0.98 Histidine/leucine/isoleucine Histidine 1.21 Leucine 1.85 Isoleucine 1.35 Total amino acid 0.86
Slope * s.d.
of individual and total
Intercept f s.d. (PM)
S,, (rM)
r
1.02 1.04 1.09 1.03
f 0.03 f 0.06 + 0.04 f 0.02
-1.02 -0.70 0.20 -0.64
* 0.50 + 0.56 f 0.60 t 0.68
0.93 1.70 1.30 1.05
0.99 0.98 0.99
0.11 1.02 1.13 1.03
f 0.04 zt 0.06 f 0.04 It 0.03
-2.90 -0.32 -0.32 -0.72
f * * f
1.10 1.82 1.02 1.05
0.99 0.97 0.99 0.99
0.60 1.00 0.59 0.65
0.99
‘25 samples, concentration of each component 5 to 30 PM, and total amino acid 15 to 50 PM, data range 8-808 s. bSix groups with 4, 6, 6, 4, 3 and 2 samples, respectively.
mixtures when reduced data ranges are used. Longer monitoring times approaching 6-8 half-lives for the slower-reacting component would likely yield some improvement. However, such long times would not be practical unless some type of multichannel sample-processing system were used. Comparison of data-processing methods The two data-processing methods reported previously [5, 6,8] were used to process data sets for selected two- and three-component samples. For eighteen different combinations of samples and data ranges, the two methods yielded results for AA, that differed by less than 0.001. A linear leastsquares fit of computed absorbance changes for the multiple-linear regression (AA L ) and nonlinear regression (AA _ ) methods yielded the equation AA:, = 1.0002 AA,
- 0.0004
with S,, = 0.002 and r = 0.99995, the two fitting methods.
indicating excellent agreement between
Conclusions It is apparent from the data presented above that, for ideal samples, there is a real loss in reliability as one proceeds from one- to two- to three-component samples. If it were possible to do separations without any loss or cross-contamination, then clearly, best results would be obtained with complete separations so that measurements would be made on single-component aliquots of the sample. However, when allowance is made for the nonideal nature of separation processes, it may be possible to exploit the multi-component kinetic data-processing methods to resolve incompletely separated
49
samples with substantially less net loss of reliability than might be implied by the results presented above. This work was supported by Grant No. CHE 8319014 from the National Science Foundation. REFERENCES 1 H. B. Mark and G. A. Rechnitz, Kinetics in Analytical Chemistry, Interscience, New York, 1968. 2 H. A. Laitinen and W. E. Harris, Chemical Analysis, McGraw-Hill, New York, 1975, p. 389. 3 J. B. Pausch and D. W. Margerum, anal. Chem., 41(1969) 226. 4 D. W. Margerum, J. B. Pausch, G. A. Nyssen and G. F. Smith, Anal. Chem., 41 (1969) 233. 5 B. G. Willis, W. H. Woodruff, J. R. Frysinger, D. W. Margerum and H. L. Pardue, Anal. Chem., 42 (1970) 1350. 6 G. M. Ridder and D. W. Margerum, Anal. Chem., 49 (1977) 2098. 7 J. B. Landis and H. L. Pardue, Clin. Chem., 24 (1978) 1700. 8 R. S. Harner and H. L. Pardue, Anal. Chim. Acta, 127 (1981) 23. 9 Y. R. Tahboub and H. L. Pardue, Anal. Chim. Acta, 173 (1985) 23.
KINETIC SPECTROPHOTOMETRIC SIMULTANEOUS QUANTITATION THREECOMPONENT MIXTURES
YAHYA R. TAHBOUBa and HARRY Department
of Chemistry,
Purdue
in The Netherlands
METHOD FOR THE OF AMINO ACIDS IN TWO- AND
L. PARDUB*
University,
West Lafayette,
IN 47907
(US A.)
(Received 22nd January 1985)
SUMMARY The development and evaluation of a kinetic method for the simultaneous quantitation of two- and three-component mixtures of amino acids are described. The method is based on reaction with ninhydrin. Multipoint kinetic data collected during one or more halflives of the slower-reacting component are processed with a nonlinear regression program to resolve the data into the concentrations of the individual components in the mixture. Results demonstrate good linearity between prepared and calculated concentrations of each component and total amino acid in the mixture (lo-50 PM). Slopes of least-squares fits of calculated vs. prepared concentrations vary from 0.98 to 1.13 and intercepts vary from -0.1 to 2.9 PM with standard errors of the estimate (S,,) between 0.67 and 1.7 MM.
