Variation of the Fourier Transform Mass Spectra ... - ACS Publications

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Variation of the Fourier Transform Mass Spectra Phase Function with Experimental Parameters Yulin Qi,† Mark P. Barrow,† Steve L. Van Orden,‡ Christopher J. Thompson,‡ Huilin Li,† Pilar Perez-Hurtado,† and Peter B. O’Connor*,† † ‡

Department of Chemistry, University of Warwick, Coventry, United Kingdom Bruker Daltonics, 40 Manning Road, Billerica, Massachusetts 01821, United States

bS Supporting Information ABSTRACT: It has been known for almost 40 years that phase correction of Fourier transform ion cyclotron resonance (FTICR) data can generate an absorption-mode spectrum with much improved peak shape compared to the conventional magnitude-mode. However, research on phasing has been slow due to the complexity of the phase-wrapping problem. Recently, the method for phasing a broadband FTICR spectrum has been solved in the MS community which will surely resurrect this old topic. This paper provides a discussion on the data processing procedure of phase correction and features of the phase function based on both a mathematical treatment and experimental data. Finally, it is shown that the same phase function can be optimized by adding correction factors and can be applied from one experiment to another with different instrument parameters, regardless of the sample measured. Thus, in the vast majority of cases, the phase function needs to be calculated just once, whenever the instrument is calibrated.

T

he Fourier transform ion cyclotron resonance mass spectrometer (FTICR) is superior to all other mass analyzers in mass resolving power and mass accuracy.1,2 Because it measures frequency, which is independent of the ions’ velocity, the precise determination of mass-to-charge ratio (m/z) is not affected by the kinetic energy. Thus, a modern FTICR can easily achieve mass accuracy less than 1 ppm and resolving power (m/Δmfwhm) greater than 1 M under normal conditions.3,4 Furthermore, the versatility and compatibility of FTICR to different fragmentation methods makes it an ideal instrument for tandem mass spectrometry analysis of large biological modules.5 Although it is wellknown that the mass resolving power of FTICR varies linearly with the applied magnetic field strength,2 it is less widely appreciated that the resolving power of FTICR can be enhanced by a factor up to 2 by phasing the magnitude-mode spectrum into an absorptionmode spectrum if the spectral data is processed accurately, which has been a long-standing problem for almost 40 years.6,7 This topic has been recently discussed by two publications last year, first by F. Xian et al., using a detailed model of the excitation pulse from the experiment,8 and second by Y. Qi et al., using a quadratic least-squares fit, iterated over the entire phase range to form a full frequency shift function for the entire spectrum.9 This paper aims to (a) review the features of an absorption-mode spectrum, (b) parametrize the phase function with variation of experimental conditions, and (c) apply the phase function from scan to scan and sample to sample in routine phase correction.

’ THEORY Absorption-Mode Spectrum and Its Advantages. An

N-point time-domain ion cyclotron resonance signal will yield a r 2011 American Chemical Society

mathematically complex spectrum consisting of two frequencydomain spectra after Fourier transformation (FT),10,11 Re(ω) and Im(ω), which correspond to the real and imaginary parts of the complex spectrum.12 The general relation is given in eqs 1a
1c. Z ð1aÞ FðωÞ ¼ FðtÞe
iωt dt ¼ AðωÞ þ iDðωÞ ΦðωÞ ¼ arctan½DðωÞ=AðωÞ

ð1bÞ

h i1=2 MðωÞ ¼ ðAðωÞÞ2 þ ðDðωÞÞ2

ð1cÞ

where ω = 2πf is the angular frequency, F(t) and F(ω) are the time and frequency domain data, respectively; A(ω) = Re(ω) and D(ω) = Im(ω) are the absorption-mode and dispersion-mode spectra respectively; and Φ(ω) and M(ω) are the phase value and magnitude-mode spectra (the mode most often used in FTICR), respectively. The frequency-domain spectrum is then converted to an m/z spectrum with less than 1 part-per-million (ppm) mass accuracy using either a linear or quadratic function based on a variety of calibration methods.13 Development of spectrometry always aims to pursue higher resolution.14 Dating back to the very first FTICR mass spectra in 1974,15,16 it was readily recognized that an absorption-mode spectral peak is inherently narrower than its corresponding Received: July 7, 2011 Accepted: October 5, 2011 Published: October 05, 2011 8477

