Mapping the regioisomeric distribution of fatty acids in triacylglycerols by hybrid mass spectrometry.

This study describes the use of hybrid mass spectrometry for the mapping, identification, and semi-quantitation of triacylglycerol regioisomers in fats and oils. The identification was performed based on the accurate mass and fragmentation pattern obtained by data-dependent fragmentation. Quantitation was based on the high-resolution ion chromatograms, and relative proportion of sn-1(3)/sn-2 regioisomers was calculated based on generalized fragmentation models and the relative intensities observed in the product ion spectra. The key performance features of the developed method are inter-batch mass accuracy < 1 ppm (n = 10); lower limit of detection (triggering threshold) 0.1 μg/ml (equivalent to 0.2 weight % in oil); lower limit of quantitation 0.2 μg/ml (equivalent to 0.4 weight % in oil); peak area precision 6.5% at 2 μg/ml concentration and 15% at 0.2 μM concentration; inter-batch precision of fragment intensities < 1% (n = 10) independent of the investigated concentration; and averaged accuracy using the generic calibration 3.8% in the 1-10 μg/ml range and varies between 1-23% depending on analytes. Inter-esterified fat, beef tallow, pork lard, and butter fat samples were used to show how well regioisomeric distribution of palmitic acid can be captured by this method.

The complexity of naturally occurring triacylglycerols (TAG) present in mammalian cells is well illustrated by previous investigations revealing multiple isobaric species having molecular weights at virtually every even mass between 600 and 900 Da ( 1 ). For example, the combination of only 30 different fatty acids (FA) would result in more than 25,000 different molecular species, including positional isomers ( 2 ). The FA composition of the TAG depends on the species, the dietary FA composition, and the carbohydrate-to-lipid ratio of the diet ( 3 ). There is a high variation in TAG stereoisomers in oils and fats of different biological origin and sometimes even species specifi city fragmentation, ESI can be also used for the analysis of TAG by adding modifi er buffers (e.g., ammonium formate, sodium-acetate) to the LC mobile phase. Such salts enhance the ionization process greatly and consequently allow lower detection limits to be reached by ESI than by APCI ( 19,21 ).
The unequivocal structural characterization of TAG requires tandem mass spectrometry and assessment of collision-induced dissociation (CID) mass spectra. The most characteristic fragmentation steps of TAG are the loss of FA residues yielding diacylglycerol (DAG) fragments, but depending on experimental conditions, the loss of fatty acyl-ketenes, various rearrangements, charge remote fragmentation involving ␤ -cleavage with ␥ -hydrogen shift, and production of acylium ions was also described ( 19,55 ). Numerous preliminary studies have reported that the neutral loss of FA from the outer sn -1(3) positions is energetically favored in comparison to cleavage from the middle sn -2 position ( 4,13,19,34,39,54,(56)(57)(58)(59). Based on this phenomenon, most studies have attempted to identify the prevailing FA in the sn -2 position by assuming that in a product ion spectrum it is represented by the lower relative abundance fragment ( 4,60 ). This simple approach is very widely applied; however, its substantial limitations and inherent errors became apparent recently. It has been demonstrated that the nature of fatty acids (mainly the double bond number and positions) ( 34,35,61,62 ) and experimental conditions, such as collision energy ( 58 ) or type of adduct ( 56 ), also affect the relative abundances of corresponding DAG fragment ions, and in this way, the favored loss from the sn -1(3) positions (higher than from sn -2) might not be necessarily true for quite different FAs. Refi ned and more accurate approaches were described on quantitating the relative abundance of regioisomeric TAG based on the construction of calibration curves using identical standards of regioisomeric pairs mixed at different ratios ( 36,39,61,63,64 ). These studies revealed encouraging quantitation possibilities, but they were restricted to TAG with commercially available standards. Holcapek et al. have utilized a range of standard regioisomeric mixtures synthesized using the microscale randomization procedure ( 34 ). Their extensive dataset measured in three different laboratories represents a good basis for the generalization of the fragmentation behavior in APCI mass spectra and the retention behavior in silver-ion chromatography.
