1986
Anal. Chem. 1985, 57, 1986-1988
in the cancellation of all errors. Integration times just covering the duration of the analytical absorbance signal can result in background errors which are larger than would be present were integration omitted. For the bracketing mode, shorter intervals from the start to the maximum of the background signal or from this maximum to the end of the background signal also produce a cancellation of all errors. However, variability in the time location of the background peak may not make this approach possible for samples with variable matrix concentrations. This study suggests that simple modifications in instrument data reduction procedures to employ the bracketing mode and careful use of the peak integration feature can significantly reduce errors in computed background-corrected absorbances caused by nonsimultaneous collection of the sample and reference signals.
ACKNOWLEDGMENT J.A.H. wishes to acknowledge the partial support of this research by National Science Foundation Grant No. CHE8409819.
LITERATURE CITED Kolrtyohann, S. R.; Pickett, E. E. Anal. Chem. 1966, 2 8 , 585. Kolzurnl, H.; Yasuda, K. Anal. Chem. 1975, 4 7 , 1679. Koizurni, H.; Yasuda, K.; Katayama, M. Anal. Chem. 1977, 4 9 , 1106. Fernandez, F. J.; Myers, S. A.; Slavin, W. Anal. Chem. 1980, 5 2 , 741. (5) Harnly, J. M.; O'Haver, T. C.; Golden, B.; Wolf W. R . Anal. Chem. 1979, 5 7 , 2007. (6) Smith, S.B.; HieftJe, G. M. Appl. Spectrosc. 1983, 37, 419. (7) Rayson, G. D.; Holcombe, J. A.; Akerlin, N., Jr. Spectrochlm. Acta, Pat? 8 1982, 378, 319. (8) Liddeil, P. R.;Brodie, K. G. Anal. Chem. 1980, 5 2 , 1256. (9) Grobenski, Z.; Lehrnann, R.; Radziuk, B.; Voellkopf, U. Af. Specfrosc. 1984, 5, 87. (IO) Lundberg, E.; Frech, W. Anal. Chem. 1981, 5 3 , 1437. (11) Siemer, D. D.;Baldwin, J. M. Anal. Chem. 1980, 5 2 , 295. (12) Harnly, J. M. Paper No. 423 Presented at the 11th Annual Meeting of the Federation of Analytical Chemistry and Spectroscopy Socletles, Philadelphia, PA, September 16-21, 1984. (1) (2) (3) (4)
RECEIVED for review March 8, 1985. Accepted May 3, 1985. Mention of trademark of proprietary products does not constitute a guarantee or warranty of the product by the US. Department of Agriculture and does not imply their approval to the exclusion of other products that may also be suitable.
Mass Spectral Analysis of Monodeuterio-Labeled Compounds Exhibiting Significant (M - H)+ Peaks Karl Blom, Jon Schuhardt, and Burnaby Munson* Department of Chemistry, University of Delaware, Newark, Delaware 19716
A method Is presented for computing the relatlve amounts of unlabeled and monodeuterlo-labeled materlals In lsotoplc mixtures for compounds whose mass spectra contain slgnlflcant (M H)' peaks. The method Is applled to the lsotoplc dllutlon experlment where It produces a llnear relatlonshlp between the measured and actual Isotope ratios. The slope of the resultlng line Is dlrectly related to the relative concentration of labeled compound In the lnltlal sample.
-
the precision of the determination. Recently, Benz described a computer program which makes approximate corrections for the presence of (M - H)+ peaks (9). While this numerical method is fairly general, it is quite complex and is, in some cases, subject to serious limitations. The purpose of this paper is to present a simple method of calculating the ratio of isotopic abundances for the special case of mixtures of unlabeled and monodeuterio-labeled compounds which produce significant (M - H)+ peaks.
