Anal. Chem. 1999, 71, 624-632
Routine Part-per-Million Mass Accuracy for HighMass Ions: Space-Charge Effects in MALDI FT-ICR Michael L. Easterling, Todd H. Mize, and I. Jonathan Amster*
Department of Chemistry, University of Georgia, Athens, Georgia 30602-2556
The effect of ion space-charge on mass accuracy in Fourier transform ion cyclotron resonance mass spectrometry is examined. Matrix-assisted laser desorption/ionization is used to form a population of high-molecular-weight polymer ions with a wide mass distribution. The density of the ions in the analyzer cell is varied using ion remeasurement and suspended trapping techniques to allow the effect of ion space charge to be examined independently of other experimental influences. Observed cyclotron frequency exhibits a linear correlation with ion population. Mass errors of 100 ppm or more in externally calibrated mass spectra result when ion number is not taken into account. By matching the total ion intensities of calibrant and analyte mass spectra, the protonated ion of insulin B-chain, 3494.6513 Da, is measured with an accuracy of 0.07 ppm (average of 10 measurements, σ ) 2.3 ppm, average absolute error 1.6 ppm) using a polymer sample as an external calibrant. Alternatively, the correction for space charge can be made by using a calibration equation that accounts for the total ion intensity of the mass spectrum. A calibration procedure is proposed and is tested with the measurement of the mass of insulin B-chain. A mass accuracy of 2.0 ppm (average of 20 measurements, σ ) 4.2 ppm, average absolute error 3.5 ppm) is achieved. Space-charge-induced mass errors are more significant for samples with many components, such as a polymer, than for single-component samples such as purified peptides or proteins. In mass spectrometry, the specificity of a measurement is often improved by increasing mass accuracy. For example, exact mass measurements have been widely used for several decades in organic mass spectrometry as a means to determine the elemental composition of low-molecular-weight samples.1 Mass accuracy is important to problems in macromolecular mass spectrometry as well. Recent work has shown that the number of proteolytic fragment masses needed to identify a protein from a search of a sequence database has an inverse relationship to the mass accuracy of the data.2 The assignment of end group chemical formulas for mid-sized polymers has also been shown to benefit from accurate mass measurements.3 Accurate mass measurements (1) McLafferty, F. W.; Turecek, F. Interpretation of Mass Spectra, 4 ed.; University Science Books: Sausalito, CA, 1993. (2) Takach, E. J.; Hines, W. M.; Patterson, D. H.; Juhasz, P.; Falick, A. M.; Vestal, M. L.; Martin, S. A. J. Protein Chem. 1997, 16, 363-369.
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play an increasingly significant role in the analysis of highmolecular-weight compounds. Accurate mass determinations require high mass resolution in order to achieve sufficient precision for accurate mass assignment. Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry is a well-known method to achieve high mass resolution.4,5 Using various ionization methods and instrument configurations, this capability has been demonstrated for a number of analyses, including the identification of unknown substances,6 identification of proteins and their proteolytic fragments,7 polymer analysis,3,8 elemental identification,9 and collisional dissociation product characterization.10-12 The high mass precision in FT-ICR measurements results from the temporal nature of ion detection. Ion masses are determined by measuring their characteristic cyclotron frequencies, which are observed as digitized data in the time domain.13 In general, determination of frequencies from digitized signals at the sub-ppm level is trivial as the associated methodologies and equipment are in widespread use in many types of laboratories. Additionally, the stability and accuracy of the electronics used for supplying dc and rf voltages to the ICR cell for ion manipulation and confinement have improved tremendously in recent years. The precision of high-resolution FT-ICR does not guarantee the accuracy of the measurement. As with other mass spectrometric methods, systematic effects can produce deviations between measured and calculated mass values. It is important to consider the nature of FT-ICR detection in order to understand the effect of experimental conditions upon mass accuracy. ICR signals are produced by measuring the image charge created by (3) Dekoster, C. G.; Duursma, M. C.; Vanrooij, G. J.; Heeren, R. M. A.; Boon, J. J. Rapid Commun. Mass Spectrom. 1995, 9, 957-962. (4) Amster, I. J. J. Mass Spectrom. 1996, 31, 1325-1337. (5) Marshall, A. G.; Hendrickson, C. L.; Jackson, G. S. Mass Spectrom. Rev. 1998, 17, 1-35. (6) Wu, J. Y.; Fannin, S. T.; Franklin, M. A.; Molinski, T. F.; Lebrilla, C. A. Anal. Chem. 1995, 67, 3788-3792. (7) Mortz, E.; Oconnor, P. B.; Roepstorff, P.; Kelleher, N. L.; Wood, T. D.; McLafferty, F. W.; Mann, M. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 82648267. (8) Easterling, M. L.; Mize, T. H.; Amster, I. J. Int. J. Mass Spectrom. Ion Processes 1997, 169, 387-400. (9) Watson, C. H.; Wronka, J.; Laukien, F. H.; Barshick, C. M.; Eyler, J. R. Anal. Chem. 1993, 65, 2801-2804. (10) Wu, Q. Y.; Vanorden, S.; Cheng, X. H.; Bakhtiar, R.; Smith, R. D. Anal. Chem. 1995, 67, 2498-2509. (11) Speir, J. P.; Senko, M. W.; Little, D. P.; Loo, J. A.; McLafferty, F. W. J. Mass Spectrom. 1995, 30, 39-42. (12) Little, D. P.; Aaserud, D. J.; Valaskovic, G. A.; McLafferty, F. W. J. Am. Chem. Soc. 1996, 118, 9352-9359. (13) Comisarow, M.; Marshall, A. J. Chem. Phys. 1976, 64, 110-119. 10.1021/ac980690d CCC: $18.00
© 1999 American Chemical Society Published on Web 12/18/1998