In summary, the quantitation of unknown intact TAG regioisomers in complex oil/fat mixes still has not been accomplished, principally because all targeted LC-MSbased quantitation approaches are restricted to TAG with commercially available standards, and these latter make up only approximately 1% of the potentially occurring TAG.
The objective of this study was to enable the untargeted detection, structural elucidation, and quantitation of the most common 28,000 TAG species in unknown oil mixtures. For this purpose, a hybrid mass spectrometry-based approach was developed and validated. The detection of TAG was performed by NARP-LC coupled with high-resolution but these approaches lack sensitivity and specifi city ( 21 ). Profi ling of intact TAG classes without chemical derivatization by GC was reported by Destaillats ( 22 ) and Guyon ( 23 ).
NARP-and Ag-LC are orthogonal separation methods and were extensively compared by Holcapek et al. ( 33 ). The retention in NARP mode is governed by the equivalent carbon number (ECN = carbon number-2*double bonds), while the retention in Ag-LC increases with the increasing number of double bonds (DB), with a clear differentiation between cis -and trans -FA ( 4,33,34 ). Unlike NARP-LC, Ag-LC can provide baseline resolution for regioisomer TAG with up to three double bonds ( 4,31 ). Resolution of Ag-LC is only partial for TAG regioisomers when the total number of double bonds higher than four (e.g., LLO and LOL) or for TAG pairs differing only by one double bond ( 5,31,40 ). Note that to date none of the existing LC methods is capable of resolving the entire complex TAG mixture of vegetable oils or animal fats.
LC-MS enables the most effi cient structural elucidation and quantitation of TAG, as using this approach the isobaric and isotopomer interferences can be separated and the interpretation of spectra becomes much more feasible. Electrospray ionization (ESI) and atmospheric pressure chemical ionization (APCI) are both commonly used for the analysis of TAG. APCI generates abundant in-source fragments, and in some cases, these can be used for structural elucidation of TAG ( 19,35,53,54 ). However, in the case of complex natural samples in which several TAGs coelute and are present in a wide dynamic range of abundances, this spontaneous and uncontrolled fragmentation rather complicates the assignment of parent-product relationship and hinders identifi cation or data-dependent tandem experiments. To minimize the spontaneous in-source according to an inclusion list containing the accurate masses of ammoniated TAG, applying parent mass width criteria of ± 5 ppm. Inclusion list criterion for data-dependent acquisition was established in MS Offi ce Excel by calculating the elemental composition and corresponding accurate mass for TAG obtained by the combination of the 40 most common FA ( Table 1 ) on the glycerol backbone. The combination of these FAs yields approximately 40,000 TAG: these species can be detected and identifi ed using the method described herein (see also supplementary material). Note however, that due to the lack of commercially available standards and published data, only TAG constituting FA with maximum three DB ( Table 5 ) could be quantifi ed, representing approximately 28,000 TAG species.
Additional mass tagging of m/z 4.95540 (between ammoniated and sodiated adducts, see Fig. 1 ) was applied in a parent intensity range of 0-100%. Intensity threshold was 100,000 cps; preview mode for FT-MS master scans was enabled. Precursor ion isolation, fragmentation, and detection were performed in the linear ion trap. Only the ammoniated adducts (low mass partner) were fragmented. Accumulation time was 50 ms, isolation width was 3 Da, normalized collision energy was 30%, activation Q value was 0.250, activation time was 30 ms. Note that the isolation width value 3 Da will result in monoisotopic isolation of the parent ion of ammoniated TAG and complete elimination of other isotopomers as experimentally confi rmed by us. The reason for this unusual behavior of the linear ion trap is described by McClellan et al. ( 65 ). The monoisotopic isolation of the parent ion is of crucial importance to eliminate unnecessary isotopomer interferences in the product ion spectra that would complicate the interpretation of the fragmentation pattern. Using a dynamic exclusion list and 30 s exclusion time, 10 data-dependent events were triggered per two scan cycles (fi ve fragmentation events per one scan cycle). The dynamic exclusion parameters were: repeat count 1; repeat duration 0 s; exclusion list size 25; exclusion duration 2.5 s; exclusion mass width ± 5 ppm.