EXPERIMENTAL SECTION Techniques using stable isotopes have become increasingly important in many areas of chemistry, biology, and geology. The isotope dilution technique is the analytical method of choice for the quantitation of a variety of materials (1). Stable isotopes are widely used as tracers in studying metabolic processes (2). Kinetic isotope effects are used as probes into the mechanisms of organic reactions (3-5). Mass spectrometry is the most commonly used method for the analysis of compounds labeled with stable isotopes. Several mathematical analyses of the general relationship between a mass spectrometrically determined ratio of ion currents and the ratio of the labeled to unlabeled compounds in the sample have been published (6, 7). The analysis, however, becomes much more difficult if the compound gives rise to an abundant (M - H)+peak. The usual ways of handling this difficulty have been either to derivatize the compound to one which does not give an (M - H)+peak or to lower the ionizing electron energy until the (M - H)+ fragment ion becomes insignificant (8). Both of these methods have potential drawbacks. Derivatization may change the ratio of labeled to unlabeled species and decreasing the ionizing electron energy lowers the overall sensitivity which may lessen
The mass spectral data were acquired with an HP5982A GC/MS. The ionizing voltage was 70 V and the source temperature was 70 f 10 O C . The benzhydrol samples were introduced with the direct insertion probe. The sample pressure could be held constant for several minutes by controlling the probe temperature. The ion currents at each of the relevant masses were cyclically sampled 1000 times over a period of approximately 3 min, simulating simultaneous detection. The ion current ratios represent 12 determinations (of 1000 measurements) for each isotopicmixture and have standard deviations of approximately 0.2%.
Under these experimental conditions the ratio, (MD - H)+/ MD+, for benzhydrol was about 0.3. This ratio was sensitive to the ionizing voltage and source temperature. Isotopic analysis under experimental conditions which gave (MD- H)+/MD+ratios ranging between 0.2 and 0.6 gave essentially identical results. Somewhat surprisingly, perhaps, the loss of H from the benzhydrol-a-d ion is favored over D loss; (MD - H)+/(MD- D)' was approximately 7 in these experiments. The benzhydrol-a-d was prepared by reduction of benzophenone with lithium aluminum deuteride and recrystallized from petroleum ether to give colorless needles with a melting range of 64-65 "C. The proton NMR of the product showed no detectable signal at 6 5.2, indicating that the benzhydrol-a-d was 0 f 3% undeuterated.
0003-2700/85/0357-1986$01.50/00 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 9, AUGUST 1985
RESULTS AND DISCUSSION The analysis of labeled compounds can be treated as a special case of mixture analysis. The ion current at a mass, k, in the mass spectrum of a mixture can be expressed as
1987
Equations 4,5b, and 6b are simultaneous equations which can be solved for the relative ion currents of the labeled and unlabeled molecular ions. We begin by rearranging eq 5b
MH+ + (MD - H)+ I, - R ~ [ ( M H- H)++ (MD - D)+] (7)
where n is the number of components in the mixture, m is the number of isobaric ionic species at mass k for component i, and Aijk is the current for every ionic species, j , at mass k for component i. In general, the proportionality constant between the absolute ion current, A,, and the molar concentration of the neutral substrate, q,will be different for different compounds. This is usually expressed as Aijk = NijksiCi
(2)
where Siis the response factor for component i and Nijk is the normalized ion current for species j at mass k from component i. It is assumed, either explicitly or implicitly, in the treatment of the isotopic analysis of complex organic molecules that (1) the total response factors for the labeled and unlabeled compounds are the same and (2) the degrees of fragmentation of the molecular ions are the same for the labeled and unlabeled compounds (3-5, 8, 9). If hydrogen elimination from the molecular ion occurs primarily at the labeled position, however, the extent of H loss from MH+ will be significantly larger than the extent of D loss from MD+. There may be differences in the total rates of decomposition of MD+ and MH+ and, therefore, the second assumption and eq 3 will be incorrect. From the general consistency of reported data (3-5) and preliminary investigations in this laboratory, this error appears to be negligible for reasonably complex organic compounds. Under these conditions,for a monodeuterio-labeled compound the mole ratio of unlabeled to labeled compounds is equal to the ratio of the currents of the molecular ions and no further calibration is needed.
/ (MD+) = (MH)/ (MD)
(3)
The ionic species contributing to the ion currents at the relevant masses for a mixture of an unlabeled and monodeuterio-labeled hydrocarbon are the following:
Im-l (MH - H)++ ( M D - D)+
(4)
I, = MH++ (MD - H)++ l 3 C ( M ~ H)++ 13C(M~- D)+ (54 I, = M H + + (MD - H)++ Ri[(MH - H)+ + (MD - D)+] (5b) I,+1 = MD+ + 13C(M~+) “C(MD - H)+ 13C2(M~ - H)+ 13C2(M~- D)+ ( 6 4 1,+1
+
= MD+ + Ri[MH+ + (MD - H)’] R~[(MH - H)+f (MD- D)+] (6b)
The unlabeled material, MH,has molecular weight m. The labeled material is MD, and 13Cand 13C2signify the naturally occurring carbon-13 and double carbon-13 isotopes of the indicated species. The I3C and 13C2species have been rewritten in eq 5b and 6b as the products of the naturally occurring 13C/12Cand 13C2/12C2 ratios for the compound, R1 and R2,and the ion currents for the 12Cspecies. The naturally occurring deuterium has been neglected since D/H = 0.015%. For compounds containing oxygen or nitrogen, the contributions of species containing the naturally occurring le0or lSNwould need to be included in eq 5a and 6a. Naturally occurring 1 7 0 can be neglected because l7O/l6O = 0.037%.
