Determining enrichments of tracers of glucose by mass spectrometry

Abstract

Provided is a method for determining, in a sample, enrichments of a first and a second stable-labeled tracer of a target substance including glucose, the first tracer and the second tracer having the same or similar chemical structure as the target substance, the method including: ionizing the first tracer, the second tracer and the target substance of the sample; measuring intensities of ions deriving from the target substance, the first tracer and the second tracer using a mass analyzer; calculating an enrichment of the first tracer from a first ratio of intensity of the ions deriving from the first tracer to the intensity of the ions deriving from the target substance employing a first calibration curve independent of enrichments of each of the second tracer; wherein the mass analyzer is operated so as to resolve an ion peak deriving from a tracer and having a width Δ(m/z) at half maximum peak height equal to or smaller than 1×10.sup.−2.

Claims

1. A method for determining, in a sample, enrichments of a first and at least one second stable-labeled tracer of at least one target substance including glucose, the first tracer and the second tracer being generated by isotopic or bioisosteric substitution in the target substance, the method comprising: ionizing the first tracer, the second tracer and the target substance of the sample; measuring intensities of ions deriving from the target substance, of ions deriving from the first tracer and of ions deriving from the second tracer using a high-resolution mass analyzer; calculating an enrichment of the first tracer from a first ratio of the intensity of the ions deriving from the first tracer to the intensity of the ions deriving from the target substance employing a first calibration curve being independent of enrichments of each of the at least one second tracer, wherein the high-resolution mass analyzer is operated so as to resolve an ion peak deriving from a tracer and having a width Δ(m/z) at half maximum peak height equal to or smaller than 1×10.sup.−2.

2. The method according to claim 1, further comprising: calculating an enrichment of the second tracer from a second ratio of the intensity of the ions deriving from the second tracer to the intensity of the ions deriving from the target substance employing a second calibration curve being independent of the enrichment of the first tracer.

3. The method according to claim 1, wherein the high-resolution mass analyzer is operated at a mass resolving power equal to or greater than 75000 when a .sup.13C-, .sup.2H-, and/or .sup.18O-labeled tracer of glucose is present in the sample, and equal to or greater than 200000 when a .sup.17O-labeled tracer of glucose is also present in the sample, wherein the mass resolving power is calculated as the quotient of the m/z value of 180 and the width of the ion peak at half maximum peak height.

4. The method according to claim 1, further comprising: at least partly separating of undesired substances contained in a raw sample by performing chromatography to obtain the sample.

5. The method according to claim 1, wherein a first mass value of the mass of the first tracer differs from a second mass value of the mass of the second tracer by between 2 mDa and 10 mDa.

6. The method according to claim 1, wherein the first calibration curve is representable by a first mathematical function that relates values of the first calibration ratios of ion intensities to enrichments of the first tracer.

7. The method according to claim 1, wherein the first calibration curve is completely independent of the enrichment of any of the at least one second tracer, wherein one of the following holds: the first tracer contains a .sup.13C-substitution and the at least one second tracer comprises at least one of: a .sup.2H- and/or .sup.17O- and/or .sup.18O-substitution the first tracer contains a .sup.2H-substitution and the at least one second tracer contains at least one of: a .sup.13C- and/or .sup.17O- and/or .sup.18O-substitution the first tracer contains a .sup.17O-substitution and the at least one second tracer contains at least one of: a .sup.13C- and/or .sup.2H- and/or .sup.18O-substitution and the first tracer contains a .sup.18O-substitution and the at least one second tracer contains at least one of: a .sup.13C- and/or .sup.2H- and/or .sup.17O-substitution.

8. The method according to claim 1, wherein the first calibration curve is practically independent of the enrichment of any of the at least one second tracer, wherein a nominal mass difference between the first tracer and the second tracer is at least 1 Da, wherein one of the following holds: the first tracer contains a .sup.2H-substitution and the at least one second tracer contains another .sup.2H-substitution, the first tracer contains a .sup.17O-substitution and the at least one second tracer contains another .sup.17O-substitution, the first tracer contains a .sup.18O-substitution and the at least one second tracer contains another .sup.18O-substitution.