Data extraction
High-resolution (5 decimals) Orbitrap and nominal-resolution linear ion trap data (two decimals) were extracted using the software Quanbrowser (ThermoFisher Scientifi c, Bremen, Germany). Chromatographic peak areas were obtained from ion chromatograms extracted in 10 ppm m/z windows. Interpretation of signals for TAG identifi cation and quantitation is described below.

RESULTS AND DISCUSSION
The global quantitation of TAG positional isomers is a long-standing and challenging problem in lipid analysis, despite the fact that TAG have strong impact on technological and nutritional properties of fats and oils. Because of these relevant aspects and most importantly due to the enormous diversity of TAG in nature, the development of a mapping method with quantitative capabilities is the objective of this study. For this purpose, we exploited i ) chromatographic retention time, ii ) accurate mass, iii ) adduct envelope, and iv ) fragmentation pattern information. We have combined these data with a quantitative fragmentation model that we have obtained based on authentic TAG regioisomer standards and data reported in the literature.
Opposite to generic lipid profi ling, the identifi cation and distinct quantitation of TAG requires their chromatographic ESI-MS, a theoretical inclusion list of TAG, and mass tagging criteria of their adduct pattern. The identifi cation of the TAG was performed based on the accurate mass and fragmentation pattern obtained by data-dependent fragmentation. Quantitation of TAG was based on the highresolution ion chromatograms, while relative proportion of sn -1(3)/ sn -2 regioisomers was calculated based on generalized fragmentation models and the relative intensities observed in the product ion spectra.

Standard solutions
Stock solutions of nonlabeled TAG were prepared at 10 mg/ ml in acetone. These were further diluted to the required concentration with acetone:methanol 4:1. Solution of 2 H 5 -1,3-dipalmitoyl-2-stearoyl-glycerol was prepared using acetone:methanol 4:1 at a concentration of 400 nmol/l.

Sample preparation
Oil/fat samples were melted at 65°C. 10 µl sample was solubilized in 990 µl n -hexane. Next, 100 µl of this solution was added to 900 µl acetone:methanol 4:1. Finally, 50 µl aliquot of this latter solution along with 250 µl stable isotope labeled internal standard solution (400 pmol/ml) was transferred into new glass vial, and 700 µl acetone:methanol 4:1 was added. A 10 µl aliquot was injected for analysis, which corresponds 1 pmol IS and 500 ng sample on-column injected absolute amount.

Mass spectrometry
An LTQ-Orbitrap XL hybrid mass spectrometer (Thermo-Fisher Scientifi c, Bremen, Germany) was used. Electrospray ionization in positive ion mode was employed to form ions at 300°C nebulizer temperature and 5 kV capillary voltage. Nebulizer and auxiliary gases were nitrogen at 40 and 20 units, respectively. Tube lens was adjusted to 110 V, and accumulation time was 100 ms. Other parameters were the typical values optimized during calibration. The Orbitrap was operated at 30,000 resolution in an m/z 100-2,000 range. Data-dependent events were triggered of butter fat) and to enable the elution of large TAG, as it is illustrated in Fig. 2 . The repeatability of this gradient was assessed by obtaining intra-batch/inter-batch precision data, see Tables 3 and 4 . The standard deviation of the relative retention time was well below 1% at both investigated concentrations. Furthermore, robustness of the method was also assessed by systematically varying the solvent composition A and B. The retention times were not affected signifi cantly when changing the ammonium formate content from 1 mM to 0.8 mM or to 1.2 mM in solvent A. The retention times were slightly shifted when changing the n -hexane content in solvent B from 50% to 45% and to 55% (see Fig. 3 , in which each data point stands for a specifi c TAG). The shift is in accordance with the classic hydrophobic interaction between the analytes and the stationary phase: the higher n -hexane content makes the solvent B stronger eluent, translating into shorter elution times. The results in Fig. 3 suggest that especially very long chain and saturated TAG might exhibit different retention times if uncontrolled fl uctuations occur in the composition of eluents.
separation to obtain good spectral purity and correct assignment of accurate masses in unknown samples. For example, to separate the isotopomer envelope TAG pairs differing in one double bond (e.g., the 2 × 13 C substitution of PPO and PPS), the required full width at half maximum mass resolution would be 90,000 and a resolution allowing determination of accurate mass would certainly exceed 100,000. Accordingly, without chromatography, the isotopomer envelope of the fi rst TAG would overlap with that of the second TAG, biasing the accurate mass of the second TAG.

