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Ion Composition Elucidation (ICE)

A Mass Peak Profile Generation Model to Facilitate Determination of Elemental Compositions Based on Exact Masses and Isotopic Abundances

Andrew H. Grange and William C. Brumley

US EPA, NERL, Characterization Research Division,
PO Box 93478, Las Vegas, NV, 89193-3478

ABSTRACT

To identify elemental compositions of ions, a mass peak profile generation model (PGM) was developed to plan data acquisitions and to interpret the data obtained by using a high resolution mass spectrometer (VG70-250SE).  The PGM provides a list of all compositions possible for the exact mass of ion M and its error range from which the user selects a hypothetical composition.  The PGM then plots [M+1] and [M+2] mass peak profiles and calculates masses and abundances of full and partial [M+1] and [M+2] profiles relative to the M profile.  All possible compositions, calculated values for the exact masses and relative abundances, and measures of profile broadening and the shape of the [M+2] profile are listed in a table.  Pass-fail results for each of six criteria based on a comparison between table entries for the hypothetical composition and each of the other compositions are indicated.  Compositions failing one or more criteria will be eliminated if the hypothetical composition is correct.  The table provides assurance that all possible compositions based on the elements specified by the user have been considered.  The PGM can be used to estimate the minimum resolution and number of determinations necessary to identify the correct composition by eliminating all others.  As multiple determinations are made and error limits become smaller, average values are entered into the PGM to determine all compositions consistent with the data, often until only one composition remains.

INTRODUCTION

The two most commonly used data acquisition methods for mass spectral analyses of samples are full scans over mass ranges of up to hundreds of units and selected ion recording (SIR), the monitoring of a number of individual mass-to-charge ratios presumed to correspond to the maxima for mass peak profiles of targeted ions, which are assumed to have Gaussian shapes.  With electron impact ionization, full scans provide mass spectra useful for compound identification by comparison with library mass spectra.  For targeted compounds, SIR provides about 100 times more sensitivity and shorter cycle times than full scans [1].  Improved chromatographic resolution and quantitative accuracy result.  Unfortunately, SIR provides no confirmation that the profiles monitored are free of interferences that inflate quantitative determinations.  For dioxin analyses (EPA Methods 8280, 8290, and 1613), two ions are monitored for a single analyte and the ion abundance ratio is used to verify an analyte's identity.  For complex samples, however, undetected interferences can alter these ratios [2].

Voltage scans with a constant magnet current at high mass resolution can reveal these interferences, but the cycle time is slow, for example, 2.7 s at 10,000 resolution over 14 u.  To decrease the cycle time, abbreviated voltage scans were employed over narrow mass domains that encompassed each of several targeted profiles.  Modified hardware and custom software acquired and processed data [2,3].  This approach revealed interferences when profiles with distorted shapes were observed.  When interferences were absent, well-defined Gaussian profiles and center masses that better confirmed each ions's identity than an ion abundance ratio were obtained [2].  In a more sensitive approach, mass peak profiling from selected ion recording data (MPPSIRD), which required no hardware modifications, multiple mass-to-charge ratios were monitored over a single profile [1, 4-8] to provide a less well-defined profile, but one that was acquired at greater mass resolution (up to 40,000 [7]).  With greater resolution, the number of possible interferences was reduced, more accurate masses were obtained, and mass peak profiles of trace components in complex mixtures were resolved more often.  Mass peak profiles for [M+1] and [M+2] ions, which are less abundant than M ions, were usually resolved at the routinely used resolution of 20,000.

These profile delineating scan methods were used primarily for quality assurance [2-6].  In some cases, exact masses determined from the profiles for interferences aided in their identification [2].  The exact mass of a small-mass ion, determined within typical error limits, corresponds to a single elemental composition.  The number of compositions possible increases rapidly with the mass of an ion, the error limit, and the number of elements considered [9].  Thus, for a large-mass ion, additional information is often required to determine a unique composition.  Recently, MPPSIRD was adapted to determine exact masses and relative abundances of the [M+1] and [M+2] profiles and the width and shape of the [M+2] profile [7,8] from which the composition of a large-mass ion can be determined.  The profile generation model (PGM) described in subsequent text was developed to rapidly and routinely plan and interpret experiments by testing criteria that utilize this information to eliminate incorrect compositions consistent with the exact mass of M.

EXPERIMENTAL

Each SIR descriptor used to acquire data contained a list of 22 mass-to-charge ratios to be monitored, the dwell time for each (30 ms), and the transition time allotted to change instrument voltages between mass-to-charge ratios (5-30 ms, depending on the mass difference).  Although 25 mass-to-charge ratios were permitted in each list by the data system, only 22 global variables were available to store chromatographic peak areas.

Two types of data acquisitions provided either a full profile as in Figure 1a [1] or partial profiles as in Figure 1b.[7]

Figure 1 - For further information contact grange.andrew@epa.gov

Figure 1.  A full mass peak profile and partial profile for a calibration ion (a), partial profiles of three analyte ions and a calibration ion (b), and (c) the six ion chromatograms used to plot the first partial profile in (b).

