Chemometric Approaches in CalibrationExperiments of Trilinolenoylglycerolby Liquid Chromatography Ion-TrapMass Spectrometry

Pedro Araujo, Thu-Thao Nguyen, and Livar FrøylandSeafood and Health Research Group, National Institute of Nutrition and Seafood Research, Bergen, Norway

The article presents a comprehensive account of the application of chemometric approaches todetermine the factors that influence the tri-�-linolenoylglycerol (TALG) ammoniated adductsignal m/z 890.6 in an ion-trap mass spectrometer coupled to a liquid chromatograph and theestimation of different sources of errors involved in TALG calibration experiments. It wasfound that by using experimental design, the influence of the nebulizer pressure on theanalytical signal is less pronounced than the influence of the drying gas flow and thechromatographic flow rate. The results revealed that without using tandem mass or atmo-spheric pressure chemical ionization, it is possible to fragment the TALG backbone and obtainthe free �-linolenic acid by varying the drying gas flow and using an electrospray interface.The error decomposition approach revealed that the preparation error was 26 times higherthan the instrumental error. (J Am Soc Mass Spectrom 2005, 16, 388–396) © 2005 AmericanSociety for Mass Spectrometry

As an essential polyunsaturated fatty acid, �-li-noleic acid (ALA, 18:3n-3) is not synthesizedde novo in animals, but must be provided in

their diets in the form of triacylglycerol [1]. Thedevelopment of analytical methods in the analysisand quantification of ALA and more general triacyl-glycerols (TAG) is of considerable importance [2, 3] inview of their involvement in many vital biochemicalprocesses and their association with the alleviation ofa wide variety of diseases [4, 5]. Quantification ofTAG using coupled techniques such as LCMS de-pends mainly on two aspects, the sample preparationtechnique and the instrumental condition settings.Well-established protocols and books [6 – 8] havebeen devoted to the former and nowadays manyresearch laboratories around the world invest timeand resources to investigate new, rapid, and simplertechniques. Works regarding the latter aspect are notwidespread in the literature, perhaps because varia-tion of the instrumental conditions can cause drasticalterations to the results obtained with a tested andoptimized method [9]. Continuity of results withinlong periods of time (years) is of paramount impor-tance in clinical studies [10], impairing in somedegree the interest in the exploration of new orexisting methodologies aiming at optimizing the set-

Published online February 4, 2005

Address reprint requests to Dr. P. Araujo, Seafood and Health Research

Group, National Institute of Nutrition and Seafood Research (NIFES), P.O.Box 2029 Nordnes, N-5817 Bergen, Norway. E-mail: pedro.araujo@nifes.no

© 2005 American Society for Mass Spectrometry. Published by Elsevie1044-0305/05/$30.00doi:10.1016/j.jasms.2004.12.006

ting of the LCMS instrumental conditions used in thequantitative analysis of TAG. Superb LCMS instru-ments equipped with automatic optimization devicescould be another reason for the limited number ofpublications on this field. It has been reported thatthe sole chromatographic system is influenced bymore than 50 factors [11], hence the complexity ofchromatography coupled to mass spectrometry over-whelms even the most sophisticated software in-tended for automatic optimization and method de-velopment. The classic one-at-the-time methodologyfor optimization has been widely used in TAG quan-tification studies. One of the drawbacks of thismethod is that it is a tedious procedure and the trueoptimum can be missed if there are important inter-actions between the factors. The optimization of aLCMS method is prone to difficulties resulting fromthe inherent high number of instrumental factorsinvolved and their interactions. The determination ofthe local response surface and exploitation of thelocal factor dependence is essential. The discoveryand application of methods to that effect are ex-tremely important. This study was undertaken, firstto estimate the optimal combination of liquid chro-matography-ion-trap-mass spectrometry (LCITMS)experimental variables, specifically nebulizer gaspressure, drying gas flow, and chromatographic flowrate involved in the quantitative determination oftri-�-linolenoylglycerol (TALG) by using the re-sponse surface methodology, in particular a Doehlert

matrix [12]; second, to study under optimal LCITMS

r Inc. Received June 23, 2004Revised December 7, 2004

Accepted December 9, 2004

389J Am Soc Mass Spectrom 2005, 16, 388–396 CHEMOMETRIC APPROACHES IN EXPERIMENTS OF TALG

condition settings, the different sources of errorsimplicated in TALG quantification experiments suchas dilution, instrumental and lack-of-fit errors, andthird, to determine quantitatively the TALG concen-tration in synthetic formulations.

