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Anal. Chem. 2001, 73, 2976-2984

Evaluation and Optimization of Ion-Current Ratio Measurements by Selected-Ion-Monitoring Mass Spectrometry Michael J. MacCoss,† Michael J. Toth, and Dwight E. Matthews*

Departments of Medicine and Chemistry, The University of Vermont, Cook Building, Burlington, Vermont 05405

Stable isotopically labeled compounds are regularly used as internal standards in quantitation and as tracers of in vivo metabolism. In both applications, the ratio of unlabeled to labeled analogues is determined from an ioncurrent ratio measured by a mass spectrometer. The precision of the ion-current ratio measurement defines the detection limit for quantitation and for tracer enrichment measurement. We have used standard models of noise to develop a method that evaluates ion-current ratio noise (i) that varies with the signal intensity and (ii) that is signal independent. This model produces a simple equation that defines the ion-current ratio precision using constants that can be evaluated empirically from the measurement of two ion-current ratios from a single standard measured multiple times. We demonstrate that our approach can predict the effect of signal intensity, ioncurrent ratio magnitude, and internal standard or tracer choice on the measurement precision. The standard deviations predicted by our method are shown to equal standard deviations of samples measured experimentally. This method allows a simple evaluation of a mass spectrometry system and can define the precision of new quantitation and tracer methods. The use of stable isotopes in biology, medicine, and chemistry has increased as a result of the greater availability of commercially available labeled compounds and easy to use economically priced mass spectrometers. Stable isotopically labeled compounds are used to measure the kinetics of in vivo metabolism, including the rate of production and disposal of a particular analyte.1,2 Stable isotopically labeled compounds are also added as internal standards to measure the amount of a compound relative to the added standard.3 Whether the application is measuring in vivo metabolism kinetics or quantifying compound concentrations, the measurements and calculations are the same: the relative amount of the labeled and unlabeled species is determined from an ioncurrent ratio measured by a mass spectrometer. * Corresponding author: (e-mail) [email protected]; (voice) (802) 6568114; (fax) (802) 656-1229. † Present address: Department of Cell Biology, The Scripps Research Institute, La Jolla, CA 90237. (1) Matthews, D. E.; Bier, D. M. Annu. Rev. Nutr. 1983, 3, 309-39. (2) Young, V. R.; Ajami, A. M. J. Parenter. Enteral Nutr. 1999, 23, 175-94. (3) Watson, J. T. In Methods in Enzymology; McCloskey, J. A., Ed.; Academic Press: San Diego, 1990; Chapter 4.

2976 Analytical Chemistry, Vol. 73, No. 13, July 1, 2001

Stable isotopically labeled compounds are generally measured using a mass spectrometer coupled to either a gas chromatograph (GC/MS) or high-performance liquid chromatograph (LC/MS). As a sample elutes from the chromatograph and enters the mass spectrometer, the ion current of two or more isotopic species (isotopomers) of a molecular or fragment ion formed in the mass spectrometer is measured over time. The peak areas from each monitored ion are integrated by the instrument data system and are then used to calculate the ion-current ratios of one ion relative to the other(s). For quantitation of compounds in complex matrixes, internal standards are used to minimize errors associated with sample isolation and preparation because the compound of interest is measured relative to the added labeled internal standard. The labeled standard mimics the measured compound during the sample isolation and preparation, therefore, accounting for any possible losses. The measurement of the ion-current ratio between the compound and the internal standard with a mass spectrometer significantly reduces errors associated with the ion source and inlet systems because the labeled and unlabeled samples are structurally identical.3 Therefore, counting or “ion” statistics resulting from the randomness in the ion beam is the limit to the quantitation of a compound with a labeled standard.4 For the measurement of in vivo metabolism, stable isotopically labeled compounds (tracers) are administered to either a human volunteer or animal with subsequent sampling of blood, urine, saliva, breath, or tissue samples. The dilution of the tracer by the natural compound (tracee) is measured as the tracer/tracee ratio (TTR) and is proportional to the measured ion-current ratio of the labeled/unlabeled material in the mass spectrometer. The TTR is used to calculate the kinetics of the system.1 In addition, tracing the fate of a specific labeled atom in biological metabolites can provide information that is diagnostic of a particular biochemical pathway or mechanism.2 Because of the large financial and time commitment in conducting metabolic tracer studies, investigators need to be able to evaluate the measurement precision of a predicted TTR for a selected method before beginning a complex in vivo tracer project. New mass spectrometric methods for quantitation using labeled internal standards and in vivo tracers are continually being developed.2 The key to these developments remains our ability (4) Peterson, D. W.; Hayes, J. M. In Contemporary Topics in Analytical and Clinical Chemistry; Hercules, D. M., Hieftje, G. M., Evenson, M. A., Eds.; Plenum Press: New York, 1978. 10.1021/ac010041t CCC: $20.00

