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Electronic Theses, Treatises and Dissertations The Graduate School
2012
Broadband Phase Correction of FourierTransform Ion Cyclotron Resanonce MassSpectraFeng Xian
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THE FLORIDA STATE UNIVERSITY
COLLEGE OF ARTS AND SCIENCES
BROADBAND PHASE CORRECTION OF FOURIER TRANSFORM ION CYCLOTRON
RESANONCE MASS SPECTRA
By
FENG XIAN
A Dissertation submitted to the Department of Chemistry and Biochemistry
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Degree Awarded: Spring Semester, 2012
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Feng Xian defended this dissertation on March 30, 2012.
The members of the supervisory committee were:
Alan G. Marshall Professor Directing Dissertation Christopher L. Hendrickson Professor Co-Directing Dissertation Stephen Hill University Representative Naresh S. Dalal Committee Member Michael Roper Committee Member
The Grduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements.
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To my parents, Huaiyun Xian and Mingxiang Gao; my wife, Donghong Min; my daughter,
Stephanie Xian, my son, Anthony Xian.
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ACKNOWLEDGEMENTS
I am sincerely and heartily grateful to my supervisor, Dr. Alan G. Marshall, for his
excellent guidance, caring and support. Dr. Marshall gives me valuable suggestions on how to
become a successful scientist and provides me with a scientific environment for doing research. I
am sure that it would have not been possible without his patient and intelligent advising.
I would also like to thank Dr. Stephen Hill, Dr. Naresh S. Dalal and Dr. Michael Roper
for their inspiring suggestions, their time and effort to serve on my examination committee.
I would also like to thank Dr. Chris Hendrickson for teaching me basically everything
that I know about mass spectrometry. His valuable suggestions and helpful discussions are very
important part in my research. I also thank Dr. Steve Beu for his expertise in the fields of FT-
ICR instrumentation and Dr. Greg Blakney for technical support in software development.
I would like to thank all the former and current members in Dr. Marshall lab for their
help and a great time we spent together. In particular, I want to thank Dr. Huan He, Dr. Amy
McKenna, Dr. Nathan Kaiser, and Dr. Joshua Savory.
I would also like to thank my parents and two elder sisters. They were always supporting
me and encouraging me with their best wishes.
Finally, I would like to thank my wife, sweet daughter and son, for their firm and
continuous love and support.
This work was supported by NSF Division of Materials Research through DMR-0654118
and the State of Florida.
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TABLE OF CONTENTS
List of Figures .............................................................................................................................. viii
Abstract ........................................................................................................................................ xiv
1. HIGH RESOLUTION MASS SPECTROMETRY............................................... 1 What Defines High Resolution and High Mass Accuracy………………………………... 1 Mass Resolution and Accuracy………………………………………………………….... 2 Time-of-Flight Mass Analyzers…………………………………………………………... 3
Orthogonal Acceleration………………………………………………………….. 3 Reflectron/Multipass TOF………………………………………………………... 5 Recent Advances in TOF Mass Analyzer……………………………………….... 6 Selected Applications………………………………………………………….......7
Fourier Transform Mass Analyzers…………………………………………………......... 8 Common Features of Fourier Transform Mass Analyzers………………………...9 Ion Accumulation and Detection………………………………………………....10 Advances in Fourier Transform Mass Analyzers ...……………………………...10
SelectedApplications………………………………………………...............….. 17
2. AUTOMATED BROADBAND PHASE CORRECTION OF FOURIER TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTRA……….... 24 Introduction…………………………………………………………………………....... 24 Problem………………………………………………………………………….. 24 Prior Solutions…………………………………………………………............... 27 Experimental Methods………………………………………………………………….. 29 Sample Description and Preparation…………………………………………….. 29 Instrumentation: 9.4 Tesla FT-ICR MS……………………………………….... 29 Mass Calibration................................................................................................... 30 Computational Method…………………………………………………………. 31 Choosing the Best Phasing Parameters…………………………………………. 32 Baseline Correction……………………………………………………………. 32 Computational Implementation............................................................................ 33 Results and Discussion..................................................................................................... 35 Absorption-Mode vs. Magnitude-Mode Spectral Display.................................... 35 Mass Accuracy..................................................................................................... 35 Filling Gaps Compositional Assignment............................................................... 37 Baseline Roll and Automated Peak Picking.......................................................... 39 Conclusions....................................................................................................................... 40
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3. BASELINE CORRECTION OF ABSORPTION-MODE FOURIER TRANSFORM ION CYCLOTRON MASS SPECTRA......................................... 41 Introduction........................................................................................................................ 41 Experimental Methods....................................................................................................... 43 Simulation.............................................................................................................. 43 Sample Description and Preparation...................................................................... 45 APPI Source........................................................................................................... 45 9.4 Tesla FT-ICR MS............................................................................................ 46 Mass Calibration.................................................................................................... 46 Baseline Correction Algorithm.............................................................................. 46 Computational Implementation..............................................................................50 Results and Discussion.......................................................................................................50 Mass Accuracy....................................................................................................... 50 Identified Peaks...................................................................................................... 51 Isotopic Distribution...............................................................................................55 4. EFFECTS OF ZERO-FILLING AND APODIZATION ON FOURIER TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTRAL ACCURACY, RESOLUTION, AND SIGNAL-TO-NOISE RATIO.................... 56 Introduction....................................................................................................................... 56 Experimental Methods...................................................................................................... 57 Sample Description and Preparation..................................................................... 57 Instrumentation...................................................................................................... 57 Mass Calibration.................................................................................................... 58 Data Processing..................................................................................................... 58 Computational Implementation............................................................................. 58 Results and Discussion...................................................................................................... 61 Full Apodization vs. Half Apodization.................................................................. 61 Mass Accuracy....................................................................................................... 65 Signal-to-Noise Ratio............................................................................................. 66 Resolving Power.................................................................................................... 66 5. PHASE SPECTRA OF FOURIER TRNSFORM ION CYCLOTRON RESONANCE MASS SPECTROMETRY............................................................. 67 Introduction........................................................................................................................ 67 Method of Stationary phase............................................................................................... 68 Phase Spectrum.................................................................................................................. 69 Chirp/Sweep Excitation Signal.............................................................................. 69 Detected Signal...................................................................................................... 72 Experimental Methods....................................................................................................... 77 Sample Preparation................................................................................................ 77 Instrumentation...................................................................................................... 77 Mass Analysis........................................................................................................ 77 SWIFT Waveform..................................................................................................79 Computational Method...........................................................................................79