Materials and Methods

Samples

Primary stock solutions of the standards tri-�-linolenoylglycerol (TALG), 1,3,-di-�-linolenoylglycerol(DAG), 1,-mono-�-linolenoylglycerol (MAG), �-linole-nic acid (FFA) and 3-sn-phosphatidylethanolamine (PE)from bovine brain (Sigma-Aldrich, Bergen, Norway)were prepared in chloroform. TALG working solutionswere prepared in chloroform by appropriate dilutionsat 10, 20, 30, 40, and 50 �g/ml. Mixtures of the MAG,DAG, FFA, and PE were prepared in chloroform andspiked with different concentrations of TALG to pro-duce the calibration curve points equivalent to 10, 20,30, 40, and 50 �g/ml.

Liquid Chromatography Ion-TrapMass Spectrometry

The LCITMS used in this study was an Agilent 1100series LC/MSD trap, SL model with an electrosprayinterface (ESI), a quaternary pump, degasser, autosam-pler, thermostatted column compartment and variable-wavelength UV detector. The column used a ZorbaxEclipse-C8 RP 150 � 4.6 mm, 5 �m (Agilent Technolo-gies, Palo Alto, CA) was kept in the column compart-ment at 40 °C. The solvent system operated in isocraticmode was 2-propanol/water (vol/vol 90/10) with am-monium acetate added at a concentration of 10 mM andUV detection at 254 nm. TALG dissolved in chloroformwas infused into the ESI source with a KD Scientificsyringe pump at a flow rate of 10 �l/min. Nitrogen wasused as nebulizing and drying gas at 350 °C. The ESIsource was operated in positive ion mode and the ionoptics responsible for getting the ions in the ion-trapsuch as capillary exit, skimmer, lens and octapolesvoltages were controlled by using the Smart Viewoption. The m/z range scanned in the MS measurementwas 100–1000 and resolution of 13,000 m/z/s (FWHM/m/z � 0.6–0.7). Complete system control, data acquisi-tion and processing were done using the ChemStationfor LC/MSD version 4.2 from Agilent.

Chemometric Approaches

Uniform shell design. The effect of the nebulizer pres-sure (z1) and the drying gas flow rate (z2) variables fromthe ion-trap along with the chromatographic flow rate(z3) on the characteristic signal of TALG ammoniatedion [M � NH4]� at m/z 890.6 was studied by using auniform shell design developed by Doehlert [12]. Figure

1 described the generation of this uniform shell design

for two and three factors whose main characteristicsare:

• The design displays an equally spaced distribution ofexperimental points circumscribed to a sphere ofradius 1; in this way the variance of the estimatedresponse is the same at all points on the spherecenterd at the origin.

• The number of experiments suggested by this designis calculated according to the general expression Z2 �Z � 1 where Z represents the number of variables tobe investigated. For instance, the study of two vari-ables (Z � 2) will involve seven experiments. Theseexperimental points are the labeled points 1, 2, 5, 8, 9,11, and 13 allocated at the center and at the vertexesof the hexagonal shape in Figure 1a.

• The selected variables are studied at different num-bers of levels. Figure 1 shows how the factors z1, z2,and z3 are studied at 5, 3, and 7 levels respectively.This characteristic is relevant when a new instrumen-tal situation arises. For instance the temperature in aparticular instrument cannot be studied at 7 levels aswas planned but at the 3 levels preset by themanufacturer.

