BIOLOGICAL MASS SPECTROMETRY, VOL. 21, 114-122 (1992)

Mass Isotopomer Pattern and Precursor-Product Relationship W.-N.Paul Lee? and E. Anne Bergner Department of Pediatrics, Harbor-UCLA Medical Center, Research and Education Institute, Torrance, California 90502, USA

ZengKui Guo Cedar-Sinai Medical Center, Los Angeles, California 90048, USA

The synthesis of a homonucleus polymer from its labeled precursor will lead to the formation of molecules with different masses. The distribution of these mass isotopomers is strictly a function of the enrichment of the 13Clabeled precursor, and can thus be used for the determination of the precursor enrichment and product dilution in the de now synthesis of the polymer. We present here a study of the isotopomer pattern of a polymer of acetate in the form of glucose pentaacetate synthesized from "C-enriched acetic anhydride. The molecular ion contains four acetyl units. Its synthesis is analogous to that of octanoic acid from acetyl coenzyme A. The process of obtaining the mass isotopomer distribution in the tetraacetyl moiety from the ion cluster of m/z 331 of glucose pentaacetate is illustrated. After correcting for the contribution of I3C natural abundance, the plot of the ratio of mass isotopomers (m4/m2) against the observed enrichment of the tetraacetate moiety yielded a straight line with a slope of 1.45. The ratio was not altered by dilution with preexisting unenriched product, as predicted. The slope of the observed linear relationship agreed with the general formula (N ( j - l))/jfor the ratio of any two consecutive mass isotopomers (m,/m,-J. Theoretical and practical aspects of determining precursor enrichment from isotopomer pattern in polymers are discussed.

-

INTRODUCTION A major limitation of studies of biosynthesis of carbohydrates and lipids with 14C-labeled substrates is the difficulty of estimating the specific activity of the intracellular precursors, such as PEP, triose-P or acetyl coenzyme A (CoA). Recently Hellerstein et al.' developed a method in v i m using 13C-labeled acetate incorporation into fatty acids and mass isotopomer analysis to obtain the enrichment of cytosolic acetyl CoA. A major complication of this elegant approach is to separate the 13C isotopomer pattern due to the added enriched precursor from that due to the natural unenriched substrate. Without such separation, precursor enrichment can only be determined graphically using empirical formulae. However, it is possible to show that, with the proper correction for isomers formed from the 13Csof the natural unenriched precursors, the mass isotopomer fractions in a polymer follow a simple binomial distribution according to the proportion of enriched to unenriched precursor species and the number of repeating units. We present here a study of the isotopomer pattern in glucose pentaacetate as a polymer of acetate linked to glucose, synthesized from acetic anhydride enriched in I3C. The molecular ion (m/z 331) contains only four acetyl groups, and the isotopomer system is analogous to that of the synthesis of octanoic acid from acetyl CoA. The crucial steps which transform spectral data to the respective corrected mass isotopomer distribution are illustrated. Theoretical and

t Author to whom correspondence should be addressed. 1052-9306/92/020114-09 %05.00

0 1992 by John Wiley & Sons, Ltd.

practical aspects of determining precursor enrichment from the correct isotopomer pattern in de nouo synthesis of homonucleus (having the same repeating unit) polymers are examined.

EXPERIMENTAL (1,2,1',2'-'3C)Acetic anhydride (99% I3C) was purchased from Isotec Inc. A series of dilution with reagent-grade acetic anhydride (containing natural abundance of 1.1% 13C)was prepared to give mixtures containing 0, 5, 10, 15, 20 and 40% of the labeled acetic anhydride by weight. Fifty microliters of the acetic anhydride was allowed to react with 0.1 mg of reagent-grade glucose in 100 pl of anhydrous pyridine to form glucose pentaacetate.2 Glucose pentaacetate was dissolved in 100 p1 ethyl acetate for injection into the gas chromatograph for analysis. Analysis of these samples by gas chromatography/mass spectrometry (GC/MS) was performed on a Hewlett-Packard 5840A gas chromatograph coupled to a Hewlett-Packard 5895 quadrupole mass spectrometer. The GC conditions were: 4-fOOt glass column (2 mm inner diameter) was packed with 3% OV-101 on 100/120 Gas Chrom Q; methane was the carrier gas at a flow rate of 14 ml min-'; injector temperature was 225"C, and column temperature was programmed from 220 "C to 22 "C at 5 "C min-'. Chemical ionization of glucose pentaacetate produces two ion clusters with respective base peaks at m/z 331 and m/z 271 corresponding to the molecular ion (glucose plus four acetyl units) and Received 18 July 1991 Revised 17 October 1991

