Tandem mass spectrometry: A novel approach for metabolic flux analysis

Metabolic Engineering 13 (2011) 225–233

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Tandem mass spectrometry: A novel approach for metabolic flux analysis Jungik Choi, Maciek R. Antoniewicz n Department of Chemical Engineering, Metabolic Engineering and Systems Biology Laboratory, University of Delaware, 150 Academy St, Newark, DE 19716, USA

a r t i c l e in f o

abstract

Article history: Received 30 August 2010 Received in revised form 17 October 2010 Accepted 23 November 2010 Available online 4 December 2010

The goal of metabolic flux analysis (MFA) is the accurate estimation of intracellular fluxes in metabolic networks. Here, we introduce a new method for MFA based on tandem mass spectrometry (MS) and stable-isotope tracer experiments. We demonstrate that tandem MS provides more labeling information than can be obtained from traditional full scan MS analysis and allows estimation of fluxes with better precision. We present a modeling framework that takes full advantage of the additional labeling information obtained from tandem MS for MFA. We show that tandem MS data can be computed for any network model, any compound and any tandem MS fragmentation using linear mapping of isotopomers. The inherent advantages of tandem MS were illustrated in two network models using simulated and literature data. Application of tandem MS increased the observability of the models and improved the precision of estimated fluxes by 2- to 5-fold compared to traditional MS analysis. & 2010 Elsevier Inc. All rights reserved.

Keywords: Mass spectrometry GC–MS/MS Metabolism Isotopomer Stable isotope tracer 13 C labeling

1. Introduction Metabolic flux analysis (MFA) has become a key concern in metabolic engineering and systems biology in the post-genomic era (Sauer, 2006). Determination of metabolic fluxes under in vivo conditions presents useful information regarding the cellular phenotype, cell function and regulation (Moxley et al., 2009). In the past two decades, MFA has been applied to many biotechnological and biomedical problems (Antoniewicz et al., 2007c; Boghigian et al., 2010; Jin et al., 2004; Sillers et al., 2009; Wisselink et al., 2010; Yoo et al., 2008). The application of stable-isotope tracers combined with measurements of isotopomer labeling represents the state-of-the-art influx determination methodology (Antoniewicz et al., 2007b; Wiechert et al., 1999). The reconstruction of a comprehensive and accurate flux map depends largely on selecting an appropriate tracer and obtaining as much information as possible about the amount and distribution of labeled atoms (e.g. 13C) in metabolic products (Suthers et al., 2010). At the moment there are two main methods for measuring isotopic labeling of molecules; namely, NMR and mass spectrometry coupled with liquid (LC–MS) or gas (GC–MS) chromatography (Burgess et al., 2003a; Des Rosiers et al., 2004; Kleijn et al., 2007). The NMR technique provides detailed positional labeling (Burgess et al., 2003b; Jones et al., 1997); however, it requires a fairly large amount of sample, long analysis times and expensive equipment.

Abbreviations: GC, gas chromatography; MS, mass spectrometry; MFA, metabolic flux analysis; CID, collision-induced dissociation n Corresponding author. Fax: + 302 831 1048. E-mail address: [email protected] (M.R. Antoniewicz). 1096-7176/$ - see front matter & 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.ymben.2010.11.006

Mass spectrometry, on the other hand, is widely accessible, less costly, and provides sensitive detection of molecular enrichment. In particular, GC–MS has been extensively used for MFA applications (Wittmann, 2002a, 2002b). In GC–MS, a sample of extracted metabolites is chemically derivatized, followed by fractionation by GC and ionization by electron impact (or chemical) ionization. The resulting ions are then characterized based on their mass-to-charge ratio (m/z). Since fragment ions usually carry a single charge, the m/z value corresponds to the molecular weight of the fragment in atomic mass units. A typical mass spectrum contains several peaks corresponding to different fragments of the detected compound (Antoniewicz et al., 2007a). Isotopomers that have incorporated the same number of labeled atoms are called mass isotopomers, denoted by M0, M1, etc. (where M is the base mass of the fragment). Using MS, the relative amount of each mass isotopomer is measured, providing the so-called full-spectrum mass isotopomer distribution of each fragment. A limitation of MS analysis is that it provides only partial information about the distribution of isotopomers. It is especially difficult to extract positional labeling information from MS data, even when multiple fragments of the same compound are detected (Dauner and Sauer, 2000). To address this limitation we explore a new approach for measuring isotopomers using tandem MS that can potentially increase the amount of labeling data for MFA. Our work builds on the pioneering research by Jeffrey et al. (2002), who were the first to suggest that tandem MS might be used for metabolic flux studies. Jeffrey et al. applied three techniques (i.e. GC–MS, GC–MS/MS, and 13C NMR) to measure 13C-labeling of glutamate from tissue extracts of hearts supplied with various 13 C-enriched substrates. Experimental results indicated that

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tandem MS could be successfully applied to analyze glutamate labeling and produce flux results similar, or better, than those obtained by 13C NMR, and significantly better than those using traditional full spectrum GC–MS. While the work by Jeffrey et al. demonstrated the potential use of tandem MS for MFA, it also highlighted some major challenges that needed to be addressed before this technique could be routinely applied for MFA. As an example, Jeffrey et al. manually derived complex non-linear expressions that related certain tandem MS measurements to flux parameters in the metabolic network model. In order to derive these expressions a number of model simplifications were necessary, such as leaving out certain isotopomers. Because these expressions were specific to the assumed network model and the specific 13C-tracers used, and because certain isotopomers and tandem MS measurements were ignored, the full potential of tandem MS analysis for MFA was not explored. Here, we present a general framework for simulating tandem MS data in complex biological network models and estimating metabolic fluxes from tandem MS measurements. Our framework is based on the wellestablished method of isotopomer balancing (Schmidt et al., 1997). In this contribution, we demonstrate that tandem MS offers significant and inherent advantages for MFA compared to full scan MS analysis.