© 2001 American Chemical Society Published on Web 05/16/2001

to measure the ion-current ratio between the isotopically labeled and unlabeled species. These new methods are usually reported and validated on a specific instrument with little discussion as to how the method may perform on another instrument or how the method may compare with a different method on the same instrument. Therefore, it is important to be able to evaluate the precision of the ion-current ratio measurement, to understand the limitations of a mass spectrometric method for a given instrument, and to compare abilities of different instruments to make these measurements. Because ion statistics should be the major limiting factor that defines the noise of an ion-current ratio measurement, Poisson’s counting statistics can be used to evaluate the ultimate precision associated with different experimental conditions.4,5 The effect of the sample size, number of ions monitored, fragment intensity, derivative type, amount of internal standard added, and tracer choice affects the number of ions collected in the ion-current ratio measurement. These effects on the precision should be predictable. In this report, we demonstrate a method to estimate accurately the precision of an ion-current ratio measurement method and use this predicted precision to assess the relative performance of a selected instrument. For simplicity, we consider ion-current ratios generated only by selected ion monitoring (SIM) on quadrupole GC/MS instruments. However, the concepts addressed here also apply to any ion-current measurement system, including LC/MS and tandem mass spectrometry experiments. EXPERIMENTAL SECTION Theory. In all experiments using stable isotopically labeled compounds, the mole ratio (na/nb) of the unlabeled and labeled species can be calculated from the ion-current ratio measured by mass spectrometry. The measured ratio (R) for two isotopic species, a and b, is a linear function of the molar ratio of a/b, in the form

R ) Rb + k(na/nb)

(1)

where na and nb are the amounts of a and b in moles, k is the molar response factor of the instrument (ideally equal to unity), and Rb is the ion-current ratio measured when pure b is injected. Rb and k are determined by the measurement of R for standard samples with a known na/nb molar ratio.6 Equation 1 can be rearranged to measure an unknown molar ratio as a function of an observed ion-current ratio:

na/nb ) [R - Rb]/k

(2)

The molar ratio of na/nb can be used either to quantitate species a as a function of added b (in the case of species b being a labeled internal standard) or to calculate the enrichment of species a in b (e.g., determination of the enrichment of labeled tracer a in unlabeled tracee b). There are conditions where the above relationship is altered. Patterson and Wolfe described a situation where R is a function (5) Lee, H. N.; Marshall, A. G. Anal. Chem. 2000, 72, 2256-60. (6) Gilker, C. D.; Pesola, G. R.; Matthews, D. E. Anal. Biochem. 1992, 205, 172-8.

of the concentration of analyte ions in the ion source and, therefore, a function of the amount of analyte injected into the GC/MS.7 Equations 1 and 2 presume that there is no relationship of amount of analyte injected and the measured ratio. Additional terms need to be added to correct for such a nonlinear relationship.8 Because such a relationship is detrimental, not beneficial, we assume that no method would be used where the ratio is significantly affected by sample amount, except when no alternative method exists. We can evaluate the noise of an ion-current ratio measurement if we can assess and predict the relative effect of the individual noise components to the total measurement. That is, the total 2 variance (σT ) of a mass spectrometric ion-current ratio measurement is equal to the sum of the variances of the individual noise components. Although there are too many individual noise sources to evaluate, we can group the total measurement noise (σT) into two different types: (1) signal-dependent noise that changes with the intensity of the ion-current signal (σS), and (2) constant noise sources (σC):

σT2 ) σS2 + σC2

(3)

2

The total variance (σT ) introduced by the measurement of an ion-current ratio can be simply calculated from replicate observations of the ion-current ratio:

σT2 )

n

(Ri - Rav)2

i)1

n-1

∑

(4)

where Ri is the ith observed ratio measurement, Rav is the mean of the ratio measurements, and n is the number of replicate measurements. To evaluate the contribution of the signal-dependent noise on the total ion-current ratio noise, we must identify the components affecting the ratio and determine their variance. Consider the case where the flow of sample into the mass spectrometer is constant, generating two ion currents (I) from species a and b. The ratio (R) of the two ion currents can be represented as a function of the total number of ions measured (N) at the detector during an observation time (t):

R)

Ia Na/ta ) Ib Nb/tb

(5)

where Na and Nb are the number of ions measured during the individual observation (dwell) times ta and tb for ion beams a and b, respectively. The signal dependent variance (σS2) of the ion-current ratio measurement is random and, therefore, dependent on Poisson’s statistics. Using propagation of errors, we can calculate the signal dependent noise for the ion-current ratio from the contribution of the individual ion beams: (7) Patterson, B. W.; Wolfe, R. R. Biol. Mass Spectrom. 1993, 22, 481-6. (8) Patterson, B. W.; Zhao, G. H.; Klein, S. Metabolism 1998, 47, 706-12.

Analytical Chemistry, Vol. 73, No. 13, July 1, 2001

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σS2 )

2

( )

( )

∂R 2 2 ∂R 2 2 σ + σ ∂Na a ∂Nb b

(6)

2

where σa and σb represent the variance of the respective ion beams. Equation 6 assumes that there is no error associated with the observation times.9 By solving the derivatives, eq 6 reduces to

[

σS2 ) R2

]

σa2

σb2

Na

Nb2

+ 2

(7)

Poisson’s statistics defines that, σ ) xN, which permits the further simplification of eq 7 to

[

σS2 ) R2

]

1 1 + N a Nb

(8)

Although eq 8 defines the signal-dependent noise for an ioncurrent ratio measurement, in GC/MS and LC/MS, the number of ions is not determined directly by the instrument data system. Rather, the signal for each ion is represented as an integrated peak area (Ai), usually in arbitrary units. The integrated peak areas are related to the measured ions by the relationship

Ai ) Rttl(N/ti)

(9)

where ti is the time spent measuring an individual ion current i, ttl is the total measurement cycle time (i.e., the time required to observe all selected masses and the time required to switch between ion beams), and R is a normalization factor that accounts for the relationship between ions collected and instrumentreported peak area. This normalization factor is constant for a given instrument under constant detector conditions (e.g., electron multiplier voltage). If only one ion beam is monitored or if the measurement is performed using array or multiple Faraday cup detection, the time values ttl and ti become equal and cancel from eq 9. Equation 9 can be used to substitute the number of ions measured with the integrated area peak in terms that can be determined easily from the data reported from the mass spectrometer’s data system: 2

σS ) R2Rttl

(

)

1 1 + Aata Abtb

(10)

where Aa and Ab are the integrated areas for species a and b, respectively. The variables ta, and tb are the times spent monitoring species a and b per measurement cycle (i.e., the dwell time) out of a total cycle measurement time of ttl. We can now rewrite our total noise equation (eq 1) and substitute eq 10 for our signaldependent noise to get (9) Schoeller, D. A.; Hayes, J. M. Anal. Chem. 1975, 47, 408-15.