Replacing the terms in brackets in eq 6b by their equivalents from eq 4 and 7 and solving for M D + gives the following:
MD+ = Im+1- R l ( I m - R1Im-J - RJm-1
(8)
Under a given set of conditions the ion current for (MD - H)+ will be a fixed fraction of the ion current for MD+; Le., (MD - H)+= F(MD+). Replacing (MD - H)+ in eq 5b with F(MD+), replacing the terms in brackets with the equivalents from eq 7 and 8 and solving for MH+ gives
MHt = 1, - F[I,+i
- R1(Im- R1lm-l) - R21,-1] - R11,-1 (9)
Finally, taking the quotient of eq 8 and 9 and simplifying give the sought equation for the ratio of the ion currents of the molecular ions (which is also the mole ratio of unlabeled to labeled compounds) MH+/MD+
{Urn- RJrn-l)/[Irn+l-
R 1 V m - R11m-J - W m - 1 1 1 - F (10)
As a simple test of eq 10we might consider the case in which the (M - H)+peaks become negligibly small. In this limit both I,-1 and F approach zero and eq 10 reduces to MH+/MD+= I r n / ( I m + l - R1Im)
(11)
This equation is just the usual one used to correct for the naturally occurring 13C overlap from the lower mass peak. The naturally occurring isotope ratios, R1 and R2, are easily calculated and the ion currents, I,, and are the experimentally determined values in eq 10 which are dependent upon the actual isotope ratio. The coefficient, F o r (MD - H)+/MD+,must be determined for each chemical system under the same conditions as those used for the isotope ratio determination. If the monodeuterio-labeled compound is available in “pure” form (199.9% isotopic purity), then F can be determined directly from the mass spectrum of this pure material. For “pure” MD the ratio MH+/MD+is zero and from eq 10 one obtains
F = (1, - RlIm-J/ [Im+1- R l ( I m - R1Im-J
- RJm-J
(12)
The “pure” labeled material may not be available and the presence of even small amounts of unlabeled compound will result in an erroneously high value of F. The value of F can, however, be determined even from isotopically impure material by isotopic dilution. Rearranging eq 10 to describe the dilution of an isotopic mixture with pure unlabeled compound gives the following: [(MH)added/(MD)oI
+ [(MH)O/(MD)O]= A - F
(13)
Where (M&ddd is the number of moles of added MH, (MH)o and ( M D )are ~ the moles of unlabeled and labeled compounds in the original mixture, and A replaces the cumbersome term in braces in eq 10. The first term on the left of eq 13 can be rewritten as [(MH)added/(MD)o) = K[1
+ ( M H ) ~ / ( M D ) ~ I(14)
where K is the extent of isotopic dilution, defined as K = (MH)added/[(MH)o+ (MD)~].Substituting eq 14 into 13 and rearranging into the form of a linear equation gives A = K[1 + ( M H ) ~ / ( M D ) ~[ ~( M H ) ~ / ( M D+) ~ Fl
(15)
1988
ANALYTICAL CHEMISTRY, VOL. 57, NO. 9, AUGUST 1985
A plot of A vs. extent of dilution, K , will be a straight line with a slope of 1 + (MH)o/(M~)o and an intercept of ( M H ) ~ / ( M D ) ~ F. The value of F is then calculated from the equation
+
F = 1 + intercept - slope
(16)
The ratio of unlabeled to labeled materials in the original sample is obtained directly from the slope of this isotopic dilution plot Mass spectral data were obtained for the isotopic dilution of high-purity benzhydrol-a-d with natural benzhydrol to test eq 15. For this oxygen-containing compound the Is0 isotope species were included in the calculation of A , i.e.