the coherent motion of a group of ions between a set of opposed electrodes in a strong magnetic field.14 For ions in a magnetic field, mass-to-charge value is derived from observed frequencies by the simple relationship, ω ) qB/m, in which the cyclotron frequency, ω, is proportional to the applied magnetic field, B, and inversely proportional to the mass-to-charge ratio, m/q. If measurements could be made in the absence of any other fields besides the applied magnetic field, then mass-to-charge determination would be trivial and accuracy limited only by the precision of the magnetic field strength measurement. However, to meet the requirement for narrow spectral line width, a static electric trapping potential must be applied to confine ions within the region of the magnetic field where they are detected. This electric field influences both the motion of the ions and the observed cyclotron frequency.15 In addition, perturbations to the trapping electric field are caused by the collective electric potential of the ions within the trapping volume. This effect is generally referred to as space charge and also impacts the measurement of cyclotron frequency.16 A similar shift due to net ion-ion interactions has been reported for quadrupole ion trap mass spectrometers.17 Space-charge effects were first proposed as a limitation to ICR mass accuracy by Sommer et al. in their seminal paper describing the first ICR mass spectrometer, the omegatron.18 Beauchamp later reported a reduction in the expected cyclotron frequency of ions in a drift cell due to space charge19 and represented this symbolically by the relationship, ωobs ) ωc - ωm - δ, where ωm describes the magnetron frequency and δ is a smaller magnitude term resulting from space charge. The terms describing these effects are negative in magnitude since the force on an ion caused by these electric fields opposes the force induced by the magnetic field, thereby reducing the observed cyclotron frequency. Jeffries et al. produced the first quantitative work to address the effect of space charge on ICR mass accuracy.16 By defining the radial electric field gradients in terms of trap electrode geometry and ion cloud shape, shifts in the observed frequency were described for idealized electric fields in several prototypical types of analyzer geometries. Although this mathematically rigorous treatment laid the groundwork for understanding these effects for trapped ions, application to modern FT-ICR is limited for a few reasons. First, the model was designed around the scanning ICR experiment and its detection scheme in which ions reside near the center of the analyzer cell and are ejected one mass at a time by resonant rf excitation. This stands in contrast to FT-ICR, in which ions are first excited into coherent cyclotron motion with a substantial radius of gyration and then detected simultaneously.13 In the Jeffries treatment, the assumption that ions are located near the center of the analyzer cell allows reasonably accurate parametrization of the static electric fields since the deviations from ideal behavior are lowest in the center of most cells.20 Despite these problems, interpretations of this model with respect to empirical observations has been used by
several investigators to formulate relationships between observed frequency and expected mass for FT-ICR experiments.21,22 McIver and co-workers used the theoretical framework of the Jeffries’ equation to develop an expression that relates observed frequencies to the mass-to-charge ratio of the ion, eq 1.22 The first
(14) Comisarow, M. B. J. Phys. Chem. 1978, 69, 4097. (15) Dunbar, R. C.; Chen, J. H.; Hays, J. D. Int. J. Mass Spectrom. Ion Processes 1984, 57, 39-56. (16) Jeffries, J. B.; Barlow, S. E.; Dunn, G. H. Int. J. Mass Spectrom. Ion Processes 1983, 54, 169-187. (17) Cox, K.; Cleven, C.; Cooks, R. Int. J. Mass Spectrom. Ion Processes 1995, 144, 47-65. (18) Sommer, H.; Thomas, H. A.; Hipple, J. A. Phys. Rev. 1949, 76, 1877. (19) Beauchamp, J. L.; Armstrong, J. T. Rev. Sci. Instrum. 1969, 40, 123.
(20) Guan, S. H.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1995, 146, 261-296. (21) Ledford, E. B.; Rempel, D. L.; Gross, M. L. Anal. Chem. 1984, 56, 27442748. (22) Francl, T. J.; Sherman, M. G.; Hunter, R. L.; Locke, M. J.; Bowers, W. D.; McIver, R. T. Int. J. Mass Spectrom. Ion Processes 1983, 54, 189-199. (23) Chen, S.; Comisarow, M. Rapid Commun. Mass Spectrom. 1991, 5, 450455. (24) Chen, S.; Comisarow, M. Rapid Commun. Mass Spectrom. 1992, 6, 1-3.
ωobs )
qB 2aV qFGi - 2 m oB aB
(1)
term is equal to the unperturbed cyclotron frequency, while the second term describes magnetron frequency for an ion in a perfectly quadrupolar static trapping field. The last term expresses the space-charge component of the mass shift, where q represents the elementary charge magnitude, F the ion density, Gi the ion cloud geometry, and o the permittivity of free space. An important feature of this equation is that the last two terms are independent of mass, predicting a constant deviation from the ideal cyclotron frequency for ions of all masses under similar experimental conditions. Using this relationship, McIver was able to demonstrate sub-ppm average mass accuracy for low mass-to-charge ions by correlating the shift between an internal reference mass and the measured mass.22 The results of Jeffries16 and McIver22 were used by Gross and co-workers to parametrize the mass-frequency relationship, eq 2, in which f is the measured frequency of an ion, a and b are
m a b ) + 2 z f f
(2)
experimentally determined constants, and m/z is the mass-tocharge ratio. This equation is currently in widespread use for FTICR mass calibration.21 The second-order frequency term parametrizes the shifts resulting from applied and induced electric fields and is used to depict the relatively small deviations at low massto-charge ratio that are not completely accounted for by a linear expression. Although these terms are included, changes in the ion population severely degrade the ability of this equation to accurately predict frequencies for externally calibrated reference masses, as b is a function of the density of the ions used to calibrate the mass spectrum.21 More recent treatments have been directed toward the simultaneous type of ion detection that is used in FT-ICR. By representing rotating ions as a pair of points, line charges, or cylinders, Chen and Comisarow were able to create a simplified description for Coulombically induced frequency shifts.23,24 The point charge model is based on the interactions between a pair of ion clouds of different mass-to-charge rotating in an orbit corresponding to the behavior of ions after an excitation event, i.e., during the FT-ICR detection process. The Coulombic force between ions of different mass-to-charge was calculated from the