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Results and Discussion...................................................................................................... 79 Phase Spectrum Method vs. Automated Broadband Phase Correction................. 80 Resolving Power and Mass Accuracy........................................................ 80 Unresolved Peaks....................................................................................... 80 SWIFT Phasing by Phase Spectrum Method......................................................... 85 Modified Phase Spectrum for SWIFT....................................................... 85 Performances..............................................................................................85 6. PHASE CORRECTION OF FOURIER TRANSFORM CYCLOTRON RESONANCE MASS SPECTRA BY SIMUTANEOUS EXCITATION AND DETECTION.......................................................................................................... 87 Introduction...................................................................................................................... 87 Phase Spectrum and Phase Correction................................................................. 87 Experimental Methods..................................................................................................... 90 Sample Preparation............................................................................................... 90 Instrumentation..................................................................................................... 90 Mass Analysis....................................................................................................... 92 SWIFT Waveform Design.................................................................................... 93 SED Experiments.................................................................................................. 93 Computational Method......................................................................................... 94 Results and Discussion...................................................................................................... 94 SED vs. Automated Broadband Phase Correction................................................ 94 Absorption Spectra vs. Magnitude Spectrum form Normal SWIFT Excitation... 97 Absorption Spectra from stepped SWIFT Excitation........................................... 97 Advantages of Broadband Phase Correction by SED.......................................... 97 7. ARTIFACTS INDUCED BY SELECTIVE BLANKING OF TIME-DOMAIN DATA IN FOURIER TRANSFORM MASS SPECTROMETRY....................... 102 Introduction..................................................................................................................... 102 Materials and Methods.................................................................................................... 103 Materials.............................................................................................................. 103 Experiments......................................................................................................... 103 Simulations.......................................................................................................... 104 Estimation of Relaxation of Time ..................................................................... 104 Results and Discussion.................................................................................................... 106 Spectral Profile without Blanking....................................................................... 106 Spectral Profile after Blanking............................................................................ 106 Effect of Noise.................................................................................................... 108 Conclusion....................................................................................................................... 109 REFERENCES...................................................................................................... 111 BIOGRAPHICAL SKETCH................................................................................ 137
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LIST OF FIGURES
Figure 1.1. High resolution time of flight mass analyzers. Top: Dual stage reflectron. Middle: Multi-pass reflectron with linear segments. Bottom: Multi-pass spiral configuration. ...................4 Figure 1.2. Standard orbitrap (left) and compact high field orbitrap (right) mass analyzers ........11 Figure 1.3. Top: Seven segment compensated ICR cell. Bottom: Dynamically harmonized ICR cell (bottom)...................................................................................................................................12
Figure 1.4. Top: Magnitude-mode and absorption-mode Lorentzian spectra, corresponding to Fourier transformation of an infinite duration time-domain signal, f(t) = A cos(ω0t) exp(-t/ ). Bottom: Magnitude (upper) and absorption-mode (lower) electrospray ionization 9.4 T FT-ICR mass spectra from the same bitumen time-domain data. The absorption display clearly resolves a mass doublet (compositions differing by C3 vs. SH4, 0.0034 Da) unresolved in magnitude mode……………………………………………………………………………………………...16 Figure 1.5. Positive electrospray ionization 14.5 T FT-ICR mass spectrum for Nannochloropsis oculata species lipid extract. Inset: Two peaks differing by 2.37 mDa are resolved and assigned…………………………………………………………………………………………..19
Figure 1.6. Positive ion atmospheric pressure photoionization (APPI) 9.4 T Fourier transform ion cyclotron resonance (FT-ICR) mass spectrum of a petroleum crude oil. Upper inset: Mass scale expansion revealing 90 singly-charged ions within a mass range of 0.32 Da. Lower inset: Baseline resolution of ions differing in mass by 1.1 mDa, made possible by ultrahigh mass resolving power of 1,000,000 at m/z 428……………………………………........................... ...22
Figure 2.1. Absorption, dispersion, and magnitude-mode Lorentzian spectra, corresponding to Fourier transformation of an infinite duration time-domain signal, f(t) = A cos(ω0t) exp(-t/ ).....26 Figure 2.2. Plots of time-domain linear frequency-sweep excitation signal (top) and instantaneous excitation frequency (bottom) vs. time, showing the time elapsed following the instant that the excitation frequency matches the ion cyclotron resonance frequency for ions of each of three different m/z values. The corresponding accumulated phase at ωi-1, ωi, or ωi+1 at the onset of detection is ωi-1 (ti-1 + tdelay), ωi (ti + tdelay), or ωi+1 (ti+1 + tdelay) Here the frequency-sweep is from low to high frequency, but a similar argument applies for sweeping from high to low frequency…………………………………………………………………………………….30 Figure 2.3. Schematic baseline flattening procedure. (A) Original absorption spectrum; (B) Fourier transform of (A); (C) Rectangular weight function to remove high-"frequency" components to yield (D); (E) Inverse Fourier transform of (D) to yield the low-"frequency"
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spectral baseline with true mass spectral peaks removed; (F) Baseline-flattened spectrum produced by subtracting (E) from (A).......................................................................................... 33 Figure 2.4. Electrospray ionization 9.4 T FT-ICR mass spectra. Top: Raw real data following Fourier transform of discrete time-domain signal. Middle: Magnitude-mode spectrum (obtained from Eq. 1.1a). Bottom: Absorption-mode spectrum. The resolving power for the absorption-mode display is equivalent to that for magnitude-mode at 13.6 Tesla. Note also higher mass accuracy for absorption-mode relative to magnitude-mode display.............................................. 34