The three variables described at the beginning of thissection will require a minimum of 13 experiments (32 �3 � 1) to model their effect on the selected response. Thegeneration and distribution of these 13 experimentalpoints is displayed in Figure 1b and the coded andnatural levels involved in the experimentation are givenin Figure 1c. A brief explanation of these levels is asfollows: the five coded levels (�1, �0.5, 0, 0.5, and 1) forvariable z1 represent five different nebulizer pressures(30, 40, 50, 60, and 70 psi), for variable z2 the three codedlevels �0.82, 0, and 0.82 represent three different dryinggas flows (8.4, 10, and 11.6 l/min), and for variable z3

the seven coded levels �0.87, �0.58, �0.29, 0, 0.29, 0.58,and 0.87 represent seven different chromatographicflow rates (0.25, 0.37, 0.48, 0.6, 0.72, 0.83, and0.95 ml/min).

The aforementioned parameters were analyzed bykeeping constant the drying gas temperature at 350 °C.This particular temperature was selected based on apreliminary investigation in our laboratory aiming atstudying the behavior of TAG, DAG, and MAG analyt-ical signals at different drying gas temperatures (250–365 °C). It was found, in all the instances, that the bestanalytical sensitivity is achieved at 350 °C. Temperaturevalues above 350 °C did not yield further significantincrease of the signals.

Linear calibration design. The description of the linearcalibration design studied in this work and representedin Figure 2 is as follows: calibration experiments werecarried out at five different concentration levels (I � 5)in order to evaluate the relationship between the TALGconcentration and its [M � NH4]� signal at 890.6 m/z.

The solution preparation error was evaluated by per-

390 ARAUJO ET AL. J Am Soc Mass Spectrom 2005, 16, 388–396

forming Ji independent standard solution replicates ateach i measurement level. The standard solution repli-cate ji is taken and Kij instrumental replicates are

Nebulizer pressure

1

2

4

5

6

9

11

12

10

13

3 7

Chromatographic

flow rate

D

r

y

i

n

g

g

a

s

f

l

o

w

radius = 1

1.03

3.97

1.

2.

1.699

-1.0

30

0.82 11.63

0.0 10.00

-0.82 8.36

Drying gas

flow rate (l/min)

a)

c)

Figure 1. (a) Generation of a Doehlert matrixexperimental points studied in this work; (c) expeach experimental point. Two scales are shownthe variables.

1

1 1

2

2 2

I concentration measurement levels

(I=5)

Jistandard solution replicates

(J1=2; J

2=3; J

3=4 J

4=3; J

5=2)

14 individual solutions

Kij

instrumental replicates

(K22

= K31

=K34

=K42

=2)

J1

J2

K11

K12

i ii iii

K21

K22

Figure 2. Experimental arrangement of the dilu

per.

performed on it. A total of 18 measurements wereperformed in order to obtain the linear relationshipwith two parameters in the model. According to the

8

13 5

11 1 8

9 2

3 7

6 4

10

12

1.043

4.110

1.359

2.566

2.060

0.787

1.829

1.932

1.846

0.58 0.83

0.29 0.72

0.00 0.60

-0.29 0.48

-0.58 0.37

-0.87 0.25

0.87 0.95

2.026

0.0 0.5 1.0

50 60 70

ulizer pressure (psi)

Chromatographic

flow rate (ml/min)

b)

wo and three variables; (b) distribution of theental [M � NH4]� area in icps�108 measured ath correspond to the coded and natural levels of

3

3 3 3 3

4

4 4 4

5

5 5

J3

J4

J5

i i i i i iiii iii iii

K31

K32

K33

K34

K41

K42

K43

K51

K52

and instrumental replicates evaluated in this pa-

2

4

232

179

-0.5

40

Neb

for terimwhic

2

i

K23

tion

391J Am Soc Mass Spectrom 2005, 16, 388–396 CHEMOMETRIC APPROACHES IN EXPERIMENTS OF TALG

notation described above, a measurement at the concen-tration level i, sample replicate j, and instrumentalreplicate k is recorded as yijk.

