Determination of intramolecular δ13C from incomplete pyrolysis fragments. Evaluation of pyrolysis-induced isotopic fractionation in fragments from the lactic acid analogue propylene glycol

Article abstract of DOI:10.1021/ac0522198

Intramolecular carbon isotope ratios reflect the source of a compound and the reaction conditions prevailing during synthesis and degradation. We report here a method for determination of relative (Δδ¹³C) and absolute (δ¹³C) intramolecular isotope ratios using the volatile lactic acid analogue propylene glycol as a model compound, measured by on-line gas chromatography-pyrolysis coupled to GC-combustion-isotope ratio mass spectrometry. Pyrolytic fragmentation of about one-third of the analyte mass produces optimal fragments for isotopic analysis, from which relative isotope ratios (Δδ¹³C) are calculated according to guidelines presented previously. Calibration to obtain absolute isotope ratios is achieved by quantifying isotope fractionation during pyrolysis with an average fractionation factor, α, and evaluated by considering extremes in isotopic fractionation behavior. The method is demonstrated by calculating ranges of absolute intramolecular isotope ratios in four samples of propylene glycol. Relative and absolute isotope ratios were calculated with average precisions of SD(Δδ¹³C) <0.84‰ and SD-(δ¹³C) <3.0‰, respectively. The various fractionation scenarios produce an average δ¹³C range of 2‰ for each position in each sample. Relative isotope ratios revealed all four samples originated from unique sources, with samples A, B, and D only distinguishable at the position-specific level. Regardless of pyrolysis fractionation distribution, absolute isotope ratios showed a consistent pattern for all samples, with δ ¹³C⁽³⁾ > δ¹³C⁽²⁾ > δ¹³C⁽¹⁾. The validity of the method was determined by examining the difference in relative isotope ratios calculated through two independent methods: Δδ¹³C calculated directly using previous methods and Δδ¹³C extracted from absolute isotope ratios. Deviation between the two Δδ¹³C values for all positions averaged 0.1-0.2‰, with the smallest deviation obtained assuming equal fractionation across all fragment positions. This approach applies generally to all compounds analyzed by pyrolytic PSIA.

Full text of DOI:10.1021/ac0522198

Anal. Chem. 2006, 78, 2752-2757
1
3
Determination of Intramolecular δ C from
Incomplete Pyrolysis Fragments. Evaluation of
Pyrolysis-Induced Isotopic Fractionation in
Fragments from the Lactic Acid Analogue
Propylene Glycol
Christopher J. Wolyniak, Gavin L. Sacks, Sara K. Metzger, and J. Thomas Brenna*
Division of Nutritional Sciences, Savage Hall, Cornell University, Ithaca, New York 14853
Intramolecular carbon isotope ratios reflect the source of
a compound and the reaction conditions prevailing during
synthesis and degradation. We report here a method for
determination of relative (∆δ13C) and absolute (δ C)
intramolecular isotope ratios using the volatile lactic acid
analogue propylene glycol as a model compound, mea-
sured by on-line gas chromatography-pyrolysis coupled
to GC-combustion-isotope ratio mass spectrometry. Py-
rolytic fragmentation of about one-third of the analyte
mass produces optimal fragments for isotopic analysis,
High-precision compound-specific isotope analysis (CSIA) is
a routine method where the analyte molecule is purified on-line
prior to isotope ratio measurement. CSIA has myriad applications,
13
1
including sourcing and determining the authenticity or purity of
a sample.2 A greater understanding of origin and biochemical
,3
history can be obtained through position-specific isotope analysis
(
PSIA), which enables observation of intramolecular isotopic
4,5
variation. Fractionation occurs during (bio)chemical processes
at sites of bond breaking and formation, with molecules containing
lighter isotopes reacting selectively over those with heavy iso-
topes.6
1
3
from which relative isotope ratios (∆δ C) are calculated
according to guidelines presented previously. Calibration
to obtain absolute isotope ratios is achieved by quantifying
isotope fractionation during pyrolysis with an average
fractionation factor, r, and evaluated by considering
extremes in isotopic fractionation behavior. The method
is demonstrated by calculating ranges of absolute in-
tramolecular isotope ratios in four samples of propylene
glycol. Relative and absolute isotope ratios were calculated
High-precision PSIA using isotope ratio mass spectrometry
(IRMS) requires off-line or on-line fragmentation of the analyte
molecule followed by isotope ratio measurement of the fragments.
