Anal. Chem. 1907, 59, 1372-1374
1372
Selavka, C. M.; Krull. I.S.;Bratln, K. J. fharm. Blomed. Anal. 1088, 4 , 83. Selavka, C. M.; Krull, I. S. J. Chromatogr. Scl. 1085,23,499. Selavka, C. M.; Krull, I. S.; Lurie. I. S . Forensic Sci. I n t . 1986,31, 301. Selavka, C. M.; Krull, I. S., submitted for publication In Anal. Chem. Lacourse, W. R.; Krull, I.S. TrAC Trends Anal. Chem. (fers. Ed.) 1985, 4 , 118. Lacourse. W. R.; Krull, I. S . Anal. Chem. 1085,57, 1810. Lacourse, W. R.; Krull. I. S . Proc. Electrochem. SOC. 1087,86(14), 181. Lacourse, W. R.; Krull, I . S. Anal. Chem. 1887,59,49-53. Sanderson, S. CV Note on Flavin MononucleotMe; Bloanalytlcal Systems, Inc.: West Lafayette, IN. Perone, S. P.; Birk, J. R. Anal. Chem. 1086,38, 1589. Birk, J. R.; Perone, S. P. Anal. Chem. 1068,40, 498. Kirschener, G. L.; Perone, S. P. Anal. Chem. 1072,4 4 , 443. Jamisson, E. A.; Perone, S. P. J. Phys. Chem. 1972, 76,830. Patterson, J. 1. M.; Perone, S. P. J. Phys. Chem. 1073. 77,2437. Johnson, D. C.; Resnlck, E. W. Anal. Chem. 1072,4 4 , 637. Lubbers, J. R.: Resnick, E. W.; Gaines. P. R.; Johnson, D. C. Anal. Chem. 1074,4 6 , 865. Albery, W. J.; Archer, M. D.; Field, N. J.; Turner, A. D. Faraday Discuss. Chem. SOC. 1074,56,28. MacCrehan, W. A.; May, W. E. Anal. Chem. 1084,56,625. Miller, F. J.; Zittel, H. E. J. Elechoanal. Chem. 1986, 7 7 , 85. Zittel, H. E.; Miller, F. L. J. Nectroanal. Chem. Interfacial Electrocbem. 1967, 73, 193. Dryhurst, G.: Elvlng, P. J. Anal. Chem. 1967,39,606. Gelssler, W.; Nkzsche, R.; Landsberg, R. €lectroch/m, Acta 1066, 7 1, 389. Beran, P.; Bruckenstein. S. Anal. Chem. lS68,4 0 , 1044. Bansai, K. M.; Gratzel, M.; Henglein, A,; Janata, E. J. Phys. Chem. 1973, 77, 16.
(30) Lacourse, W. R.; Krull, I . S., submitted for publlcatlon In J. Am. Chem. SOC. (31) Rao, P. S.; Hayon, E. J. Am. Chem. SOC. 1974,96, 1295.
RECEIVED for review October 8,1986. Accepted December 29, 1986. The photo-CV work was supported by an ACS Analytical Division Fellowship, sponsored by the Society of Analytical Chemists of Pittsburgh, a Gustel Giessen Advanced Research Award, an award from the Research and Scholarship Development Fund from Northeastern University, a Barnett Institute Innovative Research Award, and by a grant from the Analytical Research Department of Pfiier & Co., Inc., Groton, CT, to Northeastern University. Funding for the photolysis-CV work was provided by an NIH Biomedical Research Grant No. RR07143 to Northeastern University, as well as an NIH-Small Business Innovation Research Grant, 1R43ES04057-01 (in cooperation with Cambridge Analytical Associates, Boston, MA). Support for C.M.S. was provided by a National Institute of Justice, U.S. Department of Justice, Graduate Research Fellowship (86-IJ-CX-0058). Points of view or opinions stated in this document are those of the authors and do not necessarily represent the official position or policies of the U.S. Department of Justice. This is contribution number 308 from the Barnett Institute of Chemical Analysis and Materials Science at Northeastern University.