Standard solution replicates. The influence of the exper-imental errors due to inaccuracies in calibrating pi-pettes, mixing of solutions, evaporation, etc, describedin the literature as preparation error, was assessed bymaking replicate solutions of the measurement levels.These measurement levels (I) showed in Figure 2, werecoded from 1 (lowest concentration) to 5 (highest con-centration). Levels 1 and 5 (10 and 50 �g/ml TALG,respectively) were replicated twice, levels 2 and 4 (20and 40 �g/ml TALG, respectively) were replicatedthree times and level 3 (30 �g/ml TALG) was replicatedfour times, resulting in 14 individual solutions (Figure2).

Instrumental replicates. Instrumental noise, baselineproblems, spray fluctuation, etc., may lead to differentresults between replicates. This particular source oferror is estimated by measuring some concentrationlevels more than once. Instrumental accuracy becomes aproblem when very low concentrations are studied. Ithas been proposed that for a system consisting of fivemeasurement levels, a sensible number of degrees offreedom to estimate the instrumental error is four [13].Based on this observation, one of the individual solu-tions at level 2 and level 4 and two of the individualsolutions at level 3 were instrumentally replicated as isdepicted in Figure 2.

Error decomposition approaches. The mean square errorsassociated with the instrumental (Sinst

2 ) and the standardsolution (Sstd

2 ) replicates were calculated by

Sinst2 �

�i�1

I

�j�1

Ji

�k�1

Kij

�yijk � y�ij�2

��i�1

I

�j�1

Ji

�k�1

Kij

�Kij � 1�� (1)

and

Sstd2 �

�i�1

I

�j�1

Ji

Kij�y�ij � y��i�2

�i�1

I �(Ji � 1) ��j�1

Ji Kij

Ji� (2)

where the numerators of eqs 1 and 2 represent the sumof square errors for instrumental (SSinst) and standard(SSstd) solution replicates and the mean values repre-sent the instrumental average at each standard level (y�ij)and the dilution weighted average at each measure-

ment level (y��

i) calculated by

y�ij ��k�1

Kij

yijk

Kij

(3)

and

y��

i ��j�1

Ji

Kijyij

�j�1

Ji

Kij

(4)

The unequal number of standard solution and instru-mental replicates has a direct consequence on the de-grees of freedom involved in the calculation of the meansquare standard solution error (Sstd

2 ) in eq 2. To recapit-ulate briefly, each solution at level 1 was measured oncegiving an average of 1 measurement/level-1. At level 2,where three solutions were prepared, two solutionswere measured once and one solution was measuredtwice giving a total of 4 measurements and an averageof 1.33 measurements/level-2 (4 measurements dividedby 3 solutions). Similarly, at level 3, where four solu-tions were prepared, a total of six measurements wereperformed giving an average of 1.5 measurements/level-3. Hence, the sum of square errors for standardsolution replicates is divided by 11.83.

�i�1

I �(Ji � 1) ��j�1

Ji Kij

Ji��

1 ��1

2�

1

2�� 2 ��1

3�

2

3�

1

3��

3 ��1

4�

2

4�

2

4�

1

4��

2 ��1

3�

2

3�

1

3�� 1 ��1

2�

1

2�� 11.83

Calibration function. The linearity of a calibration func-tion is described by

y � �xi � � (5)

where y represents the estimated intensity in ion countsper second (icps) of the [M � NH4]� 890.6 m/z, xi theTALG concentration in �g/ml at level i, and � and � thesensitivity of the analysis and the intercept, respec-tively. The linearity of the calibration function wasinvestigated at the TALG concentration levels describedabove (10, 20, 30, 40, and 50 �g/ml).

