Anal. Chem. 1985, 57,2145-2151
2145
Table I. 6"N T 1 Standard Deviation (Relative to Atmospheric N,) for Peptone, Thiourea, Histidine, Kerogen, and Two (NHJ2S04Standards, N-1 and N-2
of laboratories have mean 615Nvalues of 0.41 and 20.19, respectively (20).
material
We thank J. Montoya and S. Horrigan for their contributions in our laboratory and I. Kaplan and D. Winter of the University of California, Los Angeles, P. Parker of the University of Texas, Austin, T. Saino of the University of Tokyo, and I. Barnes of the US. National Bureau of Standards for their participation in the interlaboratory calibration effort. Registry No. NZ,1127-31-9.
peptoneo
this study
D. Winter
T. Saino
7.12 7 0.06 6.97 T 0.20 (n = 2) (n = 11) thioureab -0.99 7 0.07 4 . 9 6 T 0.07d (n = 3) (n = 5) histidineb -5.50 T 0.09 -5.27 T 0.14d (n = 2) ( n = 4) kerogenb 7.60 F 0.01 7.35 T 0.05d ( n = 2) (n = 3) 0.41 T 0.14d N-1' 0.39 7 0.09 (n = 6) (n = 3) N-2' 20.26 F 0.17 19.81 7 0.04d (n = 6) (n = 3) T 0.10 (n = 12)
7.06
P. Parker 6.89
(n = 1)
"Obtained from this laboratory. bObtained from D. Winter. 'Obtained from I. Barnes, U.S. NBS. dAs reported for combustion method (9). aration system than analyses of nitrogen salts and organic compounds of lower molecular weight. For example, when the purification oven reagents are nearing exhaustion, it is possible to obtain satisfactory replicate analyses on materials such as (NH4)2S04but not on the peptone material. This effect is manifested by the presence of NO (mass 30), resulting from incomplete reduction of the nitrogenous sample combustion products. While this increase may be trivial ( k 2 > k-' (condition i) the estimated kl and 12, were 0.03447 and 0.011 55 mi+, respectively, and deviated from the theoretical values by less than 1% (Table 111). For k+ the estimated value was 0.001 115 min-' and was off the theoretical value (0.001 155 min-') by 3.5%. In the case where kl N k2 > (condition ii), the estimated kl (0.033 87 m i d ) and k 2 (0.034 71 mi&) mimicked their theoretical values and gave errors of less than 3%. However, the estimated k-' was 0.0003298 min-' when compared to the theoretical value of 0.001 155 m i d provided a substantial error of 70%. The reason for this large error is due to k2 being close to the sum of kl and k-', and the residual from the substraction between two numbers of close values imparts large errors. A detailed discussion on the accuracy of the values estimated by this method for a similar situation has been previously published (9). For the last case where kl> kl > It2 (condition iii), the corresponding estimated rate constants were 0.04869,0.033 87, and 0.011 55 min-l, and agreed well with the theoretical values of 0.0500,0.3465, and 0,01155 min-l, respectively; the errors were less than 5% (Table 111). In this kinetic system (Scheme IIIA) the determination of the absolute concentrations of both the reactant and intermediates are required. The overall accuracy of this method depends on the calculation of AUC and AUMC, which in turn depends on the frequency of the sampling and the length of the sampling period. Since it is usually impossible to follow the concentration of the chemical species to infinite time, the remaining area is usually assessed by dividing the terminal slope into the last concentration. To minimize error due to extrapolation, it is generally recommended that the duration of sampling should be followed to at least 10% of the peak concentration of the species (6,8,9). This would avoid an over dependency on extrapolation which may induce large errors. Although the frequency of sampling affects the accuracy of the area estimation, the result is less demanding on this factor as compared to the duration of the sampling period among these first-order systems. Generally speaking, if the data are accurate, a reasonable sampling frequency will yield acceptable estimates. A more detailed discussion on this has appeared elsewhere (9). In the present simulated kinetic schemes, 30-50
0
130
260
390
520
650
Time (m) Figure 1. Simulated data of consecutive first order kinetics with 15% errors. The symbols are as follows: 0,A,; A, A,; +, AJ.
