Anal. Chem. 2001, 73, 715-719
Estimating the Precision of Exact Mass Measurements on an Orthogonal Time-of-Flight Mass Spectrometer Karl F. Blom
Experimental Station, DuPont Pharmaceutical Company, P.O. Box 80500, Wilmington, Delaware 19880-0500
The combination of orthogonal TOF/ESI MS exact mass measurement and on-line chromatography represents a powerful analytical tool for identifying unknown components in complex mixtures and is being widely utilized. The precision of these mass data is often incorrectly estimated as the precision or mean deviation obtained for reference standards under standard conditions. But, the precision of a mass measurement is dependent on the number of ions sampled in the measurement and, thus, is likely to be different for every measurement. A simple procedure for correctly estimating the precision of a specific mass measurement is presented, the limits of the procedure are investigated, and the utility and validity of the procedure are demonstrated. Electrospray orthogonal time-of-flight mass spectrometers (oTOF/ESI MS) are capable of generating mass data of sufficient accuracy and precision to establish the elemental composition of an analyte.1-8 (For discussions on the mass accuracy and precision required to establish the elemental composition of small organic molecules see, for example, refs 9 and 10.) The combination of o-TOF/ESI MS exact mass measurement with on-line chromatography (LC) represents a powerful analytical tool for identifying components in complex mixtures and is being broadly employed by many researchers, particularly in the pharmaceutical industry.4-8 The “errors” in the measured masses of “known” components (1) Hoyes, J.; Bordolli, R.; Langridge, J.; Janssen, W.; Le Jeune, L.; Beaudry, F. Proceedings of the 46th ASMS Conference on Mass Spectrometry and Allied Topics, Orlando, FL, May 13-June 4, 1998. (2) Blom, K. Proceedings of the 46th ASMS Conference on Mass Spectrometry and Allied Topics, Orlando, FL, May 13-June 4, 1998. (3) Blom, K. J. Am. Soc. Mass Spectrom. 1998, 9, 789-798. (4) Jarvis, S.; Bateman, R.; Carruthers, P.; Doorbar, P.; Lockett, J. Proceedings of the 45th ASMS Conference on Mass Spectrometry and Allied Topics, Palm Springs, CA, June 1-5, 1997. (5) Eckers, C.; Haskins, N.; Langridge, J.; Rapid Commun. Mass Spectrom. 1997, 11, 1916. (6) Lee, M.; Monte′, S.; Sanderson, J.; Haskins, N. Rapid Commun. Mass Spectrom. 1999, 13, 216-221. (7) Hogenboom, A.; Niessen, W.; Little, D. Brinkman, U. Rapid Commun. Mass Spectrom. 1999, 13, 125-133. (8) Palmer, M.; Clench, M.; Tetler, L.; Little, D. Rapid Commun. Mass Spectrom. 1999, 13, 256-263. (9) Gross, M. J. Am Soc. Mass Spectrom. 1994, 5, 57. (10) Guidelines for Authors. J. Am. Chem. Soc. 1998, 120, 7A-11A. (11) Tyler, A.; Clayton, E.; Green, B. Anal. Chem. 1996, 68, 3561-3569. (12) Campbell, A.; Halliday, J. Proceedings of the 13th ASMS Conference on Mass Spectrometry and Allied Topics, St. Louis, MO, May 16-21, 1965. 10.1021/ac001064v CCC: $20.00 Published on Web 01/04/2001
© 2001 American Chemical Society
reported under LC-MS conditions are generally in the range of 5-10 ppm, though deviations of greater than 20 ppm have been reported. The effectiveness and validity of any procedure for establishing the elemental composition of an analyte from its measured mass depend on correctly establishing the mass error limits used to evaluate candidate compositions. If the error limits for the measured mass are underestimated, the correct composition may be rejected; and if the error limits are overestimated, the determination may not have the specificity needed to distinguish between candidate compositions. Therefore, it is important to understand the sources of error in the mass measurement, to use valid procedures for determining or estimating the error limits, and to report the mass measurement error in a meaningful manner. The error in a measured mass is composed of two components: the systematic error (the accuracy of the measurement) and the statistical or random error (the precision of the measurement). The accuracy of the measurement depends on “fixed” factors, such as the mathematical model used in the mass calibration, the granularity of the peak profile data, and the stability of the mass analyzer, and is generally a constant value for the instrument and method used. Accuracy is usually defined as the mean of the deviation in the measured mass (for a statistically significant population) of a reference standard from its actual mass. Once established, it is reasonable to presume that the accuracy for subsequent measurements is the same within certain constraints (e.g., within a certain mass range, for a certain period of time after calibration, etc.). The precision of a mass measurement depends principally on the ion statistics, that is, the number of ions sampled in making the measurement, according to the well-known relationship11,12
λppm ) 106/CRS1/2
(1)
where λppm is a suitable expression of statistical error (e.g., the 95% confidence limit in ppm), R is the resolution of the mass analyzer, C is an instrument constant, which depends on the shape of the spectral peak and the centroiding and mass correction algorithms employed, and S is the number of ions sampled in the measurement. (Note that any convenient expression of the magnitude of the measured signal can be used in place the “number of ions sampled” in eq 1. The substitution will only alter Analytical Chemistry, Vol. 73, No. 3, February 1, 2001 715
Table 1. Mean Mass Measurement Errors and 95% Confidence Limits for A by Infusiona
anal. no.