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average distance between the point charges of given magnitude and used to predict the magnetic force reduction, ultimately leading to an expression for the corresponding frequency change. Models that represented the charges as lines or cylinders provided better approximations by considering the effect of charge distribution along the magnetic field axis. A key weakness in this approach is the inability to predict a frequency shift for ions of similar massto-charge, as the average distance between these species would always be zero for most experimental conditions, and spacecharge-induced changes to the trapping potential are not considered by this model. However, experimental evidence shows that ions of similar mass-to-charge experience space-charge-induced frequency shifts.22 Another type of Coulombic interaction involves the attraction between an ion and its induced image charge of opposite polarity on cell electrodes.25 An outwardly directed net force is produced, which opposes the magnetic force in the same manner as the radial electric fields and inter-Coulombic effects. Marshall later formulated analytical descriptions of this shift for several geometries of trapping cells and determined that the magnitude of the shift was mass independent and was determined by the spatial position within the trap for ions of similar charge state.26 This effect was shown to produce very small changes in the observed frequency of an ion. Experimental elimination of the image charge by careful control of the abundances of the two groups of ions was later used to obtain greater than ppb mass accuracy for mass doublets with mass-to-charge ratios less than 20 Da.27 While this achievement represents the best example of mass accuracy in an analytical FT-ICR instrument, the method is limited to measurements where ions of only two mass-to-charge ratios are present. Here we report the results of an empirical investigation into the nature of mass measurement error due to changes in the ion density of singly charged ions in an ICR cell. In contrast to earlier work in this area, we examine the effect of space charge for mass spectra with broad distributions of high-mass ions, typical of those produced by modern ionization methods for macromolecules. With the information obtained in this study, we show that partper-million mass accuracy can be obtained for ions over a broad mass range when external calibration is used. EXPERIMENTAL SECTION All experiments were performed with a 4.7-T FT-ICR instrument with an internal source for matrix-assisted laser desorption/ ionization (MALDI) that was designed and fabricated at the University of Georgia and that has been described previously.28,29 All of the experiments reported here use MALDI ionization. Samples are applied to a target that is positioned within 1 cm of an open-ended cylindrical cell. The 355-nm line of a Nd:YAG laser (ACL-1, New Wave, Sunnyvale, CA) is focused through the cell and onto the sample. Ions formed by MALDI are captured by using gated trapping30-32 with a 200-400-µs delay between
ionization and restoration of the symmetric trapping potential. Prior to detection, nitrogen is introduced into the analyzer region through a pulsed valve for 1-3 ms, producing a peak pressure of ∼1 × 10-5 Torr, to reduce the amplitude of the axial oscillation of the ions by collisional damping. After trapping the ions with a 20-30-V potential, the end electrode voltages are lowered to 2501000 mV prior to detection. Capacitive coupling of the rf excitation to the trap plates during dipolar excitation is used to reduce the axial ejection of ions.33,34 A previously described circuit is used to achieve both gated trapping and capacitive coupling of the excitation signal to the end electrodes in the same experimental sequence.29 Reduction in the number of trapped ions was performed with alternating cycles of quadrupolar excitation (QE) and suspended trapping. After detection, all trapping electrodes were brought to ground potential for ∼1 ms to allow partial axial ion loss. Immediately following restoration of the trapping potential to 1 V, a QE pulse was applied. For narrow-band QE, a 1-Vo-p burst excitation pulse was applied at a frequency that was slightly higher than the observed frequency of the ion. Broad-band remeasurement used a 10-Vo-p arbitrary waveform with a bandwidth that covered the frequency range of interest. QE signals were usually applied for 2-3 s in the presence of nitrogen admitted through a pulse valve, providing a peak background pressure of ∼1 × 10-5 Torr. Reduction in the abundance of ions of a single mass-tocharge from a distribution of trapped masses was accomplished by collisionally activated dissociation, in which nitrogen buffer gas was admitted through a pulsed valve at a peak pressure of 1 × 10-7 Torr, followed by resonant excitation of the target ion with a 5.3-Vo-p signal for 1 ms. Experiments requiring single-ion isolation used an arbitrary waveform pulse for resonant ejection of the isotope ions. Pairs of oligomers were also isolated by using a suitably designed arbitrary waveform pulse for resonance ejection of the unwanted ions. Poly(ethylene) glycol (PEG) samples were prepared for MALDI analysis using the direct deposition method by placing 1 µL of a 1 mM PEG solution on the probe followed by 1 µL of a saturated sinapinic acid (Sigma, St. Louis, MO) solution. Both matrix and analyte were dissolved in 50% aqueous acetonitrile containing 0.1% trifluoroacetic acid (TFA), and a 1-µL amount of a 10 mM NaCl (aq) solution was added to promote sodium ion adduction. Poly(methyl methacrylate) (PMMA) samples were prepared by electrospray deposition of an acetone solution with a 1 mM polymer concentration and 0.1 M concentration of the matrix, 3-trans-indoleacrylic acid, as has been described previously.8 Insulin B-chain was prepared for MALDI in the same manner as for the PEG polymer, but without salt addition. The sample target accommodates about 10-15 sample spots, and both calibrant and analyte were applied to different spots on the same target. External calibration was performed by rotating the sample target to bring first the analyte and then the calibrant under the
(25) Wineland, D.; DeHmelt, H. J. Appl. Phys. 1975, 46, 919-930. (26) Xiang, X. Z.; Grosshans, P. B.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1993, 125, 33-43. (27) Gorshkov, M. V.; Marshall, A. G.; Nikolaev, E. N. J. Am. Soc. Mass Spectrom. 1993, 4, 855-868. (28) Easterling, M. L.; Pitsenberger, C. C.; Kulkarni, S. S.; Taylor, P. K.; Amster, I. J. Int. J. Mass Spectrom. Ion Processes 1996, 158, 97-113. (29) Easterling, M. L.; Pitsenberger, C. C.; Amster, I. J. J. Am. Soc. Mass Spectrom. 1997, 8, 195-198.