7
Most previous PSIA studies, with analytes such as amino acids,
8
9
glycerol, and components of wine, employed off-line fragmenta-
tion of samples prior to analysis. In these studies, a single position
or moiety was chemically removed and the isotope ratio was
measured independent from the rest of the compound structure;
isotope ratios for all carbon positions were not determined. Site-
specific natural isotopic fractionation-NMR has also been utilized
for intramolecular isotope ratio measurements of hydrogen,
carbon, nitrogen, and oxygen.10 However, the low sensitivity of
NMR to the heavier elements requires acquisition times signifi-
cantly longer than hydrogen as well as sample size in the gram
range,11 preventing use in situations of limited sample size.
1
3
with average precisions of SD(∆δ C) <0.84‰ and SD-
1
3
(
δ C) <3.0‰, respectively. The various fractionation
1
3
scenarios produce an average δ C range of 2‰ for each
position in each sample. Relative isotope ratios revealed
all four samples originated from unique sources, with
samples A, B, and D only distinguishable at the position-
specific level. Regardless of pyrolysis fractionation distri-
bution, absolute isotope ratios showed a consistent pat-
*
To whom correspondence should be addressed. E-mail: jtb4@cornell.edu.
(1) Asche, S.; Michaud, A. L.; Brenna, J. T. Curr. Org. Chem. 2003, 7, 1527-
543.
2) Meier-Augenstein, W. J. Chromatogr., A 1999, 842, 351-371.
1
3
(3)
13 (2)
13 (1)
tern for all samples, with δ
C
> δ
C
> δ
C
. The
1
validity of the method was determined by examining the
difference in relative isotope ratios calculated through two
(
(3) Bauer-Christoph, C.; Christoph, N.; Aguilar-Cisneros, B. O.; L o´ pez, M. G.;
1
3
Richling, E.; Rossmann, A.; Schreier, P. Eur. Food Res. Technol. 2003, 217,
independent methods: ∆δ C calculated directly using
4
38-443.
4) Schmidt, H.-L. Naturwissenschaften 2003, 90, 537-552.
(5) Brenna, J. T. Rapid Commun. Mass Spectrom. 2001, 15, 1252-1262.
1
3
previous methods and ∆δ C extracted from absolute
isotope ratios. Deviation between the two ∆δ13C values
for all positions averaged 0.1-0.2‰, with the smallest
deviation obtained assuming equal fractionation across
all fragment positions. This approach applies generally to
all compounds analyzed by pyrolytic PSIA.
(
(6) Hoefs, J. Stable Isotope Grochemistry; Springer: New York, 2004; pp 5-20.
(7) Abelson, P. H.; Hoering, T. C. Proc. Natl. Acad. Sci. U.S.A. 1961, 47, 623-
6
32.
8) Weber, D.; Kexel, H.; Schmidt, H.-L. J. Agric. Food Chem. 1997, 45, 2042-
046.
9) Savidge, W. B.; Blair, N. E. J. Agric. Food Chem. 2005, 53, 197-201.
(
2
(
(10) Martin, G. J. Isot. Environ. Health Stud. 1998, 34, 233-243.
2752 Analytical Chemistry, Vol. 78, No. 8, April 15, 2006
10.1021/ac0522198 CCC: $33.50 © 2006 American Chemical Society
Published on Web 03/10/2006

We have previously reported a purely instrumental method
1
2
for PSIA, employing a continuous flow system of analyte
separation by GC, fragmentation by pyrolysis, and GCC-IRMS
for fragment separation and isotope ratio measurement. The
method has been applied to the analysis of alkanes and fatty
1
3
14,15
acids, amino acids,
acids.
and low molecular weight organic
16,17
In many cases, optimal signal is obtained at temperatures
that produce incomplete pyrolysis (including amino acid studies)
causing the analyte to fractionate at each carbon position to an
indeterminate degree. Thus, absolute intramolecular isotope ratios
1
3
(
δ C) cannot be determined by comparison to isotopically
calibrated CO . However, each sample undergoes equivalent
fractionation, which enables the reporting of a relative isotope ratio
Figure 1. Biochemical oxidative decarboxylation of pyruvate to
acetyl-CoA and conversion of pyruvate to lactate.
2
1
3
(
∆δ C) showing isotopic variability at a single position across
1
4,15
multiple samples.
illustrated variability at the carboxyl position among four samples.
For example, a previous study of alanine
15
1
3
13
A major disadvantage of ∆δ C is that they do not reveal δ C at
each position within a single sample to enable observation of
intramolecular isotope distribution. Quantification of fractionation
during pyrolysis would enable the calculation of absolute isotope
ratios for each position and detection of isotopic distribution.