Figure 2.5. Mass error distribution for magnitude (top) and absorption (bottom) electrospray ionization 9.4 T FT-ICR mass spectra for a vacuum gas oil. Each bar represents the number of assigned masses within a 50 ppb mass error range. The same relative signal abundance threshold (peak height > 5 of baseline noise) was used for peak picking. The magnitude spectrum was produced with one zero fill and Hanning apodization1 and the absorption after one zero fill and half Hanning apodization.............................................................................................................. 36 Figure 2.6. Magnitude and absorption electrospray ionization 9.4 T FT-ICR mass spectra for the same bitumen data. The absorption display clearly resolves a mass doublet (compositions differing by C3 vs. SH4, 0.0034 Da) that appears as a single magnitude mode peak................... 37 Figure 2.7. Isoabundance-contoured plots of double bond equivalents (DBE = rings plus double bonds) vs. carbon number for species containing carbon, hydrogen, one nitrogen and one sulfur derived from magnitude-mode (left) or absorption-mode (right) electrospray ionization 9.4 T FT-ICR mass spectra. Note that absorption-mode identifies many elemental compositions missing from the magnitude-mode assignments......................................................................................... 38 Figure 2.8. Electrospray ionization 9.4 T FT-ICR absorption-mode mass spectral segments for a vacuum gas oil, before (top) and after (bottom) baseline flattening. Baseline flattening enables automated identification of additional signals from low-abundance ions..................................... 39 Figure 3.1. Zoom insets of Crude oil FT-ICR absorption-mode mass spectrum before low-pass filter (top) and after low-pass filter (bottom)................................................................................. 42 Figure 3.2. Simulated absorption-mode peaks with increased signal amplitude (left) and with increased peaks densities (right).................................................................................................... 44 Figure 3.3. Baseline flattening procedure. (A) Baseline identification from Original absorption spectrum; (B) Linear interpolation for empty spots between each two baseline points chosen in (A). (C) Boxcar smoothing of resulting (B) to yield smoothed baseline. (D) Spectrum with flat baseline after subtraction of resulting (C)..................................................................................... 47 Figure 3.4. Zoom insets of Ribonucleases A FT-ICR absorption-mode spectrum after polynomial modeling baseline correction. Note the discontinuity due to cutting whole data to each small piece.............................................................................................................................................. 49
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Figure 3.5. Zoom insets of Crude oil FT-ICR absorption-mode mass spectrum (top) and Ribonucleases A absorption-mode spectrum (bottom) showing the performance of baseline correction algorithm...................................................................................................................... 51 Figure 3.6. Mass error distribution for Crude oil FT-ICR absorption-mode mass spectrum before baseline correction (top) and after baseline correction (bottom)................................................... 52 Figure 3.7. Top: mass scale-expanded of river bitumen APPI FT-ICR absorption-mode mass spectrum showing the resulting flat baseline. Bottom: zoom insects of river bitumen APPI FT-ICR absorption-mode mass spectrum at nominal mass 746 m/z before and after baseline flattening. Note that the absorption spectrum after baseline correction improves discovery of low-abundance peaks..................................................................................................................... 53 Figure 3.8. Top: 9+ charge state isotopic distribution of Ribonucleases A FT-ICR magnitude-mode (black) and absorption-mode spectrum (red) with flat baseline. Middle: 9+ charge state isotopic distribution of Ribonucleases A FT-ICR absorption-mode spectrum before baseline correction (red) with calculated isotopic distribution profile (black cross). Bottom: 9+ charge state isotopic distribution of Ribonucleases A FT-ICR absorption-mode spectrum after baseline correction (red) with calculated isotopic distribution profile (black cross).................................. 54 Figure 4.1. Twelve full window (left) and half window (right) functions. N is the time-domain data size before zero-filling and n is the index for each data 0 ≤ n ≤ N-1.................................... 59 Figure 4.2. Data processing steps for FT-ICR magnitude-mode and absorption-mode FT-ICR spectra........................................................................................................................................... 60 Figure 4.3. Mass scale-expanded segments of electrospray ionization (ESI) FT-ICR magnitude mass spectra of distillated fraction from crude oil for half Hanning (top) and full Hanning (bottom) apodization functions. The magnitude spectrum with half hanning apodization exhibits greater width at each peak base..................................................................................................... 61 Figure 4.4. Mass error distribution for broadband magnitude-mode FT-ICR mass spectra for a distillate fraction of crude oil for half Hanning (black) and full Hanning (red) apodization functions......................................................................................................................................... 62 Figure 4.5. Mass scale-expanded segments of FT-ICR absorption spectra for a distillated fraction from crude oil for half Hanning (top) and full Hanning (bottom) apodization functions............. 63 Figure 4.6. Mass scale-expanded segments of FT-ICR absorption spectra for bitumen for half Hanning (top) and full Hanning (bottom) apodization functions.................................................. 63 Figure 4.7. Root-mean-square mass error for broadband magnitude-mode (top) and absorption-mode (bottom) FT-ICR mass spectra for a distillate fraction of crude oil, following 0, 1, and 2 zero-fills, for each of several apodization functions. The six apodization functions resulting in the least rms error are shown........................................................................................................ 64
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Figure 4.8. Peak height-to-noise ratio for peak at m/z 450.4094 (C32H52N1) for a distillate fraction of crude oil, following 0, 1, and 2 zero-fills, for each of several apodization functions.. 64 Figure 4.9. Average mass resolving power for 6 peaks above 6σ of baseline noise at nominal m/z 450 for a distillate fraction of crude oil, following 0, 1, and 2 zero-fills, for each of several apodization functions.................................................................................................................... 65 Figure 5.1. Schematic ICR cell showing the excitation, detection and magnitude field directions....................................................................................................................................... 73 Figure 5.2. A) Plots of time-domain linear frequency-sweep excitation signal (upper) and detected signal (bottom) vs. time. B) Phase spectrum profiles (phase vs. frequency) of linear-sweep excitation and detected signal. Here we only plot the phase spectrum for low-to high frequency-sweep for demonstration purpose................................................................................ 76 Figure 5.3. Distillate of crude oil 9.4T FT-ICR mass spectra. Top: Raw real data following Fourier transform of discrete time-domain signal. Middle: absorption-mode spectrum (obtained after applying analytical phase spectrum). Bottom: Optimized absorption-mode spectrum after fine tune of constant term. Note: additional 0.136 radians in constant term................................. 78
Figure 5.4. Top: Distillate of crude oil of FT-ICR absorption-mode spectra produced by broadband phase correction algorithm (upper) and phase spectrum method (lower). Middle: Plot of calculated phase value vs. frequency from broadband phase correction algorithm (blue) and phase spectrum method (red). Bottom: Plot of phase difference, ε, vs. frequency. Note that every ε value is less than 1 degree (0.0175 radians)............................................................................... 81 Figure 5.5. TOP: Mass scale-expanded segments of distillate of crude oil of FT-ICR absorption-mode spectra from broadband phase correction algorithm (upper) and phase spectrum method (lower). Bottom: Mass error distribution of absorption-mode spectra from phase correction algorithm (upper) and phase spectrum method (lower)................................................................ 82 Figure 5.6. Magnitude and absorption electrospray ionization 9.4 T FT-ICR mass spectra for the same crude oil data from phase spectrum method. The absorption display clearly resolves several mass doublets (compositions differing by C3 vs. SH4, 0.0034 Da) that appears as a single magnitude mode peak................................................................................................................... 83 Figure 5.7. A) Schematic procedure for building SWIFT waveform. B) Detailed SWIFT waveform configuration in real experiment. Note that effective waveform region is located in the middle of whole waveform and is exactly 1/2 of T1..................................................................... 84 Figure 5.8. Top: Crude oil 9.4T absorption-mode (lower) and magnitude-mode (lower) FT-ICR mass spectra excited by SWIFT waveform. Bottom: Mass error distribution for crude oil absorption-mode spectrum (lower) by modified phase spectrum method and magnitude-mode spectrum (upper). Note that much better mass accuracy for absorption-mode spectrum relative to magnitude-mode spectrum excited by SWIFT waveform........................................................... 86
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Figure 6.1. Top: Plot of time-domain linear frequency-sweep excitation signal. Middle: Plot of detection signal in SED experiments. Bottom: Plot of excitation signal in SED experiment........91