Chromatography
In this study, the chromatographic resolution of TAG pairs differing in one double bond was accomplished by NARP. This approach is simple and robust, and it allowed the use of ESI and various salt additives that were helpful in identifi cation of TAG. Several solvents were tested for the development of the fi nal gradient, including water, methanol, acetone, dichloromethane, isopropanol, and n -hexane. The fi nal gradient was optimized to allow appropriate retention of small TAG (abundant constituents    this study, we have taken advantage of the fact that ESI generates various adducts as pseudomolecular ions from TAG when used with buffers. The role of 1 mM ammonium formate and 2 µM sodium-formate was to allow generation of predominant ammonium adducts and

Ionization and mass tagging
Using NARP chromatography, it was possible to use ESI instead of APCI. ESI results in cleaner mass spectra compared with APCI, since this latter generates abundant in-source fragments from TAG ( 19,35,53,54 ). In Results obtained at 0.2 /ml and 2 g/ml are shown.

Data-dependent acquisitions based on accurate mass and mass tag
Mapping of naturally occurring TAG commenced by on-the-fl y screening of the high-resolution mass spectra for the theoretical masses present in the inclusion list (see Experimental Procedures). Once a peak possibly corresponding to an ammoniated TAG was picked, the corresponding sodiated analog was searched using the NH 4 + => Na + mass tag ( m/z 4.955395). Overall, if the i ) inclusions list, ii ) mass tag, and iii ) intensity threshold criteria were met, the system performed a product ion scan on the respective ammoniated TAG, as shown in Fig. 1 . Using this approach, fragmentation pattern of TAG could be automatically obtained without the need of knowing and specifying which TAG are in the sample.
The robustness of mass accuracy was evaluated by assessing the root mean square (RMS) mass errors in 0.2 µg/ml and 2 µg/ml standard solutions (equivalent to 0.4 and 4 weight % in an oil sample; see Table 3 ). The observed subppm mass accuracy enables a very selective way of assigning the correct elemental composition for the TAG and reduces false positives. Despite of this state-of-the art abundant sodium adducts from TAG. With the aid of these salts, both good ionization effi ciency and characteristic adduct envelope can be achieved. The adduct envelope exhibiting the characteristic m/z difference between the ammoniated and sodiated adduct ( m/z 4.955395, see Fig. 1 ) is a useful descriptor that facilitates the deduction of charge carrier and determination of exact molecular weight. Note that the relative proportion of ammoniated and sodiated forms of TAG varies depending on the types of esterifi ed fatty acids. In this work, only the peak areas of ammoniated ions are used for quantitation; the sodiated forms serve only the purpose of qualitative confi rmation.
While this type of mass tagging helps reduce the number of false positives, it also slightly compromises the absolute sensitivity of the method due to the division of analytes into two ion populations (one ammoniated and one sodiated). Then again, the implications of this negative effect to this method are minimal because the selected data-dependent triggering threshold (100,000 cps, see above) is still well above the absolute detection limits.  selectivity, specifi city cannot be achieved, and in rare cases, triggering also occurs on substances that are not TAG. In these latter cases, though, the fragmentation fi ngerprint can be used to confi rm or exclude the presence of a TAG and perform its structural elucidation as described below.