115

MASS ISOTOPOMER STUDY OF PRECURSOR ENRICHMENT

molecular ion minus an acetate group (triacetate). Scans of m/z from 330 to 339 and 270 to 277 were acquired over the entire GC peak, and normalized spectra were derived from these ion chromatograms. Samples of various mixtures of labeled and unenriched glucose pentaacetate were also analyzed to demonstrate the effect of dilution of labeled product post-synthesis. PRINCIPLE An elementary hypothetical example to illustrate the principle of the novel approach of Hellerstein is presented below. Consider the synthesis of glucose in perfused liver from a 3-carbon compound enriched with 13C carbon, which is composed of a mixture of 80% unlabeled (no 13C) and 20% labeled. The recondensation of triose-P into hexose will yield (in the absence of any discrimination between trioses) 64% unlabeled hexose, 32% hexoses labeled with one 13C either in the 1,2,3 or 4,5,6 glucose moiety, and 4% of hexose containing two 13Ccarbons per molecule, one in each 3-carbon moiety. Ideally, when examined by mass spectrometry, the distribution would be 64% mO, 32% ml and 4% m2. It is shown in algebra texts that Hellerstein’s distribution is a binomial one (0.8 + 0.2)’. It is apparent that in such a hypothetical case the enrichment can be obtained by inspection of isotopomer distribution. If the product is a polymer such as fatty acids, the isotopomer distribution would be that of the binomial distribution (p + 4)N, where p + 4 = 1, and N is the number of repeating units in the polymer, 4 for octanoic acid. However, if there is pre-existing product, such as glycogen or fatty acids, the fractional enrichment will be diluted, and frequency of isomers will no longer follow a binomial distribution. Moreover, in real systems, the istopomer distribution will be greatly affected by the natural abundance of 13C in the unenriched precursor and isotope impurity of “C in the labeled precursor. These difficulties can be overcome by the empirical formula and graphical solution of Heller~tein,~ or by the use of the proper background subtraction method of Lee et a1.4 which will be illustrated below.

(1,2-13C)acetate carbons. Since our interest is in the tetraacetate polymer, the contribution of the glucose spectrum is first derived and subtracted to obtain the mass isotopomer abundance of the tetraacetate moiety using the algorithm of Lee et d4After correcting for the contribution of background natural abundance of the unenriched acetic anhydride using the abundance matrix in Appendix 1, the mass isotopomer distribution represents the distribution of isotopomers in the tetraacetyl or triacetyl portion of the molecule due to incorporation of enriched labeled acetyl units. Enrichment per carbon is calculated from the weighted sum of the mass isotopomers using the following equation : Enrichment =

where mi is the fractional molar enrichment of mass isotopomer containing ni number of 13Ccarbons, and N is the total number of carbon atoms in the acetyl component, 8 or 6 for tetra- and triacetate, respectively.

Determination of precursor enrichment In this system of two distinct acetyl precursors (unenriched acetate with natural abundance of 13C and enriched acetate, (1,2-I3C)acetate),the mass isotopomer pattern of tetraacetyl moiety is the result of the random incorporation of acetyl units from unenriched and enriched acetic anhydride, and is given by the expansion of a binomial function: (y + c#”,where p is the fraction of unenriched acetate and q the fraction of (l,2-13C) acetate, and N = 4, the number of acetate molecules in the tetraacetate. The theoretical isotopomer distribution for the tetraacetyl group is illustrated in Table 1 expressed as functions of p and 4. Since p + q = 1, the sum of all mass isotopomer fractions is equal to one. Table 1. Theoretical mas isotopomer distribution in tetraacetyl moiety of glucose pentaacetate produced from a mixture of unenriched and (1,2,1’,2’-13C)acetic anhydride

Diluted by Q

Ion cluster of m/z 331 was used to calculate the mass isotopomer frequency distribution of the polymer enriched with labeled acetate in the tetraacetyl ion fragment, and ion cluster of m/z 271 was used to calculate the mass isotopomer frequency distribution in the triacetyl portion of the molecule. The mass spectral ion profile of the tetraacetyl fragment or the triacetyl fragment is the effect of combination of isomers of (i) the derivative (glucose) and isomers of the heteroatoms (primarily ‘*O),(ii) isomers contributed by the presence of natural abundance of 13C in the ‘unenriched‘? acetic anhydride, and (iii) isomers due to the incorporation of

(1)

i

Undiluted

Determination of mass isotopomer distribution and enrichment with correction for 13C natural abundance

1 mi ni/N

mO

m2

m4

m6

m8

P4 Q+p4

4P3q

sp2q2

4RS3

u4

SP3q 6p2q2 &q3 q4 Q+l Q+1 Q+1 Q+l

Q+1

Q is the relative concentration of pre-existing unenriched product present prior to any new synthesis with enriched precursor. The distribution is derived from the expansion of (p + q ) “ . p and 9 are fractions of unenriched and enriched acetyl precursors. Since the acetyl units are labeled in both carbons, the incremental mass of the labeled tetraacetyl moiety is 2. The mass isotopomer distribution of the mixture is obviously not a binomial distribution. The dilution factor is 1/(Q + 1 ).

t Because is present in nature comprising about 1.1% of carbon atoms, all naturally occurring organic compounds are labeled with I3C to some extent. Therefore, we use ‘unenriched’ to designate molecules having background abundance of ‘’C and ‘unlabeled’ to mean molecules containing only ”C. However, the terms ‘labeled precursor’ and ‘enriched precursor’ are used interchangeably to contrast with unenriched precursor. After correction for natural abundance of 13C due to the incorporation of the unenriched acetate, the isotopomer distribution is the result of incorporation of the enriched precursor.