Differences in the kinetic behavior of components that undergo the same or similar reactions have been used to resolve quantitatively the individual
components in mixtures for several years. Earlier methods were based on graphical or simple computational procedures [l-4]. More recent papers have described multipoint curve-fitting methods to resolve mixtures with kinetic data [5-81. Some of the curve-fitting methods were based on nonlinear regression methods [5,7] while others were based on so-called multiplelinear regression methods [6, 81. Also, all the curve-fitting methods have involved the use of data collected during 7-8 half-lives of the slowest reacting component. Although this latter approach is satisfactory for the fast reactions used as models in the earlier studies, it is less satisfactory for slow reactions for which measurement time can present a problem. The primary objective of this study was to evaluate the utility of the curvefitting methods to resolve mixtures of amino acids based on reactions with ninhydrin. Secondary objectives were to compare the two curve-fitting approaches and to evaluate the feasibility of utilizing data ranges shorter than 7-8 half-lives to resolve mixtures. Conclusions are that the curvefitting methods can be used to resolve selected two- and three-component ‘Present address: Department of Chemistry, Oklahoma State University, Stillwater,
OK 74078,
U.S.A.
0003-2670/85/$03.30
0 1985 Elsevier Science Publishers B.V.
44
mixtures of amino acids, that the two curve-fitting methods yield virtually identical results, and that satisfactory results can be obtained with data processed over as little as two half-lives of the more slowly reacting component. EXPERIMENTAL
Principles and procedures involved in the curve-fitting methods were described earlier [5, 6, 81. Briefly, signal vs. time data collected for a fixed period of time are fitted to a mathematical model that describes the kinetic behavior of the mixture. In the present study, the model involved two or three simultaneous pseudo-first-order reactions monitored by absorbance changes. The computed value of the absorbance change, AA,, for each component that gave the best fit to the experimental model was used to compute the concentration of the component. Experimental conditions required for first-order behavior for amino acids were described earlier [ 91. Briefly they involve a reaction medium consisting of 4.8 X 10m2 M ninhydrin, 4.3 X low3 M hydrindantin, 0.5 M acetate buffer at pH 5.5, and a temperature of 80°C. The acetate buffer was prepared by dissolving 54.4 g of sodium acetate trihydrate in water, adding 9.0 ml of glacial acetic acid, and diluting to 100 ml with water. A composite reagent was prepared daily by dissolving 500 mg of ninhydrin and 80 mg of hydrindantin in 20 ml of methylcellosolve (all from Sigma Chemical Co.) and adding 6.7 ml of acetate buffer. For each sample, 0.50 ml of the composite reagent and 0.40 ml of water were mixed in a cuvet and 0.1 ml of sample containing amino acids was added after the solution in the cuvet had reached 80°C. Absorbance was monitored at 10-s intervals at 570 nm with a distilled-water blank. Absorbance/time data were processed with regression programs described earlier [5,6,81RESULTS
AND DISCUSSION
Uncertainties for all quantitative results are quoted as one standard-deviation unit. Unless stated otherwise, reported results were obtained with the nonlinear least-squares curve-fitting method [ 51. Response curves Figure 1A shows response curves for three amino acids (histidine, isoleucine, and leucine). Figure 1B is a response curve for an equimolar mixture of these three components. The pseudo-first-order rate constant and absorptivity of the product for each component are computed from data such as those in Fig. 1A. Then, the experimental values of rate constants are used in the curve-fitting programs to compute values of A, and values of ff, for each acid that give the “best” (least-squares) fit of A vs. t data to the model for three simultaneous first-order reactions with known rate constants.
45 l.O(
E f 8
s ’
03
TIME (s)
808
0.3c
TIME (5)
808
Fig. 1. Response curves for selected amino acids: (A) 30 PM histidine (a), leucine (b), and isoleucine (c); (B) mixture containing 10 PM each histidine, leucine, and isoleucine.
The concentration of each component is computed from the absorbance change, AA, = A, - a,, by using a known value of absorptivity for the reaction product. The fitting process involves assumptions that there are no synergic effects among the amino acids and that all acids produce products with the same absorptivities. A bsorp tivitieshate constants Molar absorptivities for all amino acids examined except lysine are 2.24 X lo4 1 mol-’ cm-‘; the value for lysine is slightly larger at 2.37 X lo4 1 mol-’ cm-l. Pseudo-first-order rate constants for the five amino acids included in this study were 16.0, 12.5, 8.2, 6.8, and 3.9 X 10” s-l for histidine, glycine, leucine, lysine and isoleucine, respectively. It is of course important that these rate constants be independent of amino-acid concentration. For aminoacid concentrations between 10 and 50 PM, least-squares slopes of experimental values of rate constants vs. concentration (PM) were 2.6, 2.9 and 5.8 X 10” for glycine, leucine, and isoleucine, respectively, confirming the required low dependence on concentration. For isoleucine, the complete least-squares equation was h = 5.8 X 10” C? + 3.9 X 10-j For the lowest and highest concentrations (10 and 50 PM), computed values of le were 3.958 X 10” and 4.19 X 10” s-l, corresponding to a maximum difference of 0.23 X 10” s-l or 6%. This is the worst-case value; all other slopes and relative “errors” were smaller and well within the random uncertainty in experimental value of rate constants. Concentration data Results are reported here for two- and three-component samples processed with different data ranges and with the different curve-fitting approaches [5,6,81. Two-component samples. Samples contained lo-50 PM total amino acid and 5-45 PM of each component so that concentration ratios varied between 9:l and 1:9. The two different sets of mixtures evaluated were glycine with
46 50 0
40.0
0.0 0.0
10.0
20.0
PREPARED
40. 0
30.0
CONC.