Isotope ratios of compounds are easily measured, and thus,
the overall isotopic fractionation between a parent and a fragment
is readily determined. Isotopic fractionation at each position
depends on details of the potential energy surfaces and reaction
mechanisms. For pyrolytic conditions, position-specific fraction-
ation is not readily determined, and thus, it is unknown whether
fractionation distribution is equal (E) across all sites or is due to
fractionation at one site (S) with negligible fractionation at the
others. These two extremes can be considered independently by
assuming them in turn, calculating a fractionation factor, R, to be
Figure 2. Chemical reduction of lactic acid to propylene glycol.
Carbon positions (labeled as 1, 2, and 3) and isotope ratios are
preserved during this reaction.
with an extraneous additional carbon atom. Pyrolysis of that
compound is likely to yield fragments containing extraneous
carbon that would interfere with fragments containing analyte
carbon. Lactic acid can be quantitatively reduced to propylene
glycol, which is amenable to GC analysis, and here we focus on
intramolecular characterization of propylene glycol as a suitable
derivative for lactic acid.
We propose here a method to quantify pyrolysis fractionation
in propylene glycol, permitting calculation of isotope ratios for
individual carbon positions. We hypothesize that reasonable
assumptions about the range of fractionation factors, R, used to
13
used for calculation of δ C, and comparing the results to establish
whether choice of fractionation factor has an important influence
13
13
on determined δ C’s. We evaluate the influence of these assump-
tions for propylene glycol, a volatile lactic acid analogue.
calibrate relative isotope ratios, ∆δ C, will result in small differ-
13
ences in calculated δ C and compare this with calculations
Lactic acid is a key metabolic intermediate produced in humans
during anaerobic respiration, with an intramolecular isotope ratio
that is likely to reflect fractionation in pyruvate. Figure 1 shows
the conversion of pyruvate to acetyl-CoA by the pyruvate dehy-
drogenase complex in mammals. Isotope fractionation occurs for
the carbons participating in the reaction, leaving the acetate
performed independently. Finally, we characterize the absolute
δ C intramolecular in four samples of propylene glycol to test
whether the method can reliably detect natural variability.
13
EXPERIMENTAL SECTION
Synthesis of Chemical Analogue. To enable GC analysis,
lactic acid was reduced to propylene glycol (boiling point, 190
°C). Compounds were purchased as propylene glycol or lactic acid.
For convenience, each source was given a one-letter code (with
“C” omitted to prevent confusion with carbon); “A” Acros (Geel,
Belgium), “B” Aldrich (St. Louis, MO), “D” Alfa Aesar (Ward Hill,
MA), and “E” Mallinckrodt (Phillipsburg, NJ) were all purchased
1
3
18
carboxyl carbon as depleted in C. Mass balance predicts that
13
the source pyruvate should be C enriched at those two positions.
During anaerobic respiration, pyruvate is converted to lactate and
released into plasma. Lactic acid has been previously isolated from
1
3
plasma and analyzed at the compound-specific level at natural
abundance.
C
1
9,20
For GCC-IRMS analysis, the analyte was deriva-
13
tized to a volatile methyl ester, altering the observed isotope ratio
as propylene glycol and used without further reaction. C-Labeled
samples were purchased as lactic acid from Cambridge Isotope
Laboratories (Cambridge, MA) and reduced to the derivative.
Figure 2 shows the reduction reaction based upon the methods
of Nystrom21 and Wood. The reaction is performed in a three-
neck, round-bottom flask, with one neck used for a condenser
and one with a calcium chloride drying tube. Briefly, 0.5 g of lactic
(
11) Caer, V.; Trierweiler, M.; Martin, G. J.; Martin, M. L. Anal. Chem. 1991,
3, 2306-2313.
12) Corso, T. N., Brenna, J. T. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 1049-
053.
6
(
22
1
(13) Corso, T. N.; Brenna, J. T. Anal. Chim. Acta 1999, 397, 217-224.
(14) Sacks, G. L., Brenna, J. T. Anal. Chem. 2003, 75, 5495-5503.
(15) Wolyniak, C. J.; Sacks, G. L.; Pan, B. S.; Brenna, J. T. Anal. Chem. 2005,
7
7, 1746-1752.
(
(
(
16) Yamada, K.; Tanaka, M.; Nakagawa, F.; Yoshida, N. Rapid Commun. Mass
Spectrom. 2002, 16, 1059-1064.
17) Dias, R. F.; Freeman, K. H.; Franks, S. G. Org. Geochem. 2002, 33, 161-
(19) Tetens, V.; Kristensen, N. B.; Calder, A. G. Anal. Chem. 1995, 67, 858-
862.