(30) Koster, C.; Castoro, J. A.; Wilkins, C. L. J. Am. Chem. Soc. 1992, 114, 75727574. (31) Alford, J. M.; Williams, P. E.; Trevor, D. J.; Smalley, R. E. Int. J. Mass Spectrom. Ion Processes 1986, 72, 33-51. (32) Kofel, P.; Allemann, M.; Kellerhals, H.; Wanczek, K. P. Int. J. Mass Spectrom. Ion Processes 1986, 72, 53-61. (33) Beu, S.; Laude, D. Int. J. Mass Spectrom. Ion Processes 1992, 64, 177-180. (34) Beu, S.; Laude, D. Int. J. Mass Spectrom. Ion Processes 1992, 112, 215230.
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Figure 1. Frequency shift as a function of ion population for the monoisotopic peak of bradykinin, showing the change in observed frequency as a function of total ion intensity as ions from a single laser shot are remeasured.
focal point of the laser. All analytes and matrixes were obtained from commercial suppliers and used without modification. RESULTS AND DISCUSSION Previous studies of the effect of ion number on observed ICR frequency used electron ionization, which allowed the number of trapped ions to be calculated from the neutral gas pressure and electron beam geometry.21,22 Although less rigorous theoretical quantitation exists for ion generation using MALDI, random fluctuations in ion intensity prevent practical prediction of ion number. However, signal intensity in FT-ICR is a linear function of population for ions of similar charge,14 allowing the absolute number of charges to be determined from the measured ion current in a detection circuit of precisely known capacitance. Unfortunately, the uncertainty in cyclotron radius at detection time has limited the accuracy of this type of measurement to ∼(10%.35 It is therefore difficult to determine the absolute number of ions in the cell for the measurements reported here. However, since peak intensities are directly proportional to the number of ions (for singly charged ions), the total ion intensity of the mass spectrum can be used as a measure of the ion density, provided that the experimental conditions are identical for all mass spectra and that the transient duration and damping factors are the same.14 The frequency shift observed by variation of the abundance of ions in a mass spectrum that contains ions of only one massto-charge is shown in Figure 1. Several successive laser shots produced varying numbers of ions, and the mass spectra that were obtained show a linear correlation between observed frequency, ωobs, and ion intensity, with a negative slope. The total frequency change associated with the variation in absolute ion intensity in this example was ∼7.5 Hz, which could cause as much as a 110 ppm frequency error if ignored. This trend agrees with the theoretical models of space-charge behavior that predict a linear relationship between ion population and frequency shift, for example, the work of McIver, eq 1. (35) Chen, R. D.; Cheng, X. H.; Mitchell, D. W.; Hofstadler, S. A.; Wu, Q. Y.; Rockwood, A. L.; Sherman, M. G.; Smith, R. D. Anal. Chem. 1995, 67, 1159-1163.
Figure 2. Observed frequency as a function of ion intensity for substance P measured over 19 laser shots. (a) Ions captured with gated trapping (R 2 ) 0.73). (b) Ions captured with gated trapping and collisional cooling with a pulsed buffer gas show improved linearity due to damping of the trapping motion (R 2 ) 0.90). (c) Addition of quadrupolar excitation to the experimental sequence creates uniform pre-excitation conditions and provides the highest linearity in frequency versus intensity for MALDI-generated ions (R 2 ) 0.99).
The large residual spread about the linear fit in Figure 1 is indicative of the polychromatic nature of MALDI ion production.36-38 Although the mass-to-charge measured by FT-ICR is theoretically independent of ion kinetic energy in the plane normal to the magnetic field, changes in axial kinetic energy can result from velocity fluctuations of desorbed ions and ultimately dictate the extent of their axial motion within the trap boundaries. A spread in the axial energies of the ions is known to cause mass shifts for two reasons. First, ions of lower kinetic energy create a more compressed ion cloud along the magnetic axis that leads to higher ion densities and increased inter-Coulombic interactions.39 Second, for trapping cells that are not perfectly quadrupolar along the magnetic axis, ions will sample different electric field gradients as a function of their position in the analyzer cell, creating variations in the observed cyclotron frequency. These effects produce deviations from the expected linear model in the frequency versus intensity plot, as observed for the data displayed in Figure 2a, from measurements of substance P ionized by MALDI. The experimental error caused by the stochastic nature of desorption can be reduced in part by relaxation of the trapping oscillation, as shown in Figure 2b. Here, ions were allowed to undergo collisions with a pulse of nitrogen prior to detection, to allow damping of the trapping motion. The scatter of the individual frequency measurements from the best-fit line has improved significantly compared to the data of Figure 2a. The least scatter is obtained by axialization of the ions before measurement, as shown in Figure 2c. With the application of quadrupolar excita(36) Schurenberg, M.; Schulz, T.; Dreisewered, K.; Hillenkamp, F. Rapid Commun. Mass Spectrom. 1996, 10, 1873-1880. (37) Beavis, R. C.; Chait, B. T. Chem. Phys. Lett. 1991, 181, 479. (38) Juhasz, P.; Vestal, M. L.; Martin, S. A. J. Am. Soc. Mass Spectrom. 1997, 8, 209-217. (39) Guan, S. H.; Wahl, M. C.; Marshall, A. G. Anal. Chem. 1993, 65, 36473653.