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Analytical Chemistry magnitude-mode (which removed the phase information),17 and in FTNMR spectroscopy, the phasing problem was solved in the 1970s.18,19 Although the conceptual understanding is the same for both, the complexity is very different. In NMR, the phase varies over the spectrum by typically 0.1
0.3π, far less than one cycle (2π). While in FTICR, because the excitation bandwidth is 3 orders of magnitude broader (from kilohertz to megahertz), the variance of phase value is much larger (e.g., ∼10 000π for the m/z range from 200 to 2000). It is important to note that any peak can be perfectly phased at some Φ(ωi) between 0 and 2π, and this means that a small region around this peak, where the phase variance is less than 2π (perhaps several daltons), is also easily phased. Phase wrapping quickly complicates this (Figure S1 in the Supporting Information), because Φ(ωi)= Φ(ω i) + 2niπ for any integer ni at any ωi, and the phase variation for an entire spectrum is perhaps ∼10 000π. In order to solve the Φ(ω) for the entire m/z range, it is necessary to calculate all the individual values of ni before fitting the phases into a quadratic function Φ(ω) (eq 2). Note: because every addition of a frequency/phase pair to the quadratic least-squares fit also adds one value of ni, the solution to the phase function equation is not unique being under-determined by exactly one degree of freedom. However, this lack of uniqueness is clearly characterized by the same phase wrapping problem in that the set of ni integer values can always vary by (an integer, but their relative values remain constant. The above problem was recently solved using an iterative quadratic least-squares fit and iteration methodology.9 A unique feature of this method is that the user does not need to know anything about the experimental pulse sequence in order to acquire the phase function, provided there are a sufficient number of peaks (about 10, which is easily achieved in most spectra although the method becomes easier with more dense spectra). The resulting absorption-mode spectrum shows several advantages over the conventional magnitude-mode: First, the peak width at half-maximum height is narrower than its corresponding magnitude-mode by a factor depending on the damping of the transient, ranging from ∼1.7 (signal acquisition time . signal damping time, “Lorentzian” peak shape) to 2 (signal acquisition time , signal damping time, “sinc” peak shape) (Figure 1, top),20,21 which means the mass resolving power can be enhanced by the same factor. In a real experiment, the peak shape of a spectrum is always a convolution of both a “sinc” and a “Lorentzian” function. Therefore, the routine improvement in resolution by phase correction is between 1.7 and 2. Second, the mass accuracy of adjacent peaks should be improved because an absorption-mode spectrum has much reduced “tailing” compared with the magnitude-mode and, therefore, decreases the shape distortion of neighboring peaks (see below). Third, the intensity of a perfectly phased absorption-mode peak is identical to its corresponding magnitude-mode peak; thus, the increase of resolution will not greatly affect the signal-to-noise ratio (S/N) of the peak, and the much narrower shoulder at the base extends the effective dynamic range of the spectrum. Other methods to improve the peak shape such as apodization22,23 can be accomplished only at the cost of resolution or S/N. Fourth, electronic noise peaks and aliased peaks are readily recognized because they are usually incorrectly phased. Parameterization of the Phase Function. Because of the linear frequency sweep excitation (Figure 2 in ref 9), the ions’ corresponding phase angle, Φ(ω), is a quadratic function of the

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excitation frequency (eqs 2) and that such an equation could be used for phase correction,9 where A, B, and C are the fitted constants. ϕðωÞ ¼ Aω2 þ Bω þ C

ð2Þ

However, the previous published method is user-interactive,9 requiring manual peak selection and phase assignment, and it was assumed that the phase function varies from experiment to experiment if the instrument parameters are changed which means the function needs to be calculated every time. These drawbacks could potentially hinder the application of phase correction in routine work. However, because the bulk of the manual algorithm could be easily automated and computation for the phase function only has to be done when the pulse sequence parameters are changed, it was likely that the function could be parametrized by adding a few correction factors. If so, then the phase function could be applied directly to further scans without needing to be recalculated for each spectrum. Thus, a series of experiments were performed to test the variation of the phase function with particular experimental parameters such as trapping voltage, excitation amplitude, and space-charge. In the ICR trap, the reduced ion cyclotron frequency (including the electric field and the effect of space-charge) can be written in eq 3a (with ωc and k defined in eqs 3b and 3c):2,24 ωc ½1 þ ð1
4k=ωc Þ1=2  ωþ ¼ ð3aÞ 2 ωc ¼ k¼

qB0 m

ð3bÞ

qV α q2 FGi þ 2 ma ε0 m

ωþ ¼

qB0 αV V 2 α2 m
2
4 3 a B0 a B0 q m

ð3cÞ

...