Figure 6.2. Data processing steps for SED experiments. A) Zeroing of containment signal (front saturated signal induced by excitation signal). B) Complex division to produce absorption-mode spectrum. Note that exact same data processing (half apodization and zero-filling) for both zeroed detected signal and excitation signal...................................................................................92 Figure 6.3. Top: Absorption-mode from automated broadband phasing (upper) and SED phasing (lower) for linear-sweep excitation. Middle: Mass error distributions for automated broadband phasing (upper) and SED phasing (lower). Bottom: Isoabundance-contoured plots of double bond equivalents (DBE = rings plus double bonds) vs. carbon number for species containing carbon, hydrogen, one nitrogen for automated broadband phasing (left) and SED phasing (right)............................................................................................................................................. 95 Figure 6.4. Top: Magnitude-mode (upper) and absorption-mode (lower) from normal SWIFT excitation. Middle: Mass scale-expanded segments of crude oil FT-ICR magnitude-mode (upper) and absorption-mode (lower) mass spectra from normal SWIFT excitation. Bottom: Mass error distribution for magnitude (upper) and absorption (lower) electrospray ionization 9.4 T FT-ICR mass spectra for a crude oil........................................................................................................... 96 Figure 6.5. Top: Schematic design of stepped SWIFT waveform. Bottom: Magnitude-mode (upper) and absorption-mode (lower) from stepped SWIFT excitation........................................ 98 Figure 6.6. Electrospray ionization crude oil 9.4 T FT-ICR mass spectra. Top: Raw real data following Fourier transform of discrete time-domain signal. Middle: Result after automatic broadband phasing. Bottom: Absorption-mode spectrum from SED phasing...............................99 Figure 6.7. Top: Schematic automatic peak height correction in SED algorithm. Bottom: Isoabundance-contoured plots of double bond equivalents (DBE = rings plus double bonds) vs. carbon number for species containing carbon, hydrogen, one nitrogen for magnitude-mode (upper) and absorption-mode (lower).......................................................................................... 100 Figure 7.1. Generation of frequency-domain FT-ICR mass spectra from a simulated isotopic distribution with 57 frequency components................................................................................. 105 Figure 7.2. a) Experimental time-domain ICR signal from the isolated 57+ charge state isotopic distribution from electrosprayed humanized IgG1k therapeutic antibody. b) Simulated noiseless time-domain transient with 57 frequency components. c) Absorption-mode frequency spectrum for b). d) Magnitude-mode frequency spectrum for b)............................................................... 107 Figure 7.3. Top: Simulated noiseless time-domain signal after blanking of the data between the "beats". Middle: Absorption-mode frequency spectrum. Bottom: magnitude-mode frequency spectrum....................................................................................................................................... 108
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Figure 7.4. Top: Simulated time-domain ICR signal with noise. Middle: Absorption-mode frequency spectrum from the above time-domain signal. Bottom: Absorption-mode frequency spectrum after blanking was performed on the above time-domain signal................................. 109 Figure 7.5. Top: FT-ICR average peak height-to-noise ratio (S/N) for each of the 10 highest absorption-mode peaks (from the time-domain data of Figure 7.4 (top)) with (blue) and without (red) blanking. Bottom: Ion cyclotron frequency errors for the 10 highest absorption-mode peaks with (blue) and without blanking (red)....................................................................................... 110
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ABSTRACT
It has been known for 35 years that phase correction of Fourier transform ion cyclotron
resonance (FT-ICR) mass spectral data can in principle produce an absorption-mode spectrum
with mass resolving power as much as a factor of 2 higher than conventional magnitude-mode
display, an improvement otherwise requiring a (much more expensive) increase in magnetic field
strength. However, temporally dispersed excitation followed by time-delayed detection results
in steep quadratic variation of signal phase with frequency. We developed a robust, rapid,
automated method to enable accurate broadband phase correction for all peaks in the mass
spectrum. Low-pass digital filtering effectively eliminates the accompanying baseline roll.
Experimental FT-ICR absorption-mode mass spectra exhibit at least 40% higher resolving power
(and thus an increased number of resolved peaks) as well as higher mass accuracy relative to
magnitude mode spectra, for more complete and more reliable elemental composition
assignments for mixtures as complex as petroleum.
Absorption-mode FT-ICR mass spectrum, which is produced by automatic broadband
phase correction algorithm, demonstrates baseline distortion even with low-pass filter baseline
correction. Significant baseline roll affects peaks picking algorithm and results in incorrect peak
height measurement. Isotopic distribution in spectra presenting large baseline roll couldn’t
display correct information. Thus, identification and characterization of biomolecule become
much more difficult. In Chapter 2, we designed a fast, robust and automated baseline correction
process. Each minimum data point of reversed peak in absorption-mode spectrum has been
collected as bases of baseline model, and then further linear interpolation and boxcar smoothing
technique help to complete the baseline model. Finally, the baseline model is subtracted from
original spectrum to produce a flat baseline. This algorithm has been experimentally proven to
automatically flatten baseline of crude oil, environmental sample and biomolecule FT-ICR mass
spectra. More peaks have been identified from absorption-mode spectrum with flat baseline
without loss of mass accuracy. Isotopic distribution also demonstrates very accurate profile.
Apodization function and zero-filling are two basic steps in data processing of Fourier
transform ion cyclotron resonance (FT-ICR) mass spectrometry and their effect on the
conventional Fourier transform ion cyclotron resonance (FT-ICR) experimental and simulated
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magnitude-mode mass spectra and single-peak absorption-mode spectra are well known. In
Chapter 4, we examine the effects of each of twelve apodization (window) functions and 0, 1,
and 2 zero-fills for absorption-mode Fourier transform mass spectra peak height-to-noise ratio,
mass measurement accuracy, and mass resolving power for dense FT-ICR mass spectra of
petroleum. Half function windowing is best for resolving close absorption-mode doublets,
whereas full function windowing is best for resolving magnitude-mode doublets. Absorption-
mode offers significantly higher mass resolving power than magnitude-mode for any given
windowing function. Half apodization increases absorption-mode mass accuracy, irrespective of
the choice of window function. One (but not more than one) zero-fill improves mass accuracy for
absorption-mode mass accuracy but not for magnitude-mode. Peak height-to-noise ratio for both
absorption and magnitude spectra is improved by zero-filling.
Although we have successfully demonstrated the automated phase correction method for
complex Fourier transform ion cyclotron resonance (FT-ICR) mass spectrum, we can’t express
the exact quadratic phase function of frequency from calculated phase for discrete data point. In
Chapter 5, we applied stationary phase method to excitation and detection signal and derived the
accurate phase spectra for both the linear chirp excitation and detected FT-ICR signals
analytically. Because phase spectrum of detected signal represents correct variation of
accumulated phase with frequency, it could be directly used to recover the absorption-mode FT-
ICR mass spectra. Also, the phase correction of FT-ICR mass spectra from stored waveform
inverse Fourier transform (SWIFT) by phase spectrum has been experimentally described. The
analytically phase correction results are compared to the previous results produced by automated
phase correction method in terms of resolving power and mass measurement accuracy
Except for phase correction based on mathematical calculation of accurate phase for
different frequencies. Scientists have demonstrated that simultaneous excitation and detection
(SED) enable Fourier deconvolution to provide broadband phase correction with no user
interaction. However, the capacitive nulling technique which is applied in SED method for
removing the saturated excitation signal in front of detected signal is not practical due to unstable
capacitors. In Chapter 6, we describe a new data processing procedure to enable broadband phase
correction of FT-ICR mass spectra by SED without any hardware modification. The resulting
absorption-mode spectra yield improvement in resolving power as well as reduction in
assignment errors relative to conventional magnitude-mode spectra. The Fourier deconvolution
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procedure has the additional benefit of correcting for spectral variation resulting from
nonuniform power distribution over the excitation bandwidth and phasing spectra from different
excitation waveforms (e.g., SWIFT with different magnitude modulations).