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Figure 3. Observed frequency as a function of total ion intensity for the sodium-cationized peaks of a PEG 3400 sample at (a) n ) 77 (m/z 3431), (b) n ) 82 (m/z 3651), and (c) the A + 1 peak of n ) 89 (m/z 3960) taken from the same spectrum. Linear fits of all three data sets yielded a slope of ∼-0.19 Hz/AU. Repeated suspended trapping followed by quadrupolar excitation cycles of the polymer distribution provided a constant decrease in total ion number between measurements. The peak at m/z 3960 (n ) 89) was ∼1 order of magnitude less intense than the other peaks that were examined.
tion,40 the collisional relaxation period required to dampen magnetron motion in the presence of a buffer gas and center the ions in the magnetic field axis is much greater than the period needed to dampen the trapping oscillation of a given ion. Therefore, axial motion is quenched as a byproduct of the pressure used in the QE experiment without the penalty of magnetron expansion and provides greater linearity than by using a buffer gas without QE. The decoupling of ion generation effects from detection is important for the internal MALDI ion source which provides a wide distribution of ion populations and initial velocities.37,38,41,42 Figure 3 shows a similar plot for three different ions from a PEG 3400 sample that exhibit a wider range of masses and frequencies than in the previous example. For these experiments, a set of ions was trapped from a single laser pulse and then remeasured with alternate applications of quadrupolar axialization for ion centering and brief (e1 × 10-3 s) suspended trapping43 events between remeasurement cycles to reduce the overall ion population in a controlled fashion. The observed range of ion densities is comparable to the range of values that might be observed during the acquisition of a mass spectrum of an analyte and a standard used as an external calibrant. Measured frequency, when plotted as a function of the total ion abundance, is linear with a negative slope and exhibits R 2 values greater than 0.98 and slopes with values that agree within 5% of each other. These deviations provide empirical evidence that ion density produces (40) Schweikhard, L.; Guan, S. H.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1992, 120, 71-83. (41) Zhang, W. Z.; Chait, B. T. Int. J. Mass Spectrom. Ion Processes 1997, 160, 259-267. (42) Zhou, J.; Ens, W.; Standing, K. G.; Verentchikov, A. Rapid Commun. Mass Spectrom. 1992, 6, 671-678. (43) Laude, D.; Beu, S. Anal. Chem. 1989, 61, 2422-2427.
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a predictable, systematic error in mass accuracy for FT-ICR. In this example, the magnitude of the observed cyclotron frequency shift could produce an error as large as 150 ppm for mass determination using external calibration if the effect of space charge is ignored. Prior studies of space charge have not explored whether the size of the space-charge-induced frequency shift depends on the distribution of mass-to-charge values. In other words, do ions that are close in mass experience more pronounced space-chargeinduced frequency shifts than do ions that are widely spaced? Such has been found to be the case for ion coalescence, a severe spacecharge effect for ions that are closely spaced in mass and that are present at high ion density.44,45 To examine whether spacecharge-induced frequency shifts are more pronounced for ions that are close in mass, a group of closely spaced isotope peaks were significantly reduced in intensity, while other ions in the mass spectrum were reduced only marginally. We then looked for differences between the space-charge-induced frequency shift of the closely spaced ions versus ions that were well removed in mass-to-charge from those that were reduced in intensity. To achieve this result, the experiment of Figure 3 was repeated, but the suspended trapping event was replaced by a resonant collisional activation pulse directed at one oligomer and its isotopes in the polymer distribution. Collisional dissociation reduced the population of the target oligomer by a few percent upon each application either by removal of the adducted alkali metal cation (neutralization) or by fragmentation of the molecule to produce lower mass ions outside the broad-band axialization window. Following multiple remeasurements of ions generated from a single MALDI event,46 the absolute intensity of the target oligomer at m/z 2066 and its isotopes (m/z 2067-2070) are observed to decrease over 1 order of magnitude while the total ion intensity is reduced by only 25% during 13 remeasurement cycles. The top panel of Figure 4 shows the polymer mass distribution after the first axialization event and before collisionally activated dissociation (CAD), in which the peaks show the expected distribution with a number average of ∼2000 Da. The lower panel shows a decrease in the intensity of the target ion at m/z 2066, and its isotopes, after 13 remeasurement cycles. A comparison of the absolute intensities of the target ion versus that of the overall polymer distribution is plotted in Figure 5. As can be seen, the intensities of the ions near m/z 2066 are reduced much more significantly than the other ions that are present. Figure 6a shows the measured frequency plotted as a function of the total ion intensity for the n ) 41 PEG oligomer at m/z 1846. Although the relative change in the total ion intensity is fairly small, the magnitude covers more than 25 arbitrary intensity units, so the absolute shift in measured frequency is nearly 8 Hz. At a magnetic field strength of 4.7 T, this would represent a maximum mass error of ∼0.02% for an ion of m/z 1846. A linear fit of these data points indicates a slope of ∼-0.26 Hz per arbitrary unit of total ion intensity. These data are plotted in an identical fashion for the reduced target ion in Figure 6b, for which an identical frequency shift is observed for the change in total ion intensity. If space-charge-induced (44) Huang, J. Y.; Tiedemann, P. W.; Land, D. P.; McIver, R. T.; Hemminger, J. C. Int. J. Mass Spectrom. Ion Processes 1994, 134, 11-21. (45) Naito, Y.; Inoue, M. Int. J. Mass Spectrom. Ion Processes 1996, 158, 85-96. (46) Speir, J. P.; Gorman, G. S.; Pitsenberger, C. C.; Turner, C. A.; Wang, P. P.; Amster, I. J. Anal. Chem. 1993, 65, 1746-1752.
Figure 4. (a) Mass spectrum of a PEG 2000 distribution used to examine the effect of peak spacing on space-charge-induced frequency shifts. (b) The mass spectrum obtained for the ions shown above, but after 12 cycles of CAD of the ions at m/z 2066 with remeasurement of the total ion population. The CAD experiment was performed so that only a few percent of the m/z 2066 ions were lost in each cycle, to provide a small decrease per remeasurement event in the ion population at the targeted mass.