2. Theory 2.1. Isotopomer analysis using tandem mass spectrometry Fig. 1 illustrates the principles of isotopomer analysis using tandem MS, which is an extension to full scan MS analysis. In tandem MS, the first mass analyzer isolates a single mass isotopomer from the full spectrum (called the parent ion) that is then

fragmented by collision-induced dissociation (CID). The resulting daughter ions are analyzed in the second mass analyzer, operated in daughter ion scanning mode, or multiple reaction monitoring mode. For illustration purposes, the parent fragment in Fig. 1 contains all atoms of a 3-atom compound, and the daughter fragment contains atoms 2 and 3. We denote mass isotopomers of the parent fragment by M0, M1, etc., and mass isotopomers of the daughter fragment by m0, m1, etc. Note that the M2 mass isotopomer fraction is composed of three isotopomers (110, 101, and 011; with 1¼ labeled atom, 0 ¼unlabeled atom) that cannot be distinguished in the full spectrum. However, after CID two of the three isotopomers give rise to m1 signal in the daughter spectrum, while the third isotopomer yields m2. Thus, the daughter spectrum discriminates between previously unresolved isotopomers. In this case, the daughter spectrum provides one additional piece of labeling information, i.e. the abundance of the 011 isotopomer. Daughter spectra can be measured for all mass isotopomers in the full spectrum (i.e. M0, M1, M2 and M3) providing additional positional and enrichment information. These data are conveniently collected in a matrix, which we call the tandem mass isotopomer matrix (Fig. 1). The elements of this matrix represent particular parent-to-daughter ion transitions. Note that only certain transitions are possible, e.g. in this case 6 transitions are possible: one transition for M0 parent ion; two transitions for M1 and M2 parent ions, each; and one transition for M3 parent ion. In general, the number of transitions is equal to (n  m+ 1)(m+ 1), where n and m are the number of atoms for the parent and daughter fragments, respectively; specifically, (m +1) is the number of possible daughter ions and (n m +1) is the number of possible parent ions for each daughter ion. This simple example demonstrates that tandem MS provides useful additional information for determining labeling of compounds. In the next section, a mathematical framework is presented that formalizes the analysis of isotopic labeling by tandem MS.

Daughter Spectrum

Parent Spectrum 1 2 3

M2>m1 2 3 Collision - induced dissociation

M2>m2 2 3

1 M0

M1

M2

M3

2

m0

m1

m2

3

Tandem Mass Isotopomer Matrix =

Daughter Ion

M0

Parent Ion M1 M2

M3

m0

M0>m0

M1>m0

──

──

m1

──

M1>m1

M2>m1

──

m2

──

──

M2>m2

M3>m2

Fig. 1. Tandem MS analysis of isotopic labeling is an extension to full spectrum MS analysis. In tandem MS, one mass isotopomer from the parent spectrum is selected (called the parent ion) and allowed to progress to the collision cell, where the molecules are fragmented by collision-induced dissociation. The resulting daughter ions are separated in the second mass analyzer based on mass-to-charge ratio, yielding the so-called daughter spectrum. Daughter spectra for different parent ions are conveniently collected into a matrix, that we have termed the tandem mass isotopomer matrix. Each column in this matrix corresponds to a daughter spectrum and each element in the matrix corresponds to a specific parent-to-daughter transition.

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2.2. Calculation of mass isotopomer and tandem mass isotopomer distributions

2.3. Correspondence between tandem mass isotopomers and mass isotopomer distributions

It is well known that mass isotopomer distributions can be calculated from isotopomer fractions using linear mapping (Schmidt et al., 1997). Here, we demonstrate that tandem mass isotopomer distributions can also be calculated from isotopomer fractions using linear mapping. As an example, consider a three atom metabolite A, for which the isotopomer distribution vector has 23 ¼8 elements, A000, A001, A010, etc. (the subscript denotes labeling of atoms, 0¼ unlabeled atom; 1¼labeled atom). A straightforward approach to calculating the mass isotopomer distribution vector of the intact molecule A, MS(A123), which has four elements (M0, M1, M2, and M3) is by summation of appropriate isotopomer fractions as shown in Fig. 2A. Similarly, the mass isotopomer distribution for a fragment with atoms 2 and 3, MS(A23), is computed as shown in Fig. 2B. For tandem MS, the relative abundances should be computed for all possible parent-to-daughter ion transitions. Fig. 2C illustrates how the tandem mass isotopomers can be computed for parent fragment A123 and daughter fragment A23, MS/MS(A123 4A23), from isotopomer fractions using linear mapping. In general, a particular parent-todaughter transition [Mx4my] is obtained from the summation of all isotopomer fractions for which the parent fragment has x labeled atoms and the daughter fragment has y labeled atoms. Any isotopomer fraction contributes to a single tandem MS transition. The tandem mass isotopomer distribution is therefore uniquely constructed for any compound and any tandem MS fragmentation by linear mapping of isotopomer fractions.

There is an interesting relationship between the tandem mass isotopomer matrix and full-spectrum mass isotopomer distributions. Fig. 3 illustrates that column-wise summation of the tandem mass isotopomer matrix elements returns the full-spectrum mass isotopomer distribution of the parent fragment, while row-wise summation of the tandem mass isotopomer matrix returns the fullspectrum mass isotopomer distribution of the daughter fragment. This property of the tandem mass isotopomer matrix has an important implication, namely, the tandem mass isotopomer matrix always contains at least the same amount of information as can be obtained from the combined MS analysis of the parent and daughter fragments. We show next, however, that in most cases the tandem MS matrix will contain additional labeling information that cannot be obtained from full scan MS analysis.

2.4. Number of independent measurements It is important to elaborate on the number of independent measurements that can be obtained from full scan MS and tandem MS analysis. The number of measurements that can be obtained from MS analysis is limited to the number of mass isotopomers. For an n atom fragment, n +1 mass isotopomers can be measured, but only n of these mass isotopomers are independent, i.e. one degree of freedom is lost because the sum of all mass isotopomer fractions must equal 1. If two fragments are measured with n and m atoms

A000 A001

MS (A123) =

M0

A000

M1

A100 + A001 +A010

M2 M3

=

1 0 = 0 A101 + A110 + A011 0 A111

0 1 0 0

0 1 0 0

0 0 1 0

0 1 0 0

0 0 1 0

0 0 1 0

0 0 0 1

A010 x

A011 A100 A101 A110 A111

A000 A001 M0 MS (A23) =

M1 M2

A010

A000 + A100

1 0 0 0 1 0 0 0 = A001 + A010 +A101 +A110 = 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 A011 + A111

x

A011 A100 A101 A110 A111

M0 > m0

A000

M1 > m0

A100 A001+A010

M1 > m1 MS/MS (A123>A23) =

M2 > m1

=

A101+A110

M2 > m2

A011

M3 > m2

A111

A000 1 0 0 = 0 0 0

0 0 1 0 0 0

0 0 1 0 0 0

0 0 0 0 1 0

0 1 0 0 0 0

0 0 0 1 0 0

0 0 0 1 0 0

0 0 0 0 0 1

A001 A010 x

A011 A100 A101 A110 A111

Fig. 2. (A) Calculation of mass isotopomer distribution for a three atom molecule A by linear mapping of isotopomer fractions. The subscript for isotopomers denotes labeling of atoms, 0 ¼unlabeled atom; 1 ¼labeled atom. (B) Calculation of mass isotopomer distribution for a fragment containing atoms 2 and 3. (C) Calculation of tandem mass isotopomer distribution by linear mapping of isotopomer fractions, for parent fragment A123 and daughter fragment A23.