Fourier transform mass spectrometry (FTMS) of the isolated isotopic distribution for a
highly charged biomolecule produces time-domain signal containing large amplitude signal
"beats" separated by extended periods of much lower signal magnitude. Signal-to-noise ratio for
data sampled between beats is low, due to destructive interference of the signals induced by
members of the isotopic distribution. Selective blanking of the data between beats has been used
to increase spectral signal-to-noise ratio. However, blanking also eliminates signal components,
and thus can potentially distort the resulting FT spectrum. In Chapter 7, we simulate the time-
domain signal from a truncated isotopic distribution for a single charge state of an antibody.
Comparison of the FT spectra produced with or without blanking and with or without added
noise clearly show that blanking does not improve mass accuracy and introduces spurious peaks
at both ends of the isotopic distribution (thereby making it more difficult to identify
posttranslational modifications and/or adducts). Ergo, blanking should never be employed: it has
no advantages and major disadvantages.
1
CHAPTER ONE
HIGH RESOLUTION MASS SPECTROMETRY
Mass spectrometry is a powerful analytical technique for analysis of charged particles. Dr. John
B. Fenn had showed us a clear picture of mass spectrometry. “Mass spectrometry is the art of
measuring atoms and molecules to determine their molecular weight. Such mass or weight
information is sometimes sufficient, frequently necessary, and always useful in determining the
identity of a species.” Different mass analyzers coupled with different chromatography have
been powerful tools to routinely do qualitative and quantitative analysis, like, identification of
trace amount contamination in environments and food. Modern mass spectrometry application
mostly concentrated on different bio-analysis field, e.g. proteomics, lipidomics, metablomics and
drug discovery. Among characteristics of mass spectrometry, high resolution and high mass
accuracy are most interested aspects for scientists working in variety research fields in recent
decade years. Also these two characteristics are motivation for improvement of different mass
analyzers (e.g. orthogonal and multi-turn time-of-flight) and invention of new mass analyzer
(orbitrap) in recent years.
What Defines High Resolution and High Mass Accuracy?
Mass resolution determines the ability to distinguish ions with different molecular weight and the
definition of mass resolution is the minimum mass difference, m2-m1, between two mass
spectral peaks such that the valley between their sum is a specified fraction of the height of the
smaller individual peak. The most used value of the valley is the half-maximum height (∆m50%)
of either peak. So for two peaks with equal heights, the mass resolution m2-m1= ∆m50%. Mass
resolving power is another term closely related to the mass resolution. The definition of mass
resolving power could be either for a isolated peak of mass, m, as m/∆m50% or for two equal
amplitude peaks as m2/(m2-m1). For multiple charged compound, the m/z will replace m in
definition of resolving power. 2 Therefore, a greater resolving power definitely improves the
2
ability to see smaller mass difference between two ions. Although no exact boundary for
different resolution level, high resolution is usually used to described for mass analyzer with the
resolving power (m/∆m50%) larger than 10,000. Some mass analyzers, such as ion trap,
quadrupole mass filter and triple quadrupole, will not fall into this level even though they are
really useful in different application fields. Mass accuracy is a precision evaluation of mass
measurement provided by mass analyzer. It is often expressed in parts per million (ppm) and
largely depend on the stability and the resolution of different mass analyzers. High mass
accuracy (<5ppm) could provide better mass measurement and reduce the possibility of
elemental composition for each peak.
Mass Resolution and Accuracy
In most current mass spectrometer instruments, the detected signal, e.g., voltage, current or time,
will be collected as discrete data points after digital converter. Each peak has been represented
by discontinuous data points, so peak height and position usually are determined by some sort of
interpolation or fitting procedures. 3-5 The mass measurement precision of peak parameters
depends upon the spectral signal-to-noise ratio, the number of data points per peak width 6 and
different noise distribution 7. Under same signal-to-noise ratio, the peak with more data points
definitely has better mass measurement precision than the peak with less data points. Thus, the
faster data collection rate for recent time-of-flight mass spectrometer is main contribution of
improvement of mass accuracy. After determination of peak position, the whole spectrum will be
calibrated by the accurate masses of two or more different ions. Compare to the external
calibration, the internal calibration could typically gain the better mass accuracy. Because of
unknown sources of m/z-dependent systematic error, some special cared internal Calibrations are
needed, e.g., calibration of spectra in discrete m/z ranges has previously been proposed and
implemented. 8 Considering the ion abundance effect, the small segments internal calibration can
largely reduce the systematic error and improve the rms mass error. 9 Then, the accurate mass
measurement after calibration can be used to assign the elemental composition. This is not a
problem for pure simple compound, and even low resolution mass spectrometer can easily assign
the elemental composition for known chemicals.
3
However, as the number of atoms increases, the number of possible combinations also
increases. For unknown complex mixture, mass differences of different analytes become
significantly small and spectral interferences will appear. Such interferences may occur from
different possibilities, e.g., similar elemental combination, oxide chemical formation or multiple
charged ions. Peaks’ overlapping could skew the peak shape of compound and obscure the
analyte of interest, the peak centroid will no longer correspond to accurate mass. Any peak
assignment and database searching based on these peak centroids will produce erroneous results.
The straightforward method for solving this problem is improving resolving power. For
example, molecules of the same nominal mass differing in elemental composition at around m/z
700, e.g. C3 vs. SH4 (~3.4 mDa), could be separated at a resolving power m/∆m50% better than
200,000. High resolution or resolving definitely increases the confidence for assigned elemental
confirmation. In other word, the real mass measurement accuracy of complex mixture totally
relies on the high resolution or resolving power.
Time-of-Flight Mass Analyzers
The time-of-flight mass analyzer, initially proposed by Stephan in 1946,10 and reduced to
practice in 1948, 11 has evolved through several stages. Delayed ion extraction addressed the
problem of kinetic energy spread among ions of the same m/z.12 The advent of fast digitizers,
MALDI (and MALDI imaging), orthogonal ion introduction, and kinetic energy focusing by use
of a reflectron brought TOF MS to its present level of popularity.
Orthogonal Acceleration
Ideally, a TOF MS experiment should begin with all ions with the same initial position and
velocity. Orthogonal ion introduction, 13 in which ions are accelerated in a direction
perpendicular to a collimated ion beam, effectively achieves that condition, and thus improves
mass resolving power. Another advantage of orthogonal introduction is that ions can be
accumulated in the acceleration region while previously accumulated ions fly toward the
detector, thereby more efficiently enabling coupling of continuous ion sources with TOF mass
4
analysis. Further optimization of ion guides and use of an ion funnel14 with automatic gain
control (AGC) improves the ion beam quality, for higher sensitivity and mass accuracy.15
Dual Stage Reflectron
IonMirror
High FieldPusher
Ion DetectionSystem
From Ion Source
- Ion Trajectory
- One Figure-Eight Ion Trajectory
To Detector
Detector
Ion Source
Gridless Mirror
Periodic Ion Lenses
Gridless Mirror
Figure 1.1. High resolution time of flight mass analyzers. Top: Dual stage reflectron.16 Middle: Multi-pass reflectron with linear segments.19 Bottom: Multi-pass spiral configuration.17-18
5
Reflectron/Multipass TOF
The resolving power for a TOF mass analyzer is m/∆m50% = (T/2∆t), in which T is the ion total
flight time, and ∆t is the mass spectral peak width. Increasing the flight time for improved
resolving power is made possible by the reflectron, introduced by Mamyrin in 1973.20 After an
initial drift region, ions are subjected to a spatially quadratic potential that acts as an ion mirror.