The adequacy of the model is tested by calculatingthe F-test and comparing with the tabulated 95% con-

fidence level

392 ARAUJO ET AL. J Am Soc Mass Spectrom 2005, 16, 388–396

Fcalculated �

� SSlof

DFlof�

� SS�

DF�� �

Slof2

S�2 (6)

where SSlof and SS� represent the lack-of-fit and thepure error sum of squares error, respectively, DFlof andDF� the associated degrees of freedom, and Slof

2 and S�2

the mean square error respectively.SSlof is calculated by the difference

SSlof � SSr � SS� (7)

where SSr represents the residual sum of square errorcalculated by

SSr ��i�1

I

�j�1

Ji

�k�1

Kij

(yijk � yi)2 (8)

and

SS� ��i�1

I

�j�1

Ji

�k�1

Kij

(yijk � y��i)2 (9)

It is important to mention that the lack-of-fit should besmall in respect to the residual error if a genuine linearrelationship is obeyed.

The residual (Sr2) and pure error (S�

2) mean squareerror are calculated by

Sr2 �

SSr

��i�1

I

�j�1

Ji

�k�1

Kij

Kij�� p(10)

Figure 3. Response surface for nebulizer pressure and chromato-graphic flow rate at a drying gas flow of 10 l/min.

and

S�2 �

SS�

�i�1

I

(Ji � 1)(11)

where the denominators in eqs 10 and 11 represent thedegrees of freedom (16 and 9 for residual and pureerror, respectively) and their difference (16 � 9 � 7)denotes the degrees of freedom associated to the lack-of-fit error. The term p in eq 10 represents the number ofparameters in the model. In the determination of thedegrees of freedom associated to the pure error (DF� �9) used in the calibration linearity testing, the approachsuggested by the Analytical Methods Committee of theRoyal Society of Chemistry [14] was employed, that isaveraging the replicate instrumental responses at eachconcentration level. Finally, the adequacy of the modelis tested by calculating the F-test and comparing withthe tabulated 95% confidence level (F7/9 � 3.293).

Results and Discussion

Modelling of the LCITMS Variablesand Estimation of Their Optimal Combination

Figure 1c shows the experimental results obtained afterapplying the uniform shell design. A total of 15 exper-iments were run in random order. The center of thedesign was replicated three times to provide sufficientdegrees of freedom for the calculation of the pure errorsum square.

In order to determine the behavior of the threevariables studied, a full second-order polynomialmodel consisting of 10 parameters (1 intercept, 3 linear,3 squared, and 3 interaction terms) was consideredinitially but after checking the significance of the 10parameters (F-test 95% confidence level) it was possibleto simplify it to a reduced model that explains a

Figure 4. Response surface for drying gas flow and chromato-

graphic flow rate at a nebulizer pressure of 50 psi.

393J Am Soc Mass Spectrom 2005, 16, 388–396 CHEMOMETRIC APPROACHES IN EXPERIMENTS OF TALG

considerable percentage of the variability of the analyt-ical signal (r2 � 0.99). The reduced model is describedby the following equation:

y � 1.9 � 108 � 1.6 � 107z1 � 1.8 � 107z2 � 1.6 � 108z3

� 4.8 � 107z22 � 9.0 � 107z3

2 � 9.0 � 107z2z3

where y represents the estimated [M � NH4]� signal atm/z 890.6, and the terms z1, z2, and z3 represent thenebulizer pressure, the drying gas flow, and the chro-matographic flow rate in coded levels, respectively.According to the reduced model, the interaction nebu-lizer-chromatographic flow rate (z1z3) which has beenreported to have some influence on the analyticalresponse [15] was not significant at the 95% confidentlevel in the experimental range studied in this work.The reduced model also shows the significance of theinteraction drying gas flow-chromatographic flow rate(z2z3) which is generally overlooked in optimizationworks.