Structural elucidation of TAG
Parent ion isolation, fragmentation, and detection were performed at nominal mass resolution in the linear ion trap in parallel to the high-resolution scan performed in the Orbitrap. This hybrid mode of operation allowed the simultaneous acquisition of fragmentation pattern and accurate mass at the chromatographic time scale. The peaks in the TAG product ion spectra allowed the determination of FA residues within the TAG by using an Excel template (see supplementary material) that automatically calculates mass differences between the pseudo-molecular ion and the masses of the observed fragments. The calculated mass differences correspond to the masses of a fatty acid constituents and an ammonia unit. The Excel template automatically compares these mass differences to a precalculated list of fatty acids, hereby automatically identifying which fatty acids are present in a given TAG. Then, one single built-in macro constructs all possible combinations of the found fatty acids to generate TAG (e.g., 18:0-18:0-18:3). The exact masses of these hypothetical TAG are calculated and compared automatically with the measured exact mass. The list of the generated TAG is then sorted according to their mass errors. All displayed TAG are considered found which have "mass error square" < 10 ppm 2 . Ultimately, the accurate mass and the fragmentation pattern clearly identify which FA are forming which TAG species in a given sample. For more detailed explanation of the calculations, see the section Example Workfl ow of Quantifi cation Routine below, as well as the supplementary material.

Quantitation
A schematic diagram of the quantitation process is visualized in Fig. 4 . In the fi rst step, the sum concentration of TAG regioisomers was determined by integrating the corresponding peak areas in the high-resolution ion chromatograms, normalizing them to the peak area of the internal standard ( 2 H 5 -1,3-dipalmitoyl-2-stearoyl-glycerol), and substituting them into the experimentally determined generic calibration equation (described below). An Excel template can be used as a basis to calculate and express results as [weight %] and as [mM] (see supplementary material).
In the second step, the concentrations of the individual TAG regioisomers are calculated. The experimentally observed response was practically the same for the commercially available PPL (L-linoleic acid), LOO, LLS, POO, SOO, and PSS TAG regioisomer pairs at 0.5 µg/ml and 5 µg/ml concentrations (data not shown), suggesting that there is no signifi cant difference between the ESI responses of regioisomers of the same TAG. In addition, the experimentally observed fragmentation patterns of cis/trans isomers were identical (PPO and PPL cis/trans pairs; data not shown). Further, experimental data also showed that the fragmentation pattern of these TAG mixtures can be estimated by the combination of the individual fragmentation patterns of the TAG regioisomers (data not shown).
Accordingly, the relative percentage of TAG isomers contributing to a complex fragmentation pattern can be estimated if the fragmentation patterns of the individual TAG isomers are known. In this work, we have relied on the experimentally observed fragmentation pattern of commercially available TAG standards and the fragmentation pattern published in the literature using linear ion trap instruments ( 34 ) (see Table 5 ). In addition, we have evaluated the effect of fatty acid chain length on the fragmentation pattern. While the effect of fatty acid chain length is only minor on the fragmentation pattern, it can be estimated by Equation where y is the calculated correction factor in percentage that takes into consideration the chain length, and x is the carbon number of the fatty acids. These considerations altogether enabled to predict the fragmentation pattern of any TAG with the commonly occurring fatty acids up to three double bonds per fatty acid. Note that the prediction of TAG with more double bonds requires more detailed studies based on pure standards, which were not available for the current study. In summary, using the theoretical fragmentation patterns of pure TAG, one can search for their combination that will match the experimentally obtained fragmentation pattern. In this study, this was achieved by an Excel template and the Solver function of Excel (Add-in function under Data/Analysis; see supplementary material). Briefl y, the developed template automatically calculates the fragmentation pattern of pure regioisomers based on the type of fatty acids present in the TAG. This latter TABLE 4. Inter-batch precision of fragmentation pattern obtained for the commercially available TAG standards used for optimization and calibration  calculation is based on the reference patterns given in Table 5 and also takes into account the length of the fatty acids (as described above in Equation 1 ). Note that based on the name of the fatty acids (e.g., 18:2), the template automatically recognizes the degree of unsaturation and which fragmentation case applies from Table 5 . The calculated theoretical fragmentation patterns of the TAG isomers are automatically combined, and the Solver function of Excel is used to optimize the relative proportions of isomers so that the resulting fragment intensities will match the experimental pattern. The absolute concentrations of the individual regioisomers are derived automatically from the sum concentration of TAG regioisomers simply by dividing it according to the relative proportions of the individual isomers (see the last step in Fig. 4 ). A step-by-step explanation of this approach is given in the section Example Workfl ow of Quantifi cation Routine below, as well as in the supplementary material.