When ions of a given m/z but different kinetic energy fly through the reflectron region, the faster
ions penetrate farther into the reflectron (and therefore travel a greater distance to reach the
detector) than slow ions, and ions of all speeds arrive at the detector at same time. The reflectron
thus provides increased ion flight path, without defocusing due to spread in initial velocity,
thereby increasing mass resolving power. Broadband mass resolving power of 10,000 and rms
mass error of 5-10 ppm may now be routinely attained. With high field pusher and dual stage
reflectrons, commercial TOF mass analyzer can now reach mass resolving power of 40,000. 16
(Figure 1.1, top) If the ion spatial focusing can be maintained with minimal ion loss at each
reflection, the ion flight path may be extended by multiple reflections. Multi-pass 21 and spiral
(Figure 1.1, bottom)17 TOF mass analyzers now attain mass resolving power of 50,000 or higher.
Recently, an optimized multi-pass time-of-flight mass analyzer has been combined with
matrix-assisted laser desorption/ionization (MALDI) for imaging mass spectrometry. The multi-
pass time-of-flight mass analyzer consists of four electric sectors, with cylindrical side electrodes
and Matsuda configuration to generate a toroidal electric field, in which focusing is maintained
by quadrupole triplet lenses at the entrance and exit of each toroidal segment. Mass resolving
power of 130,000 has been achieved for angiotensin II [M+H]+ ions (m/z 1046.542) after 500
turns and 654.8 m total flight path.22 In a typical multi-pass time-of-flight mass analyzer, the
power supply for ion injection/ejection is very large and complicated in order to reduce
instability of voltage switching between ion injection and ejection events. A more recent multi-
pass TOF design adds two more sectors for ion injection and ejection only, thereby minimizing
the size of the power supply.23
Although a cyclic multi-pass TOF mass analyzer offers potentially high mass resolution,
the observable mass range is limited, because low-m/z ions eventually overtake higher-m/z ions,
so that the effective m/z range is reduced by a factor of N for N passes. An elliptical flight path
composed of four toroidal electric sectors works with a new segmentation method to identify the
6
number of laps transited by ions of a given m/z.24 The most recent multi-pass designs include
doughnut-shaped ion optics25, a spiral path electric reflector 26 and multiple angle reflecting
electrostatic ion mirrors. 19 (Figure 1.1, middle) The latter two designs have achieved
broadband mass resolving power of 60,000.
Recent Advances in TOF Mass Analyzer
Detection. The most commonly used TOF ion detector is the microchannel plate (MCP)
detector, which converts ions to secondary electrons, with large active area and rapid response
time. However, secondary electron generation efficiency varies directly with incident ion
velocity, and ion velocity varies inversely with the square root of accelerated ion mass, so that
MCP detection efficiency for high-mass ions is low. The mechanical nanomembrane detector
can detect the time-varying field emission of electrons from mechanical oscillation without mass
discrimination and thus improve high-mass detection sensitivity. For example, singly charged
immunoglobulin G (150 kDa) has been experimentally observed by TOF MS with
nanomembrane detection.27 A different nanomechanical resonator,28, 29 whose resonance
frequency is perturbed by surface adsorption of ions, was also recently reported as a sensitive
mass sensor, but further investigation for its practical use in TOF MS is needed. Another
potential useful detector for TOF mass analyzer is the cryodetector. When applied to TOF MS,
cryogenic detectors measure low-energy solid-state excitations, called phonons, created by a
particle impact. The energy of these phonons is less than a few meV which is much smaller than
the energy in the electronvolt range needed to produce secondary electrons in conventional
ionization detectors. The cryodetector is sensitive and good for detection of large, slow-moving
ions. 30 A strong signal at 510 kDa from disulfide liked dimmer has been experimentally
observed in MALDI TOF mass spectrometer coupled with cryodetector. 31
TOF/TOF. Two time-of-flight (TOF) mass analyzers in succession enable MS2
experiments. 32, 33 Usually, The first TOF mass analyzer selects the precursor ion for injection
into a high energy collision cell for collision induced dissociation (CID). The second TOF mass
analyzer then records the fragment ions. The most common TOF/TOF configuration is a linear
TOF mass analyzer followed by a reflectron TOF mass analyzer.34, 35 However, low resolution in
MS1 can render product ion identification difficult.
7
Multi-pass TOF/TOF has been achieved with a MALDI ion source, a multi-turn TOF
mass analyzer (TOF1), a collision cell, and a quadratic-field ion mirror,36, 18 providing resolving
power of 5000 for precursor ion selection and 1000 resolving power for product ions throughout
the mass range. The identification of lyso-phosphatidylcholine (LPC) and phosphorylation37 has
been demonstrated. Recently, a spiral ion optical TOF mass analyzer for MS1 was combined
with an offset parabolic ion reflectron TOF as MS2, providing high resolution MS1 precursor
monoisotopic ions up to m/z 2500.38
Selected Applications
Although TOF mass analyzers have lower mass resolution than FT mass analyzers (FT-ICR and
orbitrap), they have no upper m/z limit in principle and are thus particularly useful for
identifying singly charged ions of high molecular weight (as from MALDI). Fast response/scan
rate is also advantageous for applications requiring short acquisition period, e.g., analysis by
liquid or gas chromatography mass spectrometry.
A method for screening doping agents in human urine consists of solid phase extraction
followed by HPLC-TOFMS. Coupled with orthogonal electrospray ionization, 124 substances
including stimulants, narcotics, agonists, diuretics, etc., are identified in less than 30 min.39
Further development of the extraction method enabled identification of 40 more doping
compounds.40 The utility of the LC-TOF method was assessed by parallel analysis of 30
authentic urine samples by use of rapid emergency drug identification (REMEDI) and led to
identification of twice as many drugs.41 Compared to prior methods, the author concluded that
UPLC-TOFMS offers an attractive alternative toxicological screening technique. Because the
mass accuracy tolerance for broad toxicology screening has historically been quite wide (20 ppm
or more),42 TOF mass accuracy less than 5 ppm provided substantial improvement in the number
and confidence of identification.43, 44
Mass spectrometry imaging (MSI) provides rapid detection, localization, and
identification of organic components of complex biological mixtures,45 to establish chemical
correlations with biological function or morphology. MSI experiments are typically performed
with a TOF mass analyzer, due to its good sensitivity and speed. Localization of peptides by
MALDI TOF imaging reveals the distribution of their respective proteins.46 Comparison of
protein profiles from normal and tumor tissue can lead to biomarker candidates.47, 48 The
8
profiling and imaging of proteins involved in proliferation, differentiation, and apoptosis by
MALDI TOF MS generates unique and differential proteomic blueprints for implantation and
interimplantation sites.49 Lipid imaging in rat brain tissues during focal cerebral ischemia
reveals dynamic conversion from phosphatidylcholine (PC) to lyso-phosphatidylcholine (LPC)
in brain areas with ischemic injury.50 As for protein profiling, a different lipid distribution
between normal and cancer cells could diagnose disease.51, 52
In aerosol analysis, it is necessary to track changes in aerosol size and chemistry with
sub-second time resolution. A TOF mass analyzer collects high resolution aerosol mass spectra
at rates exceeding 1 kHz for determination of both aerosol size and mass.53 Alternatively, two
dimensional gas chromatography (GCxGC) mass spectrometry requires fast scanning because
the final GC peak width is typically 20-200 ms,54 making TOF the MS method of choice.