acq time (s)
est signal rate (counts/s)b
no. of spectra combined
S (no. of ions sampled)c
1 2 3 4 5 6
0.24 0.48 0.96 1.92 0.24 0.24
316.9 276.3 347.9 303.5 317.9 1303.1
5 5 5 5 20 5
380 633 1670 2913 1526 1564
1/S
mean error in measd mass (ppm) d
λppm (95% confidence limit (ppm) for N ) 12e
0.0512 99 0.0397 46 0.0244 70 0.0185 28 0.0255 99 0.0252 86
1.48 0.37 1.74 1.02 1.67 0.12
9.76 6.40 5.18 3.40 4.33 4.31
a Least-squares linear regression of mean error in mass (accuracy) data vs 1/S1/2: y ) 4 × 10-5x + 1.0146, R2 ) 0.0022. Least-squares linear regression 95% confidence limit (precision) data vs 1/S1/2: y ) 180.6x, R2 ) 0.9396. b Combined signal for 100 spectra/(100 × acquisition time). c Signal rate × acquisition time × number of spectra combined. d Statistical mean of differences between actual and observed mass, 12 determinations. e The 95% confidence limit, 1.96 × standard deviation.
the units on the constant, C.) Since number of ions sampled, S, is specific to a particular mass measurement, the magnitude of the statistical component of the error will be different for each measurement. The precision of a mass measurement can be established directly by making multiple independent measurements of the mass of interest and performing a statistical analysis of the data. In most cases, however, it is either inconvenient or not possible to make a direct determination of precision due to time limitations or limited sample availability. Consequently, precision is usually estimated indirectly, most often by incorrectly presuming that the error for all measurements is equal to the precision or the mean error observed for a set of reference masses measured under standard conditions. This practice is clearly not valid as the precision of a particular mass measurement depends on the number of ions sampled in that measurement according to eq 1 and will most likely be different for every measurement. An obvious though seldom utilized approach for estimating the precision of a mass measurement is to determine the value of the instrument constant, C in eq 1 and then use this relationship and the number of ions sampled in the measurement to estimate the precision of the mass measurement. In this note, we will (1) verify the functional relationships between the accuracy and precision of mass measurement and the number of ions sampled, (2) determine the value of the constant C for our instrument and mass measurement procedure, (3) investigate some of the limits over which the determined value of C is valid, and (4) demonstrate the validity of estimating precision with eq 1 under LC-MS conditions. EXPERIMENTAL SECTION These experiments were performed using a Micromass Q-TOF (quadrupole-orthogonal time-of-flight) hybrid mass spectrometer equipped with an orthogonal electrospray source (Z-Spray) operated in the positive ion mode. Data were acquired and exact mass measurements performed using MassLynx version 3.2, Build 004. The TOF mass correction (exact mass measurement) parameters were as follows: (background subtract) polynomial order 1, percent below curve 40; (smooth) type ) mean, smooth window 1 channel, number of smooths 1; minimum peak width at halfheight 4 channels; centroid top 70%; the deadtime correction was turned on. The single lock mass used for the TOF mass correction in the LC-MS analyses was the [M + H]+ for reserpine, m/z 609.1812, generated by adding a solution of reserpine (∼2 ng/µL 716
Analytical Chemistry, Vol. 73, No. 3, February 1, 2001
in acetonitrile) from a syringe pump (Harvard model 22) at a flow rate between 1 and 10 µL/m, as needed, through a PEEK tee connector adjacent to the Z-Spray source. The resolution of the mass spectrometer (determined for the [M + H]+ for reserpine and defined as the mass divided by the full width at half-height) was ∼5100. The mass range acquired in all experiments was 1501000 Da, the spectral acquisition times and interscan times used are specified in the Results and Discussion section. The instrument was calibrated ∼48 h before performing the exact mass measurements using a mixture of PEG 300 and PEG 600 introduced via an isocratic LC method. The liquid chromatography was carried out using an HP 1100 binary LC pump (G1312A) and HP Bonus-RP (5 µm, 2 × 50 mm) reversed-phase column. The solvents were degassed with an HP 1100 on-line vacuum degasser (G1322A) and the samples injected with an HP 1100 autosampler (G1313A). The column was maintained at 40 °C using an HP 1100 column compartment (G1316A). Solvents A and B were water and acetonitrile, respectively, with 0.1% acetic acid added. In the LC-MS analyses, the flow rate was 0.25 mL/m and the gradient was 2% B to 80% B in 1 min and then to 100% B in 2 min. The mobile phase was then returned to the initial composition (2% B) and the flow rate increased to 1 mL/m for 0.75 min before the next analysis. The total