Calibration
Response factors of commercially available TAG were determined by constructing calibration curves using standard solutions in the range from 0.1 µg/ml to 10 µg/ml (equivalent to 0.2-20 weight % in an oil sample). All calibration points were determined in triplicates. Most TAG exhibited bending calibrations that were best fi tted by cubic functions in particular at concentrations below 2 µg/ml. Weighting factor of 1/× was used in all cases to further improve accuracy at low concentrations. The precision of the replicate analyses was 4.1% on average in the 0.1-1 g/ml concentration range ( Table 2 ). The overall accuracy of the individually fi tted calibration curves was 0.1% on average (see Table 2 ).
To extrapolate the semi-quantitative analysis of TAG species beyond these commercially available analytes, a generic calibration function was optimized that allows the semi-quantitation of TAG species with up to three double bonds per fatty acid chain (see Equation 2 ): where y is the peak area ratio; x is the concentration; con- due to the lack of an appropriate matrix with the absence of the respective TAG and the low available quantity of calibration standards.

Example workfl ow of quantifi cation routine
In this section, we use the example of PSO TAG regioisomers in a beef tallow sample to demonstrate the workfl ow from data extraction, through substitution into calibration, and ultimately, to deconvolution of TAG regioisomers.
In the fi rst stage, identifi cation of TAG is performed based on its accurate mass and fragmentation fi ngerprint. The accurate mass of the ammoniated pseudomolecular ion is obtained from the raw data fi le by displaying the mass spectrum, in our case at retention time 29.66 min. The corresponding mass spectrum in Fig. 1B  The detailed accuracy values obtained by using the generic calibration ( Equation 2 ) averaged per analyte and averaged per concentration are shown in Table 2 .
The sum quantity of identifi ed triacylglycerols varied between 65% and 96% depending on the complexity of the sample (e.g., 96% for pork lard and 67% for butter fat). This variation is in accordance with the principle of the method, as more complex samples contain more lowabundance TAG that are below the triggering threshold of the method. More sensitive and faster instrumentation will enable to capture higher percentage of TAG even in most complex samples, such as butter fat.
Note that the classical yield-recovery was not tested, because this method is based only on dilution and no extraction process is involved in the sample preparation. Further, it was not possible to perform matrix-matched calibration The hit list of the possible TAG constructed from fatty acids P, S, and O clearly shows that there is only one hit with acceptable mass error. above 5%) is copied into the above-mentioned Excel template. Once the accurate mass of the ammoniated pseudomolecular ion and the fragmentation list is copied into the template, the calculation of fatty acid losses corresponding to the fragments occurs automatically by launching a fragmentation pattern is displayed for the 878 Da data-dependent channel (see Fig. 1D ). The mass difference between each fragment and the parent ion represents a fatty acid loss with an ammonia unit (see labels on Fig. 1D ). The spectrum list of the fragmentation pattern (signals   patterns. The chain length and unsaturation of the fatty acid chains is used automatically by the template to locate the relevant fragmentation pattern from Table 5 (integrated in the template). In our case, this corresponds to the scenarios of 0:0:1 and 0:1:0. The lookup process, the predicted individual intensities, and the summation of all fragment intensities originating from various TAG isomers also occur automatically in the Excel template. The deconvolution process is based on fi nding those proportions of the TAG regioisomers that will yield a sum fragmentation pattern that is practically identical to the experimentally measured fragmentation pattern. The deconvoluted proportions of TAG regioisomers are optimized using the Solver function of Excel (Add-in function under Data/Analysis). The target of Solver in our case is to minimize the differences between the calculated and experimental fragment intensities. Again, to enable the minimization process, the squared differences between the calculated and experimental fragment intensities are used. Once the relative proportions of TAG regioisomers are optimized by Solver, the sum absolute concentration of the TAG isomers (calculated above in the second stage) is divided automatically to yield the individual absolute TAG regioisomer concentrations. In our example, the optimized proportions of PSO:SPO:POS were 7.68:27.03:65.29%, which corresponds to fi nal concentrations of 12.55:44.16:106.65 mmol/1,000 g.