GCxGC TOF MS applications include identification of naphthentic acids in oil samples,55, 56
high throughput metabolic profiling,57, 58 characterization of pathogen bacteria,59 and analysis of
organic nitrogen compounds in aerosol samples.60 Moreover, fast transient temporal analysis of
catalyst kinetics targets TOF mass analysis for its sensitivity, detector response, and time
resolution.61
The TOF mass analyzer has been also been applied to polymer analysis by virtue of its
high m/z range and MS/MS capability. Evaluation of top-down TOF MS/MS for poly(α-
peptoid)s synthesized by N-heterocyclic carbine (NHC)-mediated zwitterionic ring-opening
polymerization62 showed that electrospray ionization (ESI) enabled detection of the intact
molecular species, whereas MALDI resulted in elimination of the NHC initiator in the presence
of cationizing salts. Coupled with MALDI, TOF MS can address the mechanism of polymer
backbone degradation via free radical chemistry63 and quantify residual polyethylene glycol
(PEG) in ethoxylated surfactants.64 Cation adducts generated more informative fragment ions
under CID,65 and TOF MS has characterized various polymers with ammonium adducts
generated by ESI.66 Miscellaneous other applications include characterization of C4 explosives
by TOF secondary ion mass spectrometry (SIMS),67 qualitative and quantitative analysis of
herbal medicines (HMs) LC/TOF MS68 and identification of different contamination in human
body by GC/TOF MS.69
Fourier Transform Mass Analyzers
9
The FT-ICR mass analyzer, introduced in 1974, 70 has the highest mass resolving power71, 9 and
best mass measurement accuracy9 among current mass analyzers. The orbitrap, another Fourier
transform mass analyzer, invented in 1999,72 has been widely distributed since its commercial
introduction in 2004.73
Common Features of Fourier Transform Mass Analyzers
The ion cyclotron and orbitrap each produces a spatially coherent packet of ions of a given m/z.
Coherence in FT-ICR is achieved by rf excitation at the ion cyclotron frequency, whereas
coherence in the orbitrap is achieved by injecting ions of a given m/z into the mass analyzer in a
time short compared to the ion oscillation frequency. In both devices, the periodic motion
(rotation in ICR, oscillation in orbitrap) is detected from the oscillating current induced in
opposed detection electrodes, as ions pass near each electrode. The signal from ions of a given
m/z is linearly proportional to the number of those ions, and to the radius 1, 74 or amplitude of the
ion motion. Linearity is especially important for FT-ICR, because ions of different m/z may be
selected/excited in any desired combination by a time-domain excitation waveform produced by
inverse Fourier transformation of the desired frequency-domain excitation profile ("stored
waveform inverse Fourier transform" (SWIFT) excitation). 75-77Both devices inherently detect
ions of a wide m/z range simultaneously. The time-domain signal is then digitized, apodized,
zero-filled 78, 79 (to improve digital resolution), and subjected to discrete Fourier transformation
to yield mathematically "real" and "imaginary" frequency-domain spectra, Re(ω) and Im(ω),
which are typically combined to yield a "magnitude" spectrum, M(ω) (see below).1 Spectral
frequency is then converted to m/z by an appropriate calibration equation (see below).
FTMS resolving power is ultimately limited by the acquisition period, T, for the time-
domain transient. However, the time-domain transient duration is in turn limited by magnetic and
electrical field imperfection, ion-neutral collisions, and ion-ion interactions. 79-82 Apodization
functions 83 help to detect small peaks near large peaks by reducing the magnitude of auxiliary
maxima and by narrowing the peak width near the peak base (at the cost of broadening the peak
width at half-maximum peak height).
Ion Accumulation and Detection
10
Both ICR and orbitrap mass analyzers are pulsed detectors. Because ion introduction is often
temporally continuous (e.g., ESI and APPI), ions are typically accumulated externally during
detection of ions from the preceding accumulation period. 84 In FT-ICR, ions are externally
accumulated in a multipole electric ion trap and simultaneously ejected toward the ICR cell,
whereas in the orbitrap, ions are collected in a "C" trap,85 and injected simultaneously toward the
orbitrap. In ICR, ion spatial coherence is maintained by the confining magnetic and electrostatic
fields, and by ion-ion interactions, 82 whereas in the orbitrap, ion axial coherence is achieved by
short pulsed injection from the C trap and radial coherence is lost as ions spread out to form a
rotating ring (actually, an advantage, by reducing space charge repulsions and enabling increased
dynamic range), and the ring for ions of a given m/z oscillates axially to produce an image
current on the detection electrodes. The cyclotron frequency in ICR signal varies as (m/z)-1,74
whereas the orbitrap axial frequency (like the ICR "trapping" oscillation) varies as (m/z)-1/2.85 As
a result, ICR mass resolving power varies as (m/z)-1, vs. (m/z)-1/2 for the orbitrap.
Advances in Fourier Transform Mass Analyzers
High field strength. The simplest way to improve FTMS performance is to operate at
higher magnetic field, B (ICR) or higher electric field (orbitrap). ICR mass resolving power or
scan rate increase proportional to B, whereas mass accuracy, dynamic range, and upper m/z limit
increases as B2.86, 87 The highest field FT-ICR instrument is currently 15 T, and 21 T systems are
under construction at the U.S.A. National High Magnetic Field Laboratory and Pacific
Northwest National Laboratory.
The orbitrap axial oscillation frequency can be expressed as: 88
][2
1)ln(
2
)/( 2
1
2
2
1
22 RRR
RR
U
zm
e
m
r
−−⋅=ω
[1.1]
in which e is the elementary charge (1.602 × 10-19 C), R2 is the maximum radius of the outer
barrel-like electrode, R1 is the radius of the central spindle-like electrode, Ur is the voltage
applied to the central electrode, and Rm is the "characteristic" radius at which dU(r,z)/drz=0 = 0.