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M0

M1

M2

M3

m0

A000

A100

──

──

A000+ A100

m1

──

A001 A010

A101 A110

──

m2

──

──

A011

A111

A001+ A010+ A101+ A110 Row-wise Summation A011 + A111

m0 =

m1 m2

Column-wise Summation A000

A100 A101 + A001 + A110 + A010 + A011

A111

= M1

M0

M2

M3

Fig. 3. Correspondence between tandem mass isotopomer matrix and full spectrum mass isotopomer distributions. Column-wise summation of tandem mass isotopomer matrix elements returns the full-spectrum mass isotopomer distribution of the parent fragment, while row-wise summation of the tandem mass isotopomer matrix returns the full-spectrum mass isotopomer distribution of the daughter fragment.

No independent measurements

40

Tandem MS (A>B) MS (A) & MS (B)

30

MS (A)

20 10 0 1

2

3

4 5 6 7 8 No. carbon atoms

9

10

Carbon atoms in daughter fragment

Max. independent measurements

Carbon atoms in parent fragment 0 1 2 3 4 5 6 7 8 9 10

1 1 1 -

2 2 3 2 -

3 3 5 5 3 -

4 5 6 7 8 9 10 4 5 6 7 8 9 10 7 9 11 13 15 17 19 8 11 14 17 20 23 26 7 11 15 19 23 27 31 4 9 14 19 24 29 3 34 - 5 11 17 23 29 35 - - 6 13 20 27 34 - - - 7 15 23 31 - - - - 8 17 26 - - - - - 9 19 - - - - - - 10

Fig. 4. (A) Comparison of the maximum number of independent measurements for MS and tandem MS analysis. Assuming two fragments can be measured for a compound with n (fragment A) and m (fragment B) number of carbon atoms (with n 4m), the maximum number of independent measurements for MS analysis of fragment A is n, and MS analysis of fragments A and B is n+ m. For tandem MS analysis, the maximum number of independent measurements is max((n m +1)(m+ 1)  1). (B) Number of independent measurements for tandem MS analysis is shown for varying number of carbon atoms in the parent and daughter fragments. The maximum number of independent measurements is obtained when the daughter fragment contains exactly half the number of atoms of the parent fragment (highlighted in green). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(nam), then the number of independent measurements is n+ m. For tandem MS analysis, the number of independent measurements is related to the number of possible parent-to-daughter transitions, (n  m+ 1)(m+ 1). The number of independent measurements is (n  m+ 1)(m+ 1)  1, i.e. the sum of all tandem mass isotopomer fractions must also equal to 1. Fig. 4A compares the number of independent measurements for full scan MS and tandem MS analysis for increasing number of atoms in the parent fragment. For n 43 the number of independent measurements is always greater for tandem MS analysis (with man) compared to full scan MS analysis of the same fragment(s), indicating that tandem MS measurements provide additional labeling information that cannot be obtained from MS analysis. Fig. 4B shows the number of independent measurements for tandem MS analysis for varying sizes of parent and daughter fragments. When the daughter fragment contains one atom less than the parent fragment the number of independent measurements increases by about 2-fold compared to MS analysis, and by about 3-fold when the daughter fragment contains three atoms less than the parent fragment. The

greatest number of independent measurements is obtained when the daughter fragment contains exactly half the number of atoms of the parent fragment. No additional information is obtained when the daughter fragment contains either all of the carbon atoms from the parent fragment (m¼n), or no carbon atoms from the parent fragment (m¼0).

2.5. Metabolic flux analysis For metabolic flux analysis in this study, fluxes in the model were estimated by minimizing the lack of fit between the experimental and predicted (tandem) mass isotopomer measurements using non-linear least-squares regression techniques (Antoniewicz et al., 2006). In all cases, flux estimation was repeated at least ten times starting with random initial values for all fluxes to find a global solution. At convergence, standard deviations and 95% confidence intervals for all fluxes were calculated using previously described techniques (Antoniewicz et al., 2006). A flux was

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considered non-observable if the 95% confidence interval was at least four times larger than the estimated flux value and included the value zero.

3. Results 3.1. Metabolic flux analysis in gluconeogenesis model using MS and tandem MS measurements First, we used a simplified model of gluconeogenesis, TCA cycle and glyoxylate shunt (Fig. 5) to estimate metabolic fluxes from simulated MS and tandem MS measurements. The stoichiometry and atom transitions for the reactions in the model are given in Table 1. In this network, acetyl coenzyme-A and aspartate are the two substrates, and extracellular glucose and carbon dioxide are the two products; the seven intracellular metabolites (citrate, fumarate, glyoxylate, oxaloacetate, a-ketoglutarate, succinate, and intracellular carbon dioxide) were considered to be at metabolic and isotopic steady state. We assumed the following labeling for aspartate: 25% [1,2-13C] aspartate, 25% [4-13C] aspartate, 25% [2,3,4-13C] aspartate, and 25% unlabeled aspartate. The assumed fluxes for the reactions are shown in Fig. 5. For simplicity, we only considered the labeling of carbon atoms and ignored natural isotope enrichments. To compare the performance of MS and tandem MS for flux determination, metabolic flux analysis was performed using the following five sets of simulated measurements: (i) MS data for OAC1234 fragment (4 independent measurements). (ii) MS data for OAC1234 and OAC34 fragments (6 independent measurements). (iii) Tandem MS data for OAC1234 4OAC34 (8 independent measurements). (iv) Tandem MS data for OAC1234 4OAC234 (7 independent measurements). (v) Tandem MS data for OAC1234 4OAC1234 (4 independent measurements). In practice oxaloacetate may be difficult to observe by MS due to low abundance and stability of oxaloacetate. Instead, one could

Gluc AcCoA

v11 v10

v1

[13C]Asp

OAC

Cit v9

v7

v8

v6

v3

Glyox

Fum

CO2 v2

AKG v4

v5 Suc

CO2

v12

CO2 ext

Fig. 5. Simplified gluconeogenesis network model including TCA cycle and glyoxylate shunt. Abbreviations of metabolites: Asp, aspartate; OAC, oxaloacetate; AcCoA, acetyl coenzyme A; Cit, citrate; AKG, alpha-ketoglutarate; Fum, fumarate; Suc, succinate; Glyox, glyoxylate. Assumed fluxes (arbitrary units): v1 ¼100, v2 ¼220, v3 ¼ 150, v4 ¼70, v5 ¼ 100, v6 ¼ 140, v7 ¼ 40, v8 ¼30, v9 ¼30, v10 ¼ 60, v11 ¼90, v12 ¼140.