Each profile was plotted from the areas of chromatographic peaks in ion chromatograms acquired for different mass-to-charge ratios across the profile.  For example, the shaded peaks in Figure lc were used to plot the first partial profile in Figure 1b.  The mass increment between the mass-to-charge ratios monitored was M/(R x N), where M was the mass of the ion, R was the mass resolution, and N was the number of points monitored across a full profile, which was normally 10 for unbroadened profiles.  For full profiles, 17 mass-to-charge ratios monitored the analyte profile and baseline regions around it, and 5 mass-to-charge ratios monitored the partial profile of the calibration ion formed from perfluorokerosene (PFK).  For full analyte profiles, the exact mass was determined as the weighted average of the top seven points when a point was near an apex or of the top six points when the apex fell between two points.  If the difference in amplitudes between the maximum point and the two adjacent points exceeded the amplitude difference between the top two points, seven points were included in the weighted average.

In Figure 1b, the partial profiles were plotted by monitoring 6 points across 60% of the mass range for the M, [M+1], and [M+2] profiles.  By splitting the 22 mass-to-charge ratios monitored into four groups:  six each to monitor the three analyte profiles and four to monitor the calibration ion; all three analyte ions were monitored each 0.8 s as a chromatographic peak eluted to determine the abundances of the [M+1] and [M+2] partial profiles relative to the partial M profile.  Hence, a split SIR descriptor, that is, one that monitors more than one analyte ion, was used to acquire these data.  Exact masses were again determined from similar numbers of points on both sides of the apex; either six or five points were normally used to determine a weighted average.  Similarly, the weighted average of three to five points across the partial profile of the calibration ion provided a mass correction for the exact mass of the M full or partial profile.

Exact masses and relative abundances are determined for both suspected molecular ions and fragment ions (F, [F+1], and [F+2]).  Thus, M represents any ion containing no higher isotopes, and [M+1] and [M+2] represent the ions containing one +1 isotope and one +2 or two +1 isotopes, respectively.

Maximum experimental errors for exact mass and relative abundance determinations were determined from four standards with molecular ions weighing between 536 and 766 u for data sets of 1, 2, 3, 7, and 15 determinations made at 20,000 resolution [7].  Fifteen data acquisitions with probe introduction, each calibrated independently, were collected by using normal and split SIR descriptors based on the correct composition for each standard.  Similarly, maximum errors were determined from 15 determinations of the apparent resolution for the M profile of one standard and the [M+2] profile of C24H28N2S2 found in an environmental sample [8].  The resolution (about 20,000) was determined as the average apparent resolution from two full profiles of the PFK ion most similar in mass to the analyte ion.  Data for the PFK profiles were acquired just before and after the data for the analyte profile for each probe introduction.  When partial profiles were monitored, the maximum counts from the analog-to-digital converter for the most abundant mass-to-charge ratio of the M ion did not exceed 8000 to ensure linearity of response over the abundance range of the M, [M+1], and [M+2] profiles and to ensure a signal for the [M+2] profile well above the detection limit.

A DOS batch file invoked the PGM written in QuickBASIC (Microsoft Corp., Redmond, WA) and a WordPerfect (WordPerfect Corp., Orem, UT) 5.1 macro that prepared a table of compositions with predicted masses and relative abundances for testing criteria.  A Micron (Micron Electronics Inc., Nampa, ID) personal computer containing an Intel Pentium 90 microprocessor (Intel Corp., Santa Clara, CA) was used for most simulations.

MODEL DESCRIPTION

The need for a model to evaluate data became obvious during early experiments.  Rejection of compositions based on the differences in mass defects and relative abundances among isotopes depends on the error limits of their determination.  These limits depend on several factors, including the number of determinations made, the mass resolution, the hypothetical composition used to prepare each split SIR descriptor, isotopic abundance errors, and instrumental errors. For the user to interpret the appearance of full and partial profiles, those predicted for each composition must be plotted to discern when asymmetry results from interferences or from contributions of multiple [M+1] or [M+2] ions to the profile. For large-mass ions, the number of compositions possible is often too large for manual consideration of each to be practical. Finally, to determine compositions of many ions produced from a complex mixture [8], automated data evaluation was required.

Possible Elemental Compositions

An average exact mass is determined from full M profiles and entered by the user with the resolution, number of determinations, and the elements to be considered.  The model chooses as upper limits for each element, the integer value of the mass entered divided by the atomic mass of the most abundant isomer.  The lower limit for each element is 0.  This strategy ensures that no possible composition composed of these elements and which provides greater than or zero rings and double bonds could be overlooked.  Optionally, assumed lower and upper limits for each element can be entered.  Ten elements are supported: C, Si, N, P, O, S, H, F, Cl, and Br.

The PGM compiles all possible compositions for the elements provided, within any limits provided, with masses that fall within the mass range for the number of determinations made at the resolution specified.  If only one composition is possible, the exact mass determined for M has identified the composition.

Criteria

When multiple compositions are possible, the user chooses and enters the number of a hypothetical composition from a display of all possible compositions.  For each composition in the list, the PGM then calculates (1) the masses and relative abundances of all ions contributing to the [M+1] and [M+2] profiles; (2) masses and relative abundances of [M+1] and [M+2] partial profiles; (3) ranges of relative abundances for [M+1] and [M+2] partial profiles expected by using a split descriptor having center masses based on the hypothetical composition and empirically determined or estimated error ranges in the mass, resolution, and isotopic abundances of the elements; (4) points on the [M+1] and [M+2] profiles, which are plotted; and (5) the apparent resolution and a shape parameter based on comparison between the [M+2] profiles of the hypothetical composition and each other possible composition.  A table is provided that lists the calculated values and the results of criteria testing.