Figure 5. Intensities of peaks at m/z 2022 and 2066 from a PEG 2000 distribution as a function of remeasurement number. CAD was applied to the m/z 2066 ion during each remeasurement cycle to reduce its intensity over 1 order of magnitude. The total ion intensity of the mass spectrum decreased by ∼25%, as can be seen from the intensity profile of the m/z 2022 ion, which is representative of the behavior of the ions that did not undergo CAD.
frequency shifts were sensitive to the mass (frequency) spacings between ions, then one would expect the closely spaced peaks of the isotopic distribution of the oligomer, which underwent a substantial change in intensity, to show a different frequency shift with changes in total ion intensity than do the oligomer peaks that were not reduced significantly. Since the slopes derived from a linear fit of the data in Figure 6a and b are the same, it is observed that the space-charge-induced frequency shift is independent of mass (frequency) separations of ions in the mass spectrum. As a further test of the independence of space-charge-induced frequency shifts upon the mass separation of interacting ions, pairs of oligomers were isolated from a mixture of poly(methyl methacrylate) 2000 and 3000, and the cyclotron frequency of the ions was measured while the mass spacing between pairs of oligomers
Figure 6. (a) Linear fit of measured frequency plotted as a function of total ion intensity for the n ) 41 oligomer of the PEG 2000 distribution shown in Figure 3. (b) Linear fit of the measured frequency plotted as a function of total ion intensity for the oligomer peak undergoing a systematic reduction in intensity. The calculated slope of -0.26 Hz/AU is less than a 3% deviation from the slope of the nonreduced peak.
was varied. For each pair of oligomers, frequency measurements were made for a number of values of total ion intensity, by using CAD to reduce the intensity of the lower mass oligomer in a systematic fashion, with QE-aided remeasurement of the ions for 25 or more measurement cycles, as was done in the previous experiment. Figure 7 shows mass spectra of three pairs of oligomers that were measured. Mass separations of 1000, 500, and 100 Da were examined using oligomers with repeat lengths of n ) 20 and 30, n ) 25 and 30, and n ) 29 and 30, respectively. Figure 8 shows plots of the frequency of the n ) 30 oligomer versus total ion intensity from each of the experiments. The slopes of each line agree within 1% of each other (-0.525, -0.528, and -0.529 for mass separations of 1000, 500, and 100 Da, respectively.) These experiments show that the major space-charge influence on observed cyclotron frequency is a collective effect of the total charge in the cell and does not depend on the frequency separation of the ions. Shot-to-shot differences in ion intensity for MALDI-produced ions are much greater for analytes such as polymers that have many peaks in the mass spectrum as opposed to materials that produce relatively few peaks. This is because the total ion intensity is a function of the number of different masses present as well as the abundance of the individual ions. The data in Table 1 illustrate the relationship between the number of ions present in the ICR cell for a peptide sample producing an isotopic cluster at m/z 2000 and polymer samples that produce a series of regularly spaced masses with a Gaussian distribution with a central value of 2000 Da and σ ) 300 Da. If the signal-to-noise ratio is the same for both mass spectra (i.e., the most abundant peaks have the same intensities), a distribution of PMMA ions will produce a 7.5 times greater ion density than the peptide sample, while a PEG sample will exhibit 17 times the ion density. Since the mass spacing for PEG is smaller (44 Da) than that of the PMMA sample (100 Da), the ion density increases by a factor of 3.76 for PEG relative to PMMA when peaks are present over the same mass range. For Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
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Figure 7. Mass spectra of pairs of mass-selected oligomers of PMMA, used to examine the mass spacing dependence of space charge on observed frequency. Ions were generated by MALDI of mixture of PMMA 2000 and 3000, and resonance ejection was used to remove all but the two selected oligomers. (a) The n ) 20 and 30 sodium-cationized oligomers of PMMA, with a 1000-Da mass spacing. The inset show an expansion of the n ) 30 region, with isotopic resolution of the peak. (b) The n ) 25 and 30 oligomers of PMMA, with a 500-Da mass spacing. (c) The n ) 29 and 30 oligomers of PMMA, with a 100-Da mass spacing. The principal peaks are sodiumcationized ions. Potassium-cationized ions are present at lower abundance 16 amu above the sodium cationized peaks.
Figure 8. Observed frequency for the monoisotopic ion of the n ) 30 oligomer, as a function of total ion intensity. Ions were formed in one MALDI pulse, and remeasurement was used to acquire 25-35 mass spectra, while the lower mass oligomer was subjected to CAD to systematically reduce its abundance in each measurement cycle. Data plotted are from mass spectra of the (a) n ) 20 and 30 oligomers, (b) n ) 25 and 30 oligomers, and (c) n ) 29 and 30 oligomers. The deviation between the slopes of the three plots is less than 1%.