ð3dÞ

in which B0 is the magnetic field; α is a scaling factor which depends on the trap geometry and ranges typically from 2 to 4; a is the characteristic dimension of the ICR trap usually defined as the distance between trapping plates; and V is the trapping potential applied to the ICR trapping plates. The last term in eq 3c expresses the bulk space-charge component of the frequency shifts, where F represents the ion density, Gi the generalized ion cloud geometry correction factor, and ε0 the permittivity of free space. As space-charge shifts are largely independent of m/z,25,26 the effect of electric field and space-charge are explored separately in the following section. Variation of the Phase Function with Trapping Voltage. Variation of the trapping voltage changes the electric field contribution to the ions’ frequencies (eqs 3a and 3c) and hence also alters the applied phase function. Thus, k in eq 3a is substituted by the first term in eq 3c, and eq 3a can be expanded in a Taylor series to yield eq 3d. In eq 3d, the third term can be ignored in routine calibration27,28 because it is less than 1/106 of the second term in magnitude (the error caused by ignoring the third term is less than 1 part-per-billion). Additionally, because the phase variance over an entire spectrum is >104π and because the phase function is quadratic, the order of magnitude error caused by neglecting the third term of eq 3d is squared (namely, 10
12), so that neglecting of this term in calculation of the phase function is perfectly valid. Therefore, the “ω” in the initial phase 8478

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Figure 1. (Top) Simulated time-domain ICR signals (left) and frequency-domain magnitude (black) and absorption-mode (gray) spectra (right), for τ . t, sinc function (top), for τ , t, Lorentzian function (bottom). Note that the sinc function has negative sidelobes in the absorption-mode after Fourier transform. (Bottom) A small segment from the absorption-mode crude oil spectrum; inset, zoom in for the labeled peak to show the negative blips of a sinc function.

function (eq 2) is substituted by the first two items of eq 3d, which gives eq 4. ϕðωÞ ¼ Aω2 þ Bω þ C


2αA α2 A 2 αB ωV þ V
2 V a2 B0 a4 B 0 2 a B0

ð4Þ

The resulting equation is an optimized phase function with the correction factor for trapping potential, V (average of front and back plate, usually the same). The other parameters α, a, and B0 are the constants of the instrument which can be easily acquired (see below). Variation of the Phase Function with Total Ion Number. Frequency (and phase) of ions also vary with total ion number. Easterling and co-workers used the theoretical framework of the eq 3 to demonstrate that the ion’s frequency shift is linear proportional to the number of ions in the ICR cell, which is

mostly independent of m/z.26 In the hexapole (of the FTICR), the number of ions increases linearly with the accumulation time. As the trapped ions are analyzed, space-charge is regarded as a constant shift from the ideal cyclotron frequency for ions of all masses in the cell on average, a “mean-field” approximation. Thus, we can rewrite the phase function as follows ωnew ¼

qB0 αV q2 FGi q2 FGi
2
 ω
st, s ¼ a B0 ε0 B0 m ε0 B0 t

ð5aÞ

So, substituting eq 5a into eq 2 ϕðωÞ ¼ Aω2 þ ðB
2AstÞω þ C þ As2 t 2
Bst

ð5bÞ

Here, s is defined as a space-charge factor with the unit of ion density per time; t is the accumulation time in the hexapole; eq 5b 8479

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Figure 2. (Left) Phase corrected absorption-mode spectra with the trapping potential from 0.1 to 10 V; (right) ion accumulation time from 0.01
5 s (spectrum J presents an inset figure showing its transient which has clear space-charge distortions).

is the estimation of the phase value with the space-charge effect built in. Note: eq 5 assumes that the beam current is constant, but Easterling et al. showed that space-charge frequency shifts are linear with total ion number,26 so the same excitation can be used for varying beam current based on total ion number by redefining “t” as the total ion number and “s” as a parametrization constant. Both methods introduce some error into the phase function because the total space-charge effect usually varies, which will be discussed below. In this paper, the phase function for the mass range of 200
2000 was calculated first from an oil sample and applied to small molecules and large proteins separately. The instrument parameters were changed from normal to extreme conditions (Figure 2) in order to detect the variation of phase corrected absorption-mode spectra.