data points were usually generated for a period of 300 to 500 min and the last concentration was less than 10% of the peak concentration. To examine the tolerance due to assay errors, several levels of random errors were generated and randomly added or subtracted from simple first-order kinetics data. Deviation from theoretical values of the kinetic rate constants by the statistical moment method were 0.2 and 0.94%, respectively, when 5 and 15% of the random errors were added. Figure 1is a plot for general concentration-time profiles for species in a consecutive first-order kinetic system when 15% random error was incorporated. Under reasonable sampling frequency and duration, the statistical moment method appears to tolerate a reasonable error at levels up to 20%. Experimental Data. This method was applied to estimate the kinetic rate constants of two experimental systems. On the hydrolysis of 450 pM spirohydantoin mustard at 25 "C and pH 4.0, the parent drug undergoes hydrolysis to the monohydroxy intermediate which is further hydrolyzed to yield the dihydroxy compound as the final product (15).The hydrolysis appears to follow a consecutive first-order kinetic process and the data were fitted to the appropriate integrated equations (eq 53 and 54), which gave the estmated kinetic rate constants of 0.0389 f 0.0028 and 0.0063 f 0.0012 min-l for kl and k,, respectively (Figure 2 and Table IV). By use of the statistical moment method, k , and k2 were estimated to be 0.0414 and 0.0063 min-', respectively, and compared favorably with those from the curve-fitting procedures (Table IV). Similarly, the results on the hydrolysis of AZQ at 25 OC and pH 3.0 which also forms the monohydroxy intermediate and dihydroxy final product (16) revealed that the statistical moment method furnished kl and k2 of 0.0129 and 0.0105
2151
Anal. Chem. lQ85,57,2151-2153
Spirohydantoin Mustard Hydrolysis
i
ACKNOWLEDGMENT
400
-I
E
quency and period and is quite reliable with good data (15% error). This method has been verified with simulated data of several kinetic systems as well as in two experimental examples. The authors wish to thank J. A. Kelly of the National Cancer Institute of generously providing the raw data on the hydrolyses of spirohydantoin and AZQ. Registry No. SM, 56605-16-4;SM-OH, 84393-36-2;AZQ, 57998-68-2;AZQ-OH, 77280-56-9.
2;
0 E
a
r‘ u
S
LITERATURE CITED
0
u
0
50
150
100
200
250
Time (m) Flgure 2. Concentration-time profiles of species in spirohydantoin mustard hydrolysis. The symbols are: 0,spirohydantoin mustard; A, monohydroxyspirohydantoin mustard; dihydroxysplrohydantoin
+,
mustard, ail fitted by computer regression (smooth lines) to standard equations for consecutive first-order kinetics. min-’, respectively, which compared well with the corresponding values of 0.0131 f O.OOO1 and 0.0097 f 0.00198 m i d from the curve-fitting procedure.