50.0
(10.=M*1)
Fig. 2. Comparison of computed vs. prepared concentrations for two-component mixtures: (A) glycine with a fitting range of 7.4 half-lives; (B) isoleucine with a fitting range of 1.15 half-lives.
isoleucine, and leucine with isoleucine, involving ratios of rate constants of 3.2 : 1 and 2.1: 1, respectively. Best-case and worst-case results for the glycine/ isoleucine mixture are presented in Fig. 2. Reproducibility was evaluated for fixed amounts of each component in the presence of variable amounts of the other component(s). For 5, 20 and 35 PM each of the acids, standard deviations were 0.51, 0.39 and 0.41, respectively, for glycine and 0.84, 0.81 and 0.40, respectively, for isoleucine with data ranges of 8-408 s for glycine and 8-608 s for koleucine. More complete results are presented as pooled stanTABLE 1 Least-squares statistics for calculated vs. prepared concentration total amino acid in glycine/isoleucine mixturesa Date range
Glycine 8-408 8-248 8-208 Isoleucine S-608 8-248 8-208 Total amino 8-608 8-248 8-208
Synkc (0U
rd
0.12 f 0.21 -0.25 k 0.26 -0.26 + 0.35
0.64 0.78 1.05
0.999 0.997 0.995
1.00 + 0.01 1.02 * 0.02 1.03 * 0.02
0.32 f 0.21 -0.19 f 0.33 -0.01 * 0.49
0.67 1.09 1.61
0.999 0.995 0.990
1.00 f 0.01 0.99 + 0.01 0.99 It 0.01
0.14 f 0.21 0.36 + 0.41 0.43 f 0.45
0.45 0.64 0.95
0.999 0.999 0.996
Number of half-lives
Pooled s.d.b WI)
Slope + s.d.a
7.4 4.5 3.8
0.51 0.71 0.95
0.99 f 0.01 1.01 * 0.01 0.01 f 0.02
3.4 1.4 1.15 acid -
0.69 1.21 1.51 0.43 0.75 0.91
(s)
of glycine, isoleucine and
Intercept + s.d.a (PM)
a30 samples; 5-45 MM glycine, 5-45 PM isoleucine, and 10-50 MM total amino acid. bSeven groups with 5, 5, 4, 4, 4, 3, and 3 samples, respectively. CStandard error of estimate. dCorrelation coefficient.
47 TABLE 2 Least-squares statistics for calculated vs. prepared concentration total amino acid in leucine/isoleucine mixture@ Data range (s)
Half-lives (s)
Pooled s.d. (PM)
Slope * s.d.