W.-N. P. LEE, Z. K. GUO AND E. A. BERGNER

116

The coefficients of the binomial expansion are the number of ways these combinations can occur. There are four combinations of one (1,2-13C)acetyl unit with three unenriched acetyl units, and six combinations of two (1,2-13C)acetyl unit with two unenriched acetyl units, and so on. Two important conclusions can be drawn from this illustration : (i) the mass isotopomer distribution in the tetraacetyl moiety is a function of the precursor enrichment; (ii) the relative distribution of the labeled species and their ratios is not altered by dilution by pre-existing unenriched product. Consequently, a number of isotopomer ratios can be used for the estimation of precursor enrichment. According to Table 1, these are: m4/m2 = (3/2)q/(l - q); m6/m4 = (2/3)q/ (1 - 4); and m8/m6 = (1/4)q/(l - q), for a polymer of 4 repeating doubly labeled acetyl units. The general expression for the ratio of the first two labeled species, m4/m2, is : m4/m2 = ((N- 1)/2) x (d(1 - 4)) (2) ( N - 1)/2 is 1.5 and 1 for tetra- and triacetate, respectively. In experiments where singly labeled precursors are used, the first two labeled species are m l and m2 and the ratio is m2/ml. The general expression for the other mass isotopomer ratio of mj/mj-l (where j is the numerical order of the designated isotopomer) is:

u

(3) mj/m,-, = ( N - - l))/j x (4/(1 - 4) In the present case, m6/m4, the ratio of the third isotopomer ( j= 3) to the second is given by (4 - 2)/3 = 2/ 3. Since (1,2,1',2'-13C)acetic anhydride is labeled in all carbon positions, q is the enrichment (En). If we designate En/(l - En) by r, this relationship predicts that when m4/m2 is plotted against r, one should obtain a straight line with (N - 1)/2 as the slope. Conversely, the relationship can be used for the estimation of r from the known isotopomer ratio, and the enrichment (En) is given by the equation En = r/(l + r).

Effect of two isomer species in the precursor The presence of more than one enriched isomer species (acetate containing one or two 13Cs)in the labeled precursor will greatly complicate the simple analysis shown above. We will show here the case of mass isotopomer

distribution in a polymer containing repeating units with two labeled species. Isotopic impurity of the labeled acetic anhydride will introduce a precursor containing a single 13C carbon with the formation of the tetraacetate containing an odd number of 13C(ml, m3, etc.). If we designate the fraction of acetyl molecule containing one 13Cas q1 and that of the fully labeled acetyl q2 ,(ql + q2) = q. The mass isotopomer distribution can be derived by substituting (ql + q2) for q in Table 1. The results are shown in Table 2. Because q1 is small, higher-order terms for q1 can be neglected, and these expressions can be greatly simplified: m2 = 4 x p 3 x q2 ; m3 = 6 x p 2 x 2 x q1 x q2 ; m4 = 6 x p 2 x qt2; m5 = 4 x p x 3 x q1 x q Z 2 ;m6 = 4 x p x q 2 3 ; m7 = 4 x q1 x q Z 3 ; and m8 = q24. Using these algebraic equations, we were able to estimate the fraction q1 and validate our assumption that the amount of singly labeled q1 in our labeled acetic anhydride was indeed very small.

RESULTS The stepwise transformation of spectral data of subtracting the derivative component and of correcting for 13C natural abundance to yield the mass isotopomer distribution due to incorporation of labeled precursor is shown in Tables 3, 4 and 5. The distribution of ions observed in the unenriched glucose tetraacetate fragment showed a base peak at m/z 331 corresponding to the mononucleidic species containing only "C (Table 3). The loss of a protium atom produced an ion, m - 1, at m/z 330 of about 4.5%. The presence of natural abundance of 13Cin glucose and the acetyl units gave rise to ions of m/z 332, and the presence of natural abundance of "0 accounts for a small ion peak at m/z 333, Incorporation of enriched acetic anhydride introduced (1,2l3C)acety1units, giving rise to masses 333, 335, 337 and 339. The presence of "C in unenriched acetyl units and the loss of a protium atom gave rise to even-numbered m/z (m/z 332,334,336 and 338). The first step of the data reduction algorithm removed all contributions from heteroatoms ("0) and carbons of the glucosyl moiety, the derivative component in this analysis. Intermediate results are shown

Table 2 Theoretical mass isotopomer distribution ia tetraacetyl group Efieet of "C impurity in (f,&1',Z'-13C)~ceticanhydride Fractional molar enrichment (in terms of p. q, and q2)

Iro t Op an W

mO ml m2 m3 m4 m5 m6 m7 m8

p4 4 x P' x q l 4 xp' x q2 + 6 xp2 x q 1 2 6 xp2 x 2 xql x q 2 + 4 xp x q13 + 4 x p x 3 x q12 x q2 +q14 6 xp2 x qZ2 4 xp x 3 xql x q 2 2 + 4 x q 1 J x q 4XPXqz3 + 6 xq12xqZ2 4 x q 1 xqZ3 qa4

When the 13C-labeled precursor consists of singly substituted ( q l ) and doubly substituted (q2) acetyl units, and q , + q 2 = q. the distribution is obtained by substituting ( 4 , + q 2 ) for q in the expressions of Table 1.