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Table 1 Stoichiometry and atom transitions for reactions in the gluconeogenesis network model. Reaction

Stoichiometry

Atom transitions

1 2 3 4 5 6 7 8 9 10 11

OAC +AcCoA.ext-Cit Cit-AKG+ CO2 AKG+ CO2-Cit AKG-Suc + CO2 Suc-Fum Fum-OAC OAC-Fum Cit-Glyox+ Suc Glyox+ AcCoA-OAC Asp.ext-OAC 2 OAC-Gluc.ext+ 2 CO2.ext CO2-CO2.ext

abcd + ef-dcbfea abcdef-abcde +f abcde + f-abcdef abcde-1/2bcde+ 1/2 edcb + a 1/2 abcd + 1/2 dcba-1/2 abcd +1/2 dcba 1/2 abcd + 1/2 dcba-abcd abcd-1/2 abcd +1/2 dcba abcdef-ab+ 1/2 cdef+ 1/2 fedc ab +cd-abdc abcd-abcd abcd + efgh- cbaefg+ d + h

12

a-a

The extension ‘ext’ denotes a non-balanced ‘‘external’’ metabolite. Atom transitions are defined using letter code. For each compound, atoms are identified using letters to represent successive atoms of each compound. Abbreviations of metabolites are same as in Fig. 5.

measure malate since it rapidly equilibrates with oxaloacetate and is easily detected by MS (Yoo et al., 2008). Table 2 shows the simulated mass isotopomer and tandem mass isotopomer distributions for two sets of fluxes: for the fluxes shown in Fig. 5 (Case I), and a second set of fluxes where fumarase reversibility was increased (v6 ¼200 and v7 ¼100, Case II). The last column in Table 2 shows the differences between the simulated measurements for the two cases. The differences were relatively small for mass isotopomers ( r0.2 mol% differences in enrichment), while much larger differences were observed for tandem mass isotopomers (up to 0.9 mol%), indicating that tandem MS measurements provide more sensitive information for detecting changes in the fumarase flux. It should be noted that tandem MS measurements where the daughter fragment contained all carbon atoms of parent fragment did not provide additional information compared to MS analysis. As expected, the simulated tandem mass isotopomer distributions were identical to the mass isotopomer distributions of the parent fragment (see Section 2.4). Metabolic fluxes were estimated for the simulated measurements of Case I for all five measurement sets. We assumed a standard deviation of 0.2 mol% for all mass isotopomer and tandem mass isotopomer measurements and assumed that flux v1 was measured in all cases (100 70.1). The flux analysis results are listed in Table 3. We found that the first measurement set, i.e. MS analysis of the intact oxaloacetate molecule MS(OAC1234), only allowed two fluxes to be determined. The standard deviations for the remaining 10 fluxes were very large, and these fluxes were considered non-observable. The combined measurement of two fragments of oxaloacetate, i.e. MS(OAC1234) and MS(OAC34), allowed determination of 6 out of 12 fluxes. In contrast, when tandem MS measurements were used for MFA, all 12 fluxes could be determined with high precision. The quality of flux results for tandem MS measurement sets MS/MS(OAC1234 4OAC34) and MS/MS(OAC1234 4OAC234) were similar; the standard deviations for all fluxes were at least 3-fold smaller compared to fluxes estimated using MS measurements. Note that the number of independent measurements for these tandem MS measurement sets (7 and 8 independent measurements, respectively) was similar to the number independent measurements for MS analysis (i.e. 6 independent measurements), indicating that tandem MS measurements provide inherently more informative data for flux determination. Overall, the results from this example demonstrate that tandem MS is suitable for accurate and high resolution quantification of metabolic fluxes, and can provide results that are superior compared to traditional full scan MS analysis.

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Table 2 Simulated mass isotopomer and tandem mass isotopomer distributions for oxaloacetate in the gluconeogenesis network model (molar percent abundances, mol%). Mass isotopomers were simulated for the fluxes shown in Fig. 5 (Case I), and a second case where the reversible fumarase flux was increased (Case II: v6 ¼200, v7 ¼100). Small differences were observed for simulated mass isotopomer values ( r 0.2 mol%). Much larger differences were observed for tandem mass isotopomers (up to 0.9 mol%), indicating than tandem MS analysis provides more sensitive measurements for MFA. Simulated measurements

Case I mol(%)

Case II mol(%)

Difference mol(%)

MS analysis MS(OAC1234)

M0 M1 M2 M3 M4

56.0 22.6 13.5 7.9 0.0

56.2 22.4 13.5 7.9 0.0

0.2 0.2 0.0 0.0 0.0

MS analysis MS(OAC34)

M0 M1 M2

75.7 14.3 10.0

75.5 14.4 10.2

0.2 0.1 0.2

Tandem MS analysis MS/MS(OAC1234 4OAC34)

M04m0 M14m0 M14m1 M24m0 M24m1 M24m2 M34m1 M34m2 M44m2

56.0 9.0 13.6 10.7 0.0 2.8 0.7 7.2 0.0

56.2 9.3 13.0 9.9 0.0 3.6 1.4 6.5 0.0

0.2 0.3 0.6n 0.8n 0.0 0.8n 0.7n 0.7n 0.0

Tandem MS analysis MS/MS(OAC1234 4OAC234)

M04m0 M14m0 M14m1 M24m1 M24m2 M34m2 M34m3 M44m3

56.0 4.1 18.5 10.7 2.8 0.7 7.2 0.0

56.3 4.7 17.6 9.9 3.6 1.4 6.5 0.0

0.3 0.6n 0.9n 0.8n 0.8n 0.7n 0.7n 0.0

Tandem MS analysis MS/MS(OAC1234 4OAC1234)

M04m0 M14m1 M24m2 M34m3 M44m4

56.0 22.6 13.5 7.9 0.0

56.2 22.4 13.5 7.9 0.0

0.2 0.2 0.0 0.0 0.0

n

Significant differences, above 0.5 mol%, are shown with an asterisk.