9. The method according to claim 1, wherein the first tracer contains a first isotopic substitution including one of a .sup.2H-, .sup.17O-, .sup.13C-substitution, wherein a first mathematical function representing the first calibration curve is obtained by the following steps, if no other tracer containing the first isotopic substitution is present in the sample, or if the nominal mass difference between tracers containing the first isotopic substitution is at least 1 Da or 2 Da, if the first isotopic substitution is a .sup.13C-substitution: analyzing calibration samples containing known first enrichments of the first tracer using the high-resolution mass analyzer to obtain first calibration ratios; fitting a mathematical function to the known first enrichment and associated first calibration ratios, wherein the mathematical function is linear or has the following form:
TTR=a+b RI+c d.sup.RI where a, b, c, and d are fitting parameters, TTR is the first enrichment, and RI is the first calibration ratio.

10. The method according to claim 1, further comprising: resolving, in a mass spectrum, a first ion peak caused by the first tracer from a second ion peak caused by the second tracer; deriving the enrichment of the first tracer based on the first ion peak and an ion peak caused by the target substance; and deriving the enrichment of the second tracer molecule based on the second ion peak and the ion peak caused by the target substance.

11. The method according to claim 1, wherein the target substance includes at least one further target molecule, the method comprising: ionizing a further first tracer of the further target molecule and ionizing the further target molecule of the sample; measuring intensities of ions deriving from the further target molecule and of ions deriving from the further first tracer using of the high-resolution mass analyzer; calculating an enrichment of the further first tracer from a further first ratio of the intensity of the ions deriving from the further first tracer to the intensity of the ions deriving from the further target molecule employing a further first calibration curve being independent of an enrichment of any other tracer of the further target molecule.

12. The method according to claim 1, wherein at least one of the target substance and the further target molecule comprises one of: a carbohydrate; a carbohydrate derivative; a sugar alcohol; a ketone body; a lipid; an alcohol; water.

13. The method according to claim 1, wherein at least one of a tracer of the target substance and a tracer of the further target molecule is added as an internal standard to the sample and, by taking the resulting tracer enrichment level and the known amount of added tracer, at least one of the concentration of the target substance and the concentration of the further target molecule in the sample are calculated.

14. The method according to claim 1, wherein a number of ions deriving from the tracers and entering the mass analyzer is maintained below the coalescence threshold by adjusting the mass scan window to a m/z range of one of 179 to 186 and 100 to 350 and lowering the automatic gain control to a value of one of between 10.sup.4 and 10.sup.6 and between 10.sup.3 and 10.sup.4.

15. The method according to claim 1, wherein an intensity of the ion peak deriving from the target substance is maintained above a threshold level of 1.0×10.sup.7 arbitrary units by at least one of increasing the amount of sample injected into the chromatograph to a value between 1 and 3 μl, and decreasing the mass scan window to a m/z range of one of 100 to 350 and of 179 to 186, and increasing the automatic gain control to a value of one of between 10.sup.3 and 10.sup.4 and between 10.sup.4 and 10.sup.6.

16. The method according to claim 7, wherein the first tracer and the second tracer have a same nominal mass.

17. The method according to claim 13, wherein the carbohydrate is one of a monosaccharide, a disaccharide, an oligosaccharide, a polysaccharide.

18. The method according to claim 1, wherein the target substance is glucose.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 schematically illustrates a system for determining metabolism of a target substance according to an embodiment of the present invention;

(2) FIG. 2 illustrates an example of an elution profile of a liquid chromatograph used in embodiments of the present invention;

(3) FIGS. 3A and 3B illustrate exemplary mass spectra considered in embodiments of the present invention;

(4) FIGS. 4A, 4B, 4C, 5A, 5B, 5C and 6A, 6B, and 6C illustrate examples of calibration curves as used in embodiments according to the present invention; and

(5) FIGS. 7A, 7B and 7C illustrate examples of statistical procedures for validation of the method considered in embodiments of the present invention.

DETAILED DESCRIPTION OF ILLUSTRATED EMBODIMENTS

(6) The system 1 for determining metabolism of a target substance, in particular glucose, illustrated schematically in FIG. 1, comprises a set, according to an embodiment of the present invention, of at least two tracers of the target substance which are contained in a sample 3. Further, the system 1 comprises a liquid chromatograph 5 to which the sample 3 is applied. The system 1 further comprises a high-resolution mass spectrometry apparatus 7 to which one or more fractions as derived using the chromatograph 5 are supplied or loaded.

(7) The liquid chromatograph 5 comprises an ultra-performance liquid chromatography BEH amide column (UPLC BEH amide column) equipped with a column in-line filter. For determination of the enrichment of tracers of glucose (an exemplary target substance), a sample volume of 4 μl from the sample 3 is injected and isocratic elution is performed with acetonitrile/H.sub.2O (8:2; v/v) containing 0.1 vol.-% of ammonium hydroxide solution as additive at a flow rate of 150 μL/min for 15 minutes.