[M+1] and [M+2] Ions

[M+1] ions arise from +1 isotopes and [M+2] ions result from +2 isotopes or from two +1 isotopes in an ion.  The [M+1] isotopes included in the PGM are 13C, 2H, 15N, 17O, 29Si, and 33S; the M+2 isotopes are 18O, 30Si, 34S, 37Cl, and 81Br.  For each possible composition, the model calculates the mass and relative abundance of each [M+1] and [M+2] ion and the sum of their relative abundances for each profile.  Isotopic masses and abundances from reference 10 were used in equations 1 and 2, adapted from reference 11 to calculate relative abundances.

equation 1 & 2 - For further information contact grange.andrew@epa.gov

n is the number of elements in the ion; Ni is the number of atoms of each element; and Ai1 Ai2, and Ai3 are the percentage abundances of each +1 isotope, +2 isotope, and +3 isotope, respectively.  For example, Ai3 is 0.02 for S and 0 for the other elements included in the model.

At low mass resolution, the small mass differences between multiple [M+1] or [M+2] ions are unresolvable, but at resolutions >10,000 valleys appear between different [M+1] or [M+2] ions in the [M+1] or [M+2] profile, depending on the mass of M.  The mass differences between [M+2] ions are larger than between [M+1] ions, and for high mass ions, [M+2] profiles become broad and asymmetric at experimentally achievable resolutions when the M ion contains one or more S or Si atoms.  Only one composition is usually possible at masses small enough for significant profile broadening or valleys to appear in the [M+1] profile.  Accordingly, width and shape parameters are calculated by the PGM only for the [M+2] profile.

Gaussian Distribution

The mass peak profile for M ions observed experimentally resembles the Gaussian distribution with a rounded apex and tails.  Thus, the Gaussian distribution calculated by equation 3 [12] was adapted to model the appearance of profiles:

Equation 3 - For further information contact grange.andrew@epa.gov

Equation 4 was used to calculate 101 points across a mass range that included the profile.  At 20,000 resolution, a mass range of 100 ppm was plotted.

Equation 4 - For further information contact grange.andrew@epa.gov

Mp is the mass on the x axis, Mc is the center mass, and R is the resolution.  (Mp-Mc) and (R/(0.020397 x Mc)) correspond to (x-xmean) and sigma in the Gaussian distribution equation.  The normalization term is not necessary to observe profile shapes.

[M+1] and [M+2] Profiles

The [M+1] and [M+2] profiles calculated at 20,000 resolution for tetraphenylsilane (C24H20Si) are shown in Figure 2.

Figure 2 - For further information contact grange.andrew@epa.gov

Figure 2.  The monitor display for calculated [M+1] (a) and [M+2] profiles (b) for C24H20Si at 20,000 resolution.  (c) Profiles for the three ions that contribute significantly to the [M+2] profile.

Because 10 mass-to-charge ratios delineate the full profile for a single ion, 6 mass-to-charge ratios monitor almost 60% of the [M+1] profile's mass range, but much less of the [M+2] profile's mass range.  The mass ranges monitored are marked by the vertical lines in Figure 2a and b.  In Figure 2c are shown the profiles for the three [M+2] ions (thin lines) whose sum produces the shape of the [M+2] profile (thick line).  The profiles of three other ions, C242H2H18Si+, 13CC232HH19Si+, and C242HH1929Si+, were also summed, but did not significantly affect the shape of the [M+2] profile.

When multiple [M+1] or [M+2] ions contribute to a profile, the amplitudes due to each ion are summed at each mass along the profile by using equation 5:

Equation 5 - For further information contact grange.andrew@epa.gov

y is the sum of relative abundances from all [M+1] or [M+2] ions at a point along the profile; n is the number of [M+1] or [M+2] ions; Ai is the abundance of the [M+1] or [M+2] ion relative to M; Mi is the mass of the [M+1] or [M+2] ion; Mp is the mass of the point along the profile; and the other parameters are the same as for equation 4.

Profile broadening is observable, because 101 points provide a mass range twice the width of a single ion's profile at 5% of its maximum.

Center Masses and Predicted Masses

The center mass (CM) is the weighted average mass of a profile.  A predicted mass (PM) is determined that will provide the largest area when only 6 m/z ratios are monitored.  The PM is the weighted average mass determined from the points between the vertical lines in Figure 2a or b.  The PM is initially calculated by:

Equation 6 - For further information contact grange.andrew@epa.gov

Mwa is the weighted average; Mi and Ai are the mass and amplitude coordinates of each point between the vertical lines.  All indices in the denominator are incremented and decremented by 1 or more to find the center point that provides the maximum area.  The predicted mass (PM) is then calculated by using equation 6 centered about this point.  When a deep valley between two maxima is present, the mass range monitored is centered on the larger maximum.

The PM is the mass used by the PGM for criteria testing.  Neither the CM nor the PM need correspond exactly to the mass of an individual [M+1] or [M+2] ion.  At low resolution the CM and PM are the same, but for profiles that broaden at higher resolution, the CM and PM will have slightly different values as illustrated by the header for Figure 2b.

Relative Abundances

The ratio of the area under the [M+1] or [M+2] profile relative to the area under the M profile times 100% is %[M+1] or %[M+2].  The percentage on the left of Figure 2a (32.1%) indicates the %[M+1] expected based on the areas of full profiles.  The %[M+1] or %[M+2] under a profile is based on the areas between the vertical lines in Figure 2a or b.  Without profile broadening, the same fraction (0.86) of the full profile areas corresponds to the partial profiles.  In Figure 2b, the partial profile includes only 54% of the full profile's area and the predicted %[M+2] is 5.4%, much less than 8.2% based on the areas of full profiles.