Table 3 MFA results for the gluconeogenesis network model using simulated mass isotopomer and tandem mass isotopomer data from Table 2, Case I. Estimated fluxes are shown as: best fit flux7 SD. Only 6 fluxes were observable with MS measurements. Using tandem MS measurements all 12 fluxes were observable and the precision of the estimated fluxes was improved by at least 3-fold. Flux

V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12

Mass spectrometry measurements

Tandem MS measurements

MS(OAC1234)

MS(OAC1234) + MS(OAC34)

MS/MS(OAC1234 4OAC34)

MS/MS(OAC1234 4OAC234)

MS/MS(OAC1234 4OAC1234)

1007 0.1 n/o n/o n/o 1007 0.1 n/o n/o n/o n/o n/o n/o n/o

1007 0.1 n/o n/o 707 17 1007 0.1 n/o n/o n/o n/o 607 10 907 26 1407 34

1007 0.1 2207 64 1507 66 707 5 1007 0.1 1407 7 407 7 307 5 307 5 607 3 907 8 1407 11

1007 0.1 2207 70 1507 73 707 5 1007 0.1 1407 6 407 6 307 5 307 5 607 2 907 7 1407 9

1007 0.1 n/o n/o n/o 1007 0.1 n/o n/o n/o n/o n/o n/o n/o

The same standard deviations of 0.2 mol% were assumed for all mass isotopomer and tandem mass isotopomer measurements. In addition, flux v1 was assumed to be measured (1007 0.1). A non-observable flux is indicated by ‘‘n/o’’.

3.2. Metabolic flux analysis in perfused hearts using tandem MS measurements As a second example, we used a simplified model of glycolysis, TCA cycle and anaplerosis to estimate fluxes in perfused hearts using MS and tandem MS measurements from Jeffrey et al. (2002). The reconstructed metabolic network model is shown in Table 4. The model is based on the description by Jeffrey et al. (Jeffrey et al., 2002)

and a previous publication (Malloy et al., 1990). Jeffrey et al. performed three tracer experiments with perfused hearts: (i) glucose+[2-13C]acetate; (ii) [1-13C]glucose+insulin; and (iii) glucose+[3-13C]pyruvate; and measured the labeling of intracellular glutamate using GC–MS and GC–MS/MS. Specifically, the mass isotopomer distribution of the intact glutamate molecule was measured, i.e. MS(Glu12345), and two daughter fragments of glutamate were quantified, namely glutamate C2–C5 fragment and glutamate

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parent ions, M+1, M+2 and M+3 (Table 5). A complicating factor in the analysis of glutamate daughter spectra was the fact that the daughter fragments partially overlapped in the m/z domain, i.e. the first daughter fragment was detected at m/z 155–158 and the second fragment was detected at m/z 157–160. Jeffrey et al. (Jeffrey et al., 2002) accounted for this overlap by determining relative abundances of the fragments and using an empirical ratio to deconvolute the overlapping daughter spectra. A detailed description of the deconvolution can be found in the original paper by Jeffrey et al. (2002). From these measurements, two model parameters were determined, the fractional anaplerosis flux Y (i.e. the ratio of anaplerotic flux relative to the flux of TCA cycle) and the enrichment of the acetyl-CoA pool (Fc2). We used the MS and tandem MS data in Table 5 to estimate metabolic fluxes in the network model using our method. We obtained statistically acceptable fits for all data sets. The fitted mass isotopomers and tandem mass isotopomers are also shown in Table 5. The estimated anaplerotic flux (v10) and the estimated steady-state enrichment of acetyl-CoA are given in Table 6. The enrichment of acetyl-CoA was calculated from fluxes v1 (influx of glucose), v2 (influx of pyruvate) and v4 (influx of acetate). The precision of the estimated fluxes for tandem MS measurements was 2- to 5-fold improved compared to MS measurements.

C1–C3 fragment, i.e. MS/MS(Glu12345 4Glu2345) and MS/MS (Glu12345 4Glu123). The data reported by Jeffrey et al. consisted of the relative mole fractions (RMF) of labeled mass isotopomers of glutamate (i.e. the M+0 isotopomer of glutamate was not reported and not fitted), and normalized daughter spectra for three of the five Table 4 Stoichiometry and atom transitions for reactions in the perfused heart model. Reaction

Stoichiometry

Atom transitions

1 2 3 4 5 6 7 8 9 10 11

Gluc.ext-2 PYR PYR.ext-PYR PYR-AcCoA+CO2 AC.ext-AcCoA OAC +AcCoA-Cit Cit-AKG+ CO2 AKG-Suc + CO2 Suc-Fum Fum-OAC Asp.ext-OAC AKG-Glu

abcdef-cba +def abc-abc abc-a + bc ab-ab abcd+ ef-dcbfea abcdef-abcde + f abcde-1/2 bcde + 1/2 bcde + a 1/2 abcd + 1/2 dcba-1/2 abcd + 1/2 dcba 1/2 abcd + 1/2 dcba-abcd abcd-abcd abcde-abcde

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Abbreviations of metabolites: PYR, pyruvate; AC, acetate; other abbreviations same as in Fig. 5.

Table 5 Measured and fitted MS and tandem MS measurements for perfused heart experiments. Normalized full scan mass isotopomer and tandem mass isotopomer data were obtained from Jeffrey et al. (2002). The ‘‘best fit’’ column shows the simulated mass isotopomer and tandem mass isotopomer values for the estimated fluxes in the perfused heart model using our method. Glucose + [2-13C] Acetate

[1-13C] Glucose + Insulin

Glucose + [3-13C] Pyruvate

Best fit (our method)

Measured data (Jeffrey et al., 2002)

Best fit (our method)

Measured data (Jeffrey et al., 2002)

Best fit (our method)

Measured data (Jeffrey et al., 2002)

Full scan mass spectra RMF (M+ 1) RMF (M+ 2) RMF (M+ 3) RMF (M+ 4)

0.05 0.12 0.47 0.35

0.057 0.02 0.13 70.03 0.46 70.03 0.36 70.03

0.46 0.37 0.15 0.02

0.46 7 0.03 0.37 7 0.01 0.15 7 0.01 0.03 7 0.01

0.18 0.30 0.37 0.15

0.18 70.04 0.307 0.03 0.37 70.03 0.15 70.03

Tandem mass spectra M+ 1 (m/z 231) C1155 C1156 C1157 C1158

0.00 1.00 0.87 0.13

n/a n/a n/a n/a

0.10 0.90 0.36 0.64

0.11 7 0.02 0.89 7 0.02 0.36 7 0.02 0.64 7 0.02

0.06 0.94 0.40 0.60

0.087 0.02 0.92 70.02 0.47 70.11 0.53 70.11

M+ 2 (m/z 232)