(8) The mass spectrometry apparatus 7 is an Orbitrap mass spectrometer that is connected to the liquid chromatograph 5 through a heated-electrospray ionization interface. For determination of the enrichment of tracers of the exemplary target substance (i.e., glucose), the heated-electrospray ionization interface is operated in the negative ionization mode using the following electrospray parameters: source voltage, 3.8 kV; a source heater temperature, 250° C.; sheath, auxiliary and sweep gas, 30, 12 and 1 arbitrary units, respectively; capillary temperature, 300° C. Thereby, the Orbitrap mass analyzer 7 is operated in full scan mode at a target resolution of 100,000 with a scan window of m/z 100-350. Automatic gain control is set to allow 10.sup.5 ions to enter the mass analyzer. Using the water loss of monoisotopic glucose (m/z 161.0455) as lock mass, deprotonated ions of glucose and sorbitol/mannitol are then monitored at mass-to-charge values as given in Table 1 below. The integration of the observed ion peaks is performed using a software tool.

(9) TABLE-US-00001 TABLE 1 Tracers of Glucose as well as Natural Abundance & Exact Mass of Stable Isotopologues of Glucose Natural Nominal Mass Tracers of Glucose Isotopologues of Abundance Mass Exact Mass (Da) Difference No. Type Glucose.sup.a (%).sup.b (Da) M [M − H].sup.− (mDa).sup.c .sup.12C.sub.6.sup.1H.sub.12.sup.16O.sub.6 100.00000 180 180.06339 179.05611 1 [1-.sup.13C.sub.1]glucose .sup.13C.sub.1.sup.12C.sub.5.sup.1H.sub.12.sup.16O.sub.6 6.48944 181 181.06674 180.05947 2.922 .sup.12C.sub.6.sup.1H.sub.12.sup.17O.sub.1.sup.16O.sub.5 0.22856 181 181.06761 180.06033 2.060 2 [1-.sup.2H.sub.1]glucose .sup.12C.sub.6.sup.2H.sub.1.sup.1H.sub.11.sup.16O.sub.6 0.13802 181 181.06966 180.06239 0.000 .sup.12C.sub.6.sup.1H.sub.12.sup.18O.sub.1.sup.16O.sub.5 1.23300 182 182.06763 181.06036 8.308 3 [1,6-.sup.13C.sub.2]glucose .sup.13C.sub.2.sup.12C.sub.4.sup.1H.sub.12.sup.16O.sub.6 0.17547 182 182.07010 181.06282 5.844 .sup.13C.sub.1.sup.12C.sub.5.sup.1H.sub.12.sup.17O.sub.1.sup.16O.sub.5 0.01483 182 182.07096 181.06368 4.982 .sup.12C.sub.6.sup.1H.sub.12.sup.17O.sub.2.sup.16O.sub.4 0.00022 182 182.07182 181.06455 4.119 .sup.13C.sub.1.sup.12C.sub.5.sup.2H.sub.1.sup.1H.sub.11.sup.16O.sub.6 0.00896 182 182.07302 181.06574 2.922 .sup.12C.sub.6.sup.2H.sub.1.sup.1H.sub.11.sup.17O.sub.1.sup.16O.sub.5 0.00032 182 182.07388 181.06661 2.060 4 [6,6-.sup.2H.sub.2]glucose .sup.12C.sub.6.sup.2H.sub.2.sup.1H.sub.10.sup.16O.sub.6 0.00009 182 182.07594 181.06867 0.000 .sup.12C.sub.6.sup.1H.sub.14.sup.16O.sub.6 .sup.d n.a. 182.07904 181.07176 3.097 5 [U-.sup.13C.sub.6]glucose .sup.13C.sub.61H1.sub.2.sup.16O.sub.6 <0.00001 186 186.08352 185.07624 .sup.aIsotopologues used as tracers are underlined. .sup.bRelative to monoisotopic glucose. .sup.cDifference to the ion mass of [.sup.12C.sub.6.sup.2H.sub.1.sup.1H.sub.11.sup.16O.sub.6] or [.sup.12C.sub.6.sup.2H.sub.1.sup.1H.sub.10.sup.16O.sub.6]. .sup.d Monoisotropic sorbitol and mannitol

(10) Application of the sample 3 containing the at least two tracers of the target substance results in an elution profile 9 from which individual fractions may be transferred to the mass spectrometry apparatus 7. For one or more fractions eluting from the chromatograph 5, the high-resolution mass spectrometry apparatus 7 determines a mass spectrum 11 wherein the ionized constituents of the respective fraction are separated according to their mass-to-charge values.