MASS ISOTOPOMER STUDY OF PRECURSOR ENRICHMENT

117

Table 3. Normalized ohserved spectra of glucose tetraacetate prepared from acetic anhydride containing varioup enrichments of (1,2,1',2'-'3C)a~ydride The highest ion is set to 100 Enrichment (Yo)

0

5 10

15 20 40

m-1

m

m+l

m +2

m+3

m+4

m+S

m+6

m+7

330

331

332

333

334

336

336

337

338

339

0.36 0.02 3.32 0.17 6.68 0.11 10.93 0.18 16.14 0.31 21.67 0.12

0.70 0.02 2.43 0.08 8.55 0.06 19.73 0.22 37.60 0.58 96.54 0.44

0.02 0.01 0.31 0.02 1.09 0.01 2.60 0.03 5.13 0.05 15.79 0.06

0.02 0.01 0.16 0.03 0.95 0.04 3.06 0.05 7.61 0.06 45.32 0.20

0.01 0.00 0.04 0.01 0.13 0.02 0.35 0.01 0.87 0.01 5.66 0.03

0.02 0.01 0.03 0.01 0.09 0.01 0.30 0.02 0.87 0.05 10.36 0.12

4.53 0.31 4.61 0.07 4.56 0.06 4.72 0.31 4.81 0.22 2.10 0.14

15.68 0.09 17.11 0.09 18.59 0.08 20.16 0.13 22.05 0.26 13.12 0.15

1 00

100 1 00

100 100 40.39 0.50

3.08 0.13 22.68 0.28 44.76 0.87 69.17 1.11 96.69 1.68 1 00

m+8

Normalized intensities are averages of six separate GC/MS determinations. Standard deviations of the observed intensities are provided under the mean values.

in Table 4, which are the mass isotopomers due to "C from labeled precursor and natural acetate in the tetraacetyl group. The values in each row are the frequency distribution of mononucleidic and other molecular species containing different numbers of I3C atoms. Since there are eight carbons in the polymer, the presence of natural abundance of 13C in the unenriched compound gave rise to about 8.8% of ml as expected. The ml/mO mass isotopomer ratio increased from 9% in the unenriched compound to 14% in the 40% enriched compound as unenriched acetyl units were substituted by some of the singly labeled impurity of the enriched species. The application of Eqn (1) to these values will give I3C abundance of the tetraacetyl moiety, which corresponds to 13C abundance as determined by isotope ratio mass spectrometric analysis of C 0 2 from combustion of the sample. Finally, with the correction of isomers formed from 13C natural abundance of the unenriched acetyl group, the mass isotopomer distribution represents only the isotopomers due to incorporation of 3C from labeled acetyl units (Table 5). Now, mO stands for the percentage of unenriched tetraacetate. The effect of 13C from

unenriched acetic anhydride on ml isotopomer and other odd-numbered labeled isomers has been removed (comparing ml, m3 and m5 of Table 4 with those of Table 5). The amount of m l remaining is due to the incorporation of a small amount of singly labeled acetic anhydride contaminant. The ratio of singly labeled to doubly labeled species of acetyl unit of labeled anhydride can be calculated from the ratio of ml/m2 as suggested by the formulae in Table 2. About 3% of the labeled acetic anhydride was made of the (l3C1)acetyl unit, and the enrichment of the acetic anhydride was estimated to be 98.5%, which is in good agreement with the manufacturer's specification. The observed enrichment depends on isotope purity as well as chemical purity. The observed enrichments of the different acetic anhydride preparations (column 11, Tablt 5 ) were slightly different from those expected (column 1, Table 5). After adjusting for the difference in molecular weights of the labeled anhydride, the chemical purity is estimated to be better than 99%. The advantage of using uniformly labeled acetate of high purity in this demonstration can be seen by comparing the results in Table 4 with those in Table 5.

Table 4. Fractional molar abundance of tetraacetyl isotopomers 0%

5% 10%

15% 20% 40%

mO

ml

m2

m3

91.52 0.19 75.22 0.15 61.09 0.33 49.08 0.40 38.89 0.39 13.04 0.18

8.15 0.11 7.10 0.05 6.07 0.04 5.10 0.02 4.29 0.05 1.90 0.04

0.32 0.11 14.98 0.19 25.65 0.38 32.54 0.35 36.42 0.32 31.75 0.03

0.01 0.02 1.16 0.13 1.92 0.03 2.58 0.04 3.04 0.05 3.40 0.03

m4

m6

m6

0 0 1.38 0.06 4.52 0.02 8.79 0.05 13.60 0.09 30.17 0.15

0 0 0.07 0.01 0.25 0.01 0.51 0.01 0.83 0.01 2.30 0.01

0 0 0.07 0.02 0.44 0.03 1.25 0.03 2.58 0.05 13.79 0.06

m7

0 0 0.01 0.01 0.03 0.01 0.05 0.01 0.10 0.01 0.65 0.01

m8

0 0 0.01 0.01 0.03 0.01 0.10 0.01 0.26 0.02 2.98 0.04

The values of Table 3 are subtracted for the glucose derivative moiety and the natural abundance of l80. The isotopomer distribution is due to the contribution of the labeled and the 13C natural abundance in unenriched acetyl units. mO stands for the mononucleidic lzC species. ml stands for the polymer with one "C atom, m2, polymer with two "C atoms, and so on.