analysis time (including the injector cycle) was ∼4 min. Exact mass measurements were performed on the oligomers of polyanaline infused at ∼5 µL/m from a solution of ∼2 ng/µL in 50% acetonitrile and on two proprietary compounds obtained from the Discovery Chemistry group within DuPont Pharmaceuticals. These two compounds will be designated A and B. The reported mass defects for these compounds have been offset by a fixed amount (less than 5 mmu) to conceal their compositions. This manipulation does not affect qualitatively or quantitatively the results or conclusions reported here. Infusion studies were performed using mixtures of reserpine with either A or B at concentrations of ∼2 ng/µL per each compound in 50% acetonitrile and 0.1% acetic acid. For the data reported in Table 1, the exact concentration of A was adjusted slightly so that the mass spectrometric responses of the two components were equal (10%. The LC-MS experiments were performed on a mixture of A and B in 10% acetonitrile. The amount of material used in each analysis is specified in the Results and Discussion section.
RESULTS AND DISCUSSION A mixture of reserpine and A was infused into the Z-Spray source. The [M + H]+ for the reserpine, m/z 609.2812, was used as the lock mass for the measurement of the mass of A. The signal rates for the two components were approximately equal and were held constant throughout the analysis to minimize distortions due to differences in the rate of coincidental ion strikes, detector deadtime, etc. In the first five analyses, rows 1-5 in Table 1, the component concentrations and infusion rates were set such that the signal rates (the number of ions striking the detector per unit time) were maintained within the range recommended by the manufacturer, i.e., less than 400 counts/s. In these analyses, the numbers of ions sampled, S, were adjusted by varying the acquisition time and the number of spectra combined. In analysis 6, the number of ions sampled was increased by increasing the infusion rate of the analyte/reserpine mixture, thereby increasing the signal rate. The accuracy (the mean of the deviation) and precision (the 95% confidence limit) data reported in Table 1 are for 12 independent measurements made under each set of conditions. The functional relationships between the experimentally determined accuracy and precision data in Table 1 and the number of ions sampled, 1/S1/2 were assessed using a nonweighted linear least-squares analysis. The results of these analyses are summarized in Table 1. The slope and correlation for the linear fit of the accuracy data and 1/S1/2 are essentially zero (slope 4 × 10-05 ppm, R2 ) 0.0022) indicating that the accuracy of the measurement procedure is independent of the number of ions sampled (within the range of values evaluated). The accuracy or mean error in the measurement at this mass is 1.1 ppm. The functional relationship between precision and 1/S1/2 is well approximated by the linear fit (R2 ) 0.9396, intercept 0 ppm, slope 180.6 ppm), consistent with eq 1. The slope of the linear fit, 180.6, corresponds to the combination of terms 106/RC in eq 1. Thus, for this instrument, operated at this resolution, and using this centroiding and mass measurement algorithm, the 95% confidence limit for a mass measurement made using a given number of ions, s, is simply
λppm ) 180.6/S1/2
(2)
The precision of the mass measurement depends only on the number of ions sampled and not on the specific acquisition parameters (i.e., the scan time, number of scans combined, and signal rate) utilized to achieve a given value of S. It is particularly interesting that no decrease is noted in either accuracy or precision in analysis 6 in which the value of S was increased by raising the signal rate well beyond the recommended level. This result is a consequence of the somewhat unrealistic condition of maintaining the analyte and lock masses at approximately the same signal rate. Under these conditions, the distortions to the peak shape caused by coincident ion strikes at the detector and/ or detector deadtime are approximately the same for analyte and lock mass and the mass measurement routine apparently compensates for the distortion. However, at signal rates greater than ∼400 counts/s, the error in the mass measurement does increase significantly when the intensities for the analyte and lock mass differ significantly. This is illustrated in Figure 1. The signal rate
Figure 1. Dependence of mass measurement error (accuracy) on relative responses of analyte and lock mass peaks at low and high signal rates. Squares represent data obtained at a lock mass signal rate of 760 counts/s; diamonds represent data obtained at lock mass signal rate of 330 counts/s. The solid lines are linear nonweighted least-squares fits of the data; the dashed lines represent mass measurement errors of (5 ppm.