’ EXPERIMENTAL METHODS Sample Description and Preparation. A crude oil sample (SRM 2721, light-sour) was purchased from NIST, diluted 2000 times in a 50:50:1 toluene
methanol
formic acid mixture. Ubiquitin, purchased from Sigma-Aldrich (Dorset, England), was diluted into 0.1 μM and 0.2 μM in a 50:50:1 water
acetonitrile
formic acid mixture for the molecular ion charge state distribution and electron capture dissociation (ECD)29 spectra, respectively. Collagen type I and sequencing-grade trypsin were purchased from Sigma-Aldrich; collagen was digested and then run at approximately 2.5 μM concentration in 50:50:1 methanol
water
formic acid. ESI-L low concentration tuning mix (external calibration) is purchased from Agilent Technologies (Palo Alto, California) without dilution. All solvents were HPLC-grade, obtained from Sigma-Aldrich Chemical Co. (Dorset, England). Instrumentation. All spectra were recorded using a solariX 12 T FTICR mass spectrometer (Bruker Daltonik GmbH, Bremen,

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Figure 3. (A) Ubiquitin charge state spectra in absorption-mode initially phase corrected using the phase function from the oil spectrum (Figure 2B) using the same instrument parameters; (B) zoom in of the 11+ charge isotope peaks (m/z ∼779) in part A; (C) rephased absorption-mode spectrum generated by correcting the phase value of 3 (or more) peaks in the spectrum and recalculating the quadratic phase function; (D) zoom in of the 11+ charge isotope peaks in part C.

Germany) by positive-mode electrospray ionization (ESI). Broadband frequency sweep excitation (92
922 kHz (m/z 2000
200) at 125 Hz/μs sweep rate) was followed by a prescan delay of 3.5 ms and image current detection to yield 4 mega-point time-domain data sets. The ion accumulation time in the hexapole was varied from 0.01 to 10 s, trapping voltage in the ICR cell from 0.1 to 10 V, and excitation power from 10 to 100 V. The data sets were coadded (10 acquisitions each to increase S/N), zero-filled, and fast Fourier transformed without apodization. All data sets were then processed using MatLab R2010a (MathWorks, Natick, MA). Mass Calibration. The observed frequency is converted into m/z by means of a three term quadratic equation.13,28 The instrument was externally calibrated first using ESI tuning mix before each experiment. The oil spectrum is internally calibrated using a series of homologous compounds throughout the m/z range from 200 to 800. Both ubiquitin and collagen spectra are calibrated internally using the molecular ions of different charge states.

’ RESULTS AND DISCUSSION Optimize Phase Function. The original phase function for a m/z range from 200 to 2000 was calculated based on the oil spectrum (Figure 2B) using the quadratic least-squares fit and iteration.9 The instrument parameters from Figure 2B were then applied to acquire a ubiquitin molecular ion spectrum, and the absorption-mode spectrum of ubiquitin was then corrected using the same phase function from Figure 2B. As shown in Figure 3, the phase value of spectrum shifts constantly probably due to the slight difference in space-charge conditions; however, the variation of phase value for every point was definitely within one cycle 8480