Apparent Resolution

Mass resolution is defined as R = Mave/deltaM for a 10% valley between overlapping profiles of equal height, where Mave is the average center mass of the two profiles and deltaM is the mass difference between the maxima of the two profiles [13].  The width of each profile is determined by the constant (0.20397) in equation 4, which provides calculated multi-ion profiles very similar in appearance to those observed.  For a Gaussian peak, the mass difference between points at 5% of the maximum on the two sides of either peak, deltaM5% is equal to deltaM [13].  The apparent resolution is the exact mass divided by deltaM5% and is a measure of the profile broadening that occurs when multiple [M+1] or [M+2] ions contribute to a profile.  For broadened profiles the apparent mass resolution is much less than the resolution specified by the user, as illustrated in Figure 2b.  When the mass range initially examined by the PGM is insufficient to view all of a broadened [M+2] profile, 50 additional points are calculated for the side of the profile that does not fall below 5% of maximum to calculate the apparent resolution.

Shape Parameter

Whether two [M+2] profile shapes can be distinguished visually is a subjective judgment, especially when only 17 points are monitored across the mass range containing a full profile.  A shape parameter provides a measure of shape differences between profiles.  The parameter is the sum of the absolute differences between the amplitude of two normalized [M+2] profiles with overlapping center masses - that of the hypothetical composition and that of each other possible composition.  In Figure 3a and b are shown two [M+2] profiles with the same apparent resolution, that are easily distinguishable by their shapes.

Figure 3a & 3b - For further information contact grange.andrew@epa.gov

Figure 3.  Calculated [M+2] profiles for (a) C24H44N2PS and (b) C28H41NS at 21,400 resolution.

The shape parameter was 13.9 for these profiles.  When the shape parameter exceeds 2 for two compositions that are otherwise indistinguishable, the calculated [M+2] profiles should be examined to determine if their shapes are sufficiently different to distinguish between them.

ERRORS

Two types of errors must be considered:  those accounted for in the model and those that must be observed by the operator.  Before data are considered to be valid, three visual, quality assurance tests must be passed.  The maximum in the partial profile of the calibration ion must not be the first or last point, the third or fourth point must be the maximum in the M, [M+1], and [M+2] profiles, and the ion chromatograms used to construct each profile must overlap after each is normalized.  These requirements confirm that instrument calibration was acceptable to within l mass-to-charge ratio step for all profiles and that no obvious interferences were present.

The goal of the PGM error treatment is to ensure the correct composition is never rejected, while providing criteria narrow enough to reject as many other compositions as possible.  At the same time, the error ranges used should not falsely reject other possible compositions.  Thus, conservative estimates of the errors considered by the PGM were made and the total error was taken as the sum of all errors, rather than as the square root of the sum of the squares [14].  Generous error ranges for %[M+1] and %[M+2] resulted.  If multiple compositions passed all criteria based on experimental data, but most observed values agreed best with values calculated for one composition, that composition would probably be the correct one.

Mass Offset Error

Predicted masses are first calculated for the hypothetical composition.  The PMs of the [M+1] and [M+2] profiles are then used as center masses in the SIR descriptor and are different from the PMs for the other compositions.  These mass offsets for all other compositions contribute error to the determination of relative abundances based on partial profiles.  Three other errors are also considered by the PGM:  mass calibration error, resolution error, and isotopic abundance errors.  These errors influence the relative abundances determined for all compositions.

Mass Calibration Error

For full profiles, the effect of profile shifts on determining the exact mass of the analyte profile is corrected by calibration against the PFK ion to provide an error almost always within 2.5 ppm at 20,000 resolution.  The exact masses of the [M+1] and [M+2] partial profiles are calibrated against the exact mass of the M partial profile to provide better accuracy and precision.  Because shifts in partial profile maxima occur in the same direction, they are compensated by calibration against M.  Mass calibration error is not important for determining exact masses of the [M+1] and [M+2] partial profiles.

Mass calibration error significantly affects the relative abundance determinations when profile broadening occurs, because the sum of the amplitudes of all six points on each partial profile provides the area under the partial profile.  A shift of M, [M+1], and [M+2] profiles causes less of their total area to be monitored by six mass-to-charge ratios, but, as illustrated in Figure 4, the reduction in area monitored is less for broad profiles.  A high estimate of %[M+2] based on partial profiles would result.

Figure 4 - For further information contact grange.andrew@epa.gov

Figure 4.  An unbroadened M profile (a) and a broad [M+2] profile (b).  A shift of -1 mass increment results in less area on the left of the M profile being monitored than the area lost on the right side of the profile.  For the [M+2] profile the difference in these areas relative to the total area is much less.

Resolution Error

The resolution is tunable to within 10% and is determined from the width of the M profile for a PFK ion at 5% of its maximum.  As long as a single maximum is observed in a profile, the dependence of the exact mass determined on resolution is insignificant.  However, %[M+1] and %[M+2] values are dependent on the resolution when profile broadening is present.  At higher resolutions, the fraction of the total area under the profile monitored by only six mass-to-charge ratios becomes less for broadened profiles and the observed relative abundance is reduced.

Isotopic Abundance Errors

Relative abundances result from the isotopic abundances of the +1 and +2 isotopes.  Although mass and resolution errors are partially responsible for the observed precision, isotopic abundance errors depend on the origin of each compound and are constant for all %[M+1] and %[M+2] determinations.  Isotopic abundances and errors were taken from reference [10].