(20) Khalfallah, Y. Biol. Mass Spectrom. 1993, 22, 707-711.
(21) Nystrom, R. F.; Brown, W. G. J. Am. Chem. Soc. 1947, 69, 2548-2549.
(22) Wood, G.; Srivasta, R. M.; Adlam, B. Can. J. Chem. 1973, 51, 1200-1206.
1
68.
18) DeNiro, M. J.; Epstein, S. Science 1977, 197, 261-263.
Analytical Chemistry, Vol. 78, No. 8, April 15, 2006 2753

13
acid was dissolved in 10 mL of diethyl ether. The lactic acid
solution was added dropwise over 5 min to a solution of 0.16 g of
δ CV-PDB values. It has been previously demonstrated that
SAXICAB produces isotopic results identical to ISODAT, the
proprietary software from Thermo Finnigan.23 Data were collected
using high-precision NI435x data acquisition boards (National
Instruments, Austin, TX). Background levels were taken into
account using “dynamic” background correction.25 The mass 45
4
LiAlH in 6 mL of diethyl either. The resulting solution was stirred
for 30 min with the reaction quenched by adding 2 mL of distilled
water. Six milliliters 15% (w/w) of NaOH followed by 6 mL of
distilled water was added and the resultant mixture stirred for an
additional 15 min. The ether layer containing the product was
separated and vacuum filtered, rinsing three times with 4 mL of
ether. The resulting white solid product was dissolved in 100 mL
of methanol. A 40-µL aliquot of the solution was diluted with 60
µL of methanol to create a concentration appropriate for analysis
1
7
signal was adjusted to account for the presence of O prior to
1
3
26
final δ CV-PDB calculation.
Isotope Ratio Reporting. Absolute isotope ratios are reported
13
using conventional δ C notation,
Rspl - RV-PDB
RV-PDB
1
3
(2 µg/µL). The reaction produces product at 97% yield.
δ C
)
] × 1000
(1)
V-PDB
[
Instrumentation. Analysis was done using a home-built GC-
Py-GCC-IRMS system previously described.1 A 1-µL aliquot of
solution (2 µg of propylene glycol) was injected splitless using a
Varian 8200 autosampler (Varian, Inc., Walnut Creek, CA). The
analyte was separated from the solvent in GC1 (HP 5890, Hewlett-
Packard, Palo Alto, CA) on a VB-1 capillary column (15 m × 0.32
mm × 3 µm, VICI, Gig Harbor, WA). The oven was initially held
at 60 °C for 5 min and ramped at 20 °C/min to 180 °C. An
electronically triggered rotary valve (Valco, Houston, TX) was used
to direct column flow either to isotope analysis or to a flame
ionization detector (FID). The FID was used to determine reten-
tion time of the analyte peak and, therefore, trigger times of the
rotary valve to send the analyte to pyrolysis and isotope analysis.
One continuous length of 0.32-mm fused-silica capillary column
stretched from the output of GC1, through the pyrolysis furnace,
to the input of GC2. A resistively heated Fibercraft furnace
2
where Rspl is the isotope ratio of the sample and RV-PDB is the
isotope ratio of Vienna-PeeDee Belemnite, the international
standard for carbon with RV-PDB ) 0.011 179 6. In bulk and
compound-specific analysis, the analyte is assumed to be quanti-
13
tatively combusted, so that the resulting CO
the analyte. Subsequent transfer of the analyte CO
source is assumed to introduce no major isotopic fractionation
differing from that of the isotopically calibrated CO gas, which
typically takes a transfer path different from that of the analyte
2
δ C is identical to
2
to the ion
2
13
CO
accurate. Incomplete pyrolysis introduces isotopic fractionation
to the analyte to which the CO calibrant gas is not subject. A
2
. By this reasoning, the resulting δ CV-PDB is considered
2
13
relative isotope ratio, ∆δ C, can be accurately calculated compar-
ing a single position across several samples, making the reason-
able assumption that pyrolysis-induced fractionation is constant.
(
Thermcraft, Winston-Salem, NC) created a pyrolysis zone of ∼20
cm. To secure the capillary in the pyrolysis furnace, the capillary
was held in a 0.5-mm-i.d. ceramic tube. The pyrolysis furnace was
held at 700 ( 1 °C and controlled by a CN9000A series
temperature controller (Omega Engineering, Stamford, CT).
Following pyrolysis, the effluent passed through a heated transfer
line to the GC2 column.