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Analytical Chemistry (2π) (Figure 3B). Therefore, the phase wrapping effect does not exist in the spectrum, which means that, using the same instrument parameters as before, the previous phase function can provide a very close approximation for the phase value of the new spectrum, and thus, the phase function can be reused easily from experiment to experiment. Correction of the phase function is achieved by choosing three (or more) peaks in the spectrum, calculating their phase values from eq 1b, and adding the resulting values to the predicted phase from the provisional phase function. A new, corrected phase function is then calculated by quadratic least-squares fitting. This result clearly shows that computation of the phase function must be done only when the pulse sequence is changed, so that in the vast majority of cases, it only has to be calculated once whenever instrumental drift requires recalibration of the instrument. Since the original phase function is now defined, subsequent experiments endeavored to determine the phase function variance as a function of the following parameters: trapping potential, accumulation times, and excitation power from normal to extreme conditions. Then the variance of the phase function was applied to correct the phase of spectra using the predicted functions mentioned above. The majority of the spectra used for demonstration were acquired from crude oil, because such samples have high intensity peaks throughout the entire mass range which would clearly capture any error resulting from incorrect phase correction. Trapping Potential. Equation 4 is applied to predict the phase shift caused by variance of the trapping potential; the resulting spectra are shown separately (Figure 2, left). A rough estimation of eq 3 tells that a change of 0.1 V in the trapping potential will cause a cyclotron frequency shift of several hertz, which is about 10π for the frequencies used (eq 4); as a consequence, the phase function varies significantly with a small change in trapping voltage. Figure 2 shows that a properly parametrized eq 4 can effectively convert the phase function for different trapping potentials (from 0.1 to 10 V). The maximum setting for the instrument is 10 V and is sufficient to show the relationship, particularly because detection is normally performed with a trapping potential below 1 V. Number of Ions. An important feature in eq 5a is that the space-charge effect on the frequency is linear with the ion population, and moreover, the accumulation time is independent of m/z.26 The value of “s” in eq 5a is calculated by choosing any peak in the spectrum and recording its observed frequency change with accumulation time; the value is acquired by linear regression with a related coefficient (R2) greater than 0.99. Given the R2 > 0.99, the error of the predicted phase value from eq 5 is within 0.01π, which is a sufficiently good approximation to eliminate the phase wrapping effect. With such an approximation, the exact phase value for each point can be easily calculated, thus, the entire m/z range is then rephased as before. Figure 2 shows the application of eq 5b with different ion accumulation times. As is shown, the phase function remains fairly stable throughout the entire time scale from 10 ms to 5 s of accumulation time. Surprisingly, the phase function is still stable even in the extreme space-charge condition which already shows the spontaneous loss of coherence catastrophe or “nipple effect” in the transient (Figure 2J).30 However, in such an extreme case, the peak shift and artifacts caused from the space-charge effect are much more severe than the phase correction itself. Excitation Radius. Ideally, an ion’s frequency is a function of the excitation radius, but this is only true in a perfect,

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hyperbolic cell.30,31 The new shaped cell designs from Rempel,32 Tolmachev33 and Nikolaev34 greatly improve the adherence to the ideal. However, the data herein was generated from the Infinity cell,35 in which the electric field is not shimmed in any way. Thus, frequency does change slightly with excitation radius. An ion packet’s orbital radius is determined by the applied excitation potential; however, change of the cyclotron radius has effects on both the electric field and space-charge conditions which make prediction of the exact cyclotron frequency difficult.36 According to the experimental data, the shift of ion cyclotron frequency was recorded, which roughly follows a quadratic relation with the ion excitation potential (Figure S4 in the Supporting Information); however, these plots show that, in the Infinity cell, the resulting quadratic function varies substantially for different ions and thus is not sufficiently accurate to reach a reliable prediction for the ions’ frequency to be used for a proper evaluation of the phase function. For that reason, the ion excitation potential was held as a constant throughout the experiment. Furthermore, since the newer, improved cell designs will largely eliminate this effect, a full evaluation of this multidimensional frequency shift function is not warranted at this time. Effect of Zero-Filling on Absorption-Mode Spectra. During the FT data processing, the time-domain transient is recorded discretely and numerically transformed to generate a discrete m/z spectrum, thus mass error occurs when the apex of a continuous peak falls between two adjacent sampled points in the discrete spectrum. One solution is to use zero-filling, which is a computational trick used to increase the sampling points of a spectrum. It can be viewed as adding N zeros at the end of N observed points in the time-domain (T); thus, the Fourier transform is calculated at intervals of 1/(2T) rather than 1/T and visual resolution of the spectrum is doubled.20 As is originally pointed by Comisarow,37 peak picking algorithms improve dramatically with the first zerofill and slightly with more zero-fills when the transient signal decayed significantly during the acquisition (is Lorentzian peak shape, τ , t). For this reason, most FTICR data analysis zero-fills the original N-points data once by default before the Fourier transform. Additionally, it is been proved by the NMR community that the causality principle requires that one zerofill is needed for the absorption-mode spectrum to recover the information lost in the dispersion-mode. Figure 4 (inset) shows, for one zerofill, that the phase corrected absorption-mode spectrum exhibits less information than its corresponding magnitude-mode (the peak splitting is not well resolved), and a smaller and better resolved absorption-mode spectrum appears only with a second zero-fill. This is because the computed absorption and dispersion-mode spectra are independent for a periodic pulse excitation, and the causality principle requires an extra zerofill to transfer the information residing in the dispersion-mode FT into the absorption-mode.38 Therefore, an extra zerofill is best for absorption-mode ICR spectra. Phasing Artifacts. Phase corrected spectra always show negative wiggles in both sides of the peak (Figure 1, bottom) because an absorption-mode spectrum has a “sinc” peak shape (Figure 1, top). In the previous paper, negative-valued peaks were incorrectly attributed to the resolution of the frequency sweep waveform and/or the centroiding algorithm used.9 As mentioned above, the peak shape resulting from the Fourier transform is a convolution of both a “sinc” and a “Lorentzian” function; thus the negative wiggles are the nature of an absorption spectrum which cannot be eliminated except by apodization.20,39 8481