Figure 5. The effect of increasing the drying gadduct signal m/z 890.6. The nebulizer pressure, d

constant at 50 psi, 350 °C and 10 �l/min respectively

The multilinear equation given above is used togenerate the response surfaces of the estimated re-sponse y against the variables. The behavior of the [M �NH4]� signal as a function of the nebulizer pressureand the chromatographic flow rate (Figure 3) and thenebulizer pressure and the drying gas flow (not shown)give evidence that at constant levels of either the dryinggas flow or the chromatographic flow rate, variations ofthe nebulizer pressure do not affect the magnitude ofthe analytical signal. When a constant nebulizer pres-sure is set and the chromatographic flow rate is in-creased (Figure 3) the signal decreases rapidly; howeverbetween 0.8 and 1 ml/min (0.5 and 1 in coded levels)the signal changes slightly with the chromatographicflow rate. Figure 4 represents the behavior of theanalytical signal as a function of the drying gas flowand the chromatographic flow rate. It can be seen fromthis figure that when the chromatographic flow rate iskept constant at 1 ml/min (coded level 1), an increase inthe drying gas flow produces an enhancement on the

ow on the tri-�-linolenoylglycerol ammoniatedg gas temperature and infusion speed were kept

as flryin

.

394 ARAUJO ET AL. J Am Soc Mass Spectrom 2005, 16, 388–396

analytical signal; however there is a region around 8and 10 l/min of drying gas flow in which the signal isalmost constant. In contrast to this result, Figure 4shows that keeping constant the chromatographic flowrate at 0.2 ml/min (coded level 1) the signal decreaseswhen the drying gas flow rate is increased. A remark-able enhancement of the 890.6 m/z signal is achievedwhen the levels of the nitrogen drying gas flow and thechromatographic flow rate are kept in the lowest mag-nitudes used in this work, 8 l/min and 0.2 ml/min,respectively. This result was contrary to our expecta-tions, due to the fact that the main role of the drying gasflow is to evaporate solvents in the spray chamberwithout decomposing the analytes thermally [15]. Fur-ther investigation aiming at studying the effect of thedrying gas on the analytical signal, in order to clarifythe divergence between the aforesaid reported observa-tion and our experimental results, was carried out byinfusing a sample of TALG and changing the levels ofthe counter-current drying gas flow between 8–12l/min. The results obtained (Figure 5) suggest that themain process involved at 8 l/min is the reduction of thekinetic energy of the ions formed from charged dropletsby collision with molecules of the drying gas leading tothe formation of intact [M � NH4]�. Based on thebehavior of the system at 10 l/min, it is highly probablethat the increase in drying gas flow causes an increasein pressure in the atmospheric pressure interface, whichmight lead the ions to undergo more collisions whichresults in an increase in the internal energy of a consid-erable fraction of the intact ions and in this way both�-linolenic FFA (296.2 m/z) and precursor ions (890.4

Table 1. Results of the tri-�-linolenoylglycerol LCITMS calibrati

Measurementlevel (�g/ml)

Codedmeasurement

level (I)

Standardsolution

replication (Ji)

Instrumentareplication

(Kij)

10 1 2 11

20 2 3 12

130 3 4 2

112

40 4 3 12

150 5 2 1

1

All the responses in icps � 109 units.

m/z) ammoniated adducts are formed. At 12 l/min the

increasing of the internal energy is more dramatic andall the precursor ions are over the threshold of fragmen-tation; therefore, the formation of the FFA dominates. Itis important to mention that fragmentation of TALGhas been observed by using atmospheric pressurechemical ionization [2] and tandem sector MS [3] but inany of these works the FFA ammoniated adduct wasobserved. The fragmentation of TALG into FFA as aresult of varying the drying gas flow in ESI-MS exper-iments, to our knowledge, has not been previouslyreported.

Estimation of the Sources of Errors in ESI LC-Ion-Trap-MS Under Optimal Variable Conditions

Based on the behavior of the analytical signal with thevariables studied (Figures 3 and 4) the coded levels 1,�1, and �1 for z1, z2, and z3, respectively, whichcorrespond to the experimental condition 70 psi fornebulizer pressure, 8 l/min for drying gas flow, and 0.2ml/min for chromatographic flow rate, were suggestedto estimate the main errors involved in linear calibra-tion experiments for the quantitative estimation ofTALG. The results after measuring the dilution andinstrumental replicates are shown in Table 1 with theirrespective instrumental average, dilution weighted av-erage and estimated response.