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Analytical Chemistry, Vol. 73, No. 13, July 1, 2001

[ (

σT ) R2Rttl

)

1 1 2 + + σC Aata Abtb

]

1/2

(11)

This equation has terms that we know (ta, tb, and ttl) or can measure (R, Aa, Ab, and σT). Thus, if we can measure R, Aa, Ab, and σT for two or more points (where R ) Aa/Ab) that satisfy eq 11, the constants R and σC can be determined. Because R and σC are constants related to the noise contribution from signaldependent and constant noise sources, respectively, we can apply these constants to define the precision of an ion-current ratio measurement for the instrument and method used. These constants can also be used to predict the precision for other ratio measurements to be measured by the same system or to compare the performance of two different systems. Materials. Leucine and phenylalanine were purchased from Sigma Chemical. [1-13C]Leucine, [1,2-13C2]leucine, and [ring-2H5]phenylalanine were obtained from Mass Trace (Woburn, MA). [5,5,5-2H3]Leucine was purchased from MSD Isotopes (formerly from Montreal, Canada). Chemical and isotopic purities of each stable isotopically labeled compound were determined by gas chromatography/mass spectrometry (GC/MS). The reagents N-methyl-N-(tert-butyldimethylsilyl)trifluoroacetamide (MTBSTFA) and heptafluorobutyric anhydride were obtained from Regis (Morton Grove, IL). Overview of Experiments. Four different experiments were performed to assess the effect of different types of ion-current ratio measurements on the overall precision and to confirm that eq 11 accurately models the SIM-GC/MS ion-current ratio precision. Different analytes, derivatives, instruments, and ionization techniques were tested. All experiments were performed on either a Hewlett-Packard model HP5988A or model HP5971A gas chromatograph/mass spectrometer (Palo Alto, CA). The gas chromatographs in all experiments were operated with isothermal oven conditions optimized for each analyte being studied using a 20:1 injector split ratio. Unless otherwise noted, all measurements were made by SIM with dwell times of 50 ms for the two monitored ions (ta and tb) and a total cycle time (ttl) of 156 ms. Experiment 1. To both demonstrate the calculation of R and σC from eq 11 and confirm that the ion-current ratio precision is a function of the ion-current ratio, standards of natural leucine were prepared containing different known amounts of either [1-13C]leucine or [5,5,5-2H3]leucine. The [1-13C]leucine had a [1-13C]leucine/leucine mole ratio range of na/nb ) 0-8.6%, and the [5,5,52H ]leucine standards were made up with a [5,5,5-2H ]leucine/ 3 3 leucine mole ratio range of na/nb ) 0-3.0%. Aliquots of each standard solution were placed into conical-bottom reaction vials, and the samples were dried under a constant stream N2. The leucine was then derivatized by adding 100 µL of MTBSTFA/ acetonitrile (1:1 by volume) to each vial; the vials were capped and heated at 105 °C for 30 min to form the tert-butyldimethylsilyl derivatives of leucine (tBDMS-leucine). All ion-current ratios in experiment 1 were measured using the HP5988A GC/MS by electron ionization (EI) at 70 eV. An aliquot of each sample containing ∼2 nmol of tBDMS-leucine was injected 10 separate times, and the m/z ) 302 [M - 57]+ fragment ion (corresponding to the loss of a tert-butyl group) and related isotope ions were measured in all cases. To produce the data shown in Table 1, a single natural leucine sample was injected and measured multiple times. For the first

Table 1. Measurement of the [M + 1]/M and [M + 3]/M Ion-Current Ratios by SIM-GC/MS for an Unlabeled Leucine Samplea [M + 1]/M ratio injection

A302

R ) A303/A302

[M + 3]/M ratio A302b

R ) A305/A302

1 2 3 4 5 6 7 8 9 10

9 568 070 9 171 170 9 810 230 9 804 830 9 572 920 9 052 970 9 331 140 9 761 850 8 749 710 8 467 570

0.263 89 0.264 00 0.263 64 0.263 40 0.263 12 0.262 50 0.263 19 0.263 35 0.263 15 0.263 21

4 986 120 6 072 740 5 033 470 5 013 270 5 267 340 5 189 560 5 786 490 5 525 060 6 017 550 5 413 420

0.017 13 0.017 12 0.017 45 0.017 15 0.017 17 0.017 13 0.017 15 0.017 15 0.017 28 0.017 20

average σT

9 329 046

0.263 35 4.29 × 10-4

5 430 502

0.017 19 1.39 × 10-4

a A leucine standard was injected 10 times for measurement of the [M + 1]/M ratio and 10 times for measurement of the [M + 3]/M ratio as described in experiment 1. b The area values (A302) are presented for m/z ) 302. The values are in arbitrary units from the instrument data system. The σT term is the standard deviation computed from the ratio measurements for each group of measurements.