(11) FIG. 2 illustrates an example of elution profile 9 as obtained after injecting 5 μg/ml of glucose, mannose, and galactose as well as 100 μg/ml of glucose into the chromatograph 5. Thereby, the abscissa 13 denotes the time in minutes, while the ordinate 15 denotes the intensity of the fractions eluting from the column contained in the chromatograph 5. The elution profile 9 comprises a number of peaks 17, 19, 21 and 23. In particular, the peak 17 corresponds to fructose, the peak 19 corresponds to mannose, the peak 21 corresponds to glucose and the peak 23 corresponds to galactose. Fructose, mannose, and galactose have the same elemental composition and mass as glucose (hexoses) and, therefore, cannot be separated from each other using the mass spectrometry apparatus 7 alone. As can be appreciated from the liquid chromatography elution profile 9 illustrated in FIG. 2, fructose and mannose are completely resolved from glucose, but glucose and galactose are only partially resolved on the column. However, since galactose may most often be present in negligible concentrations in the sample 3, the determination of glucose tracer enrichments may not be affected by an incomplete separation of glucose and galactose.

(12) Thus, fractions containing the peak 21 are then loaded into the mass spectrometry apparatus 7 to determine levels of at least a first and a second tracer contained within the sample 3. Besides the naturally occurring isotopologues of glucose (i.e., isotopologues of the exemplary target substance), the sample 3 may also contain tracers of glucose, for example, those listed in Table 1, in particular combinations thereof. Since the chemical properties of the listed tracers are the same as those of the isotopologues of glucose, the tracers are also comprised in the peak 21. Fractions containing the peak 21 are then transferred to the mass spectrometry apparatus 7 to determine enrichments of at least a first and a second tracer contained within the sample 3.

(13) The tracers listed in Table 1 and labeled as tracer number 1 to tracer number 5 may be present in the sample in particular combinations thereof. As can be seen, these tracers contain at least one .sup.13C-, or .sup.2H-substitution in specific carbon positions. Tracer 1 contains one .sup.13C-substitution in the first carbon position, whereas tracer 2 contains exactly one .sup.2H-substitution in the first carbon position. Furthermore, tracer 3 contains two .sup.13C-substitutions, one in the first and one in the sixth carbon position, and tracer 4 contains two .sup.2H-substitutions, both in the sixth carbon position. Finally, tracer 5 contains .sup.13C-substitutions in all six carbon positions of the tracer molecule.

(14) As can be taken from Table 1, the most abundant naturally occurring isotopologue of (unlabeled) glucose has a nominal mass of 180 Da. Most abundant isotopologues of the tracer 1 and 2 have a nominal mass of 181 Da, the most abundant isotopologues of the tracer 3 and 4 have a nominal mass of 182 Da and the most abundant isotopologue of tracer 5 has a nominal mass of 186 Da. Although the isotopologues of tracer 1 and 2 have the same nominal mass, they may be resolved using the high-resolution mass spectrometry apparatus 7. The same holds for the isotopologues of tracer 3 and 4.

(15) FIGS. 3A and 3B show high-resolution negative-ion mass spectra 11a and 11b acquired using the Orbitrap Velos mass analyzer 7 illustrated in FIG. 1. Thereby, the ordinates 25 indicate the relative ion intensity, while the abscissas 27 indicate the mass-to-charge (m/z) values.

(16) The mass spectrum 11a, illustrated in FIG. 3A, was recorded from a blank human blood plasma sample containing naturally abundant levels of glucose isotopologues, while the mass spectrum 11b, shown in FIG. 3B, was recorded from a human blood sample that contained the tracer 2, 3, 4 and 5 at enrichment levels of 2%. Insets in FIGS. 3A and 3B show magnified views of the m/z-ranges containing the ion peaks arising from the isotopologues of natural glucose and of tracers 2, 3, 4 and 5. Also shown are the isotopic composition and the exact m/z-value of the individual ion peaks arising from the isotopologues of the natural glucose and the tracers. The mass spectra 11a and 11b were acquired with a resolution or resolving power exceeding 175,000 (defined at m/z 180).