W.-N. P. LEE, Z. K. GUO AND E. A. BERGNER

118

Table 5. Fractional molar enrichment of tetraacetyl isotopomers due to incorporation of label. The contribution of isomers from unenriched acetyl unit has been subtracted Enrichment

0% 5% 10%

15% 20% 40%

mO

ml

m2

99.96 0.21 82.18 0.17 66.74 0.37 53.62 0.44 42.48 0.44 14.25 0.20

0.00

0.00

0.13 0.43 0.06 0.68 0.03 0.78 0.05 0.88 0.08 0.80 0.05

0.01 15.70 0.21 27.14 0.41 34.54 0.38 38.71 0.35 33.83 0.03

m3

0.00 0.01 0.18 0.15 0.24 0.02 0.44 0.01 0.65 0.02 1.35 0.04

m4

0.01 0.01 1.41 0.06 4.66 0.02 9.10 0.05 14.12 0.09 31.42 0.16

in6

m6

m7

ma

0.00

0.00

0.00

0.00

0.00 0.01 0.01 0.06 0.01 0.13 0.01 0.23 0.01 0.98 0.01

0.00 0.07 0.02 0.45 0.03 1.27 0.03 2.63 0.05 14.06 0.07

0.00 0.00 0.00 0.01 0.01 0.02 0.01 0.05 0.01 0.35 0.01

0.00 0.01 0.01 0.04 0.01 0.10 0.01

0.36 0.02 2.99 0.04

("/a)

0 4.82 0.07 9.71 0.07 14.60 0.09 19.50 0.08 39.21 0.09

After correcting for natural abundance of unenriched acetyl units, isotopomers from the combination of unenriched acetate are removed. mO stands for the fraction of unenriched tetraacetate polymer. m l and m2 are the fractions of polymers with one enriched acetate (having one or two "C atoms). m3 and m4 are the fractions of polymers with two enriched acetates.

Because of the small number of repeating units (N = 4), the higher-order terms drops off rather rapidly (see the distribution for the unenriched in Table 4). Consequently, the corrections for m2, m4 and m6 are small. However, the effect of correcting for 13C abundance in the natural acetate is substantial by comparing values of mO of Table 4 with those of Table 5. Since most of the labeled acetic anhydride molecules contain two 13C atoms, the number of polymer molecules containing an odd number of I3C atoms is virtually negligible after background correction. It is only after the correction of natural abundance of the unenriched acetyl units that the isotopomer distribution can be modelled by a binomial distribution. The results of 40% enriched pentaacetate are used to illustrate the application of the expansion of the binomial function of Table 1. The fractional molar enrichment of mO (the unenriched species) is 14.25%. Therefore, the fraction of starting unenriched acetic anhydride is given by the fourth root of 14.25%, which is 6l.44%, and the fraction of the enriched species is 38.56%. The fractional molar enrichment of m2, m4 and m6 can be calculated using expressions for undiluted tetraacetate in Table 1 and substituting 0.6144 and 0.3856 for q and p. The calculated values of 35.77%, 33.68%, 14.09% and 2.21% are in excellent agreement with the observed values of 33.83%, 31.41%, 14.06% and 2.98%. The slight discrepancy is probably due to the presence of a small amount of the singly labeled acetic anhydride. Since the contamination by the singly labeled acetyl precursor is quantitatively not significant, the mass isotopomer distribution of tetraacetate polymer should follow the theoretical distribution of Table 1. The observed m4/m2 ratios determined from m/z 331 and m/z 271 clusters were plotted against the observed enrichment ratio (r) according to Eqn (2) (Fig. 1). As predicted from the equation, we observed two straight lines with slope of 1.46 and 1, respectively, for the tetraacetyl and the triacetyl groups. The excellent agreement of the observed slopes with the theoretical values of 1.5

and 1 suggests that the relationship can be used for the determination of precursor enrichment. The method of using mass isotopomer distribution to determine precursor enrichment and dilution by preexisting unenriched product is illustrated by the following experiment. Quantities of compound synthesized from lo%, 20% and 40% enriched acetic anhydride were mixed with unenriched glucose pentaacetate. The composition of these mixtures is presented in Table 6. The spectral data were processed according to the steps outlined above. The observed m4/m2 mass isotopomer ratios of the tetraacetate mixture and the calculated enrichments are shown in columns 2 and 3 of Table 6. Since the m4/m2 ratios depend only on the respective precursor enrichments, they were almost identical to those of the undiluted enriched samples from which the diluted samples were prepared (see Fig. 1). It is important to note that it is only after the proper correction for isomers of the unenriched precursor that the m4/m2 ratio will not be affected by the presence of pre-existing unenriched compound. Samples C, D and E were three different dilutions of the 40% enriched tetraacetate, and the m4/m2 ratios of these samples are the same regardless of dilution. The enriched-to-unenriched ratio (r) of the precursor is then derived from the linear relationship shown in Fig. 1. Precursor enrichment (En,) is calculated from the ratio as r/(l + r) (column 4). The principle for the estimation of tracer dilution is the same for non-radioactive (stable) and radioactive isotopes. In radioisotope studies, the dilution factor is given by the specific activity of the product divided by the specific activity of the precursor. In stable isotope studies involving more than two isotopomers, more than one ratio can be used. In our example, three methods are presented for the determination of dilution by pre-existing product. These are: enrichment ratio; mass isotopomer ratio, and regression analysis of mass isotopomer distribution. The enrichment ratio, which is the observed enrichment En, divided by the respective precursor enrichment En,, is directly analogous to taking the ratio of specific activities of radioisotopes.