10 injections, m/z ) 302 and 303 were measured, the corresponding peak areas were integrated, and the [M + 1]/M ion-current ratio R ) A303/A302 was determined. For the second 10 injections, m/z ) 302 and 305 were measured, the respective peak areas were integrated, and the [M + 3]/M ion-current ratio R ) A305/ A302 was calculated. To produce the data shown in Figure 1, a series of unlabeled, [1-13C]leucine, and [5,5,5-2H3]leucine samples were measured. In this case, different pairs of ions were measured for the various samples. The ion-current ratios that were measured were [M + 1]/M (A303/A302), [M + 2]/M (A304/A302), [M + 3]/M (A305/A302), [M + 4]/M (A306/A302). When the unlabeled leucine standard was injected, the natural abundance ratio produced a range of ion current ratio values of [M + 1]/M ) 26.3%, [M + 2]/M ) 10.0%, [M + 3]/M ) 1.7%, and [M + 4]/M ) 0.3%. The enriched samples of [1-13C]- and [2H3]leucine increased these ratio values to provide a range of measured ion-current ratios from 0 to 33%. Experiment 2. To demonstrate that the precision of an ioncurrent ratio measurement varies predictably with signal intensity, 10 derivatives of unlabeled phenylalanine were prepared in different amounts of the amino acid. The samples were prepared as the tBDMS derivatives as described in experiment 1. The standards had final concentrations with a range of 0.5-7.1 nmol/ µl. The measurements were made by EI using the HP5988A GC/ MS with a constant electron multiplier voltage for all injections. A 1-µL aliquot of each derivatized tBDMS-phenylalanine sample was injected 10 separate times. The [M - 57]+ fragment ion of m/z ) 336 was monitored for the unlabeled tBDMS-phenylalanine along with the m/z ) 337 ion. The natural abundance ion-current ratio of R ) A337/A336 was calculated from the integrated areas for each measurement. Experiment 3. The ion-current ratio was measured by SIMGC/MS of 10 different standards to demonstrate that the ratio measurement precision can be assessed for a different instrument and that the assessment is independent of the analyte and ion measured. Standards of known mole ratios of [1-13C]leucine/

Figure 1. Effect of ion-current ratio (R) on the ion-current ratio precision. Standards of leucine enriched with varying amounts of [1-13C]leucine and [5,5,5-2H3]leucine were prepared as the tBDMS derivatives and measured by EI-GC/MS. Five ions of one fragment were measured (M, M + 1, M + 2, M + 3, and M + 4) and the ratios [M + 1]/M (circles), [M + 2]/M (triangles), [M + 3]/M (inverted triangles), and [M + 4]/M (diamonds) were measured in replicate for each sample (values displayed on the y-axis). The mean ratio for each sample was also determined (Rav, values displayed on the x-axis). The y-axis of the upper panel A plots the absolute deviation of each individual measurement (Ri) from the mean value of each sample (eq 12). The y-axis of the lower panel B plots the relative deviation of each measurement from the mean value of each sample (eq 13). The broken and solid lines are the theoretical 1σT and 2σT envelopes, respectively, calculated using eq 11.

leucine, [5,5,5-2H3]leucine/leucine, and [ring-2H5]phenylalanine/ phenylalanine were prepared in the range of na/nb ) 0-9%. Each standard was derivatized to form the tBDMS derivatives as described above. An aliquot of each sample containing ∼1 nmol of either tBDMS-leucine or tBDMS-phenylalanine was injected 10 separate times into the HP5971A GC/MS and measured by EI. The [M - 57]+ fragment ions m/z ) 336 and 341 were monitored for unlabeled and [ring-2H5]phenylalanine, respectively, and the [M - 57]+ fragment ions m/z ) 302 and 303 were monitored for unlabeled and [1-13C]leucine, respectively. In addition, m/z ) 200 and 203, corresponding to a loss of a COOtBDMS group, were monitored for unlabeled and [5,5,5-2H3]leucine, respectively. As with the previous experiments, the electron multiplier voltage was kept constant for all injections. The ion-current ratios of [M + Analytical Chemistry, Vol. 73, No. 13, July 1, 2001

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1]/M, [M + 3]/M, and [M + 5]/M for [1-13C]leucine, [2H3]leucine, and [2H5]phenylalanine standards, respectively, were calculated from the integrated areas of the monitored ions. As in experiment 1, the [M + 1]/M and [M + 3]/M ion-current ratio measurements for the unlabeled leucine standard were used to evaluate R and σC. These values were then used to predict σT. The predicted values of σT were then compared against the experimentally determined values for σT. Experiment 4. Standards of [1-13C]leucine and [5,5,5-2H3]leucine (0-3.0 mol % excess) from experiment 1 were remeasured for measurement of tracer enrichment detection precision. In addition, a different derivative and different ionization process was used to make the measurements. Standard samples were derivatized as the N-heptafluorobutyryl, n-propyl ester (HFBP) derivatives as described previously.10 Injections of ∼2 nmol of derivatized HFBP-leucine were made into the HP5988A GC/MS, operated using electron capture negative chemical ionization (NCI) with methane as the reagent gas. The [M - HF]- fragment ion was monitored at m/z ) 349 and 350 for unlabeled and [1-13C]leucine and at m/z ) 349 and 352 for unlabeled and [5,5,5-2H3]leucine. The two different tracer standards have different starting natural abundance ion-current ratios (Rb), corresponding to the [M + 1]/M and [M + 3]/M ratios. First, 10 replicate injections of natural leucine were made and the [M + 1]/M ion-current ratio was measured. Next, 10 injections were made and the [M + 3]/M ion-current ratio was measured. From these measurements, R and σC were determined as described above. Finally, replicate measurements of the [1-13C]- and [2H3]leucine-enriched samples were made and the mean ion-current ratios and standard deviations determined. The enriched sample enrichment precision measurements were then compared against the predicted precision measurements based upon measurement of the unenriched leucine sample evaluation of R and σC. Data Analysis. A key element to data analysis is the measurement of deviations of individual measurements around mean values for each sample measured. Deviations of individual measurements are presented as both absolute and relative deviations from the mean. The absolute deviation (∆Ri) of an individual ion-current ratio measurement (Ri) is expressed as