(17) The ion peak 29 in FIGS. 3A and 3B arises from the most abundant naturally occurring isotopologue of glucose. Furthermore, ion peak 31, which has a relative intensity of about 6.45%, arises from the .sup.13C-containing, second most abundant naturally occurring isotopologue of glucose (i.e., .sup.13C.sub.1.sup.12C.sub.5.sup.1H.sub.12.sup.16O.sub.6). Since tracer 1 contains one .sup.13C-substitution (i.e., [1-.sup.13C]glucose), ions arising from the most abundant isotopologue of tracer 1 will have exactly the same m/z value as the ions of peak 31 and, hence, will contribute to this ion peak. The ion peak 33 in the mass spectrum 11b arises from the most abundant isotopologue of the singly .sup.2H-labeled tracer 2. As can be seen, ions of this peak and ions of peak 31, which may arise from the singly .sup.13C-labeled tracer 1 and the second most abundant naturally occurring isotopologue of glucose, can be distinguished from each other. Importantly this distinction can be achieved despite the very small mass difference between the ions of peak 31 and 33 (i.e., 2.922 mDa, see Table 1). Thus, enrichments of the singly .sup.13C-labeled tracer 1 and the singly .sup.2H-labeled tracer 2 can be determined independently of one another, since the ion peaks associated with these tracers (i.e., peaks 31 and 33) can be completely distinguished from one another using the high-resolution mass analyzer 7. Furthermore, ion peak 35 in mass spectra 11a, 11b arises from the .sup.18O-containing, third most abundant naturally occurring isotopologue (i.e., .sup.12C.sub.6.sup.1H.sub.12.sup.18O.sub.1.sup.16O.sub.5 with a natural abundance of 1.23%). Ion peak 37 arises from the most abundant isotopologue of the doubly .sup.13C-labeled tracer 3 and from the .sup.13C-containing, less abundant naturally occurring isotopologue of glucose (i.e., .sup.13C.sub.2.sup.12C.sub.5.sup.1H.sub.12.sup.16O.sub.6 with a natural abundance of 0.18%). Ion peak 39 in the mass spectrum 11b arises from the most abundant isotopologue of the doubly .sup.2H-labeled tracer 4. Again, ions of this peak and ions of peak 37 can be distinguished from each other, despite the very small mass difference between them (i.e., 5.8 mDa, see Table 1). Therefore, enrichments of the doubly .sup.13C-labeled tracer 3 and the doubly .sup.2H-labeled tracer 4 can also be determined independently of one another, since the ion peaks associated with these tracers (i.e., peaks 37 and 39) can be completely distinguished from one another using the high-resolution mass spectrometry apparatus 7, Finally, the ion peak 41 in mass spectrum 11b arises from the most abundant isotopologue of tracer 5 incorporating six .sup.13C-substitutions.

(18) In the sample, different tracer combinations according to embodiments of the present invention may be present. For example, tracer 2, 4, and 5 may be concurrently present in the sample. For this combination, termed triple-tracer combination 1, calibration curves are illustrated in FIGS. 4A, 4B and 4C. Furthermore, calibration curves for another tracer combination, termed triple-tracer combination 2 and comprising tracer, 2, 4 and 3, are illustrated in FIGS. 5A, 5B and 5C. Moreover, calibration curves for a third tracer combination, termed triple-tracer combination 3 and comprising tracer 1, 4, and 5, are illustrated in FIGS. 6A, 6B and 6C.

(19) In FIGS. 4A, 4B, 4C, 5A, 5B, 5C and 6A, 6B, 6C, abscissas 43 denote the relative ion intensity (RI) or ion intensity ratio (calculated as the intensity of ions deriving from the respective tracer divided by the intensity of ions deriving from the tracee, i.e., unlabeled glucose), while ordinates 45 denote the tracer enrichment (expressed as the tracer-to-tracee ratio TTR). Furthermore, the circles, diamonds and triangles shown in the panels of FIGS. 4 to 6 denote the experimental data points obtained from the analysis of the calibration samples. In addition, also shown are fitting parameters of the mathematical representation of the calibration curves, insets with enlarged views of curve fits in the enrichment range from 0 to 2%, and the uncertainty in the TTR-determination (expressed as the one-sided lower and upper 95%-confidence intervals; 95%-CI) for the case that for a sample with unknown enrichments, the mean of the results of duplicative relative ion intensity measurements is used.