Mass Spectral Analysis of Isotopically Labeled Compounds: Average Mass Approach Karl Blom,’ Cecil Dybowski, and Burnaby Munson* Department of Chemistry, University of Delaware, Newark, Delaware 19716
Bruce Gates and Lori Hasselbring Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Stable isotope labels are used in many areas of chemistry, geology, biology, and pharmacology. Their roles as probes into the mechanisms of organic reactions (1-3)and metabolic pathways (4),as environmental (5,6)and process tracers (7), and in the quantitation of trace components in mixtures (8) are well documented. Mass spectrometry is the most commonly used method of analyzing the isotopic content of labeled compounds. For relatively simple compounds containing predominantly monoisotopic elements (e.g., C, N, 0,etc.) the degree of labeling is easily calculated from the ratio of the intensities of the relevant peaks in the mass spectrum (9). However, for larger molecules or compounds containing polyisotopic elements (e.g., inorganic or organometallic compounds containing Mo, Sn, Pt, Hg, etc.), the complexity of the isotopic cluster often makes direct analysis of the isotopic content difficult. Sophisticated computational procedures have been reported for estimating the isotopic enrichment of these compounds (lG12). In general, these approaches attempt to ”fit” the experimentally determined isotopic pattern to a pattern calculated for an estimated isotopic composition. These approaches have some drawbacks since the results will depend upon the particular method used to calculate the difference between the experimental and calculated patterns and upon the criterion used to determine a match. All of the methods for determining isotopic content reported in the literature require mass spectral data with unit resolution.
The average mass or “centroid” of complex isotope clusters can be measured very precisely even at high mass (13)or when
unit mass resolution is not available (14-16). It has been proposed that the most useful mass for characterizing compounds with high molecular weights is the average mass, which can be combined with the shape of the isotopic cluster (e.g., full width at half height) to verify the elemental composition of the ion (11-14). This approach should also be applicable to lower molecular weight compounds, particularly those which contain polyisotopic elements. The purpose of this communication is to present a simple method for calculating the total isotopic content of a sample directly from its mass spectrometrically determined average mass.
EXPERIMENTAL SECTION The C H I chemical ionization mass spectra were obtained for “natural” 2,5-dichlorophenyl azide, double 13C enriched 2,5-dichlorophenyl azide, a mixture of the natural and labeled azides, and an osmium carbonyl, H40s4(C0)12,partially enriched with 13C. The data were acquired oscillographically with a Du Pont 21-492B mass spectrometer operated at unit mass resolution. The masses of the peaks were determined to the nearest 1 amu (nominal mass precision). Peaks less than 0.5% of the base peak were not included in the analysis. Triplicate determinations were made for each sample. The estimated average uncertainty in the intensity measurements (one standard deviation) was about 2%. The average mass for a cluster was calculated with n
Present address: E. I. du Pont de Nemours & Company, Medical Products Department, Experimental Station, Wilmington, DE 19898.
n
Ma = X I i M , / E I , I-1
(1)
,-1
where n is the number of peaks in the cluster and Ii and M , are
0003-2700/87/0359-1372$01.50/00 1987 American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 59, NO. 9, MAY 1, 1987
the intensity and mass for peak i, respectively. The (M + H)+cluster was used for the analysis of the osmium carbonyl. The (M + C2H5)+adduct ion was used for the analysis of the 2,5-dichlorophenyl azide samples because the (M H)+ cluster was distorted by the presence of a significant M+ ion.