for the analyte, B, was varied by changing its concentration in the infusion mixture while holding the concentration of the reference material, reserpine, constant. Data were obtained at two signal rates for the lock mass (about 330 and 760 counts/s) by changing the infusion rate for the reserpine/analyte mixtures. The data in Figure 1 are for 100 spectra; the acquisition time was 0.24 s, and the interscan time was 0.01 s. At the lower signal rate for the lock mass, the error in the mass measurement is ∼0 when the ratio of intensities, analyte/lock mass, is 1 and changes slightly as the ratio of intensities changes. The rate of change is ∼-1.6 ppm (the slope of the line in Figure 1). Thus, if the signal rate for the analyte is 50% that of the lock mass, the systematic error or accuracy of the measured mass (due primarily to distortions in the peak shape) will be ∼0.8 ppm. At the higher signal rate, the error in the mass measurement is, again, ∼0 when the intensity ratio is 1. But, as the signal rate for the analyte changes relative to that for the lock mass the size of the error increases at a greater rate, ∼-10.6 ppm. Under these conditions, if the signal rate for the analyte is 50%, that of the lock mass the systematic error in the measured mass will be ∼-5.3 ppm. Increasing the signal rate does improve the ion statistics and hence the precision of the exact mass measurement, but using signal rates above 400 counts/s can result in a significant decrease in the accuracy of the mass measurement. Equation 2 is only valid if the signal rates for both the analyte and the lock mass are less than 400 counts/s or are approximately equal. The solution of polyanaline was infused into the Z-spray source at a rate sufficient to produce a signal rate for the m/z 587 peak, (8(ALA)OH2 + H)+, of ∼350 counts/s . This oligomer peak was used as the lock mass to measure the exact masses of the other polyanaline oligomers between m/z 161 and 942. The signal rates for these peaks ranged between 50 and 100% that of the lock mass. Exact mass measurements were made on combining 20 spectra with an acquisition time of 0.48 s. The results for six replicate measurements are summarized in Table 2. The average absolute error is 1.3 ppm. A nonweighted least squares linear fit of the mean error vs peak mass gives a slope of 0.001 ppm/Da and an Analytical Chemistry, Vol. 73, No. 3, February 1, 2001
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Table 2. Mean Mass Measurement Errors and 95% Confidence Limits for Polyanaline Oligomers by Infusion actual mass of oligomer
mean measd mass
error in mean mass (ppm)
95% confidence limit (ppm)
precision coeff (ppm)
161.0926 232.1297 303.1668 374.2039 445.2411 516.2782 658.3524 729.3895 800.4266 871.4637 942.5008
161.0927 232.1300 303.1660 374.2042 445.2412 516.2772 658.3533 729.3901 800.4280 871.4660 942.5021
0.35 1.08 -2.74 0.56 0.34 -1.96 1.35 0.81 1.69 2.57 1.36
2.60 3.03 4.60 6.01 4.28 4.51 3.70 3.77 5.60 6.95 6.91
172.6 177.9 182.9 184.6 191.0 181.3 167.7 192.6 169.7 169.8 185.0
Table 3. LC-MS/Exact Mass Measurementa analyte A (actual mass 474.2253)
a
analysis no.