13
When close to natural abundance levels, ∆δ C can be calculated
13
as the difference of the sample and standard δ C values as shown
in eq 2,
13
(x)
13 spl,(x)
13 ref,(x)
∆
δ C ) δ C
- δ C
(2)
Pyrolysis fragments were separated in GC2 (Varian 3400) on
a CarbonPLOT column (30 m × 0.32 mm × 1.5 µm, J&W
Scientific, Folsom, CA). The oven was initially held at 30 °C for
1
3
ref, (x)
where δ C
is the δ value for the reference source at carbon
13
spl,(x)
position x (source D in the current study) and δ C
is the δ
value for the sample source at carbon position x. This notation
has been discussed in detail previously.14 Pyrolysis introduces
artifactual isotopic fractionation, which will be taken into account
using the method discussed later.
1
0 min, ramped at 10 °C/min to 200 °C, and held for 3 min. A
manually controlled rotary valve directed separated peaks either
to isotope ratio measurement or molecular analysis for fragment
identification. Molecular analysis was accomplished using a Varian
Saturn III QISMS ion trap operating in positive ion electron impact
mode. Fragments were identified with the assistance of the Wiley
mass spectral database (Palisades, Newfield, NY). For isotope ratio
measurement, fragments were quantitatively combusted in a
second resistively heated Fibercraft furnace (940 °C) consisting
of a 30 cm × 0.5 mm i.d. ceramic tube containing oxidized Cu.
Products continued through a Nafion water trap to an open split
with a 10:1 split ratio into a Finnigan-MAT 252 IRMS (Bremen,
Germany) for isotope ratio measurement.
1
3
Fidelity of Pyrolysis Fragments. Calculation of ∆δ C and
13
δ CV-PDB values requires knowledge of pyrolysis fragment origin
in the parent molecule. We use the term isotopic fidelity to
describe the extent to which the isotope ratio of a fragment reflects
the isotope ratio of a specific position or moiety in the parent
compound.1
fragment originating from a position or moiety in the parent.
Utilizing previously established methods based on isotopic label-
ing, fidelity was calculated for each fragment formed as follows.
Separate standards were made with lactic acid labeled exclu-
sively in the 1 or 3 position. The derivatized compound was added
to an unlabeled solution with total 13C label at a concentration
between 0 and 200‰. Three labeled solutions were used, one
4,15
The fidelity of a compound is the percent of a
The system was controlled and data collected using SAXI-
CAB,23 a home-written Labview 6i-based program with controls
to trigger GC ovens, GC1 rotary valve, pyrolysis furnace, and
standard gas pulses and with data reduction routines to calculate
24
(25) Ricci, M. P.; Merritt, D. A.; Freeman, K. H.; Hayes, J. M. Org. Geochem.
(
(
23) Sacks, G. L., Brenna, J. T., Sepp, J. T. 48th ASMS Conference, Chicago, IL.
001.
24) 6i ed.; National Instruments, Austin, TX, 2000.
1994, 21, 561-571.
(26) Santrock, J.; Studley, S. A.; Hayes, J. M. Anal. Chem. 1985, 57, 1444-
2
1448.
2754 Analytical Chemistry, Vol. 78, No. 8, April 15, 2006

Table 1. Fidelity of Fragments Formed during Pyrolysis
C(1)
C(2)
C(3)
methanola
CH4
77.9 ( 0.7%
35.9 ( 1.0%
6.9 ( 0.5%
10.9 ( 0.2%
35.2 ( 3.6%
11.6 ( 1.9%
27.3 ( 0.7%
10.2 ( 0.7%
11.9 ( 0.4%
64.1 ( 0.8%
54.2 ( 0.2%
89.1 ( 1.3%
34.7 ( 0.7%
71.8 ( 1.7%
37.4 ( 0.8%
ethylene
acetaldehyde
propylene
38.9 ( 0.5%
30.1 ( 3.7%
16.6 ( 2.6%
35.4 ( 1.1%
a
ethanol
propanola
a
Used in calculation of relative and absolute δ values.
Figure 3. ∆δ13C for the three positions of propylene glycol
measured for four different sources. Error bars represent SD. Within
a position (1, 2, or 3), error bars that do not overlap are significantly
containing no labeled compound, one at ∼50‰ and one at ∼150‰.
The observed isotope ratio of a fragment (Robs) is a weighted sum
13
different (p <0.05). - - - represents ∆δ C ) 0.
of the isotope ratios of the carbons it contains (R
i
),
1
3
Relative Isotope Calculation. Relative isotope ratios (∆δ C)
15
Robs R [X ]
)
(3)
were calculated using previously developed methods, arbitrarily
using source D as the standard and setting relative isotope ratios
at each position to zero. Equations 5-7 show the mass balance
equations for methanol, ethanol, and propanol, respectively, used
for the calculation.