Table I. Average Masses of Several Elements” calcd av massesb for the following mass mecisions 1 amu 0.0001 amu
+
THEORY Consider the cluster of peaks corresponding to a “pure” molecular ion in the mass spectrum of a sample compound in which one element has been enriched in the heavy isotopic form of that element. The average mass, Ma,for this cluster can be expressed as the sum of the average masses of the elements in the enriched compound
Ma = C N j M j I
+ NXHMH + N ( 1 - XH)ML
(2)
where N j and M, are the number of occurrences and average masses for those elements not involved in the isotopic enrichment, N is the number of sites within the ion which contain the enriched population of the label element, ML and MH are the nuclidic masses for the light and heavy isotopic forms of the label element, and X H is the mole fraction of the heavy isotope in the enriched population. The product, NXH, is the fraction of label sites within the ion which contain the heavy isotope label, averaged over the entire sample. Thus, the term NXHMH represents the average mass of the heavy isotope label in the ion. Similarly, the term N ( l - XH)ML represents the average mass of the light isotope in the ion, and the sum of N,Mis in eq 2 represents the average mass for the remainder of the ion, i.e., the average mass for the atoms not involved in the isotopic enrichment. Replacing the summation in eq 2 with Mo and solving for the mole fraction of the heavy isotope gives
XH = (Ma- Mo - N M L ) / N ( M H - ML)
(3)
The average mass for the nonenriched portion of the ion, Mo, is easily calculated from standard tables of the average masses of the elements (see Table I) and N , ML, and MH are usually known a priori. Thus, the mole fraction of the heavier isotope in the enriched population can be calculated directly from the experimentally determined average mass of the ionic cluster using eq 3. The “exactn average mass for a distribution of peaks or isotopic forms can be expressed as the sum of a “nominal” average mass which is the average of the nominal masses of the species in the distribution and a “defect” average mass which results from the mass defects of the species. Thus, if the masses of the peaks in the mass spectral analysis are measured with nominal mass precision (integral masses), then the average mass which is calculated with eq 1 will be the “nominal” average mass of the ionic cluster. Mathematically, the “nominal” and “defect” average masses have the same properties as the “exact” average mass. Consequently, the “nominal” average mass of an ionic species can be expressed as the sum of the ”nominal” masses of its component elements, as in eq 2; and eq 3, which describes the isotopic content of an enriched sample in terms of ita average mass, is valid even if the masses of the peaks in the cluster are only measured with unit precision. However, if the “nominal” average mass is used, then all of the quantities in eq 3 must be expressed in terms of their nominal masses; i.e., MH and ML must be the nominal masses of the light and heavy isotopic forms of the label element and Mo must be calculated from the “nominal” average masses of the elements. Table I shows the “exact” and “nominal” average masses for a few common elements as calculated with n
(4)
where Pjiand Mji are the normalized abundance and mass
1373
element H C N
1.000 15 12.011 10 14.003 70
1.007 97 12.011 14 14.006 76
0
16.004 45 19.0000 28.108 80
15.999 37 18.99840 28.085 61
31.0000 32.090 64 35.489 4
30.993 76 32.062 53 35.453
F Si
P S
c1 Br
79.989 2 127.000 190.278
I
os ”Data from ref
17.
*Calculated with eq
79.906 5 126.9004 190.237 4, in
amu.
(either exact or nominal) for isotopic form i of element j . The uncertainty in the isotopic content calculated from eq 3 results primarily from the uncertainty associated with the measured average mass
AXH = AMa/N(MH - ML)
(5)
The major source of uncertainty in the experimental determination of an average mass lies in the measurement of the ionic intensities. Propagating the error through eq 1gives the uncertainty in Ma as where AI is the average relative uncertainty in the intensities of the peaks, n is the number of peaks in the cluster, and Mi is the mass of peak i. The most obvious implication of eq 5 and 6 is that the uncertainty in the calculated isotopic content is inversely related to the number of peaks in bhe cluster; i.e., the precision is better for larger clusters. The term in the brackets in eq 6 is related to the symmetry of the cluster; the precision of the average mass analysis increases with increasing symmetry of the cluster.