Table 2 shows the results of the different source oferrors studied in this work. Comparison between thesum square errors for instrumental and standard solu-tion replication seems to indicate that instrumental

periments

xperimentalresponse

(yijk)

Instrumentalaverageresponse

(yij)

Standard solutionweighted average

response (y��i)

Estimatedresponse

(yi)

1.19 1.19 0.90 0.730.61 0.611.45 1.45 1.43 1.421.44 1.401.361.46 1.461.99 2.00 1.95 2.112.001.91 1.912.00 2.001.96 1.911.872.93 2.93 2.93 2.812.84 2.862.883.07 3.073.59 3.59 3.56 3.503.53 3.53

on ex

l E

stability is not of major concern in LCITMS calibration

395J Am Soc Mass Spectrom 2005, 16, 388–396 CHEMOMETRIC APPROACHES IN EXPERIMENTS OF TALG

experiments compared to standard solution replication.The preparation error is 26 times larger than the instru-mental error; for this reason TAG calibration experi-ments where the number of instrumental replicates ishigher than the number of dilution replicates are notadvisable and can be considered as poor calibrationstrategies.

Tri-�-Linolenoylglycerol ESI LC-Ion-Trap-MSCalibration Study

The linear calibration was estimated by calculating thelinear functional relationship between the analyticalsignal at 890.6 m/z and the instrumental average at eachdilution level. The error analysis, presented in Table 2,revealed that the ratio lack-of-fit to pure error variances(F7/9 � 1.586) gives evidence to support the adequacy ofthe model described by eq 5. The calibration graph waslinear between 10 and 50 �g/ml (r2 � 0.96) and theanalytical characteristics of the calibration graph deter-mined by unweighted least-squares regression werey � 3.20 � 107 � 6.94 � 107 xi. The determination ofTALG in synthetic mixtures at different analytical con-centrations was successfully achieved without detri-mental side effects from the matrices tested. The recov-eries from synthetic mixtures spiked with TALG rangedfrom 94.6 to 99.4% and the detection limit correspond-ing to three times the standard deviation of the blankwas found to be 9.5 � 10�2 �g/ml.

Conclusions

The application of an experimental design in LCITMSexperiments aiming at measuring, modeling, and opti-mizing the different parameters involved in the analysisof TAG has resulted in a substantial reduction of timeand resources. It is important to highlight how theuniform shell design used in this work has permitted toestimate the experimental response as a function of theexperimental variables considered at a cost of about14% of the full 5 � 3 � 7 � 105 design and has provento be a good component in high dimensional experi-mental work.

The described approaches have demonstrated thatefficient experimentation is based on experimental de-sign and subsequent quantitative evaluation of therelationship between factors and responses. The de-scribed uniform shell design and error decomposition

Table 2. Error terms studied in this work

Instrumentalreplicates

Standarrep

Sum of square errors (icps)2 7.74 � 1015 2.02Degrees of freedom 4 1Mean square errors (icps)2 1.93 � 1015 1.71

approaches can be applied to the study of others

parameters different from those considered in thiswork. The reader interested in the implementation ofthese or other kind of designs is referred to a series oftutorials with examples taken from the literature byAraujo and Brereton [16–18].

By applying experimental design we have demon-strated that it is possible to fragment the backbone of thetri-�-linolenoylglycerol and obtain the free �-linolenicfatty acid by using ESI MS alone. The application ofmultivariate approaches, in order to study the effect of thedrying gas in combination with other MS variables such asthe voltages in the electrospray source and high order MScoupled to liquid chromatography, could offer a greatdeal of potentialities in the structural characterization ofFFA and the identification of the relative disposition of theacyl groups on the glycerol backbone. Such studies canpave the way for the development of selective TAGfragmentation methods which are essential to gain a clearunderstanding of the dynamic of TAG and FFA in areassuch as human nutrition.

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