∆Ri ) (Ri - Rav) × 100

(12)

for the ith measurement, where Rav is the mean of the ion-current ratio measurements. The relative deviation (RDi) of the ith ioncurrent ratio measurement is the absolute deviation divided by the mean:

RDi )

∆Ri Ri ) -1 Rav Rav

(13)

The above calculations define the uncertainty or noise in a single ratio measurement. In most cases where the stable isotopically labeled compound is added to serve as an internal standard, only the one ratio measurement is required because the internal standard will contain multiple isotopes and the (10) Matthews, D. E.; Pesola, G.; Campbell, R. G. Am. J. Physiol. Endocrinol. Metab. 1990, 258, E948-56.

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contribution of the labeled material to the unlabeled ion will be small (Rb ≈ 0). To determine the amount of tracer enrichment present in a sample (i.e., defining the TTR of a sample from a stable isotope tracer study), the amount of natural abundance background has to be considered. In this case, two measurements are required to define the TTR1: (i) measurement of the ioncurrent ratio of a sample before the tracer was administered and (ii) measurement of the ion-current ratio of a sample during or after the tracer was administered. This two-measurement system is highlighted in eq 2 where na/nb is the TTR. When Rb is not negligible and must also be measured, then the na/nb mole ratio is the difference between two measurements (∆Ri ) Ri - Rb) and the error in the mole ratio or TTR measurement is equal to the error in ∆Ri (σ∆R): 2 + σT,i2 ]1/2 σ∆R ) [σT,0

(14)

where σT,0 and σT,i are the standard deviations of the ion-current ratio measurement for a sample prior to the administration of a stable isotopically labeled compound (Rb) and after the start of the tracer administration (Ri), respectively. RESULTS Determination of the Constants r and σC. The constants R and σC provide valuable information regarding the signal-dependent and constant noise sources, respectively. These constants can be easily calculated for a specific mass spectrometer from two or more points that satisfy eq 11. Data from the replicate measurement of two different ion-current ratios of tBDMS-leucine from experiment 1 are presented in Table 1. Some of the parameters in eq 11 are constants and are known (ta, tb, ttl). The ion-current integrated areas were measured for each sample (Aa, Ab) and the ion current ratio formed (R ) Aa/Ab). From a series of measurements (Table 1), σT can be computed for each sample and eq 11 solved for R and σC. This process was performed using a single sample and measurement of different ion-current ratios of that sample. In this example, the [M + 1]/M and [M + 3]/M ratio measurements were made. Using these two sets of ratio measurements, the constants R ) 1.63 and σC ) 5.28 × 10-5 were determined for the HP5988A GC/MS. These constants can then be used to predict σT for different ion-current ratios on the same mass spectrometer, to compare different mass spectrometers for ion-current ratio measurements or to evaluate the instrument’s performance over time. Effect of R on Ion-Current Ratio Precision. Several leucine standards containing varying amounts of [1-13C]- and [2H3]leucine were measured by EI-GC/MS. The ion current ratios for [M + 1]/M and [M + 3]/M were measured for these samples, and the data are displayed in Figure 1. The ratio data for each injection are plotted as both the absolute (top panel A) and relative deviations (lower panel B) versus the mean ion-current ratio (Rav) for each sample. The natural abundance [M + 1]/M ratio starts at 26.3% and the [M + 3]/M ratio starts at 0.3% for the unlabeled leucine standard, and these ratios increase as [1-13C]- and [2H3]leucine enrichments are added. Even with ∼10% [2H3]leucine added, the [M + 3]/M ratio is considerably lower than the starting natural abundance [M + 1]/M ratio. Using these two different tracers with different starting natural abundance ion-current ratios

Figure 2. Effect of sample size (ion-current intensity) on the precision of the ion-current ratio. Different amounts of phenylalanine were prepared as the tBDMS derivative, measured multiple times (N ) 67) by EI-GC/MS, and the [M + 1]/M ion-current ratio was measured. The x-axis shows the tBDMS-phenylalanine peak area from the [M - 57]+ fragment ion at m/z ) 366 (A336). The y-axis shows the absolute deviation of each ion current ratio measurement (Ri) from the mean of all measurements (Rav, eq 12). The broken and solid lines are the theoretical 1σT and 2σT envelopes, respectively, calculated using eq 11.