(20) FIGS. 4A, 4B and 4C illustrate the calibration curves 47, 49, 51 obtained for the tracer 2, 4, and 5, respectively. Furthermore, FIGS. 5A, 5B and 5C depict the calibration curves 53, 55, 57 obtained from the tracer 2, 4, and 3, respectively, and FIGS. 6A, 6B and 6C depict the calibration curves 59, 61 and 63 obtained for the tracer 1, 4 and 5, respectively.

(21) It can be well appreciated from the calibration data points (i.e., circles, triangles, and diamonds) plotted in FIGS. 4 to 6 that in all cases a linear relationship between TTR and RI values exists for TTR values larger than ˜1%. However, in the TTR range between 0 and ˜1%, deviations from linearity occur in all but one of the plots, the exception being the plot for tracer 1 (i.e., [1-.sup.13C.sub.1]glucose in FIG. 6A). Therefore, to obtain the calibration curve 47, 49, 51, 53, 55, 57, 61 and 63, the above-defined linear-exponential function (i.e., TTR=a+b RI+c d RI) was fit to the calibration data for the respective tracer 2, 4, 5, 2, 4, 3, 4, and 5, whereas to obtain calibration curve 59, the parameter values of the exponential component of the linear exponential function were set to 0 and only its linear component was fit to the calibration data for tracer 1. The calibration curve 47, 49, 51, 53, 55, 57, 59, 61 and 63 are, thus, represented by the above-defined linear-exponential function together with the obtained fitting parameter values given in the panels of FIGS. 4 to 6.

(22) The calibration data illustrated in FIGS. 4 to 6 were obtained by analyzing a set of 12 standards ranging in the TTR values from 0 to 15% (i.e., 0, 0.25, 0.5, 0.75, 1, 1.5, 2, 4, 6, 8, 10, 15%). This set of calibration standards was prepared for each of the three triple-tracer combinations as described above. To calculate the RI values (i.e., the relative intensity values), the ion peak intensity arising from the tracer (e.g., intensity of the peak 33 for the tracer 2 in FIG. 3B) is divided by the ion peak intensity arising from the tracee (e.g., the intensity of the peak 29 in FIG. 3A or FIG. 3B). To fit the linear-exponential function to the calibration data and to get the numerical values of the (unknown) fitting parameters, a nonlinear least-squares technique (i.e. Levenberg-Marquadt method), that incorporated the above-described inverse effective variance weighting, was applied. However, to perform the inverse effective variance weighting, the uncertainty in the RI measurement (expressed as variance, σ.sub.RIi.sup.2, or coefficient of variation, CV) has to be known. Therefore, prior to the curve fitting, the uncertainty in the RI measurement was experimentally determined by analyzing replicates of human plasma samples enriched with known amounts of the tracers. To prepare the replicates, a series of 13 human plasma samples ranging in the TTR values from 0 to 15% (i.e., 0, 0.1, 0.2, 0.3, 0.4, 0.5, 1, 2, 4, 6, 8, 10, 15%) was first produced for each triple-tracer combination as described above for calibration standards. Afterwards, each plasma sample was aliquoted, and 10 aliquots of each sample were purified and analyzed. Measures of uncertainty (σ.sub.RIi.sup.2, CV) were then calculated from the obtained RI values. Results of this uncertainty evaluation for the individual tracers are shown in Table 2.

(23) TABLE-US-00002 TABLE 2 Uncertainty Values Obtained for Relative Ion Intensity Measurements CV for Measuring Relative Ion Intensity (%).sup.a,b TTR-Level [1-.sup.2H.sub.1] [6,6-.sup.2H.sub.2] [1-.sup.13C.sub.1] [1,6-.sup.13C.sub.2] [U-.sup.13C.sub.6] (%) glucose glucose glucose glucose glucose 15 2.1 1.5 1.9 1.5 2.1 10 2.7 2.1 1.8 1.4 1.7 8 2.3 1.9 2.1 1.4 1.8 6 2.5 1.6 2.1 1.7 1.9 4 3.8 2.9 1.2 3.4 2.0 2 5.4 4.1 1.7 3.3 2.9 1 12.1 8.1 1.3 7.5 5.9 0.5 12.3 9.8 1.8 3.0 10.6 0.4 11.5 11.0 1.7 7.5 13.6 0.3 25.1 10.8 2.0 7.1 10.9 0.2 23.1 19.6 2.1 8.0 30.3 0.1 34.7 34.9 2.1 18.2 35.0 0 33.1 N/D 1.8 14.7 N/D .sup.aCV . . . coefficient of variation defined as: standard deviation/mean × 100; .sup.bN/D . . . not defined (CV is not defined if sample mean is zero);