Applications
A commercially available inter-esterifi ed fat was analyzed using the present hybrid MS-based method for its P content at the sn -2 position. Results showed that 57.3% of the overall P content was esterifi ed at the sn -2 position. This number was practically identical with the result provided in the Certifi cate of Analysis of the product (56.9%).
Similarly, the regiodistribution of P was compared between pork lard and beef tallow samples (see Fig. 5 ). In the investigated pork lard sample, 83% of the overall P was found to be esterifi ed to the sn -2 position, whereas this value was only 17% in beef tallow sample. These results are in accordance with the literature, as pork lard was reported to contain 80-90% P at the sn-2 position, and beef tallow only at 15% ( 4,6 ). Note that in addition to this information, the hybrid MS analysis also provides the regioisomeric balance of other FA (e.g., S, O), as illustrated in Fig. 5 . Further, the TAG data was interrogated to derive the quantity of FA present in the samples. This latter was then compared with the results obtained by the classical GC-FID analysis following transmethylation of the samples. Despite the fact that hybrid MS and GC-FID methods analyze different compounds (TAG versus FA), good agreement was found between the results ( Table 7 ), suggesting that majority of FA were captured during TAG analysis and that FA profi le can be also deducted from the TAG profi le.
Finally, butter fat was analyzed using the described hybrid MS-based method. The complexity of this sample and thus the key role of chromatographic separation is illustrated in Fig. 2B , depicting the ion chromatograms of the detected TAG extracted at 10 ppm extraction window. macro in the Excel template. This macro calculates the differences between all fragments and the parent ion, and it assigns the identifi ed fatty acid loss by looking up these values on a precalculated list of fatty acid masses (integrated in the template). In the same process, the macro also constructs all possible combinations of the found fatty acids to generate TAG (e.g., PPP, SSS, OOO, PPS, OOS, PSO) and calculates their accurate masses (see the hit list for our example in Table 6 ). Finally, the exact masses of these hypothetical TAG are compared (automatically) with the experimentally measured exact mass (878.81769 Da). The hits of TAG are sorted according to their mass errors. All displayed TAG are considered possible hits that have "mass error square" < 10 ppm 2 . In our case, the only such TAG is PSO; all others have mass errors > 5 million ppm 2 .
In the second stage, the sum concentration of TAG isomers (in our case, PSO, SPO, and POS) that have the same accurate mass and same retention time is calculated based on the peak area of the corresponding accurate mass ion chromatogram. In our case, the ion chromatogram of 878.81769 Da ( Fig. 1C ) yields a peak area of 697541884. This peak area is divided with the peak area of the internal standard (11538828) and is substituted into Equation 2 using the template QUANTIFICATION_BY_CALIBRA-TION.xls (see supplementary material). Note that the carbon number (CN) and unsaturation (number of DB) is required by the template to adjust the calibration parameters to the chemical nature of the respective TAG. Once these data are entered into the Excel template, the calibration parameters are calculated automatically as described in Equation 2 . In our case, the CN is 52, and the DB is 1. The calculated calibration parameters are A = Ϫ 0.00726274; B = Ϫ 0.09882424; C = 9.67708010; and D = Ϫ 0.17629132. The resulting concentrations are derived using the Solver function of Excel (Add-in function under Data/Analysis). Briefl y, the basic principle of Solver-based quantifi cation is fi nding iteratively a concentration that returns a peak area ratio that is practically identical with the experimentally measured peak area ratio. This way, any type of calibration (e.g., cubic, quadratic, weighted by 1/x, 1/X 2 ) can be applied without sophisticated calculations. In our case, we use Solver to minimize the difference between the calculated and experimental peak area ratio. Note that to enable this minimization, the squared difference between the calculated and experimental peak area ratio is used. In our example, the solution was 7.03 g/ml concentration in the vial, which corresponds to 163.36 mmol/1,000 g in the original sample.
In the third stage, the distinct quantifi cation of TAG regioisomers occurs by deconvoluting the experimental fragmentation pattern (maximum 20 fragments) and dividing the above calculated sum concentration of TAG isomers accordingly. The deconvolution process is facilitated by the template REGIOISOMER_CALCULATOR.xls (for fi lling the template, see the supplementary material). Briefl y, fi rst the theoretical fragmentation patterns of all identifi ed TAG are predicted. In our example, this means the calculation of PSO, SPO, and POS fragmentation Altogether 565 TAG were identifi ed and quantifi ed, from which approximately 200 TAG were present at greater than 1 mM concentration. The regioisomeric balance of various FA is shown in Fig. 6A . The results show that in butter fat the vast majority of the short-chain fatty acyl groups (C4-C6) are at the sn -1(3) position, which is in accordance with the literature ( 57,66 ). The most abundant odd carbon number FA were C17:0, C15:0, and C17:1, all of which were found enriched on the sn -2 position. Another advantage of the present hybrid MS-based method is that TAG are characterized in their intact form, enabling overview of the size distribution (e.g., sum carbon number of acyl chains) of TAG present in the sample. This is illustrated in Fig. 6B , showing that the observed size distribution comprised a 24-54 CN range in the investigated butter fat sample. The fact that the carbon number of acyl chains in the smallest detected TAG was 24 suggests that butyric and caproic acids occur in butter fat almost exclusively in combination with medium-and long chain-fatty acids, which is again in accordance with the literature ( 67 ).