C2156 C2157 C2158 C2159

0.03 0.60 0.28 0.08

0.057 0.02 0.607 0.05 0.27 70.04 0.107 0.03

0.17 0.47 0.22 0.15

0.16 7 0.01 0.42 7 0.01 0.22 7 0.00 0.15 7 0.01

0.12 0.52 0.23 0.14

0.11 70.03 0.51 70.01 0.24 70.03 0.14 70.02

M+ 3 (m/z 233)

C3156 C3157 C3158 C3159 C3160

0.00 0.08 0.53 0.35 0.02

n/a 0.107 0.01 0.54 70.02 0.35 70.02 0.017 0.01

0.00 0.32 0.32 0.29 0.07

0.02 7 0.01 0.29 7 0.03 0.33 7 0.01 0.30 7 0.04 0.06 7 0.01

0.00 0.26 0.38 0.31 0.05

0.017 0.00 0.24 70.03 0.38 70.02 0.31 70.01 0.077 0.02

RMF (M +i), relative mole fractions of glutamate mass isotopomers (note: M + 0 values were not reported, and were not fitted). Ci155–Ci160, normalized tandem mass isotopomer data (the first digit denoted the parent ion M +i, and the next three digits denote the m/z value of the daughter ion); ‘‘n/a’’ indicates that a measurement was non-available in Jeffrey et al. (2002).

Table 6 MFA results for the perfused heart model using mass isotopomer and tandem mass isotopomer data from Table 5. The precision of estimated flux parameters was improved by 2- to 5-fold using tandem MS measurements compared to MS measurements. Parameter Anaplerotic flux (v10)a Estimated using MS data Estimated using tandem MS data 13

C Enrichment of AcCoA (mol%) Estimated using MS data Estimated using tandem MS data a

Glucose + [2-13C]Acetate

[1-13C]Glucose+ Insulin

Glucose + [3-13C]Pyruvate

5.0 72.3 3.7 70.9

14.7 7 7.2 5.8 7 1.4

12.1 7 5.6 2.17 1.3

95.9 71.0 94.4 70.6

49.8 7 2.4 43.6 7 0.5

82.3 7 2.2 71.07 0.7

Anaplerotic flux was normalized to citrate synthase flux of 100.

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The estimated flux values corresponded quantitatively well to the values reported by Jeffrey et al. This provides support for the manually derived expressions by Jeffrey for calculating fluxes in this simplified model using MS and tandem MS measurements. However, as we noted in the introduction, Jeffrey et al. did not explore the full potential of tandem MS for flux analysis. For example, only three (M +1, M+ 2, and M+ 3) of the five parent ions were analyzed by tandem MS. Furthermore, expressions were only derived for one metabolite, i.e. glutamate, and it was assumed that C5 of glutamate never became labeled, which greatly simplified the analysis of tandem MS data. Flux analysis would have been more difficult if other tracers had been used that could label C1 of acetylCoA, and if other metabolites had been measured. By using our method, flux analysis is more convenient because all isotopomers are computed for all metabolites in the model (i.e. using the isotopomer/cumomer method, Wiechert et al., 1999) regardless of model complexity and the choice of the tracer. We should note that in these experiments the assumption that C5 of glutamate was unlabeled was largely valid considering that anaplerotic flux was relatively small and acetyl-CoA only became labeled at C2 position due to the particular choice of tracers in this study.

4. Discussion Tracer experiments are a powerful technique for elucidating the structure, stereochemistry and fluxes of metabolic pathways (Crown et al., 2010). The application of stable isotopes for the study of metabolism goes back to the work by Schoenheimer in the 1930s (Schoenheimer and Rittenberg, 1935, 1938). In the early work, dissection of metabolic pathways was largely qualitative and often required laborious analytical techniques and chemical conversions to determine labeling of molecules. It was not until the 1980s when a combination of advances in mass spectrometry and NMR accompanied by an increase in computing power allowed quantitative models of metabolism and isotope redistribution to be constructed. First, 13C NMR analysis was used to detect fractional enrichment of carbon atoms (Walsh and Koshland, 1984). Later, the use of 13C NMR fine spectra was developed to obtain a finer level of detail of isotopic labeling (Carvalho et al., 1999; Malloy et al., 1987). Currently, the most advanced NMR techniques make use of two dimensional NMR spectra, the so-called 2D [13C,1H]-COZY technique, developed by Szyperski to take full advantage of labeling information in both 13C and 1H NMR spectra for MFA (Szyperski, 1995; van Winden et al., 2001). In recent years, however, the focus has shifted more toward MS based techniques, such as GC–MS and LC–MS, due to the higher sensitivity of MS. Traditional full scan MS analysis allows measurement of mass isotopomer distributions of metabolites for MFA. A major limitation of mass isotopomer analysis, however, is the lack of positional labeling information, which can severely limit the resolution of fluxes in complex biological systems. This is the problem that we addressed here. Specifically, we developed a new framework for high-resolution MFA based on the additional labeling information that can be obtained from tandem MS. The development of tandem MS techniques for MFA parallels earlier developments in NMR techniques for improving flux determination using 2D-NMR analysis, as opposed to previous 1D-NMR techniques for MFA. At present, tandem MS is mainly used for structural analysis of small and medium sized molecules, including organic molecules, lipids and fatty acids, peptides, carbohydrates, as well as DNA and RNA adducts (Ma et al., 2006; Robbe et al., 2006; Wellemans et al., 1994), however, its application for MFA has not been fully explored yet. Our first goal here was to establish a universal mathematical framework that takes full advantage of the additional labeling