(24) To assess the uncertainty associated with the determination of the fitting parameters, a Monte Carlo simulation was performed. In this simulation, 5000 synthetic data sets were generated for each calibration data set by randomly drawing new RI values from Gaussian distributions with the experimentally determined standard deviations (i.e., σ.sub.RIi.sup.2 values obtained for the 12 enrichment levels of a set) and locations (i.e., means of the triplicate RI values observed at the 12 enrichment levels of a set). Each synthetic data set was then fit with the linear-exponential function, and the 5000 values thus obtained for each fitting parameter were used to calculate measures of location (mean.sub.MC) and uncertainty (SD.sub.MC). Results of the assessment of the uncertainty associated with the determination of the fitting parameters are shown in Table 3.

(25) TABLE-US-00003 TABLE 3 Parameter Results Obtained From Fitting the Linear-Exponential Function to Calibration Data Sets Triple Glucose Combination Linear-Exponential Function Parameters (mean.sub.MC, SD.sub.MC).sup.a,b Tracer (TC) .sup.a .sup.b .sup.c .sup.d [1-.sup.2H.sub.1]glucose TC 1   0.702 (0.064) 0.969 (0.010) −0.872 (0.068) 0.04656 (0.05307) TC 2   0.695 (0.038) 0.959 (0.009) −0.842 (0.069) 0.05928 (0.02954) [6,6-.sup.2H.sub.2]glucose TC 1   0.545 (0.038) 1.002 (0.007) −0.548 (0.038) 0.01062 (0.00755) TC 2   0.540 (0.020) 1.001 (0.005) −0.545 (0.020) 0.01426 (0.00599) TC 3   0.541 (0.025) 0.993 (0.007) −0.545 (0.025) 0.01244 (0.00643) [1-.sup.13C.sub.1]glucose TC 3 −6.428 (0.083) 0.984 (0.010) [1,6-.sup.13C.sub.2]glucose TC 2   0.358 (0.024) 0.968 (0.006) −0.515 (0.027) 0.01952 (0.00872) [U-.sup.13C.sub.6]glucose TC 1   0.344 (0.017) 0.949 (0.005) −0.350 (0.017) 0.00099 (0.00125) TC 2   0.358 (0.016) 0.941 (0.006) −0.365 (0.017) 0.00416 (0.00344) .sup.aShown are means and standard deviations of the parameter's frequency distributions obtained by applying the Monte Carlo method; .sup.bNo significant differences were found between parameter values obtained for calibration sets with low tracee concentration (i.e., sets prepared from plasma pool 2; upper part) and those obtained for calibration sets with high tracee concentration (i.e., sets prepared from plasma pool 3; bottom part);

(26) FIGS. 7A, 7B and 7C illustrate further statistical procedures for the validation of the method considered in embodiments of the present invention. To compare the fitting parameter values obtained for the individual calibration sets with one another (e.g., parameters obtained for triple-tracer combination 1 with those obtained for triple-tracer combination 2), the z statistic (z=δ/σ.sub.δ) was used in which the mean of the difference between the parameters obtained for the combination 1 and 2, δ, as well as the standard deviation of this difference, σ.sub.δ, were calculated from the Monte Carlo simulation results. Any z value whose absolute value was less than 1.96 resulted in the acceptance of the null hypothesis that δ=0. A representative example of the comparison of fitting parameters using the z statistic is shown in FIG. 7A.

(27) To assess the linear ranges of the method, one-sided lower and upper 95%-CI for linear-exponential function fits were calculated for each tracer by determining the 5 and 95 percentile values from the frequency distribution of the 5000 calibration curve fits obtained for each tracer in a triple combination. These 95%-CI values were compared to those derived from the frequency distribution of curve fits obtained by using the linear part of the linear-exponential function only (i.e., terms containing parameter a and b). The lower bound of the linear range of the enrichment determination was then determined for each tracer as the point where the lower 95%-prediction band obtained for the linear curve fits crosses the upper 95%-prediction band obtained for the linear-exponential curve fits. A representative example of the determination of the linear range is shown in FIG. 7B. Results of the assessment of the linear ranges of the calibration curves for the individual tracers are shown in Table 4.