MASS ISOTOPOMER STUDY OF PRECURSOR ENRICHMENT

1

loo

MIZ=331

119

/

r, % Figure 1. Observed m4/m2 ratio is plotted against r calculated from the individual enrichment for tetraacetate and triacetate moieties. The slopes correspond to (N - 1 )/2 as predicted by Eqn (2).

The results are shown in column 5 of Table 6. Another consequence of the algebraic relationship of Table 1 is that the dilution by unenriched compound is given by the fractional molar enrichment of a mass isotopomer (mi,) in a sample divided by the fractional enrichment of the isotopomer of its precursor (mip). When two or more isotopomer ratios are used in the calculation, multiple linear regression analysis can be applied as the proper averaging method. Dilutions determined by these two methods are shown in columns 6 and 7. The last two methods of determining dilution by pre-formed product assume the knowledge of mass isotopomer dis-

tribution of the precursor, which may not be readily available. When the distribution in the precursor is known, any of these three methods can be used for the estimation of dilution post-synthesis. The dilution factors calculated by the three methods are in good agreement with each other.

DISCUSSION Mass isotopomer analysis is a relatively new technique for the quantification of 13C tracer in nutrient sub-

Table 6. Calculation of precursor enrichment and product dilution Sample

A

B C

D E

Approx. dilution

m4/m2

9.09% 9.09% 20.00% 33.33% 66.67%

0.1720 0.3690 0.9300 0.9370 0.9340

Observed enrich (En,)

Precursor enrich. (En,).

0.65% 1.42% 6.68% 10.92% 24.06%

9.71Yo 19.50% 39.20% 39.20% 39.20%

Dilution calculated from

EndEn,

6.69% 7.28% 17.04% 27.86% 61.38%

mZ,Jm2,0

RegressionC

6.57% 7.24% 16.89% 27.66% 60.95%

6.57% 7.24% 16.91Yo 27.77% 61.87%

The samples were prepared by mixing labeled with unenriched glucose pentaacetate as follows: A: 2 pl of 10% enriched pentaacetate mixed with 20 pI of unenriched pentaacetate; 8 : 2 pI of 20% enriched pentaacetate mixed with 20 pI of unenriched pentaacetate; C: 2 pI of 40% enriched pentaacetate mixed with 8 pI of unenriched pentaacetate; D: 3 pI of 40% enriched pentaacetate mixed with 6 pl of unenriched pentaacetate; E: 6 pI of 40% enriched pentaacetate mixed with 3 pI of unenriched pentaacetate. Precursor enrichment was calculated from r obtained from m4/m2 ratio using Fig. 1. bm20/rn2,stands for the observed m2 in the product divided by the m2 in the precursor from Table 5. Dilution by unenriched product can be estimated by multiple linear regression analysis using the mass isotopomer distributions of unenriched and enriched as the independent variables and the observed mass isotopomer distribution in the sample as the dependent variable. An example is provided in the Appendix 2. a

W.-N. P. LEE, 2. K. GUO AND E. A. BERGNER

120

strates. Since its introduction for the study of glycogen synthesis by Kalderon et al.' the technique has only been applied in very few metabolic studies and its potential use in metabolic studies is largely unexplored. Early applications of mass isotopomer analysis focused on processes by which mass isotopomers are generated from uniformly labeled compounds.6-8 Thus glucose labeled in all positions with 13C((U-'3C)glucose) is used to generate uniformly labeled 3-carbon precursors. Intramolecular dilution of the labeled 3-carbon precursor produces intermediates labeled with 1, 2 or 3 I3Cs. Many mass isotopomers can also be formed from the combination of simple labeled precursors. For example, cholesterol with masses up to m + 22 can be formed in its synthesis in the presence of deuterated water, and m + 4 glucose can be formed from (2,3-l3C2)lactateof high enrichment. The distribution of these isotopomers formed by the combination of two or more labeled precursors carries information which can be exploited for the study of precursor enrichment and biosynthesis of compounds. Recently, Hellerstein et al.' reported a new method of determining hepatic cytosolic acetyl CoA enrichment using the frequency distribution of isotopomers in fatty acid. The method is based on the well-known fact that mass isotopomer distribution in a polymer follows a binomial distribution according to the proportion of the unenriched ( p ) to the enriched (q) precursor, and the number of repeating units (N). Since most experimental samples are essentially mixtures of newly synthesized and pre-existing products, the mass isotopomer distribution in such a mixture is the average of two binomial functions, which cannot be subjected to simple analysis. For this reason, Hellerstein et al. employed the concept of 'excess isotopomer frequency,$ which is the simple subtraction of background molar fraction of an ion species from the observed mass isotopomer fraction, and precursor enrichment was determined graphi~ally.~ In this paper, we have used the synthesis of glucose pentaacetate as an example of mass isotopomer formation of a polymer from its simple labeled precursor. The synthesis is analogous to lipid synthesis from typical 2carbon acetyl units. Our method differs from that of