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Figure 4. Isotopic distribution of a fragment from collagen; (inset) 1N (top) and 2N (bottom) zerofills of the labeled peak in both magnitude (gray) and absorption-mode (black) display; the left peak is the deamidated peptide, the right one with is the undeamidated precursor (A + 4 isotope).

These wiggles are also present in the magnitude-mode spectrum but are only positive valued because of the square calculation, broadening the base of a peak which tends to distort neighboring peaks and can confound peak detection algorithms.40 Mass Accuracy and Resolution. Figure S2 in the Supporting Information shows the mass error41 distribution for ESI magnitude and absorption-mode spectra of the oil sample (peaks were accumulated for 10 scans and picked at S/N over 10). A total of 3498 peaks (m/z 187
995) were assigned in the magnitudemode with a root-mean-square (rms) error of 81 ppb, and these peaks were reassigned in the absorption-mode which achieved an error of 80 ppb. It is interesting to notice the absorption-mode does not improve the mass accuracy for these peaks. To test the result further, the same approach was applied to an ECD spectrum of 11+ charged ubiquitin, with 215 peaks (m/z 537
1580) assigned, which achieved an rms error of 446 ppb (magnitude-mode) versus 440 ppb (absorption-mode), see Figure S3 in the Supporting Information. One possible reason for this surprising lack of improvement is that the intensity of a perfectly phased peak is identical to its corresponding magnitudemode (see Figure 1, top); therefore, the position of peaks picked by centroiding is almost the same if the peak is intense and not distorted by neighboring peaks. Additionally, these data in the absorption-mode show a random error distribution rather than the m/z-dependent systematic error described by Savory et al.,42 which need to be corrected in order to observe a mass accuracy improvement.27,28 The discrepancy in mass errors from this work compared with Savory et al.42 are likely to arise from use of different ICR cell designs which will likely cause different systematic errors. However, noting the absorption-mode has much narrower baseline compared with magnitude-mode, this feature should significantly change the centroiding when peaks are sufficiently close and such a case is shown in Figure 4, inset. After phase correction, it is surprising to see that, although the peak shape becomes much narrower, the overlapping part has not been split at all and the peak intensities are even decreased. However, it is also interesting to notice the apexes of the two peaks are shifted in the absorption-mode which indicates the change of mass accuracy! Anecdotally, it appears that low intensity peaks next to high intensity peaks show an increase in mass accuracy, but a

detailed analysis has not yet been done. This improvement is considered to be systematic, depending on the degree of peak distortion and different compound types. Magnetic Field and Geometry Factor. In most commercial FTICR instruments, the mass calibration from frequency to m/z consists of fitting either the Ledford (eq 6)28 or Francl equation,27 and information on the magnetic field and geometry factor are accommodated within the calibration parameters below, where e is the elementary charge. m=z ¼