CONCLUSIONS The statistical moment method offers means of estimation of rate constants in several kinetic systems alternative to curve fitting procedures when the kinetics are known. This method only requires simple area calculations from the experimental data without solving differential equations or employing computer curve-fitting procedures. In application of statistical moment theory to multiple consecutive first-order kinetics, it does not require the determinations of the absolute concentrations of the intermediates or in some cases the reactant. The accuracy of this method depends on the sampling fre-
van der Laan, E. Th. Chem. Eng. Sci. 1957, 7, 187. McQuarrie, D. A. J . Chem. Phys. 1983, 38, 437. Yamaoka, K.; Nakagawa, T. J . Chromatogr. 1974, 9 2 , 213. Perl, W.; Samuel, P. Circ. Res. 1959, 25, 191. Oppenhelmer, J.; Schwartz. H.; Surks, M. I. J . Clin. Endocrinol. Metab. 1975, 4 1 , 319. Yamaoka, K.; Nakagawa, T.; Uno, T. J . Pharmacokinet. Biopharm. 1978, 6 , 547. Cutler, D. J. J . Pharm. Pharmacol. 1978, 30, 476. Riegelman, S.; Collier, P. J . Pharmacokinet. Biopharm. 1980, 8 , 509. Chan, K. K. Drug Metab. Dlspos. 1982, 10, 474. Benet, L. 2.; Galeazzi, R. L. J . Pharm. Sci. 1979, 68, 1071. W e b , M. J . Pharmacokinef. Bipharm. 1983, 1 1 , 63. Bauer, L. A.; Gibaldi, M. J . Pharm. Sci. 1983, 72, 978. Knott, G. Comput. Program Biomed. 1979, 10, 271. Bolger, Mlchael B., School of Pharmacy, University of Southern California, Los Angeles, CA, unpublished results. Flora, K. P.; Cradock, J. C.; Kelley, J. A. J . Pharm. Sci. 1982, 71, 1206. Poochlkian. G. K.; Kelley, J. A. J . Pharm. Sci. 1981, 70, 162. Pang, K. S.;Gillette, J. R:, Drug Metab. Dispos. 1980, 8 , 39. Gibaldi, M.; Perrier, D. Pharmacoklnetics”; Marcel Dekker: New York, 1975; pp 84-86.
RECEIVED for review January 31,1985. Accepted May 6,1985. This work is supported by the USC Cancer Center Core Grant CA 14089and Grant CA 31693, both from the National Cancer Institute (K.K.C.), by Biomedical Research Support Grant SO7 RR05792 from the National Institute of Health (M.B.B.), and by the Medical Research Council of Canada, Development Awards, DG-262, 263, and 264, and Canadian Liver Foundation (K.S.P.).
CORRESPONDENCE Use of Electron-Impact Ion Directing (Diethy1amino)ethyl Esters in Gas Chromatography/Mass Spectrometry of Carboxylic Acids Sir: Selected ion monitoring gas chromatography/mass spectrometry (GC/MS) has become a standard technique for the measurement of drugs in body fluids because it permits speciation of analyte and reference compound from coeluting extracted components. While many compounds have intense electron-impact ionization (EI) diagnostic ions, amenable to low level detection limits, other compounds have numerous fragmentation pathways that result in ions of marginal intensity. In these cases, either positive or negative chemical ionization (CI) has been employed as the method to enhance the signal-to-noise of the diagnostic ions. The introduction of low-cost E1 instruments has made them generally available for use in GC/MS body fluid analyses. Selective extraction techniques and capillary column GC contribute to better speciation of the analyte and reference compounds. Various methods (1-6) previously developed for
packed column E1 GC/MS have been transposed to capillary GC/MSD with an accompanying reduction in sample required, amount injected, and multiplier voltage applied. Unfortunately,the lack of reasonably intense diagnostic ions still limits the use of E1 detection methods. A pilot study of a derivatization scheme for several model carboxylic acids was investigated as one example of a way to maximize the intensity of one fragment ion.
EXPERIMENTAL SECTION Reagents and Chemicals. The model carboxylic acids S-
methylcaptopril (I,Table I,Figure l),S-acetylcaptopril (11,Table I, Figure l), and a prostanoid, SQ 28668 (111,Table 11, Figure 2), were characterized pharmaceutical grade materials obtained from E. R. Squibb & Sons (Princeton, NJ). 2-(Diethylamino)ethyl (XII),was chloride, hydrochloride salt (CzH5)2NCH2CH2Cl~HCl used as received (Aldrich Chemical Co., Milwaukee, WI). A
0003-2700/85/0357-2151$01.50/00 1985 American Chemical Society