information obtained from tandem MS for MFA. To this end, we developed a modeling framework based on isotopomer balancing (Schmidt et al., 1997) for simulating tandem MS spectra and estimating fluxes from these data. This is in contrast with the previous attempts to use tandem MS data for MFA, which relied on manually derived expressions in simplified models. While it may be possible to derive analytical expressions that relate certain fluxes and tandem MS spectra in a simple network and for specific labeling of substrates, the complexity of these expressions grows exponentially with increase in model size and the number of labeled atoms. This problem can easily become intractable. For example, Jeffrey et al. (2002) assumed that only singly labeled acetyl-CoA entered the TCA cycle, which greatly simplified the interpretation of tandem MS data. However, it is known that the use of multiply labeled isotopic tracers often provides more information for MFA (Metallo et al., 2009), and thus will require a more general modeling framework that scales better with increase in model size and number of labeled atoms. Here, we build our framework upon isotopomer balancing method since techniques for simulating isotopomers in complex biological systems are well established (Antoniewicz et al., 2007b; Wiechert et al., 1999). We demonstrated the inherent advantages of tandem MS, compared to full spectrum MS, by comparing the number of independent measurements. The advantage of tandem MS was evident for molecules with more than three carbon atoms, which includes most molecules of biological interest, and increased with increase in the size of molecules. Thus, tandem MS technique has great potential for tracing complex biological pathways beyond central carbon metabolism. For example, if suitable daughter fragments can be obtained for fatty acids, it should be possible to perform detailed studies of fatty acid metabolism, which has been a difficult problem to address using traditional MS techniques (Kelleher and Masterson, 1992; Kharroubi et al., 1992; Young et al., 2008). A challenge that should be addressed in future work is the selection of appropriate daughter fragments for MFA studies. One complicating factor that was evident from the work by Jeffrey et al. is that daughter spectra can overlap in the m/z domain. This increases the complexity of data analysis significantly. It would be valuable to evaluate alternative derivatization methods and select these daughter fragments that are well separated and provide the most informative data for MFA. Our analysis demonstrates that daughter fragments should have about half the number of carbon atoms of parent fragments in order to maximize the number of independent measurements. However, even daughter fragments with suboptimal fragmentation patterns are expected to provide useful information for MFA. As an example, in Section 3.1 we found that tandem MS fragmentations MS/MS(OAC1234 4 OAC34) and MS/MS(OAC1234 4OAC234) produced flux results that were of similar quality. We have demonstrated that tandem MS analysis of daughter fragments that have the same number of carbon atoms as the parent fragment, or no carbon atoms of the parent fragment, provides no new labeling information for MFA. However, there are practical advantages for measuring mass isotopomer distributions using tandem MS, as was demonstrated by Kiefer et al. (2007), who developed a tandem MS method for measuring full spectrum mass isotopomer distributions of phosphorylated compounds. In that case, the parent fragment contained the intact molecule, while the daughter fragment contained no carbon atoms. Kiefer et al. demonstrated that mass isotopomer distributions were measured with much higher precision compared to traditional MS analysis due to less interferences and higher signal-to-noise ratio in tandem MS analysis, resulting in typical measurement errors of 0.05 mol% for tandem MS analysis compared to  0.2 mol% for full scan MS analysis (Antoniewicz et al., 2007a, 2007c; Kiefer et al., 2007).

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To demonstrate practical advantages of tandems MS for MFA we used two simplified model systems in this study. In the first case, we used simulated MS and tandem MS data to determine fluxes in a gluconeogenesis model. In the second case, we used experimental tandem MS data to estimate fluxes in a perfused heart model. In both case studies, we found that flux results obtained from tandem MS measurements were improved compared to results obtained from MS measurements, i.e. the standard deviations of fluxes were 2-fold to 5-fold smaller using tandem MS measurements. In both studies, we assumed similar measurement precision for MS and tandem MS measurements. If we take into account the higher measurement precision that is possible with tandem MS (Kiefer et al., 2007), we project that fluxes could be determined with even higher precision using tandem MS. With further development, we believe that it should be possible to improve the precision of flux estimates by more than 10-fold. If this is indeed the case, then tandem MS analysis could become the new gold standard for metabolic flux analysis in the coming years.

Acknowledgments This work was supported by the DuPont Young Professor grant and the University of Delaware Research Foundation (UDRF) grant. References Antoniewicz, M.R., Kelleher, J.K., Stephanopoulos, G., 2006. Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements. Metabolic Engineering 8, 324–337. Antoniewicz, M.R., Kelleher, J.K., Stephanopoulos, G., 2007a. Accurate assessment of amino acid mass isotopomer distributions for metabolic flux analysis. Analytical Chemistry 79, 7554–7559. Antoniewicz, M.R., Kelleher, J.K., Stephanopoulos, G., 2007b. Elementary metabolite units (EMU): A novel framework for modeling isotopic distributions. Metabolic Engineering 9, 68–86. Antoniewicz, M.R., Kraynie, D.F., Laffend, L.A., Gonzalez-Lergier, J., Kelleher, J.K., Stephanopoulos, G., 2007c. Metabolic flux analysis in a nonstationary system: fed-batch fermentation of a high yielding strain of E. coli producing 1, 3-propanediol. Metabolic Engineering 9, 277–292. Boghigian, B.A., Seth, G., Kiss, R., Pfeifer, B.A., 2010. Metabolic flux analysis and pharmaceutical production. Metabolic Engineering 12 (2), 81–95. Burgess, S.C., Nuss, M., Chandramouli, V., Hardin, D.S., Rice, M., Landau, B.R., Malloy, C.R., Sherry, A.D., 2003a. Analysis of gluconeogenic pathways in vivo by distribution of H-2 in plasma glucose: comparison of nuclear magnetic resonance and mass spectrometry. Analytical Biochemistry 318, 321–324. Burgess, S.C., Weis, B., Jones, J.G., Smith, E., Merritt, M.E., Margolis, D., Sherry, A.D., Malloy, C.R., 2003b. Noninvasive evaluation of liver metabolism by H-2 and C-13 NMR isotopomer analysis of human urine. Analytical Biochemistry 312, 228–234. Carvalho, R.A., Babcock, E.E., Jeffrey, F.M.H., Sherry, A.D., Malloy, C.R., 1999. Multiple bond C-13-C-13 spin-spin coupling provides complementary information in a C-13 NMR isotopomer analysis of glutamate. Magnetic Resonance in Medicine 42, 197–200. Crown, S.B., Indurthi, D.C., Ahn, W.S., Choi, J., Papoutsakis, E.T., Antoniewicz, M.R. 2010. Resolving the TCA cycle and pentose-phosphate pathway of Clostridium acetobutylicum ATCC 824: Isotopomer analysis, in vitro activities and expression analysis. Biotechnology Journal 10.1002/biot.201000282. Dauner, M., Sauer, U., 2000. GC–MS analysis of amino acids rapidly provides rich information for isotopomer balancing. Biotechnology Progress 16, 642–649. Des Rosiers, C., Lloyd, S., Comte, B., Chatham, J.C., 2004. A critical perspective of the use of C-13-isotopomer analysis by GCMS and NMR as applied to cardiac metabolism. Metabolic Engineering 6, 44–58. Jeffrey, F.M.H., Roach, J.S., Storey, C.J., Sherry, A.D., Malloy, C.R., 2002. C-13 isotopomer analysis of glutamate by tandem mass spectrometry. Analytical Biochemistry. 300, 192–205. Jin, E.S., Jones, J.G., Merritt, M., Burgess, S.C., Malloy, C.R., Sherry, A.D., 2004. Glucose production, gluconeogenesis, and hepatic tricarboxylic acid cycle fluxes measured by nuclear magnetic resonance analysis of a single glucose derivative. Analytical Biochemistry 327, 149–155. Jones, J.G., Naidoo, R., Sherry, A.D., Jeffrey, F.M.H., Cottam, G.L., Malloy, C.R., 1997. Measurement of gluconeogenesis and pyruvate recycling in the rat liver:

233

a simple analysis of glucose and glutamate isotopomers during metabolism of [1,2,3-C-13(3)]propionate. Febs Letters 412, 131–137. Kelleher, J.K., Masterson, T.M., 1992. Model equations for condensation biosynthesis using stable isotopes and radioisotopes. American Journal of Physiology 262, E118–25. Kharroubi, A.T., Masterson, T.M., Aldaghlas, T.A., Kennedy, K.A., Kelleher, J.K., 1992. Isotopomer spectral analysis of triglyceride fatty acid synthesis in 3T3-L1 cells. American Journal of Physiology 263, E667–75. Kiefer, P., Nicolas, C., Letisse, F., Portais, J.C., 2007. Determination of carbon labeling distribution of intracellular metabolites from single fragment ions by ion chromatography tandem mass spectrometry. Analytical Biochemistry 360, 182–188. Kleijn, R.J., Geertman, J.M.A., Nfor, B.K., Ras, C., Schipper, D., Pronk, J.T., Heijnen, J.J., van Maris, A.J.A., van Winden, W.A., 2007. Metabolic flux analysis of a glyceroloverproducing Saccharomyces cerevisiae strain based on GC–MS, LC–MS and NMR-derived C-13-labelling data. Fems Yeast Research 7, 216–231. Ma, S.K., Chowdhury, S.B., Alton, K., 2006. Application of Mass Spectrometry for Metabolite Identification. Current Drug Metabolism 7, 503–523. Malloy, C.R., Sherry, A.D., Jeffrey, F.M., 1990. Analysis of tricarboxylic acid cycle of the heart using 13C isotope isomers. American Journal of Physiology 259 (3 Pt 2), H987–95. Malloy, C.R., Sherry, A.D., Jeffrey, F.M.H., 1987. Carbon Flux through Citric-acid Cycle Pathways in Perfused Heart by C-13 NMR-Spectroscopy. Febs Letters 212, 58–62. Metallo, C.M., Walther, J.L., Stephanopoulos, G., 2009. Evaluation of 13C isotopic tracers for metabolic flux analysis in mammalian cells. Journal of Biotechnology 144, 167–174. Moxley, J.F., Jewett, M.C., Antoniewicz, M.R., Villas-Boas, S.G., Alper, H., Wheeler, R.T., Tong, L., Hinnebusch, A.G., Ideker, T., Nielsen, J., Stephanopoulos, G., 2009. Linking high-resolution metabolic flux phenotypes and transcriptional regulation in yeast modulated by the global regulator Gcn4p. Proceedings of the National Academy of Sciences 106, 6477–6482. Robbe, C., Michalski, J.-C., Capon, C., 2006. Structural Determination of O-glycans by Tandem Mass Spectrometry. Methods in Molecular Biology (Clifton, N.J.) 347, 109–123. Sauer, U., 2006. Metabolic networks in motion: C-13-based flux analysis. Molecular Systems Biology, 2. Schmidt, K., Carlsen, M., Nielsen, J., Villadsen, J., 1997. Modeling isotopomer distributions in biochemical networks using isotopomer mapping matrices. Biotechnology and Bioengineering 55, 831–840. Schoenheimer, R., Rittenberg, D., 1935. Deuterium as an Indicator in the Study of Intermediary Metabolism. Science 82, 156–157. Schoenheimer, R., Rittenberg, D., 1938. The Application of Isotopes to the Study of Intermediary Metabolism. Science 87, 221–226. Sillers, R., Al-Hinai, M.A., Papoutsakis, E.T., 2009. Aldehyde-alcohol dehydrogenase and/or thiolase overexpression coupled with CoA transferase downregulation lead to higher alcohol titers and selectivity in Clostridium acetobutylicum fermentations. Biotechnology and Bioengineering 102, 38–49. Suthers, P.F., Chang, Y.J., Maranas, C.D., 2010. Improved computational performance of MFA using elementary metabolite units and flux coupling. Metabolic Engineering 12 (2), 123–128. Szyperski, T., 1995. Biosynthetically Directed Fractional C-13-Labeling of Proteinogenic Amino-Acids—an Efficient Analytical Tool to Investigate Intermediary Metabolism. European Journal of Biochemistry 232, 433–448. van Winden, W., Schipper, D., Verheijen, P., Heijnen, J., 2001. Innovations in generation and analysis of 2D [C-13, H-1] COSYNMR spectra for metabolic flux analysis purposes. Metabolic Engineering 3, 322–343. Walsh, K., Koshland, D.E., 1984. Determination of Flux through The Branch Point of 2 Metabolic Cycles—The Trycarboxlic-Acid Cycle and The Glyoxylate Shunt. Journal of Biological Chemistry 259, 9646–9654. Wellemans, J., Cerny, R.L., Gross, M.L., 1994. Tandem Mass-Spectrometry for The Determination of Deoxyribonucleic-Acid Damage by Polycyclic AromaticHydrocarbons. Royal Soc Chemistry, pp. 497–503. Wiechert, W., Mollney, M., Isermann, N., Wurzel, M., de Graaf, A.A., 1999. Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. Biotechnol. Bioeng. 66, 69–85. Wisselink, H.W., Cipollina, C., Oud, B., Crimi, B., Heijnen, J.J., Pronk, J.T., van Maris, A.J., 2010. Metabolome, transcriptome and metabolic flux analysis of arabinose fermentation by engineered Saccharomyces cerevisiae. Metabolic Engineering 12 (6), 537–551. Wittmann, C., 2002a. Metabolic Flux Analysis Using Mass Spectrometry, Tools and Applications of Biochemical Engineering Science, pp. 39–64. Wittmann, C., 2002b. Metabolic flux analysis using mass spectrometry. Advances in Biochemical Engineering/Biotechnology 74, 39–64. Yoo, H., Antoniewicz, M.R., Stephanopoulos, G., Kelleher, J.K., 2008. Quantifying reductive carboxylation flux of glutamine to lipid in a brown adipocyte cell line. Journal of Biological Chemistry 283, 20621–20627. Young, J.D., Walther, J.L., Antoniewicz, M.R., Yoo, H., Stephanopoulos, G., 2008. An elementary metabolite unit (EMU) based method of isotopically nonstationary flux analysis. Biotechnology and Bioengineering 99, 686–699.