ALedford BLedford þ ω ω2

ALedford ¼ eB0

ð6aÞ ð6bÞ

eV α ð6cÞ a2 The exact magnetic field of the instrument can be extracted from eq 6b. Also the geometry factor, α, is a constant dependent on the shape of the ICR cell (cylindrical Infinity cell35 in this project). Values of α for different ICR trap designs commonly used were listed in a recent review.2 The value of “α” is determined by rearranging eq 3d to yield eq 7 and then plotting frequency versus trapping voltage. BLedford ¼

ω¼


α a2 B0

V þ

qB0 m

ð7Þ

The slope (
α/a2B0) and intercept (qB0/m) were calculated using linear regression by varying the trapping potential, V, and monitoring the corresponding observed frequency, ω. The measurement was carried out by monitoring two peaks in the Agilent ESI tuning mix, with one in the high mass range (reference m/z: 1821.9523), the other in the low mass range (reference m/z: 622.0290). Table S1 in the Supporting Information lists the result, and the value of α = 2.841 was applied in the phase equations above.

’ CONCLUSIONS This manuscript discussed the parametrization of broadband phase correction for FTICR mass spectra with trapping voltage, 8482

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Analytical Chemistry ion accumulation time, and excitation amplitude including experimental data and a theoretical treatment. These experiments show that the phase function can be applied directly from scan to scan and from sample to sample (with slight modification) in cases where (1) the pulse sequence does not change or (2) the pulse sequence change is limited to modest variation to trapping voltage or ion accumulation. The present method was successfully applied to complex mixtures ranging from petroleum to protein ECD spectra. It is clear that, in the vast majority of cases, the phase function need be calculated only once, whenever the instrument calibration changes, and it can then be applied directly to almost all spectra with little effort to yield 70
100% resolution increase at no cost. While the initial investigation on mass accuracy before magnitude-mode and absorption-mode shows no differences, these data suggest that a significant improvement will be observed for low intensity peaks on the shoulders of higher intensity peaks due to changes in peak shape between the two modes. This broadband phase correction can be easily automated in routine work as is already done in NMR. The current results were performed offline as postprocessing of existing transients, but once the phase function is known and the parametrizations discussed above are applied, phase correction requires a single point-by-point vector complex number multiplication on the transient, which takes less than a millisecond on modern processors. Thus, the method is, in principle, fast enough to be applied online on a chromatographic time scale.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Phone: +44 02476 151008. Fax: +44 02476 151009. E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the University of Warwick, Department of Chemistry, and the Warwick Centre for Analytical Science (EPSRC funded by Grant EP/F034210/1). The authors would also like to thank Joseph Meier, Tzu-Yung Lin, Rebecca Wills, Andrea Lopez Clavijo, and Andrew Soulby for help with the instrument. ’ REFERENCES (1) Amster, I. J. J. Mass Spectrom. 1996, 31, 1325–1337. (2) Marshall, A. G.; Hendrickson, C. L.; Jackson, G. S. Mass Spectrom. Rev. 1998, 17, 1–35. (3) Ledford, E. B., Jr.; Ghaderi, S.; White, R. L.; Spencerr., B.; Kulkarni, P. S.; Wilkins, C. L.; Gross, M. L. Anal. Chem. 1980, 52, 463–468. (4) Schaub, T. M.; Hendrickson, C. L.; Horning, S.; Quinn, J. P.; Senko, M. W.; Marshall, A. G. Anal. Chem. 2008, 80, 3985–3990. (5) O’Connor, P. B.; Speir, J. P.; Senko, M. W.; Little, D. P.; McLafferty, F. W. J. Mass Spectrom. 1995, 30, 88–93. (6) Comisarow, M. B. J. Chem. Phys. 1971, 55, 205–217. (7) Marshall, A. G. J. Chem. Phys. 1971, 55, 1343–1354. (8) Xian, F.; Hendrickson, C. L.; Blakney, G. T.; Beu, S. C.; Marshall, A. G. Anal. Chem. 2010, 82, 8807–8812.

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