7.05 4.75 3.60
0.76 1.26 0.94
1.03 f 0.02 1.00 f 0.03 0.95 f 0.04
-0.32 -0.10 -0.24
8-608 3.4 8-408 2.3 8-308 1.75 Total amino acid 8-608 8-408 8-308 -
0.69 1.68 2.24
1.07 f 0.02 1.05 f 0.03 0.98 i 0.05
-1.20 -0.36 -2.20
0.71 0.98 1.26
1.02 f 0.02 1.00 f 0.02 1.02 f 0.03
a30 samples; 5-45
PM leucine, 5-i5
Leucine 8-608 8-408 8-308
of leucine, isoleucine and
Intercept * s.d. (rM)
S &,
’
* 0.36 f 0.60 * 0.46
0.67 1.00 0.86
0.998 0.996 0.996
f 0.33 * 0.71 i 0.98
0.67 1.45 2.00
0.998 0.992 0.983
-0.43 f 0.55 0.32 f 0.81 0.39 * 0.98
0.69 1.00 1.25
0.999 0.998 0.997
Isoleucine
PM isoleucine, and lo-50
PM total amino acid,
dard deviations and least-squares statistics for fits of computed vs. prepared concentrations in Tables 1 and 2 for these two-component mixtures. In each case, best results were obtained for the faster-reacting component with data processed over longer times and worst results were obtained for the slowerreacting component with data processed over shorter times. To provide a basis for comparison, single-component samples were processed over similar data ranges by the predictive kinetic method described earlier [9]. The least-squares statistics for a fit of computed concentration (e) vs. prepared concentration (co) of glycine were C?’ = (1.007 + O.OOS)b - 0.16 f 0.21 with a standard error of the estimate (S,,) of 0.35 PM and correlation coefficient of 0.9996. All results for two-component samples are degraded relative to those for the single-component sample. However, when the standard error of the estimate is used as a measure of the scatter about the best fit to the data, results are degraded by little more than a factor of 2 as long as ratios of rate constants are 2:l or larger, and the data range includes three or more half-lives of the slower-reacting component. Shorter reaction times can be used with a corresponding increase in uncertainty. Three-component mixtures. Results obtained for two sets of three-component samples are summarized in Table 3. To obtain reasonably reliable results with these mixtures, it was necessary to process data over some 4.5 half-lives of the slower-reacting component. Results are substantially degraded relative to results for single-component samples and the best results for two-components mixtures but are similar to those for two-component
48 TABLE 3 Least-squares statistics for calculated vs. prepared concentration amino acid in three-component mixturesa Amino acid
Pooled s.d.b (fiM)
Hi&dine/lysine/isoleucine Histidine 1.12 Lysine 1.66 Isoleucine 1.25 Total amino acid 0.98 Histidine/leucine/isoleucine Histidine 1.21 Leucine 1.85 Isoleucine 1.35 Total amino acid 0.86
Slope * s.d.
of individual and total
Intercept f s.d. (PM)
S,, (rM)
r
1.02 1.04 1.09 1.03
f 0.03 f 0.06 + 0.04 f 0.02
-1.02 -0.70 0.20 -0.64
* 0.50 + 0.56 f 0.60 t 0.68
0.93 1.70 1.30 1.05
0.99 0.98 0.99
0.11 1.02 1.13 1.03
f 0.04 zt 0.06 f 0.04 It 0.03
-2.90 -0.32 -0.32 -0.72
f * * f
1.10 1.82 1.02 1.05
0.99 0.97 0.99 0.99
0.60 1.00 0.59 0.65
0.99
‘25 samples, concentration of each component 5 to 30 PM, and total amino acid 15 to 50 PM, data range 8-808 s. bSix groups with 4, 6, 6, 4, 3 and 2 samples, respectively.
mixtures when reduced data ranges are used. Longer monitoring times approaching 6-8 half-lives for the slower-reacting component would likely yield some improvement. However, such long times would not be practical unless some type of multichannel sample-processing system were used. Comparison of data-processing methods The two data-processing methods reported previously [5, 6,8] were used to process data sets for selected two- and three-component samples. For eighteen different combinations of samples and data ranges, the two methods yielded results for AA, that differed by less than 0.001. A linear leastsquares fit of computed absorbance changes for the multiple-linear regression (AA L ) and nonlinear regression (AA _ ) methods yielded the equation AA:, = 1.0002 AA,
- 0.0004
with S,, = 0.002 and r = 0.99995, the two fitting methods.
indicating excellent agreement between
Conclusions It is apparent from the data presented above that, for ideal samples, there is a real loss in reliability as one proceeds from one- to two- to three-component samples. If it were possible to do separations without any loss or cross-contamination, then clearly, best results would be obtained with complete separations so that measurements would be made on single-component aliquots of the sample. However, when allowance is made for the nonideal nature of separation processes, it may be possible to exploit the multi-component kinetic data-processing methods to resolve incompletely separated
49
samples with substantially less net loss of reliability than might be implied by the results presented above. This work was supported by Grant No. CHE 8319014 from the National Science Foundation. REFERENCES 1 H. B. Mark and G. A. Rechnitz, Kinetics in Analytical Chemistry, Interscience, New York, 1968. 2 H. A. Laitinen and W. E. Harris, Chemical Analysis, McGraw-Hill, New York, 1975, p. 389. 3 J. B. Pausch and D. W. Margerum, anal. Chem., 41(1969) 226. 4 D. W. Margerum, J. B. Pausch, G. A. Nyssen and G. F. Smith, Anal. Chem., 41 (1969) 233. 5 B. G. Willis, W. H. Woodruff, J. R. Frysinger, D. W. Margerum and H. L. Pardue, Anal. Chem., 42 (1970) 1350. 6 G. M. Ridder and D. W. Margerum, Anal. Chem., 49 (1977) 2098. 7 J. B. Landis and H. L. Pardue, Clin. Chem., 24 (1978) 1700. 8 R. S. Harner and H. L. Pardue, Anal. Chim. Acta, 127 (1981) 23. 9 Y. R. Tahboub and H. L. Pardue, Anal. Chim. Acta, 173 (1985) 23.