∑i
i
i
i
where X is the fraction of carbon from carbon i. Separating the
labeled position yields,
1
3
∆
∆
∆
δ C(MeOH) )
Robs
)
R [X ] + R [X ]
(4)
∑i
i
i
lab
lab
1
3
(1)
13 (2)
13 (3)
0.78∆δ C
+ 0.10∆δ C + 0.12∆δ C (5)
13
δ C(EtOH) )
where Rlab is the isotope ratio of the labeled compound and Xlab
is the mole fraction of the labeled compound. Equation 4 can be
plotted linearly as Robs versus Rlab, where slope is the fidelity of
the labeled carbon position for the fragment. Errors of slopes were
determined using the linear regression tool in Microsoft Excel
13
(1)
13 (2)
13 (3)
0
.12∆δ C + 0.17∆δ C + 0.72∆δ C (6)
13
δ C(Prop) )
0.27∆δ C + 0.35∆δ C + 0.37∆δ C (7)
13
(1)
13 (2)
13 (3)
2
000.
The system of three equations and three unknowns is solved for
the relative isotope ratios for each position. Errors were calculated
via standard propagation methods and took into account errors
in fidelities and fragment isotope ratio measurements. The
isotope ratio of each position was calculated independently to
eliminate compounded errors.
Figure 3 shows the relative isotope ratios for each position
and relative compound-specific data for each of the samples
analyzed. At the compound-specific level, all sources were within
RESULTS AND DISCUSSION
Pyrolysis Fragmentation. At 700 °C, 33% of the propylene
glycol present was pyrolyzed. Table 1 shows fidelities of pyrolysis
fragments formed from lactic acid. Each value listed is the quantity
of a fragment originating from the specified carbon. For example,
in the methanol fragment, 77.9 ( 0.7% of the carbon originated
2
7
(
1)
from position 1 (C ). Lower temperatures do not produce the
quantities of fragments necessary for high-precision measure-
ments, while higher temperatures exhibit more carbon atom
1
3
13
scrambling, and therefore, less ideal fidelity.14
a δ C range of 2.3‰, with sources A (∆δ C
D
) -0.04 ( 0.31‰),
) 0.00‰) statistically
) 2.28 ( 0.31‰) was the only unique
source. In contrast, at the position-specific level, the sources were
13
13
B (∆δ C
indistinguishable; E (∆δ C
D D
) 0.03 ( 0.32‰), and D (∆δ C
Fidelities of the fragments formed reflect the parent compound
structure, though evidence of scrambling is present. The majority
of methanol is formed from carbons that contain hydroxyl groups
13
D
(1)
in the parent compound, C( (77.9 ( 0.7%) and C (10.2 ( 0.7%).
1)
(2)
unique, with source D distinguished from all other sources at C
and source B distinguished at C( . The unique origin of source A
3)
Ethanol had a significant contribution from C(3) (71.8 ( 1.7%),
(1)
only becomes apparent in examining differences at two positions;
which presumably contributed to the methyl carbon, while C
11.6 ( 1.9%) and C(2) (16.6 ( 2.6%) primarily contribute to the
at C( , A is isotopically unique from source D, while at C , A is
1)
(3)
(
isotopically unique from source B. Relative isotope ratios were
hydroxyl-containing carbon. Propanol was formed from all three
13
(
2)
(3)
calculated with an average precision of SD(∆δ C) <0.84‰.
Absolute δ13C Calculation. Calibration for pyrolytic isotopic
carbons with C (35.4 ( 1.1%) and C (37.4 ( 0.8%) slightly
(
1)
favored over C (27.3 ( 0.7%). Methanol, ethanol, and propanol
13
fractionation is necessary for calculation of δ C. The critical
component of absolute isotope ratio calculation is the pyrolysis
fractionation factor (R) quantifying the influence of incomplete
fragmentation on isotope ratio due to partial pyrolysis. Ideally,
were used for the calculation of positional isotope ratios; average
1
3
precisions of the fragment isotope ratios were SD(δ C) <0.14‰,
1
3
13
SD(δ C) <0.34‰, and SD(δ C) <0.28‰, respectively. These
fragments had the most desirable combination of orthogonal
fidelities and isotope ratio precision to minimize propagated error
in positional isotope ratio calculations.
(27) Meyer, S. L. Data Analysis for Scientists and Engineers; Wiley: New York,
1975.