(28) TABLE-US-00004 TABLE 4 Limits of Detection and Linear Ranges Glucose Limit of Lower Bound of Tracer Detection (%) Linear Range (%) [1-.sup.2H.sub.1]glucose 0.200 1.26 [6,6-.sup.2H.sub.2]glucose 0.037 0.99 [1-.sup.13C.sub.1]glucose 0.310 0.00 [1,6-.sup.13C.sub.2]glucose 0.071 0.87 [U-.sup.13C.sub.6]glucose 0.040 0.63

(29) To assess the uncertainty associated with the TTR determination when it is based on the use of the mean of the results of duplicate RI measurements, a second Monte Carlo simulation was performed in which 1000 new RI values were generated for enrichment levels of 0, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5, 0.75, 1.0, 1.5, 2, 4, 6, 8, 10, and 15% by drawing random samples from Gaussian distributions centered at locations equal to the means of the observed RI values and with standard deviations equal to the obtained σ.sub.RIi values divided by √{square root over (2)}. Following this, for a given calibration set, the obtained RI values and the corresponding 5000 calibration curve fits generated as described above were used to calculate 5×10.sup.6 TTR values for each enrichment level. The CV and the one-sided lower and upper 95%-CI for the TTR determination were then calculated from the frequency distribution of the 5×10.sup.6 TTR values obtained for each enrichment level. Results of the assessment of the uncertainty associated with the TTR determination for the individual tracers are shown in Table 5 and in FIGS. 4 to 6.

(30) TABLE-US-00005 TABLE 5 Uncertainty Values Obtained for Determination of Tracer Enrichments CV for Determining Tracer Enrichment (%).sup.a,b,c,d TTR-Level [1-.sup.2H.sub.1] [6,6-.sup.2H.sub.2] [1-.sup.13C.sub.1] [1,6-.sup.13C.sub.2] [U-.sup.13C.sub.6] (%) glucose glucose glucose glucose glucose 15  1.6  1.1  2.1  1.1  1.5 10  2.0  1.4  2.2  1.1  1.2 8  1.6  1.3  2.7  1.0  1.3 6  1.7  1.0  3.0  1.3  1.3 4  2.3  1.8  2.3  2.2  1.4 2  3.0  2.3  5.0  2.2  1.8 1  6.8  3.7  7.8  4.2  3.2 0.5  9.9  6.1 17.1  2.4  5.8 0.4 10.6  7.3 22.5  5.8  8.2 0.3 24.7  7.8 32.4  6.4  8.1 0.2 29.8 13.5 50.1  9.4 20.2 0.1 71.4 25.4 93.4 30.3 25.4 0 N/D N/D N/D N/D N/D .sup.aCV . . . coefficient of variation defined as: standard deviation/mean × 100; .sup.bN/D . . . not defined (CV is not defined if sample mean is zero); .sup.cCalculated for the case when the mean of duplicate RI measurements are used for the TTR determination; .sup.dCVs for enrichment levels that are equal or close to the LOD levels are underlined;

(31) From the obtained 95%-CI values, the lower limits of detection (LOD) were calculated for each tracer by employing the procedure graphically illustrated in FIG. 7C. It involves the drawing of a horizontal line from the lower end of the upper 95%-prediction band to the lower 95%-prediction band, and the adding of a vertical line at the point where the horizontal line crosses the lower 95%-prediction band. The obtained intersection point on the fitted linear-exponential curve is then regarded as the LOD. Results of the assessment of the LOD for the individual tracers are shown in Table 4.

(32) The samples used according to embodiments of the present invention are not necessarily of human origin.

(33) In other embodiments, the sample derives from human blood, in particular plasma of human blood. According to these embodiments, also a method for determining metabolism of a target substance, including glucose, by high-resolution mass spectrometry may be provided. Thereby, the method may comprise administering at least one tracer molecule to a living organism, each one of the at least one tracer molecule having a chemical structure and an elemental composition of the target substance. The method may further comprise extracting at least one sample from a body fluid of the living organism and analyzing the at least one sample using high-resolution mass spectrometry, to detect an enrichment of the at least one tracer molecule in the sample. In particular, more than one tracer molecule may have been administered and more than one tracer molecule may then be analyzed to detect the respective enrichment. One or more of the tracer molecules may have been supplied to a blood stream of the living organism and one or more of the tracer molecules may have been supplied to a digestive tract of the living organism. The enrichment of one or more tracer molecules may be determined in dependence of time elapsed after administering the respective target molecules to the living organism. However, the method for determining the enrichments of the tracers may also be performed without the sample being of human origin.