provided a wide range of measured enrichments in Figure 1 from near 0 to ∼33%. The values for R and σC obtained in Table 1 were used to calculate σT as a function of the ion-current ratio via eq 11. Contour lines for 1σT and 2σT were then inserted into Figure 1 as broken and solid lines, respectively. If eq 11 accurately models the noise of the ion-current ratio measurement, then 68% of the points in Figure 1 should fall within 1σT and 95% within 2σT. Experimentally, 125 of 175 observations (71.4%) lie within the 1σT contours, and 167 of the 175 points (95.4%) lie within the 2σT contours. The agreement of our experimental ion-current ratio measurements within the theoretical standard deviations demonstrates that eq 11 accurately predicts the precision of ion-current ratios on this mass spectrometer. Effect of Sample Size on Ion-Current Ratio Precision. Different amounts of the same unlabeled phenylalanine standard were prepared and measured, as described in experiment 2, to demonstrate the effect of the signal intensity on the ion-current ratio precision. The absolute deviation of the ion-current ratio for each measurement relative to the ion-current ratio of the entire group (Rav ) 29.3%) is shown in Figure 2. These deviations are plotted as a function of the measured integrated peak area, which represents signal intensity and the number of measured ions (eq 9). The broken and solid lines in Figure 2 represent the predicted deviations calculated from eq 12 for 1σT and 2σT, respectively. Experimentally, 46 of 67 observations (68.6%) lie within the 1σT contours while 62 of the 67 (92.5%) lie within the 2σT contours. Figure 2 shows good agreement between the measured and predicted errors in the ion current ratio as a function of signal intensity. The error assessment shown for phenylalanine was based upon measurements of a different compound, leucine, and different measured ions. These results show (i) that results from one

Figure 3. Comparison of measured and predicted ion-current ratio measurement precision of different amino acid standards. The standard deviations were both measured and predicted (based upon prior evaluation of the constants R and σC). The closed triangles, the closed circles (b), and open circles (O) represent the standard deviations of 10 replicate measurements of three different [1-13C]leucine-, five different [5,5,5-2H3]leucine-, and two different [ring-2H5]phenylalanine-enriched standards, respectively. A linear regression was measured using the predicted standard deviation (σT(pre)) as the dependent versus the measured standard deviation (σT(meas)). The regression line was σT(pre) ) 0.0009 ( 0.0019 + 0.999 ( 0.098σT(meas) and r2 ) 0.929.

measurement condition on a given instrument can be extrapolated to other measurement conditions and (ii) that our model accurately predicts the effect of the sample size (signal intensity) on the precision of an ion-current ratio measurement. However, it is important to remember that the constant R in eq 11 requires that the intensity of both ion currents used to calculate the ioncurrent ratio are within the linear “working” range of the measurement system. If one of the measurements is beyond the linear amplification range of either the electron multiplier or subsequent amplifiers, then the predicted precision will not accurately reflect the actual precision of the samples. Predicting Precision of a Different GC/MS. Measurements were also made on the HP5971 GC/MS system and R and σC determined as per Table 1 for the HP5988 GC/MS from a single leucine standard. The standard deviation from 10 measurements of the [M + 1]/M ratio and 10 measurements of the [M + 3]/M ratio of the same unlabeled leucine standard were used (individual values not shown) as the two points to satisfy eq 11. The values determined were R ) 0.16 and σC ) 4.18 × 10-5. These values from the single leucine sample were then used to predict the precision that the HP5971 would provide in measuring other labeled leucine and phenylalanine standard samples. These predictions were confirmed experimentally (experiment 3) by injecting 10 samples 10 times each into the HP5971 and determining the ion-current ratios and their standard deviations. In Figure 3 we show these measured standard deviations (σT(meas)) on the x-axis and plot the corresponding predicted standard deviations (σT(pre)) based upon the R and σC values on the y-axis. The predicted uncertainties are not significantly different from the experimentally determined uncertainties as demonstrated by the regression line having a slope not different from unity and an intercept not different from zero. Analytical Chemistry, Vol. 73, No. 13, July 1, 2001

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Figure 4. Precision of measurement of stable isotopically labeled tracers. Standards of similarly enriched [1-13C]leucine and [5,5,5-2H3]leucine were prepared and measured by NCI-GC/MS as described in experiment 4. The ion-current ratios of [M + 1]/M and [M + 3]/M were measured for the [1-13C]leucine and [5,5,5-2H3]leucine samples, respectively. Each sample was measured multiple times, and the relative standard deviation of the mean of each sample was determined and plotted as a function of the mole ratio (na/nb) of tracer enrichment for the [1-13C]leucine samples (O) and the [5,5,5-2H3]leucine samples (b). The R and σC values were determined separately from measurement of the [M + 1]/M and [M + 3]/M of a natural abundance leucine sample. The measurement precision (predicted relative standard deviations) based upon the R and σC values are shown as the solid and broken lines for [5,5,5-2H3]leucine and [1-13C]leucine, respectively.