A= V m
- ~ l L ) / [ Z m + l - Rl(Zm - fiJm-1) - (R, + R0)Zm-ll (18)
in which Ro is the naturally occurring 1sO/160ratio. Leastsquares linear regression of these data gave a slope and intercept ( f l standard deviation) of 1.010 f 0.006 and 0.282 f 0.008 with a correlation coefficient of 0.999 94. From eq 17 and 16 we calculate the starting material to be 99.0 f 0.6% deuterated and the value of F as 0.272 f 0,010. This result is consistent with but of higher precision than the proton NMR analysis of the original benzhydrol-a-d which indicates that it is 100 f 3% deuterated. The value of F obtained directly from the mass spectrum of the undiluted labeled compound and using eq 12 modified to include l80is 0.290 f 0.013. This value is slightly high as expected, because of the small amount of unlabeled material in the “pure” labeled sample. The determination of F by isotopic dilution is analogous to constructing the calibration graphs relating apparent and “actual” isotope ratios usually associated with isotopic dilution experiments. The calibration plot (184/185 ratio vs. the extent of dilution) for the isotopic dilution of benzhydrol-a-d with natural benzhydrol is shown in Figure 1. The relationship is a nonlinear one as expected. The calibration curve only relates the measured isotope ratio with the relative concentrations of the starting and added materials used in the isotopic dilution. Obviously, this relationship can only be used to determine the relative concentrations of labeled and unlabeled compound in an unknown mixture if the isotopic compositions of the materials used in the dilution are precisely known. No information as to the isotopic purity of the labeled material is directly available from this analysis. One difficulty exists with the isotopic dilution experiment in the calculation of the extent of dilution, K. Operationally, K may be written as
0
0
1
2
K , extent of dilution Flgure 1. Uncorrected calibration graph for the dilution of hlgh-purity benzhydrol-a-d with natural benzhydrol.
weights of the indicated species. If the composition of the initial sample is not known, then the denominator in eq 19 cannot be calculated. In this case the usual procedure is to assume that the initial sample is completely labeled (6, IO). This is the assumption we used to estimate K for the experiment shown in Figure 1. The error in the estimated value of K will depend on the isotopic purity of the labeled material. For benzhydrol, as an example, the estimated value of K is less than the correct value by about 1 part in 10000 for a 90% deuterio-labeled sample and is low by 2.3 parts per 1000 for a 50% deuteriolabeled sample. This small error can be eliminated by iteratively estimating the composition of the initial labeled material using eq 17 and recalculating K.
LITERATURE CITED (1) Horning, E. C.; Thenot, J. P.; Hornlng, M. G. “Quantitative Mass Spectrometry in Life Sclences”; DeLeenheer, A. P., Roncucci, R. R., Eds.; Elsevier: New York, 1977; pp 1-14. (2) Knapp, D. R.; Gatfney, T. E.; Compson, K. R. ”Advances in Biochemical Psychopharmacology”; Costa, E., Holmstedt, B., Eds.; Raven: New York, 1973; Vol. 7, pp 83-94. (3) Bencivenao, D. J.; Sen FIIIDDo, J., Jr. Organometalllcs 1983, 2 , .. 1907-1969. Kwart, H.; Stanulonis, J. J . Am. Chem. SOC. 1978, 98, 4009. Shine, H. J.; Hobdas, J.; Kwart, H.; Brenchbiei, M.; Gaffney, A,; San Fliippo, J., Jr. J . Am. Chem. SOC. 1983, 105, 2823-2827. Pickup, J., F.; McPherson, K. “Quantitative Mass Spectrometry in Life Sciences”; DeLeenheer, A. P., Roncucci, R. R., Eds.; Elsevier: New York, 1977; pp 209-213. Gentry, C. Anal. Chem. 1973, 45, 505-511. Biemann, K. “Mass Spectrometry: Organic Chemical Appllcations”; McGraw-HIII: New York, 1962; Chapter 5. Benz, W. Anal. Chem. 1980, 52, 248-252. Jonckheere, J. A.; DeLeenheer, A. P. Anal. Chem. 1983, 5 5 , 153-155.
K=
[(WtH)added/MWHI / [ (WtH)o/MWH + (WtD)o/MWDI (19)
where Wt and MW represent the weights and molecular
RECEIVED for review March 25,1985. Accepted May 6,1985. This work was supported by Grant CHE-8212197 from the National Science Foundation.