RESULTS AND DISCUSSION As a simple test of the average mass approach, the isotopic contents of several 13C-enriched samples were calculated by using eq 3 and using standard ratio and pattern matching methods. The results are summarized in Table 11. These results represent the average for three determinations *1 standard deviation. The isotopic contents calculated by using the average masses of the clusters and eq 3 are the same as those calculated by the standard methods within experimental error. The agreement establishes the validity of eq 3. The accuracy and precision of the results in Table I1 are reflective of the small data sets used in these calculations and should not be interpreted as indicative of the ultimate obtainable by either procedure. However, one may note that, for these data, the uncertainties for the average mass results are approximately the same or slightly better than those for the ion ratio results. A simple analysis of the likely errors indicates that this improvement is due to the larger number of peaks used in the average mass analysis and should be general. The advantage of an average mass approach is illustrated by the osmium carbonyl example, H.,OS,(CO)~~. Figure 1 shows the (M + H)+ cluster for the natural and %-enriched materials. The clusters for these species are very complex. The most intense peak containing a manageable number of isotopic forms is m / z 1085 (predominantly 1H51860s4(12C160)12+). However, this peak is C0.17’ of the base peak.
1374
ANALYTICAL CHEMISTRY, VOL. 59,
T a b l e 11. Comparison Methods
NO. 9, MAY 1, 1987 Average Masses
of Average M a s s a n d C o n v e n t i o n a l
1106.84
1102.19
no. o f peaks in clustern
sample
labels
ClZH8N2ClZ Cl2H8N2ClZ ClzHsNzClz H40s,(CO)12
"natural" double I3C mixture 13C enriched
mole fraction o f 13Cb av mass method
0.013 0.984 0.565 0.390
6
7 7 24
conventional method
i 0.001 0.012 f 0.001 f 0.007 0.983 f 0.015' f 0.007 0.556 f 0.011' f 0.002 0.38ad
"Number of peaks w i t h intensities 20.5% of base peak. bAverage of three determinations il standard deviation. Calculated from X H = [ I , 2(IzS1 - R1279)]/[21z79 2I,, 2(Izsl- R1279)], where I represents the measured intensity for the indicated mass in the (M CZH6)+ cluster and R is the naturally occurring abundance o f 37Cl for two chlorines. Estimated by systematically varying the 13C abundance, calculating the resulting isotope pattern (assuming statistical distribution of W ) , comparing calculated and measured patterns, and determining the abundance which produces the "best fit"; Le., when AF = ~ : J ( Z o ~ , i / ~ I o ~-d(Ic~c~,i/EIca~~,i)l ,l) is a minimum. AF for the best fit was 6.8%.
+
+
T a b l e 111. Partial L i s t i n g
+
+
+
of I s o t o p i c F o r m s P r e s e n t at m / z
1104 for ( H 4 0 s 4 ( C 0 ) 1 2 HI+
I -
Natural
C Enriched
Figure 1. (M -I- H)' clusters for H,Os,(CO),,.
also be applicable in those cases in which the mass analyzer cannot provide unit mass resolution.
ACKNOWLEDGMENT The authors thank Henry J. Shine, Texas Tech University, for supplying the natural and double I3C labeled 2,5-dichlorophenyl azide and Henry Lamb, University of Delaware, for supplying the I3C-enriched H40~4(C0)12. Registry No. I3C, 14762-74-4;H,OS,(CO),~, 12375-04-1;2,5dichlorophenyl azide, 75458-15-0.
LITERATURE CITED
etc. Every peak of reasonable intensity is composed of an enormous number of isotopic forms. Table I11 gives a partial listing of the significant forms that are found in the I3C-enriched species at a nominal mass of 1104 amu. Obviously, it will be very difficult to solve this system directly to obtain any reasonable estimate of the isotopic content from a ratio of ionic intensities. The isotopic content could be approximated by a pattern matching or least-squares approach. However, all of these methods either are difficult to apply or involve approximations which could lead to large errors (18). The average mass method, on the other hand, avoids most of these approximations and is easy to apply. For the clusters shown in Figure 1,Mo is the average mass for H50s4OI2and is easily calculated from Table I (Mo= 958.166 amu for nominal mass precision); N is 12; and MLand M Hare 12 and 13 amu (again, for nominal mass precision), respectively. Inserting these values into eq 3, along with the average masses given in Figure 1,we immediately obtain I3C abundances of 0.2% and 39.0% for the natural and enriched samples, respectively.