3 For such calculation, the spectral intensities are normalized to the sum of all ion intensities of the cluster. The algebraic entity of 'excess isotopomer frequency' is used. 'Excess isotopomer frequency' is defined as the (m/z + i), of the sample minus the (m/z + i)b of the background or unenriched product when the ion intensities are norm a l i d to the total ion current, i.e. sum of all m/z equals 1. 'Excess isotopomer frequency' thus calculated is not equal to the enrichment as generally accepted. The excess frequency ratio of m2 and ml is given by : C(dz +

- (m/z + l)bl/c(m/z

+ 2)s

-

+ 2)bl

which can be shown not to be altered by dilution by preexisting unenriched product. This quantity can be approximated by a linear function of enrichment when precursor enrichment is small (< 10%). Enrichment of cytosolic acetyl CoA was determined from such an excess isotopomer frequency ratio, and the expected excess isotopomer frequency ratio of a standard. The fraction of newly synthesized palamitate was calculated by dividing the observed excess enrichment by the expected excess enrichment, (EF) = [(m/z + l), - (m/z + l)b]cxpderived from theory for different enrichments:

Hellerstein3 in that the isotope contribution from the derivative component of the compound and the natural abundance of the unenriched 2-carbon units is subtracted, and the simple binomial probability function of Table 1 is used. The method of background correction is equivalent to converting the spectral data of a product into a simple mass isotopomer distribution resulted from the combination of two (enriched and unenriched) precursor species. Only when this background correction method is applied can Eqn (2) or (3) be used for the estimation of precursor enrichment. When the labeled precursor consists of two enriched species, Eqn (2) or (3) needs to be replaced by the algebraic formula of Table 2 for the estimation of the two enrichments, q1 and qz . Once the precursor enrichment is determined, any one of three methods shown in Table 6 can be used to determine dilution by pre-formed unenriched product. The ability to determine precursor enrichment and dilution of product from mass isotopomer pattern is another unique feature of the application of stable isotope and GC/MS analy~is.'.'~When total 13C incorporation is known, the rate of synthesis can be determined as well. Another potential application of the isotopomer ratio involves the determination of the number of repeating units (N) of a polymer. When the stoichiometric relationship between the precursor and product (N) is not firmly established, such as in the case of using deuterated water to study biosynthesis, other methods are often used to determine N-the number of positions which can accept a labeled precursor. Wadke et al. used the maximum average mass of palmitate and stearate synthesized in the presence of 100% enriched deuterated water to estimate the number of exchangeable protium atoms of these fatty acid molecules.'' Javitt and Javitt determined the number of exchangeable protium atoms in cholesterol using a binomial distribution model of the mass isotopomers produced from deuterium during its synthesis.l 2 In situations where the precursor enrichment can be controlled, Eqn (2) can also be used to solve for the largest number of labeled species possible (N); m2/ml is plotted against q/p, and N is calculated from the slope by the equation: slope = (N - 1)/2. In summary, we have demonstrated the use of mass isotopomer analysis in determining precursor enrichment and product dilution in the synthesis of a homonucleus polymer. The method is not suitable for studies of synthesis of compounds from direct conversion such as pyruvate to alanine, nor from several precursor units such as in protein synthesis. Generally infusion of large amounts of highly enriched precursor is required to allow for the recombination of the label precursor to occur in the product. Despite these limitations, the application is suitable for studies of glucose and fatty acid synthesis which are underway.

Acknowledgements This work was supported by National Institutes of Health grants DK 6824 to Dr Joseph Katz and CA 4271 to the UCLA Clinical Nutrition Research Unit. The authors are deeply grateful to Dr Joseph Katz for his critical input and his invaluable editorial assistance throughout the preparation of this manuscript. The authors also thank Dr Marc Hellerstein for his permission to cite his articles prior to their publication.

MASS ISOTOPOMER STUDY OF PRECURSOR ENRICHMENT

121

REFERENCES 1. M. K. Hellerstein, K. Wu, S. Kaempfer, C. Kletke and C. H. L. Shackleton, J. Biol. Chem. 266, 10912 (1991). 2. P. R. Wolfe, Tracers in Metabolic Research: Radioactive and Stable Isotope/Mass Spectrometry Methods, p. 282. Liss, New York (1984). 3. M. Hellerstein, J. Biol. Chem. 266, 10920 (1991 ). 4. W. N. P. Lee, L. 0. Byerley, E. A. Bergner and J. Edmond, Biol. Mass Spectrom. 20,451 (1991). 5. B. Kalderon, A. Gopher and A. Lapidot, FEBS Lett. 204. 29 (1986). 6. J. Katz, W.-N. P. Lee, P. A. Wals and E. A. Bergner, J. Biol. Chem. 264,12994 (1989).