Relative Abundance Ranges

To establish ranges for %[M+1] and %[M+2] for the hypothetical composition, the model predicts %[M+1] and %[M+2] values in the absence of errors and for errors of plus or minus 1 mass increment and/or plus or minus 10% of the resolution determined (nine conditions in all).  Relative abundances are calculated after shifting the center point for all three partial profiles 1, 0, and -1 mass increments at resolutions 10% less than, 10% greater than, and at the resolution specified.  Without peak broadening, the same %[M+1] and %[M+2] are predicted under all conditions, since the shape of the M, [M+1], and [M+2] profiles are the same and mass calibration and resolution errors change the fraction of each profile monitored in unison.

For broadened profiles, these errors alter the observed relative abundances and contribute to the relative abundance ranges.  For C24H20Si, %[M+2] ranges of 7.2-7.7% and 5.0-6.1% were calculated at 10,000 and 20,000 resolution, respectively, when only mass calibration and resolution errors were considered.  At the higher resolution, profile broadening was greater and a wider range resulted.

Wider ranges are predicted when the split SIR descriptor based on the predicted masses of the M, [M+1], and [M+2] profiles for the hypothetical composition is used to monitor the partial profiles of the other compositions.  Different mass offsets between the predicted masses in the SIR descriptor and the profiles for each composition result in different fractions of the area being monitored for each profile.  Even for unbroadened profiles, the fractions no longer change in unison for mass calibration and resolution errors.  Proportionally wider %[M+1] and %[M+2] ranges are calculated for greater resolution, because the mass offsets are larger relative to the profile width at high resolution.  For C24H20Si, using C18H27P3 as the hypothetical composition, the predicted %[M+2] ranges expand to 5.4-8.9% and 3.9-7.0% at 10,000 and 20,000 resolution, respectively.

After %[M+1] and %[M+2] ranges are calculated by the model by considering mass and resolution errors, the isotopic abundance errors are calculated.  Each isotopic abundance is reduced and then increased by the maximum error possible [10].  The %[M+1] and %[M+2] are recalculated by using equations 1 and 2 to provide the largest possible negative and positive errors.  The absolute value of the larger error for each composition is then added to the upper limit and subtracted from the lower limit of the %[M+1] and %[M+2] error ranges.  For C24H20Si as the hypothetical composition, %[M+1] and %[M+2] ranges of 6.6-8.3% and 4.5-6.7% result after considering maximum isotopic abundance errors of 0.6% and 0.5%, respectively.

Apparent Resolution

When only 10 points are monitored across an unbroadened profile, the resolution will be underestimated by no more than 4% for a single determination.  This error results from the maximum point not corresponding exactly to the maximum of the profile and to the linear interpolation made between the points that bracket 5% of the maximum on each side of the profile.  This error occurs for both calibration and analyte ions and tends to cancel.  Fifteen determinations of the apparent resolution for the full M profile of C36H38O6N4 (m/z 622.2791) and the full [M+2] profile of C24H28N2S2 (m/z 410.1665) were made at 20,000 resolution to estimate the experimental error.  Peak broadening was nonexistent for the first profile and substantial for the second.  The largest observed errors in the apparent resolutions obtained were 5.2% and -10.2% for triplicate sets of successive determinations, respectively.  For all 15 determinations, the errors were +3.2% and -8.0%.  The model might slightly underpredict the extent of broadening, but data for more [M+2] profiles are required to verify and estimate this tendency.  For now, the apparent resolution criterion is based on the maximum errors observed; it distinguishes well between compositions that contain Si and S atoms and those that do not.

Accuracy

A model only predicts error ranges based on the influence of important independent variables upon measured quantities.  Experimental error ranges must also be considered.  In Table 1 are listed the estimates of the maximum errors used in the PGM for different numbers of determinations of exact masses, relative abundances, and the apparent resolution.

Table 1.  Maximum errors observed at 20,000 resolution

Table 1 - For further information contact grange.andrew@epa.gov

The maximum exact mass errors are those observed for the molecular ion profile and [M+1] and [M+2] partial profiles for four standards.  The experimental ranges for the relative abundances were determined from these ions by using the predicted masses for their compositions in the split SIR descriptors.  The [M+2] profiles had minimal peak broadening.  These ranges were added to the ranges calculated by the PGM that arise from peak broadening, mass offsets in the split SIR descriptor, and isotopic abundance errors.  The apparent resolution errors are the maximum differences between the model prediction and the observed apparent resolution for the broadened [M+2] profile of C24H28N2S2.  For all maximum errors, the largest observed error was rounded upward to the nearest 0.5 ppm or 0.5%.

Experiments are run routinely at 20,000-25,000 resolution, but also at lower or higher resolution, depending on the concentration of analytes and the relative abundance of the ions studied.  To estimate the influence of resolution on the error ranges in Table 1, 15 full and partial profile data acquisitions were made at 10,000 resolution for the m/z 766.3942 ion.  The mass error range for the exact mass of M was 1.8 times larger when the data were treated as 13 sets of triplicate determinations.  As an approximation, the mass error limits in Table 1 are multiplied by 20,000/R and correspond to one half of the mass increment used to monitor profiles for triplicate determinations.  Mass increments smaller than 5 ppm are avoided to ensure no repeated points are observed in the profile due to round-off limitations of the 16-bit digital-to-analog converter that controls the accelerating potential in the SIR mode.  Thus, if R is >20,000, the mass error ranges used in the model are still those for 20,000 resolution.  No resolution dependence has been observed for the error ranges in %[M+1] or %[M+2] or in the apparent resolution.  Hence, no factor is used to adjust the error limits observed at 20,000 resolution.  Until a larger data base is acquired, the model is used with greatest confidence near resolutions of 20,000.