Effect of Tracer Choice on Enrichment Detection Limits. A common belief that has not readily been proven is that lower tracer enrichments can be determined from ion-current ratios that have a lower natural abundance value. That is [M + 1]/M with a higher natural abundance background contribution will produce a higher uncertainty of measurement compared to [M + 3]/M. This concept is illustrated in eq 11 and can be seen in Figure 1A where the absolute deviations increase with increasing ion-current ratios. When stable isotopically labeled tracers are used for metabolic studies, the tracer enrichment (i.e., TTR) is measured as the difference in the ion-current ratio after tracer administration and the ion-current ratio measured from a sample taken before the tracer administration (eq 2). Under these circumstances, the precision includes uncertainties from both ion-current ratio terms (eq 14). Experiment 4 was conducted to use our method to examine the effect of natural abundance isotopes on the ion-current ratio measurement of labeled tracers. Two tracers with large differences in natural abundance background measurement were chosen: [1-13C]leucine with a higher [M + 1]/M natural ratio and [5,5,52H ]leucine with a much smaller [M + 3]/M ratio. Enriched 3 [1-13C]- and [2H3]leucine samples were measured above natural abundance in the range 0-3.5 mol % excess. Figure 4 shows the measured relative standard deviation as a function of the enrichment measurements. The [5,5,5-2H3]leucine measurements produced significantly lower relative standard deviations (higher precision) than the [1-13C]leucine measurements at low enrichments, but the results were comparable above ∼2 mol % excess tracer. 2982 Analytical Chemistry, Vol. 73, No. 13, July 1, 2001

The measurements presented in Figure 4 were performed using the HP5988 and negative chemical ionizationsnot EI as shown in the prior experiments. The R and σC determined for this system, using ratio measurements for [M + 1]/M and [M + 3]/M for a natural abundance leucine sample, were R ) 0.257 and σC ) 4.05 × 10-5. The σC value by NCI is similar to the σC reported in experiment 1 for the HP5988 operated in EI mode with a different leucine derivative, but the R for NCI is much smaller than the R for EI (R ) 1.63). As described above, R should be constant under constant detector conditions. The difference in R between the NCI and EI can be found in differences in the instrument detector gain during experiments 1 and 4. The electron multiplier voltage was decreased in experiment 4 to compensate for the increased signal intensity of the HFBP-leucine by NCI over tBDMS-leucine by EI on our HP5988. The decrease in detector gain produces a smaller signal intensity and proportional decrease in R (eq 9). The R and σC values determined from measurement of the natural abundance leucine alone were then used to predict the measurement precision for the labeled [2H3]- and [1-13C]leucine samples. These predicted lines are shown in Figure 4 and approximate the actual uncertainties of the labeled standard measurements. Figure 4 demonstrates two key points: (i) eq 11 can be evaluated to determine values for signal-dependent (R) and constant (σC) noise terms using a single unlabeled sample. Those measurements can then be used to predict the measurement precision of any tracer by that same measurement system without having to complete a laborious and time-consuming set of measurements. (ii) Figure 4 demonstrates that a small TTR can be measured with greater precision using multiply labeled tracers than singly labeled tracers but that this advantage disappears as the tracer enrichment approaches ∼2 mol % excess. DISCUSSION The use of selected ion monitoring for the measurement of ion-current ratios is a well-established technique for measuring both the levels of compounds relative to an internal standard for quantitation3,11,12 and the enrichment of an infused isotopically labeled tracer for in vivo kinetic analysis.13 To set up a method to measure mole ratios from mass spectrometer-derived ion-current ratios, the analyst chooses a characteristic ion from the mass spectrum that contains the atom or atoms that are labeled. This ion is usually the most intense ion in the spectrum. Next, the base isotope peak of that ion is monitored for the unlabeled compound (i.e., m/z ) M) and for the labeled compound that produces an “i” increase in mass (i.e., m/z ) M + i). The data system is set to step back and forth between these masses while recording the ion intensities at the detector.11 Although criteria for the selection of a fragment ion to maximize sensitivity of a single ion current in complex mixtures has been discussed and reviewed,3 very little has been reported on the instrument limitations of ion-current ratio measurements by SIM. In this report, we show that the ioncurrent ratio precision is predictable and dependent on the measured R and signal intensities (Aa and Ab) for a given instrument, derivative type, and ionization technique. (11) Sweeley, C. C.; Elliott, W. H.; Fries, I.; Ryhage, R. Anal. Chem. 1966, 38, 1549-53. (12) Hammer, C. G.; Holmstedt, B.; Ryhage, R. Anal. Biochem. 1968, 25, 53248. (13) Matthews, D. E.; Ben-Galim, E.; Bier, D. M. Anal. Chem. 1979, 51, 80-4.

Quantitation Using Labeled Internal Standards. Isotopically labeled analogues are regularly used as internal standards for quantitation of a range of compounds. Usually the internal standard is a deuterated analogue of the compound to be determined. This technique for quantitation is commonplace in most analytical mass spectrometry laboratories and is colloquially referred to as “isotope dilution mass spectrometry”. The technique requires that the measured ion-current ratio (R) increases proportionally with an increase in the mole ratio (na/ nb) of the unlabeled compound (na) to the deuterated internal standard (nb). The method proposed here makes it possible to assess the mass spectrometric noise terms associated with this mole ratio measurement for a given mass spectrometer and ionization conditions. Because we can usually control the amount of internal standard added to a sample, we have the ability to add an amount of internal standard that produces a measured mole ratio with the least amount of error. The least amount of error for a mole ratio measurement will occur when the relative deviation of the individual measurements about the mean is minimized. This condition is shown in the lower panel B of Figure 1. In this figure, we can see that the relative error is rapidly minimized when the ion current ratio is greater than ∼20%. Figure 1B shows a dramatic increase in the relative deviation as the ion-current ratio increases from below 10%. The data in this figure demonstrate that for this GC/MS instrument the internal standard should not be added in more than a 5-fold increase over the unlabeled compound to be measured if we wish to keep na/nb g 0.2 and nb e 5 na. Obviously, the greatest precision for the measurement of compound levels by isotope dilution mass spectrometry will be when the amount of internal standard is present in the same amount as the compound to be measured (i.e., R ≈1). However, the method we present allows for a more complete evaluation of a specific instrument from measurements of one sample alone. Those measurements will define the R and σC parameters, and these parameters can be used to predict the measurement of all other conditions or to construct anticipated confidence limits as shown in Figure 1. The evaluation of predicted error after determining R and σC is sensitive to the effects of sample amount and signal intensity. Equation 11 contains terms for the peak area of the measured ions that effect the uncertainty (σT) of the ion-current ratio measurement. Thus, the predicted lines for σT in Figure 1 are sensitive to the amount of material injected into the system. If 4 times less material were injected and measured, then σT would increase by a factor of 2 (eq 11). While this point is straightforward and is demonstrated in Figure 2, it has a more subtle effect upon defining the amount of internal standard that should be added to produce the best precision. To keep nb e 5na, the amount of labeled internal standard should be decreased as the amount of unlabeled analyte decreases. However, decreasing the amount of internal standard also decreases the measured peak area and causes σT to increase (Figure 2). The effect of sample amount enters into the evaluation of instrument precision via R and σC in eq 11. Once R and σC have been evaluated, eq 11 can be used to predict precision and the optimum amount of labeled internal standard for an assay without requiring extensive testing of sample sets of different amounts of analyte and internal standard.