CONCLUSIONS
This work describes a new approach to detect, identify, and semi-quantitate individual regioisomers of TAG in fats and oils. The method is based on hybrid mass spectrometry that enables the global detection and identifi cation of TAG without the need of defi ning which TAG are present in the sample. As this method characterizes TAG in their intact form, the overview of TAG size distribution is possible, and the regioisomeric distribution of various FA, including that of P, can be measured simultaneously. Furthermore, there is no need for enzymatic treatment using this method, so fats/oils above melting point of 45°C can be characterized in contrast to conventional lipasebased methods. Limitation of the present approach is that positional and geometrical isomers of FA (e.g., 18:3 n-3/18:3 n-6 or cis/trans confi guration) cannot be distinguished, and currently only TAG containing FA with no more than three double bonds (meaning maximum of nine double bonds per TAG) can be quantifi ed due to the limited availability of commercial standards.

OUTLOOK
The continuously expanding range of commercially available standards and the next generation of faster and more sensitive instrumentation will enable the characterization of more complex oils (e.g., fi sh oil) at even higher selectivity (e.g., MS 3 ). Further, the integration of ozoneinduced dissociation ( 68 ) to the present approach would bring information on FA isomerism. This work points out that radical future software developments are needed to facilitate the interpretation and exploit the identifi cation/ quantitation potential of hybrid datasets, including various chromatographic, ion mobility, high-resolution, and multistage fragmentation information.