RESULTS AND DISCUSSION

An Example

Table 2 provides the PGM output for m/z 536.2621 assuming triplicate determinations and a resolution of 20,000.

Table 2.  Elemental compositions and quantities useful for distinguishing among them

Table 2 - For further information contact grange.andrew@epa.gov

aRings and double bonds.
bCalculated mass defect.
cBased on partial profiles centered about the calculated mass for the composition.
dBased on partial profiles centered about the calculated mass of the hypothetical composition, plus or minus 1 mass increment at plus or minus 10% of resolution, isotopic abundance error, and maximum observed experimental error.
eCalculated apparent resolution.
fSum of the absolute differences at 1-ppm intervals along normalizad [M+2] profiles of the hypothetical composition and each other composition.  An "X" indicates application of this criterion will reject this composition if the hypothetical composition is correct.  The hypothetical composition is in bold print.

An "X" next to a value indicates failure of the criterion based on comparison of the value with that of the hypothetical composition, and the composition is rejected.  The compositions are listed in three groups separated by blank lines:  compositions for which the ranges of values for the hypothetical composition and each other composition do not overlap for at least one criterion, compositions that pass all criteria based on partial overlap of the ranges, and those compositions that pass all criteria based on inclusion of the calculated values for the hypothetical composition within their ranges.  Range overlaps consider the minimum and maximum possible values of the hypothetical composition, whereas testing of the calculated values recognizes that single values will be compared after data are acquired.  For the example in Table 2, eight compositions passed all criteria based on overlap of ranges, but only the hypothetical composition in bold print and one other remained after testing the correct values.  For average values from single triplicate determinations, however, one or more of the other six compositions might not be eliminated and additional determinations would be required to improve the averages and to reduce the error limits.

In Table 2, the mass of the [M+2] partial profile criterion is violated more often (51) than the mass of the [M+1] partial profile criterion (13) because the differences between the mass defects of the most abundant isotopes and +2 isotopes are larger than the differences between the most abundant isotopes and +1 isotopes.  With low numbers of C atoms, the first 41 compositions fail the %[M+1] criterion, since the relative abundance of 13C (1.10%) [10] is much larger than the relative abundances of the other +1 isotopes, which are present in lower numbers.  The apparent resolution criterion was failed by 24 compositions.  One or more S atoms and at least 15 C atoms provided broadened [M+2] profiles relative to the hypothetical composition.

In Table 2, the mass of the [M+2] partial profile criterion is violated more often (51) than the mass of the [M+1] partial profile criterion (13) because the differences between the mass defects of the most abundant isotopes and +2 isotopes are larger than the differences between the most abundant isotopes and +1 isotopes.  With low numbers of C atoms, the first 41 compositions fail the %[M+1] criterion, since the relative abundance of 13C (1.10%) [10] is much larger than the relative abundances of the other +1 isotopes, which are present in lower numbers.  The apparent resolution criterion was failed by 24 compositions.  One or more S atoms and at least 15 C atoms provided broadened [M+2] profiles relative to the hypothetical composition.

Usually, for organic compounds found in the environment, at least one third of the mass of the largest mass ion is due to carbon.  By specifying a lower limit of 14 C atoms, the time required to produce an abridged table lacking the first 23 compositions was reduced from 23.3 to 4.9 min.  With one third of the total mass of the ion already accounted for as C atoms, the time required to account for the remaining mass was much less than for the entire mass.

In Table 2, the proportionally largest relative abundance ranges are calculated for %[M+2], since the largest mass offsets are calculated for [M+2] profiles.  For all possible compositions and triplicate determinations, the mass offset for M is no greater than 2.5 ppm or one half mass increment at 20,000 resolution.  However, [M+2] mass defects with offsets up to 21.4 ppm or 4.3 mass increments are listed.  Hence, the fraction of the area monitored under the M profile changes only slightly, whereas the fraction monitored for an [M+2] profile decreases sharply for a large mass offset.  Although the range for %[M+2] of the hypothetical composition is only 1.6%, ranges up to 14.8% are observed for compositions with large mass offsets.  If the center mass in the SIR descriptor was offset by 4.3 mass increments, no maximum would be observed for the [M+2] profile and would indicate that either the wrong hypothetical composition had been used or a major interference was present.

For the compositions in Table 2, %[M+1] isotopic abundance errors between plus or minus 0.3 and plus or minus 1.2% were calculated, of which 0.0 to plus or minus 1.2% were due to the 13C abundance error of +0.03%.  The %[M+2] isotopic abundance errors ranged from 0.0 to plus or minus 0.7% and are included in the ranges listed.