Measurement of in Vivo Tracer Enrichment. Stable isotopically labeled tracers are routinely administered to animals and humans to measure their dilution in the body and assess in vivo kinetics of various metabolites and pathways.1,2 The measurement of in vivo kinetics requires measuring the ratio of the administered “tracer” to the endogenous “tracee” (i.e., the TTR ) na/nb).14,15 In most cases where a tracer is used, it must be measured from a fragment ion in the mass spectrometer that has an isotope peak of substantial natural abundance already present. Thus, tracer enrichments generally have to be measured as difference or “increase” in the ion-current ratio over the naturally abundant isotope distribution (i.e., we measure a ∆Ri ) Ri - Rb). Figure 1A shows that as the natural abundance background (Rb) increases, the uncertainty or absolute error in the ion-current ratio increases. It is this error that effects the ∆Ri measurement required for the tracer enrichment determination. The effect of a larger background (Rb) on the measurement of a TTR is illustrated in Figure 4. The relative error in the TTR measurement is considerably greater at low enrichments for measurement of [1-13C]leucine (where Rb ) 15.0%) than for measurement of [5,5,52H ]leucine (where R ) 0.14%). However, as the enrichment of 3 b tracer rises above ∼2 mol % excess, the errors for each tracer are similar. The method described here allows for a quick and easy determination of these tracer considerations from simple measurements of an unlabeled sample without requiring measurement of numerous samples of different tracers. Application of r and σC in Evaluating Instrument Performance. The direct comparison of different instruments for the measurement of ion-current ratios is not straightforward. Different commercially available instruments have both different instrumental designs and usually different data processing systems that make it difficult to assess the quantitative performance between different instruments. In addition, there are many factors that can effect an ion-current measurement by a mass spectrometer.4 We have shown that the error in an ion-current ratio measurement can be simplified to signal-dependent and constant noise sources. The signal-dependent noise is governed by ion statistics and, therefore, inversely related to the number of ions measured. Consequently, any ion-current measurement system can be thoroughly evaluated if the ionization efficiency and contribution of constant noise sources can be determined. The precision of an ion-current ratio measurement can be evaluated for any instrument using the variable R, which relates arbitrary area values from the mass spectrometer data system to the number of ions measured, and the constant σC that defines the constant noise sources. Therefore, after assessing R for a mass spectrometric measurement, eq 9 from above can be rearranged to solve for the number of ions measured (N) from any measured area (A): N ) A (t/ttl) /R, where t/ttl is the fraction of the cycle time spent collecting ions on a particular mass. The efficiency of the ion source can then be calculated from the number of ions measured and the amount of material injected onto the GC column. Furthermore, the constant σC can be used to directly compare constant noise sources between different instruments. Therefore, the constants R and σC can be used to quantitatively compare the performance of different mass spectrometers beyond predicting the relative (14) Bier, D. M. Eur. J. Pediatr. 1997, 156, S2-8. (15) Bier, D. M. Diabetes Metab. Rev. 1989, 5, 111-32.

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precision of an ion-current ratio measurement on the same instrument. CONCLUSIONS The precision of an ion-current ratio measurement of organic molecules by selected-ion-monitoring mass spectrometry is predictable and is dependent on the ion-current ratio and the total number of ions measured. The relative precision can be predicted and evaluated for different compounds with different ion-current ratios and signal intensities. When compound levels are tobe measured, the method and fragment ion should be chosen that produce the largest signal. In quantitation, the measured ioncurrent ratio is determined by the addition of the internal standard and, therefore, does not need to be considered in the selection of a method. However, in the measurement of a TTR, the ion-current ratio is fixed by the measurement method. In a tracer infusion study, the method used to measure the stable isotopically labeled

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compound needs to carefully consider (i) the natural abundance isotope background of the derivatized compound, (ii) fragment ions with different elemental compositions, and (iii) the number of labeled atoms in the tracer. Finally, we have presented an approach to evaluate methods of quantitation using stable isotopically labeled internal standards rapidly and simply from measurement of single samples and to compare methods across instrument platforms or measurement conditions. ACKNOWLEDGMENT This work was supported by National Institutes of Health grants DK-38429 and RR-00109.

Received for review January 10, 2001. Accepted April 17, 2001. AC010041T