Analytical Chemistry, Vol. 78, No. 8, April 15, 2006 2755

fractionation factors would be available for each site; however, in
practice, it is only possible to determine isotope ratios at the
compound-specific level. The thus determined average fraction-
ation can be the result of equal (E) fractionation occurring at all
sites, in which case a single R can be applied to calibrate to each
position. The opposite extreme is to assume that fractionation
occurs only at one site (S), with negligible fractionation at the
other sites. If fractionation occurs at a single site within a fragment
containing n carbons, fractionation for that fragment changes by
a factor of 1/n as the isotope ratio of all other carbons remains
constant. Each fragment may independently fractionate between
the S and E extremes. For propylene glycol, we evaluate the
Table 2. Calculated r Values Used in Eq 12 To Correct
13
δ
C of Pyrolysis Fragments
fractionation scenario
source
EE
ES
SE
SS
A
B
D
E
3.6
4.5
3.4
3.4
5.3
6.6
5.1
5.0
4.1
5.2
3.9
3.9
6.6
8.2
6.3
6.2
1
3
magnitude of uncertainty by calculating R and δ C for both
extreme scenarios.
The isotope ratio of pyrolyzed carbon used in the calculation
was compared to that of the parent compound, with each factor
weighted appropriately for the pyrolysis scenario used, to obtain
R values, as follows. To accomplish this, first the relative
abundances of carbon contributed by methanol, ethanol, and
propanol in the pyrogram were calculated. Fractional abundances,
Figure 4. Range of absolute isotope ratios enabling comparison
between positions within the same molecule. The central box spans
the range of δ13C values, while the error lines extend to the extremes
of standard deviation.
ø
n
, of the fragments were calculated through eq 8,
An
øn )
(8)
AMeOH + AEtOH + AProp
and (1,1), respectively. Calculated R’s range from 3.3 to 8.2‰,
and their specific values can be found in Table 2.
Following calculation of R, fragment δ values are corrected
for pyrolysis fractionation using eq 12,
where A is peak area of fragment n in the m/z 44 pyrogram. The
1
3
isotope ratio of carbon used in the absolute δ C calculations,
13
δ Cpyr, was calculated using the weighted sum in eq 9,
1
3
13
13
δ C
)
δ C ) δ C - R/n
uncorr
(12)
pyr
corr
1
3
13
13
øMeOHδ C
+ øEtOHδ C
+ øPropδ C
(9)
MeOH
EtOH
Prop
13
13
where δ Cuncorr is the uncorrected fragment isotope ratio, δ Ccorr
is the corrected fragment isotope ratio, and n is either the number
of carbons in the fragment (for site-specific fractionation, S) or 1
1
3
with fragment δ C
is the difference between the parent δ value, δ CCSIA, and δ Cpyr
Including the 1/n term to account for site-specific fractionation
as shown in Appendix 1, Supporting Information), R is calculated
as,
n
values directly measured. Total fractionation
1
3
13
.
(for equal fractionation, E).
Utilizing corrected fragment isotope ratios, absolute position-
(
specific isotope ratios were calculated using a method similar to
that of the relative isotope ratio calculation. Equations 13-15 show
weighted sum equations with coefficients based on fidelity for
methanol (δ CMeOH), ethanol (δ CEtOH), and propanol (δ CProp),
respectively,
1
3
13
δ C
- δ C
)
pyr
CSIA
13
13
13
R
R
nEtOH
R
nProp
øMeOH
+ øEtOH
+ øProp
(10)
nMeOH
1
3
13 (1)
13 (2)
13 (3)
δ C
) 0.78δ C + 0.10δ C + 0.12δ C
(13)
(14)
(15)
MeOH
where n is the number of carbons in the specified fragment for
site-specific fractionation, or in the case of average fractionation,
n ) 1. Solving eq 10 for R yields eq 11.
1
3
13 (1)
13 (2)
13 (3)
δ CEtOH ) 0.12δ C + 0.17δ C + 0.72δ C
1
3
13 (1)
13 (2)
13 (3)
δ C
) 0.27δ C + 0.35δ C + 0.37δ C
Prop
1
3
13
δ C
- δ C
CSIA
pyr
R )
(11)
øMeOH
øEtOH øProp
+
+
13 (1)
13
(2)
13
(3)
are δ values of C(1), C(2), and
where δ C , δ C , and δ C
nMeOH
nEtOH nProp
(3)
13
C , respectively. Calculated δ C values for all pyrolysis scenarios
are shown in Figure 4, to be discussed below.