An Occasional Complication:  Proton Loss

When a significant fraction of M ions lose protons and the resolution is insufficient to discriminate among M, [13CM-H] and [13C2M-2H] ions, %[M+1] and %[M+2] will be decreased, since the abundance of M will be inflated by loss of an H atom from the [M+1] ion or by the loss of two H atoms from the [M+2] ion.  The exact masses observed will also be decreased, since ions containing a 13C atom and one less H atom have slightly less mass than those that do not.  For (S, S)-(+}-tetrandrine (C38H42O6N2), an error in %[M+2] of -2% was observed, despite a standard deviation of only 0.3% for 15 determinations.  A full scan revealed large abundances of [M-H] (67% of M) and [M-2H] ions (11% of M).  After correcting for bias, corrections in the masses and relative abundances were made for proton losses based on ion balance equations.  In addition, the reduction in area monitored under the partial profile for M, [M+1], and [M+2] for the ions that have lost one or two protons by only six mass-to-charge ratios centered about the normal M, [M+1] or [M+2] profile was considered.  These calculations were done manually and are not included in the PGM.  For the correct composition, two of the corrected masses and both corrected relative abundances fell outside of the maximum error ranges established from the four standards.  When the maximum errors were doubled for all 6 criteria, only the correct composition remained after the set of 15 determinations.  When proton loss is prominent and resolution is insufficient to discriminate against ions having lost a proton, confidence in the identification is reduced.  Fragment ions can then be identified to confirm the identity of the target ion.  Although proton loss caused problems only in this example, a single determination of [M-2] and [M-1] relative abundances by using a split SIR descriptor is a prudent precaution.  None of the other four standards had %[M-2] and %[M-1] values greater than 2% and 3%, respectively.

(The preceding topic is examined in greater detail in a more recent reference.[16])

Resolution, Number of Determinations, and the Number of Possible Compositions

To examine the utility of MPPSIRD for determining unique compositions for molecular ions over a broad mass range, the PGM was used to provide tables similar to Table 2 for the ions studied in references 1 and 7 and for 22 compounds containing C, H, O, N, P, or S atoms found in the formula index of a chemical catalog [15], which may or may not provide abundant molecular ions.  At least one third of the mass of the ion was assumed to be carbon and the upper limits ensured that all combinations of the other elements having zero or more rings and double bonds were examined.  In Table 3 are listed the number of compositions that passed all six criteria and in parentheses the total number of possible compositions for each compound.

Table 3.  Compositions, molecular weights, the number of compositions passing all six criteria, and the total number of possible compositions containing C, H, O, N, P or S atoms

Table 3 - For further information contact grange.andrew@epa.gov

About one half as many compositions were possible for triplicate determinations made at 20,000 resolution (mass error limits 2.5 ppm) than at 10,000 resolution (mass error limits 5 ppm).  Fewer compositions remained viable as the number of determinations increased and the error limits for the criteria decreased.

In general, the number of compositions possible increases with the mass of an ion.  Triplicate determinations at 20,000 resolution with the list of elements considered will usually provide a unique composition for masses less than 300 u, about half the time for masses between 300 and 600 u, and less often at higher masses.  Table 3 indicates that with 15 determinations, unique compositions are probable up to 600 u.

Two compounds in Table 3 provided surprisingly few possible compositions: C36H75N and C37H70O3.  The number of compositions possible was calculated by using the PGM for masses between 499.5 u and 501.5 u at 0.05-u increments with 20,000 resolution for triplicate determinations to prepare Figure 5.

Figure 5 - For further information contact grange.andrew@epa.gov

Figure 5.  The number of compositions possible assuming at least one third of the ion's mass is due to C atoms for masses between 499.60 u and 501.60 u calculated by the PGM at 0.05-u intervals for triplicate determinations at 20,000 resolution.  The number of remaining compositions was calculated by the PGM by using composition N/2 (even number of compositions) or (N+1)/2 (odd number of compositions) as the hypothetical composition.

For even and odd numbers of possible compositions, the N/2 and (N+1)/2 composition was chosen, respectively, as the hypothetical composition.  Clearly, the number of possible compositions is also highly dependent on the mass defect.  For all of the masses for which compositions were found, only one composition was predicted to pass all criteria.

Planning and Interpreting Experiments

For trace compounds present at very low concentrations, a resolution lower than 20,000 might be needed to provide greater sensitivity.  The PGM can be used to estimate the number of determinations necessary at a given resolution to exclude all but the hypothetical composition.  After data acquisition, the average values for the quantities used to distinguish between compositions are entered into the model, which then lists the possible compositions and applies the criteria.  Usually, only one composition passes all criteria based on the data.  When lower resolution is used, more determinations might be required to provide sufficiently narrow error limits to reject all but the correct composition.

The PGM reveals which data can eliminate other compositions.  After a single exact mass determination for M, a hypothetical composition is chosen and a table similar to Table 2 is prepared by the PGM.  Additional exact mass determinations for M would usually eliminate only a fraction of the other compositions by providing smaller maximum error limits.  Instead, the other values in the table are examined.  If only one criterion can reject all but the hypothetical composition, then the next data acquisition should provide the value for that criterion.  Generally, acquisition of partial profiles is indicated to provide values to apply four of the remaining five criteria.  After each data acquisition, updated average exact masses and relative abundances can be entered into the PGM until a unique composition is found based on more accurate values and smaller error limits.

If multiple compositions remain for M, fragment ion compositions can be determined by the same procedure.  The exact masses of neutral loss fragments determined as the difference between the exact masses of M and each F generally correspond to only one composition.  In the absence of fragments ions, other instruments such as gas chromatographs with nitrogen-phosphorus detectors or inductively coupled plasma-atomic emission spectrometers can be used to distinguish among compositions containing or not containing heteroatoms.