CONCLUSIONS The average mass approach to isotopic analysis is valid for both partially enriched materials which contain a statistical distribution of isotopic labels (such as the osmium carbonyl) and specific mixtures of labeled and unlabeled compounds (such as the azide mixture). The calculation is simple even for compounds that produce very complex clusters of peaks. For relatively simple systems (like the 2,5-dichlorophenyl azide examples) the standard ionic ratio methods are easy to use and work well. However, an average mass approach might find wide application in the isotopic analysis of inorganic, organometallic, and higher molecular weight samples which produce complex clusters. An average mass approach should
Knapp, D. R.; Gaffnay, T. E.; Compson, K. R. Advances in Biochemical Psychopharmacology; Costa, E., Holmstedt, B., Eds.; Raven: New York, 1973; Vol. 7, pp 83-94. Bencivengo, D. J.; San Fillppo, J., Jr. Organometall/cs 1983, 2, 1907-1 909. Kwart, H.; Stanulonis, J. J. Am. Chem. SOC. 1978, 98, 4009. Shlne, H. J.; Hobdas, J.; Kwart, H.; Brechbiel, M.; Gaffney, A.; San Fllippo, J., Jr. J. Am. Chem. SOC. 1983, 105, 2823-2827. Halverson, J. E. Energy Res. Abstr. 1982, 7 , Abstr. No. 4820. Rokop, D.; Alei, M.; Cappis, J.; Mroz, E.; Mason, A,; Norris, T.; Paths, J.; Guthals, P.;Bryant, E.; Cowan, G.; Dye, S.; Goldbiatt, M.; Jefferles, R.; Mills, T. Presented at the 33rd Annual Conference on Mass Spectrometry and Allied Topics; Sen Diego, CA; May 26-31, 1985. Maurer, 0. A.: Parent, G.; Laporte, R. Presented at the 33rd Annual Conference on Mass Spectrometry and Allied Topics; San Diego, CA; May 26-31, 1985. Horning, E. C.; Thenot, J. P.; Horning. M. G. Quantitative Mass Spectrometry in Life Sciences; De Leenheer, A. P., Roncucci, R. R., Eds.; Elsevier: New York, 1977; pp 1-14. Biemann, K. Mass Spectrometry: Organic Chemical Applications ; McGraw-Hill: New York, 1962; Chapter 5. Sukharev, Y. N.; Nekrasov, Y. S. Org. Mass Specfrom. 1976, 1 1 , 1239-1241. Lee, W. N. P.; Whiting, J. S.; Fymat, A. L.; Boettger, H. G. Biomed. Mass Spectrom. 1983, 10, 641-645. Benz, W. Anal. Chem. 1980, 52, 248-252. Yergey, J.; Helier, D.; Hansen, G.; Cotter, R. J.; Fenselau, C. Anal. Chem. 1983, 55, 353-356. kkansson, P.; Kamensky, I.; Sundqvist, B.; Fohlman, J.; Peterson, P.; McNeal, C. J.; MacFarlane, R. D. J. Am. Chem. SOC. 1982, 104, 2948-2949. McNeal, C. J.; Ogilvie, K. K.; Theriault, N. Y.; Nemer. M. J. J. Am. Ch8m. SOC. 1982, 104, 976-980. Ens, W.; Standing, K. G.; Westmore, J. B.; Ogilvie, K. K.; Nemer, M. J. Anal. Chem. 1982. 5 4 , 960-966. Handbook of Chemistry and Physics, 54th ed.; Weast, R. C., Ed.; CRC Press: Cleveland, OH, 1974. Jonckheere, J. A,; De Leenheer, A. P.; Steyaert, H. L. Anal. Ch8m. 1983. 55, 153-155.
RECEIVED for review July 21, 1986. Accepted February 10, 1986. Bruce Gates and Cecil Dybowski acknowledge the support of the National Science Foundation under Grant CPE82-17890.