7. J. Katz, P. A. Wals and W. N. P. Lee, Proc. Nat. Acad. Sci. USA 88,2103 (1991). 8. J. Katz, and W. N. P. Lee,Am. J. Physiol. 259, E757 (1991). 9. J. Edmond, R. A. Korsak, E. A. Bergner and W. N. P. Lee, FASEB J. 4, A1 922 (1990). 10. W. N. P. Lee, E. A. Bergner, L. Byerley, R. A. Korsak and J. Edmond, Clin. Res. 39,133A (1991). 11. M. Wadke, H. Brunengraber, J. M. Lowenstein, J. J. Dolhun and G. P. Arsenault, Biochemistry12,2619 (1973). 12. N. B. Javitt and J. I. Javitt, Biomed. Environ. Mass Spectrom. 18,626 (1989).

APPENDIX 1

The abundance matrix for the correction of background enrichment is constructed based on the assumption of distribution of mass isotopomers contributed by the unenriched species. These distributions are suggested from the expressions of Table 2, and form the basis of the abundance matrix shown in Table 7. In the unenriched tetraacetate there are four unenriched acetyl units, and the distribution of carbon mass isotopomers

is given by the binomial expansion of (0.989 + 0.01 1)8 given in column 1 of the abundance matrix. The combination of one labeled acetyl unit and three unlabeled acetyl units will give rise to mass isotopomer distribution following the binomial expansion of (0.989 0.011)6 with base mass at m l and m2 (columns 2 and 3 of the abundance matrix).

+

Table 7. Abundance matrix used for the correction of unenriched acetyl units mO

ml

m2

17-13

0.91 53 0.0814 0.0032 0.0001 0 0 0

0 0.9358 0.0624 0.0017 0

0 0 0.9358 0.0624 0.0017 0 0

0 0 0 0.9567 0.0426 0.0007 0 0 0

0 0

0

0 0

0

0

0

13C natural

m4

0 0 0 0 0.9567 0.0426 0.0007 0 0

m6

m5

0 0

abundance of the

0 0 0

0 0 0

0.9781 0.0217 0.0001 0

0 0 0 0.9781 0.0217 0.0001

m7

m8

0 0 0 0

0 0 0 0

0 0 0 1 0

0 0 0 0 1

APPENDIX 2

From expressions in Table 1 it is clear that the mass isotopomer enrichment in the diluted sample (mi,) divided by the isotopomer enrichment in the undiluted Table 8. Enrichment of even-number mass isotopomers of tetraacetyl moiety of mixtures of enriched and unenricbed glucose pentaacetate Samples

mO

m2

m4

m6

m8

A B

0.9777 0.9578 0.8528 0.7610 0.4737

0.01 78 0.0280 0.0571 0.0934 0.2064

0.0031 0.0103 0.0532 0.0876 0.1930

0.0002 0.0019 0.0239 0.0393 0.0965

0.0001 0.0003 0.0051 0.0082 0.0182

0.1425 0.4248 0.6674

0.3383 0.3871 0.2714

0.3142 0.1412 0.0466

0.1406 0.0263 0.0045

0.0298 0.0026 0.0001

C D

E Precursorse

40% En 20% En 10% En

'Values are from Table 5 corresponding to the different precursor enrichment.

Table 9. Determination of dilution factor by multiple linear regression analysis of mass isotopomer data of sample C

mO m2

m4 m6 m8

40% En precursor

Unenriched product

Sample C mixture

0.1424 0.3380 0.31 40 0.1403 0.0298

1 0 0 0 0

0.8528 0.0571 0.0531 0.0240 0.0051

Regression output

0 0.0001 63 0.999999 5 3

Constant Std Err. of y est. R2 No. of observations Degrees of freedom

x coefficient@) Std Err. of coeff.

0.1 69195 0.000338

0.828706 0.000170

Thex coefficient for the enriched species, 0.169, is the fraction of the enriched species in the mixture.

122

W.-N. P. LEE, Z. K. G U O A N D E. A. BERGNER

sample (precursor) gives the dilution 1/(Q + 1). The relationship can be summarized by : m l J m l = m2dm2 = m3Jm3 =

= 1/(Q

+ 1)

By algebraic manipulation, it can be shown that the sum of all the numerators divided by the sum of all the denominators will give the same ratio 1/(Q + 1). The sum of the numerators is the enrichment of the sample, and the sum of the denominators is the enrichment of the precursor. Therefore, the enrichment of the diluted

sample divided by the enrichment of the precursor will give the same result. The enrichment of even-number mass isotopomers of experimental samples and their precursors are used to demonstrate the application of regression analysis, and the data are shown in Table 8. The x coefficients are the fractions of precursor and pre-existing product. A multiple linear regression analysis using the Lotus 123 program of sample C is shown in Table 9. Multiple linear regression analysis allows one to properly average the results from several mass isotopomer ratios.