Other Data Systems

Due primarily to the limited number of mass-to-charge ratios available in a SIR group, the PGM was written to predict and evaluate data based on partial profiles.  Six mass-to-charge ratios monitored most of the area under unbroadened profiles and maintained a narrow mass increment to provide more accurate masses.  An advantage of this approach was the fast cycle time of 0.8 s, which better revealed partially coeluting interferences [8].  To retain this cycle time and to use the PGM without modification, other data systems that allow more mass-to-charge ratios in SIR groups could be used, providing only the same 22 mass-to-charge ratios were monitored.  To examine full M, [M+1], and [M+2] profiles simultaneously, at least 10 mass-to-charge ratios would be required for M and perhaps 13 and 18 mass-to-charge ratios for the [M+1] and [M+2] profiles to allow for peak broadening and mass offsets when the hypothetical composition is incorrect.  Monitoring six mass-to-charge ratios for the partial profile of the calibration ion would also be helpful to ensure its maximum was never missed.  Using 47 mass-to-charge ratios and the same dwell time, the cycle time would be more than doubled, which is a major disadvantage when studying closely eluting components.  However, three advantages would be gained.  Smaller relative abundance ranges determined only from isotopic abundance errors and experimental errors would result, since mass offsets and peak broadening would no longer be important if %[M+1] and %[M+2] were determined from full profiles; error estimates by the PGM could be simplified; and location of maxima (third or fourth of six mass-to-charge ratios for partial profiles) would not be a concern.

As demonstrated by Table 2, the largest relative abundance ranges were associated with the largest mass offsets, which, when >2.5 ppm at 20,000 resolution, already eliminated a composition.  For cases in Table 3 where multiple compositions passed all criteria, we conjecture that use of more mass-to-charge ratios to provide full profiles would occasionally reject additional compositions when the hypothetical composition or the other compositions have broadened [M+2] profiles.

Possibly of greater value would be use of smaller mass-to-charge ratio increments and proportionally more mass-to-charge ratios.  Mass increments of 5 ppm were used, limited primarily by the 16-bit digital-to-analog converter (DAC) that set the accelerating potential for each ratio.  If smaller mass errors were obtained at 20,000 resolution by using a 20-bit DAC, better discrimination against incorrect compositions would result.  We encourage others with newer data systems to investigate this possibility.  The PGM is available from the authors by request, as are the data acquisition and processing procedures, which are specific to the VG data system.

CONCLUSION

A profile generation model (PGM) was written to plan and interpret experiments for determining elemental compositions of ions by using mass peak profiling from selected ion recording data (MPPSIRD) at high mass resolution (at least 10,000).  The PGM listed all possible elemental compositions for an ion based on the exact mass specified, from which the user selected a hypothetical composition.  Each other composition was rejected if the range of values predicted for the exact masses of the [M+1] and [M+2] partial profiles, the relative abundances of the [M+1] and [M+2] partial profiles relative to the M partial profile, and the apparent resolution of the [M+2] profile were not consistent with the values predicted for the hypothetical composition.  A shape parameter was also calculated to estimate the degree of difference between the shapes of [M+2] profiles.  Occasionally, the shape of the [M+2] profile is unique for the hypothetical composition.

Ranges for the exact masses determined were estimated from experiments with four standards.  Relative abundance ranges were calculated based on errors in mass calibration, mass resolution, isotopic abundance, center mass offsets in the split SIR descriptor for non-hypothetical compositions, and maximum error ranges observed for four standards with nearly unbroadened [M+2] profiles.  Apparent resolution ranges were estimated from results for a compound providing a broad [M+2] profile. For all quantities measured, precision and accuracy improved for larger numbers of determinations.  For exact mass determinations, precision and accuracy also improved at higher resolution.  Consequently, fewer compositions were possible as the resolution and the number of determinations increased.  The PGM predicted whether a chosen resolution and number of determinations would eliminate all but the correct composition.  Considering C, H, O, N, P, and S atoms, the PGM predicted that unique compositions can be determined for ions weighing up to 600 u.  The PGM is a valuable theoretical tool for assessing mass peak profiles for multiple compositions as a function of the mass resolution.  It enables routine determination of compositions of ions produced from numerous compounds in mixtures.  Together, the PGM and MPPSIRD utilize efficiently and fully the information about elemental compositions available in the mass peak profiles of M, [M+1], and [M+2] ions obtained at high mass resolution and provide a new technique for characterizing environmental samples and other complex mixtures.

Acknowledgment.  A. H. Grange currently holds a National Research Council/NERL-CRD-LV Senior Research Associateship.

REFERENCES

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  8. Grange, A. H.; Brumley, W. C. Liquid Chromatogr. Gas Chromatogr. 1996, 14, 978-986.

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  10. Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, 74th ed.; CRC Press: Boca Raton, FL, 1994 pp 1-110-1-111.

  11. Beynon, J. H.; Williams, A. E. Mass and Abundance Tables for use in Mass Spectrometry; Elsevier: New York 1970, pp VIII-IX.

  12. Dixon, W. J.; Massey, F. J., Jr. Introduction to Statistical Analysis, 3rd ed.; McGraw-Hill: New York, 1969.

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  16. Grange, A.H.; Sovocool, G.W. Rapid Commun. Mass Spectrom. 1999, 13, 673-686.

Analytical Environmental Chemistry
ICE Home Page

Environmental Sciences | Office of Research & Development
 National Exposure Research Laboratory
Author: Andrew Grange
Email: grange.andrew@epa.gov


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