measd mass (Da)
error in measd mass (ppm)
measd mass (Da)
error in measd mass (ppm)
1 2 3 4 5 6
474.2234 474.2255 474.2263 474.2244 474.2240 474.2248
-4.01 0.42 2.11 -1.90 -2.74 -1.05
481.1516 481.1494 481.1513 481.1499 481.1527 481.1512
3.04 -3.44 2.15 -1.97 6.27 1.85
mean 95% confidence limits direct estimate estimate using eq 2
474.2247
-1.2
481.1504
1.3
3.9 4.4
6.3 6.5
Acquisition time 0.96 s; five combined spectra. Signal rate for lock mass ∼320 counts/s.
R2 of 0.1651. This result suggests that the accuracy of the measurements has little or no dependence on the mass of the peak over this mass range. The instrument constant term for the precision calculation, 106/RC in eq 1, was calculated from the observed 95% confidence limit at each mass. A nonweighted linear least-squares fit of these coefficients with the peak masses indicates that this term, 106/RC, is essentially independent of the mass of the peak (R2 ) 0.0085, slope -0.003 ppm/Da, intercept 181.9 ppm). Thus, eq 2 is valid over the mass range of m/z 161942, essentially the entire calibrated mass range. The utility of this indirect method for estimating the precision of an exact mass measurement is easily demonstrated by example. Data for six replicate LC-MS analyses of a simple two-component mixture are presented in Table 3. The mass correction reference material, reserpine, was added to the LC stream postcolumn at a rate sufficient to produce a signal rate of ∼320 counts/s for the lock mass, m/z 609. The quantities of material analyzed, ∼5 ng of A and less than 1 ng of B, were chosen so that the maximum intensity of A would be significantly greater than that for the lock mass while the maximum intensity for B was less than that for the lock mass. The spectral acquisition time was 0.96 s. and the interscan time was 0.04 s. The LC method is described in the Experimental Section and typical chromatographic traces for the relevant ions are shown in Figure 2. Five spectra were combined from the trailing edge of the LC peak for A so that the combined signal for the analyte was about equal to that for the lock mass. For B, the five spectra from the top of the peak were combined; the integrated signal for B was ∼50% that for the lock mass. The 718
analyte B (actual mass 481.1505)
Analytical Chemistry, Vol. 73, No. 3, February 1, 2001
Figure 2. Selected ion traces for lock mass, m/z 609 from reserpine, and A, m/z 474, and B, m/z 481, in fast gradient LC-MS analysis under simulated parallel acquisition conditions.
mean errors in the mass measurements are ∼1 ppm for both analytes, consistent with the accuracy observed in the infusion studies. The 95% confidence limits estimated directly by statistical analysis of the replicate measurements are 3.9 and 6.3 ppm for A and B, respectively. The precision estimated indirectly using eq 1 and the average number of ions sampled per analysis are 4.4 and 6.5 ppm, respectively. Considering the relatively small population used in the direct statistical determination of the precision the agreement between the direct and indirect estimates of precision is quite reasonable.
CONCLUSIONS The accuracy and the precision of the o-TOF/ESI mass spectrometer and mass measuring procedure used in these experiments are found to have the expected dependence on the number of ions sampled in the mass measurement. The mass accuracy is ∼1 ppm over the entire calibrated mass range and is independent of the number of ions sampled and of the specific acquisition parameters, e.g., the signal rate (up to 400 counts/s), the acquisition time, etc. The relationship between mass measurement precision and the number of ions sampled is consistent with eq 1, is constant over the entire calibrated mass range, and is independent of the specific acquisition parameters within the same constraints. The precision of a mass measurement can be accurately estimated from the number of ions sampled using eq 1 and the previously determined instrument constant, C.
The statistical error usually dominates the total error in a mass measurement and is solely dependent upon the number of ions sampled in the measurement. Therefore, it would be of great value if researchers reporting LC-MS exact mass data would include estimates of signal rate (for both analyte and lock mass) and either the number of ions sampled or (if the instrument constant, C, has been determined) the 95% confidence limit as calculated with eq 1. This information is vital in order to judge the validity and the significance of an elemental composition analysis based on the exact mass measurement. Received for review September 7, 2000. Accepted October 19, 2000. AC001064V
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