a variation in ion intensity of 10%, typical of the shot-to-shot behavior in a MALDI experiment, the PMMA sample would exhibit a 2.3-Hz frequency shift while the PEG sample would undergo a 5.1-Hz shift, by extrapolating from the experimentally observed trend of ∼-0.3 Hz/AU. If unaccounted for, these shifts would result in mass errors of 63 ppm for the PMMA sample and 141 ppm for the PEG sample at m/z 2000. Analytes such as petroleum distillates, combinatorial libraries, and copolymers can 630 Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
produce greater mass compression due to the high density of mass-to-charge values, accentuating the effects of normal MALDI fluctuations in signal intensity on mass accuracy. This ion distribution consideration to space-charge effects is significant for the MALDI experiment in that the small relative changes in total ion intensity due to variations in ion production between laser shots are magnified by the number of peaks in the mass spectrum to produce large absolute changes in ion intensity and this is particularly significant when polymers are used for external calibration. Because the space-charge effect on observed frequency produces a well-behaved and linear systematic error, appropriate calibration methods should allow one to account for this effect and thus achieve good mass accuracy. This can be achieved either by establishing a calibration curve by using a mass spectrum with a total ion intensity that is close to that of the analyte or by accounting for total ion intensity explicitly in the calibration procedure. As a test of the first of these approaches to correct for ion population effects on mass accuracy, a PEG 3400 sample was used to externally calibrate a single peptide mass, and the results are shown in Figure 9. The PEG 3400 sample was ionized by MALDI, and several stages of ion remeasurement with intervening suspended trapping events were used to reduce the ion population to a level in which the calibrant and analyte had nearly similar total ion intensities. This procedure was performed to calibrate 10 different mass spectra of insulin B-chain, and a representative pair of calibrant and analyte mass spectra are shown in Figure 9. Because the polymer sample produces so many more ions in its mass spectrum than the peptide, the base peak of the polymer sample is more than 80 times less intense than that of the peptide when the total ion intensities are nearly the same for the two mass spectra. As a result of this matching, the average of 10 measurements, each externally calibrated, of the monoisotopic peak of insulin B-chain is 3494.6510 Da, which is within 0.07 ppm of the calculated value of 3494.6513 Da. For the 10 measurements, the average absolute error was 1.6 ppm and the standard deviation was 2.2 ppm. The initial polymer (calibrant) mass spectra total ion intensities were ∼3 times greater than for the corresponding peptide mass spectra. If the effect of space charge was ignored in applying the polymer calibration to the peptide sample, the error would have been 220 ppm, based on the intensity of the initial polymer mass spectra and the known variation of measured frequency with total ion intensity. This result is particularly remarkable in that the desorption dynamics of cation-attached polymers and protonated peptides are quite different, and thus polymers are considered to be poor standards for calibration of peptide samples when using time-of-flight mass spectrometry, which is sensitive to the initial kinetic energy of desorbed ions. The mass accuracy obtained here compares favorably to an earlier result from our laboratory that used this approach to obtain 1.7 ppm average mass error with a polymer external calibrant for the oligomers in a PMMA distribution in the 6200-7200-Da mass range.8 The measurements described above achieve high mass accuracy by acquiring the data in a manner in which the calibrant and the analyte mass spectra have the same total ion intensity. It would be more convenient to account for space charge with a calibration equation that takes into account space-charge effects,
Table 1. Calculation of Mass Error as a Function of Changes in Total Ion Intensity for a Peptide, and Similar Gaussian Distributions of PEG and PMMAa
Table 2. External Calibration of 20 Measurements of the Monoisotopic Molecular Weight of Protonated Insulin B-Chaina
∆f (10% mass base peak total ion intens error at intens intens change) m/z 2000 (AU) (AU) (Hz) (ppm) Peptide PMMA 2000 (100-Da repeat) PEG 2000 (44-Da repeat)
1.00 1.00 1.00
1.00 7.52 17.01
0.30 2.26 5.10
8.5 63 141
a The multiple masses of the polymer distributions greatly increase the number of trapped ions for a given S/N ratio of the most intense peak. A 10% fluctuation in signal, typical with MALDI ionization, produces a greater impact on ion density for the polymer samples, which is predicted to create a much greater deviation in the mass accuracy for these species. Measurement errors are calculated assuming a slope of -0.3 Hz/AU for the frequency versus total ion intensity plot.
analyte TII
measured frequency
calibrant TII
estimated frequency
calcd mass (Da)
error (ppm)
2.454 5.362 6.512 6.874 7.183 7.842 8.324 9.874 9.924 10.036 10.277 10.34 10.523 10.537 11.379 11.515 12.022 12.477 14.166 14.462
20 586.806 20 586.311 20 586.219 20 586.226 20 586.104 20 586.053 20 585.995 20 585.817 20 585.887 20 585.987 20 585.811 20 585.928 20 585.885 20 585.833 20 585.721 20 585.616 20 585.703 20 585.625 20 585.416 20 585.445
10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400 10.400
20 585.957 20 585.773 20 585.804 20 585.849 20 585.760 20 585.780 20 585.773 20 585.761 20 585.836 20 585.948 20 585.798 20 585.922 20 585.898 20 585.848 20 585.826 20 585.735 20 585.876 20 585.847 20 585.818 20 585.879
3494.638 3494.670 3494.664 3494.657 3494.672 3494.668 3494.670 3494.672 3494.659 3494.640 3494.665 3494.644 3494.648 3494.657 3494.661 3494.676 3494.652 3494.657 3494.662 3494.652
-3.7 +5.2 +3.7 +1.5 +5.8 +4.9 +5.2 +5.8 +2.2 -3.3 +4.0 -2.0 -0.8 +1.6 +2.7 +7.1 +0.2 +1.6 +3.0 +0.1
3494.659
+2.3
0.011
3.1
av SD
a The measurements are sorted by increasing total ion intensity (TII) of the analyte mass spectra. The measured frequencies were converted to estimated frequencies using eq 4, using a value of c ) -0.1068 Hz/ AU, which is the slope of the least-squares fit to a plot of the measured frequencies (column 2) versus total ion intensity (column 1). Masses were calculated using eq 3. The calibration constants were obtained by fitting data from a PEG 3400 mass spectrum with a total ion intensity of 10.400. The calibration constants used for the calculation of mass are A ) 7.2203717 × 107, B ) 1.07837 × 1010, and C ) 1.104356 × 1014.