For methanol, S and E are equivalent since there is only one
carbon, and nMeOH ) 1 always. We then use a two-letter code
to describe specific pyrolysis scenarios for the three frag-
ments. The four possible combinations are SS, SE, ES, and EE,
which correspond to values of nEtOH and nProp of (2,3), (2,1), (1,3),
Check of Method Validity. Method validity was checked
13
through a comparison of relative isotope ratios (∆δ C). One set
13
was calculated directly from fragment δ C and fidelities in eqs
13
5-7 (∆δ C-dir), and the other set was calculated from absolute
isotope ratios of different pyrolysis scenarios (eqs 8-10) and
2756 Analytical Chemistry, Vol. 78, No. 8, April 15, 2006

Table 3. Average Deviation of ∆δ13C Calculated by
Assuming Various Scenarios Compared to Those
Determined by Direct Calibration of Fragment Isotope
Ratios Weighted by Fidelities
CONCLUSIONS
A method is presented to calculate absolute intramolecular
isotope ratios, demonstrated using the lactic acid analogue
propylene glycol as a model compound. Four samples of propylene
13
1
3
(1)
13 (2)
13 (3)
glycol were analyzed, for which relative (∆δ C) and absolute
∆
δ C
∆δ C
∆δ C
av abs
dev
13
dev
dev
dev
(δ C) isotope ratios were calculated. Relative isotope ratios
showed all samples originated from different sources, with sources
A, B, and D distinguishable only at the position-specific level.
EEa
ES
SE
SS
-0.37
-0.55
-0.43
-0.69
-0.20
-0.29
-0.23
-0.36
0.23
0.32
0.26
0.39
0.27
0.39
0.31
0.48
13
Absolute isotope ratios revealed the same δ C pattern, with
(3)
(1)
13
enrichment at the C position, with C most depleted in C.
13
a
Absolute δ C calculations required quantification of fraction-
ation due to pyrolysis. The degree of fractionation is dependent
on whether fractionation is exclusive to one carbon site in a
fragment or distributed among all carbons. Four different sce-
narios were explored, with different combinations of site-specific
and average fractionation for each fragment. We find that use of
an average fractionation factor yields minimal error and absolute
Smallest average absolute deviation.
13
converted to relative isotope ratios using eq 2 (∆δ C-check). This
1
3
is an independent check because ∆δ C-check incorporates an
13
independent mean R, and ∆δ C values thus derived are indepen-
1
3
13
dent of ∆δ C-dir. Table 3 presents all results for the differences
δ C within (1.5‰ of that calculated under assumptions of
1
3
13
(
∆δ C-dir) - (∆δ C-check). The average absolute deviation is
extreme fractionation. Although this figure is higher than com-
monly reported for high-precision IRMS, we note that the
∼
0.4‰, positions 1 and 2 are biased to lower values, and position
is biased to higher values. This value is modest compared to
13
3
difference in ∆δ C is determined with much less error and is
usually the quantity of most interest. In addition, intramolecular
variability is high compared to compound-specific or bulk isotope
the magnitude of differences for the means and is about twice
1
3
the precision expected for direct δ C measurement of frag-
ments. The EE combination, where fractionation is distributed
evenly across all carbon sites, yields the smallest deviation, which
we take as evidence that variation among R are closer to E than
to S.
13
δ C, providing greater tolerance for error. This analysis indicates
that on-line PSIA by GC-Py-GCC-IRMS can provide useful in-
tramolecular 13C/ C for a single analyte without resorting to
intramolecularly calibrated isotopic standards.
12
Intramolecular Isotope Distribution. Figure 4 shows the
intramolecular isotope ratios grouped by source incorporating R
factors for all pyrolysis scenarios. In the figure, central rectangles
span the range of δ C calculated by assuming all four fractionation
scenarios, and the error lines extend to the extremes of means
plus and minus SDs. Each source exhibits a similar pattern of
ACKNOWLEDGMENT
This work was funded by NIH grant GM49209. C.J.W.
acknowledges support from NIH training grant DK07158.
13
SUPPORTING INFORMATION AVAILABLE
Additional information as noted in text. This material is
1
3
(3)
13 (2)
13 (1)
isotope distribution, with δ C > δ C > δ C , though the
degree of variability is different. Although no biological statements
can be made concerning these propylene glycol samples, we note
available free of charge via the Internet at http://pubs.acs.org.
13
Received for review December 15, 2005. Accepted
February 7, 2006.
that all samples show a clear pattern of increasing δ C with carbon
number. Average precision was calculated with an average SD-
1
3
(
δ C) <3.0‰.
AC0522198
Analytical Chemistry, Vol. 78, No. 8, April 15, 2006 2757