Figure 9. (a) MALDI mass spectrum of bovine insulin B-chain externally calibrated with the PEG 3400 mass spectrum shown in (b). The average of 10 individual externally calibrated measurements yields a value of 3494.6510 Da, demonstrating a mass accuracy of 0.1 ppm.
that would have been measured if the total ion intensity was the same as that of the calibrant mass spectrum. Estimated frequencies are obtained using eq 4, where c is the slope of the frequency
festimated ) fmeasured + c(Icalibrant - Ianalyte) so that mass spectra of arbitrary total ion intensity can be properly assigned. Because there is a linear relationship between ion intensity and space-charge-induced frequency shifts, a calibration equation could easily incorporate a correction that accounts for the effect of total ion intensity based on the measured cyclotron frequency. With the data system that is used for the experiments described in this paper, calibration is achieved by fitting three or more mass standards to a third-order polynomial expression, as shown in eq 3, which is recognized to be the calibration equation
m A B C ) + 2+ 3 z f f f
(3)
proposed by Gross,21 with the addition of a higher order correction term. The calibration constants A, B, and C are accurate only for mass spectra which have the same total ion intensity as that of the calibrant mass spectrum from which the constants were derived. However, one can take the cyclotron frequencies that are measured in a mass spectrum of arbitrary total ion intensity and estimate from these by linear extrapolation the frequencies
(4)
versus total ion intensity plot, obtained from plots such as that in Figure 2, and Icalibrant and Ianalyte refer to the total ion intensities of a calibrant and analyte mass spectrum, respectively. The estimated frequencies can then be used in eq 3 to determine an accurate mass-to-charge value. In other words, a new calibration equation that is sensitive to total ion intensity can be derived by replacing the frequency variable in the three terms on the right side of eq 3 with the expression on the right side of eq 4. Using this approach, 20 measurements of insulin B-chain with total ion intensities ranging from 2.5 to 14.5 arbitrary units (AU) were calibrated using a single PEG 3400 mass spectrum with a total ion intensity of 10.4. Table 2 shows the data used for this measurement. The value of the constant, c, from eq 4 was obtained from the slope of the least-squares fit of a plot of the measured frequencies of the base peak of insulin B-chain versus total ion intensity, which for these experimental conditions, was found to be -0.1068 Hz/AU. This constant is independent of mass and can be obtained from plots generated from mass spectra of either the analyte or a standard, obtained over a range of total ion Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
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Figure 10. Observed frequency as a function of ion intensity for a single remeasured ion with chirp excitation at 30 and 60 Vp-p. The dashed line corresponds to the 30-V data, corrected for the difference in signal response as a function of excitation voltage.
intensity values. The average of 20 measurements of the molecular mass of the protonated peptide yielded a value of 3494.6592 Da, in error by 2.3 ppm from the theoretical value, with an average absolute error of 3.2 ppm, and a standard deviation of 3.1 ppm. While this result produced a larger (but still small on an absolute scale) error than did calibration by using mass spectra of the same total ion intensity, the experimental effort expended was considerably less by this method. Experimental methods and instrument configurations that reduce the charge density by increasing the volume occupied by the ions can reduce the influence of space charge on observed frequencies. Figure 10 shows an example of the manner in which excitation radius affects the observed frequency. Since the cyclotron radius is linearly proportional to the dipolar excitation electric field magnitude, the volume of the three-dimensional cylinder occupied by the excited ions would be at least 4 times larger if the excitation voltage were doubled, neglecting changes in potential along the z axis at different radii. The plot of observed frequency versus total ion current is compared in Figure 10 for excitation voltages of 30 and 60 Vp-p under similar experimental conditions. The 60-Vp-p amplitude, which closely approximates the excitation conditions of previous examples, results in an observed slope of -0.33 Hz/AU, while the 30-Vp-p excitation provides about half the normal excitation radius and results in a slope of -1.28 Hz/AU for a linear fit of the data points, ∼4 times larger than for 60 V. However, the ions that have received 30-V excitation induce a signal that is half as strong as that induced by the ions that have received 60 V of excitation. If one corrects for this effect, then the slope of the frequency ion number response of the 30-V data is twice that of the data obtained at 60-V excitation amplitude. The reduction in space-charge-induced frequency shifts can be attributed to two factors. First, the larger radius orbit allows ions of different mass-to-charge to achieve a wider spatial separation in the plane perpendicular to the magnetic field. Second, because of the approximately quadrupolar shape of the trapping potential in the plane that lies parallel to the magnetic field, ions
632 Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
that have a larger cyclotron orbit can assume a wider spatial distribution along the magnetic field axis. Both of these factors cause a reduction in ion density when a given number of ions is present in the analyzer cell. These data suggest that the use of larger diameter analyzer cells would be useful for reducing spacecharge-induced mass errors. However, a larger volume cell will allow ions to sample regions of the magnetic field of greater inhomogeneity, which could offset gains in mass accuracy from reduced space charge. Further experimentation will be required to determine the benefit of this approach to improving mass accuracy. It is necessary to accurately calculate the total ion intensity of a mass spectrum for correction of space-charge effects either by matching calibrant and analyte mass spectra or by using the calibration equation presented above. This task is not trivial to perform manually when there are large number of peaks present in the mass spectrum, but should be more readily accomplished by automated methods. Internal calibration provides the best method to account for space charge, as both the calibrant and the analyte are exposed to the identical total ion intensity. However, addition of an internal calibrant is not always feasible, especially for samples with low sensitivity or unknown ionization efficiencies. It is thus important to be able to employ external calibration and still achieve comparable mass accuracy. CONCLUSIONS We have shown that the mass accuracy obtained by FT-ICR can be improved by correcting for the differences in the number of trapped ions when external calibration methods are used. Mass accuracy less than 2 ppm can be obtained for ions up to m/z 6000 when external calibration is used. This improvement is important for ions formed by MALDI, as the chaotic nature of laser desorption often produces wide shot-to-shot variations in the number of ions that are produced. A sample characteristic such as mass distribution is also an important factor for analytes or calibrants such as polymers in which small changes in the abundance of peaks in the mass spectrum (and in their signalto-noise ratio) produce large changes in the overall number of trapped charges. For a given signal-to-noise ratio, the total ion intensity increases as the number of components in the sample increases. Thus, complex mixtures such as polymers, tryptic digests, or combinatorial libraries will exhibit a much greater total ion intensity than a single component sample, for a given value of signal-to-noise ratio. By accounting for the total number of ions in the cell, samples of any type can be examined with low-ppm mass accuracy. ACKNOWLEDGMENT Financial support by the National Science Foundation (Grant CHE-9412334) and the Rohm and Haas Corp. is gratefully acknowledged. Received for review June 26, 1998. Accepted November 5, 1998. AC980690D