From Eq. 1.1, it is clear that orbitrap resolving power may be increased by increasing the central
11
electrode voltage or decreasing the R2/R1 ratio. The newest orbitrap exhibits increased Ur and
optimized R2/R1 ratio to provide ~2-fold improvement in resolving power (for a given data
acquisition period) or similar reduction in data acquisition period (for faster on-line LC
sampling, for a given mass resolving power). With careful balancing of construction tolerances
and experimental parameters, the new orbitrap resolved an isotopic distribution at a resolving
power in excess of 600,000 at m/z 196. 88
12
mm
30
mm
10
mm
20
mm
Standard Orbitrap High Field Orbitrap
Figure 1.2. Standard orbitrap (left) and compact high field orbitrap (right) mass analyzers.88
12
Electric field optimization. The orbitrap mass analyzer is composed of a spindle-like
central electrode and a barrel-like outer electrode (Figure 1.2). Application of a dc voltage to the
two axial electrodes produces an electrostatic potential that ideally is the sum of a quadrupolar
ion trap potential and a logarithmic potential of a cylindrical capacitor. For ICR, a strong
homogeneous static magnetic field confines ion motion transverse to the magnetic field, and an
ideally three dimensional quadrupolar electrostatic potential confines ion motion parallel to the
magnetic field.
Compensation Segments
Trapping Segments
Central S
egment
Figure 1.3 Top: Seven segment compensated ICR cell. 89 Bottom: Dynamically harmonized ICR cell (bottom). 90
13
In practice, the potentials in both mass analyzers deviate from ideal, because the
electrodes are truncated, imperfect in shape and alignment, and must have apertures to admit ions
(both) and electrons or photons (ICR). In ICR, an imperfect (anharmonic) quadrupolar
electrostatic potential produces an axially dependent, nonlinear radial electric field (Er) that
makes the observed cyclotron frequencies depend on ion radius and axial amplitude. Different
approaches to the cell anharmonicity problem have been investigated since the 1980s. 91-98 One
approach is to insert compensation rings into an open cylindrical cell. 99, 89, 100-102 (e.g., Figure
1.3, top). Another idea relies on ion cyclotron motion to average the electric potential from
curved segmented electrodes90 (Figure 1.3, bottom). Both cell designs in Figure 1.3 have
achieved baseline unit mass resolution for proteins up to 150 kDa.103 Moreover, a coaxial multi-
electrode cell (O-trap),104 with separate compartments for ICR excitation and detection, has been
experimentally demonstrated. The potential benefit from that design is enhancement of
resolving power equal to detected frequency multiple order that could alternatively yield shorter
detection period for correspondingly higher throughput. (e.g., for LC/MS)
Compared to a standard orbitrap geometry, the outer electrode dimensions of the compact
high-field orbitrap analyzer are scaled down by a factor of 1.5, whereas the central electrode
dimensions are scaled down by a factor of 1.2 (Figure 1.2). The entrance aperture cross-section
is reduced by more than a factor of 2; thus, to avoid a corresponding loss in sensitivity, a new
miniature lens system focuses ions to a much smaller spot. The capacitance of the orbitrap drops
in proportion to size, which results in improved image current detection sensitivity. New
transistors in the preamplifier further increase sensitivity. In spite of higher ion density, the
relatively thicker central electrode results in smaller space charge shifts than for the standard
orbitrap.
Software Development. Calibration. FTMS mass accuracy is determined by signal-to-
noise ratio and number of data points per peak width,6 and by "calibration", namely the
conversion of a frequency-domain spectrum to an m/z spectrum. For FT-ICR, calibration
typically relies on a two-term equation based on a perfectly homogeneous magnetic field and a
purely quadrupolar electrostatic field.105, 106 Other equations incorporating variation in ion
abundance107 and space-charge effects108, 109 have also been evaluated. External calibration
(performed for a different sample than for analyte) is typically 2-3x less accurate than internal
14
calibration (based on multiple ions of known m/z values in the analyte sample). Systematic error
has been reduced by a factor of up to 3 (and the number of assigned peaks increased by ~25%)
by separate calibration for each of up to ~30 individual mass spectral segments.8,9 Addition of an
ion abundance-dependent term to the calibration equation can reduce systematic error by another
factor of ~2-3. 89, 9 For a high vacuum gas oil sample with ~5,200 peaks, FT-ICR rms mass error
for an absorption-mode spectrum (see below) drops from 107 ppb to 27 ppb by essentially
eliminating systematic error. For the orbitrap, m/z is to first order proportional to (ω)-1/2, leading
to a one term calibration equation. As for ICR, orbitrap mass calibration may be improved by
considering the effect of space charge, leading to a mass measurement error as low as ~80 ppb
over an m/z range of 100-2,000. 110
Phase Correction. Fourier transformation of a time-domain signal produces
mathematically real and imaginary frequency-domain spectra, Re(ω) and Im(ω), which may be
combined to yield magnitude-mode (also known as absolute-value) and phase spectra, M(ω) and
φ(ω), related according to Eq. 1.2.1
M(ω) = [[Re(ω)]2 + [Im(ω)]2]1/2 [1.2a]
φ(ω) = arctan[Im(ω)/Re(ω)] [1.2b]
If the "phase spectrum", φ(ω), is known, absorption- and dispersion-mode spectra, A(ω)
and D(ω), may in turn be obtained as linear combinations of Re(ω) and Im(ω).
A(ω) = cos[φ(ω)] Re(ω) - sin[φ(ω)] Im(ω) [1.3a]
D(ω) = sin[φ(ω)] Re(ω) + cos[φ(ω)] Im(ω) [1.3b]
An absorption-mode spectral peak is inherently narrower than its corresponding magnitude-mode
spectral peak (Figure 1.4, top) by a factor that depends on the presence and mechanism of signal
damping, 79-82 for an improvement in mass resolving power by a factor of up to 2. In FT-ICR,
temporally dispersed excitation and the delay between excitation and detection result in complex
variation of phase with frequency. For that reason, magnitude-mode has been the conventional
15
display for FT-ICR mass spectra. The advantage of absorption-mode display was recognized
from the outset.111 Efforts to achieve broadband phase correction112, 113 culminated in a phase
correction algorithm that can automatically account for first- and second-order phase
accumulation from excitation parameters and iterates the zero-order term.114 An experimental
FT-ICR absorption-mode mass spectrum 40% higher resolving power (and thus an increased
number of resolved peaks) as well as higher mass accuracy relative to its corresponding
magnitude mode spectrum is shown in Figure 1.4, bottom. Another approach for phase
correction is to assume a quadratic relation between phase and frequency, and iteratively solve
for zero-, first-, and second-order coefficients.115
Compared to ICR, the phase "wrapping" (i.e., phase variation by more than 2π across the
frequency spectrum) for the orbitrap is less severe due to the short ion injection period from the
C trap but complicated by the change in central electrode voltage (and therefore resonant
frequency) during ion injection. A "pseudo" phase correction based for the orbitrap combines
absorption-mode display for the top part of the peak with an increasing magnitude-mode
component for the bottom part. Although the peak width at half peak height is thus narrower,116
improvement vanishes for low abundance peaks that are near the base of a high abundance peak,
and the mass measurement accuracy does not improve.
Improved Data Station. Continued improvement in FT mass analyzers requires optimized
control of multiple experimental events, precisely timed data acquisition, and efficient data
analysis to accommodate new hardware modifications and ion optics configurations. A recent
Predator data station117 exploits improved PC bus speed to transfer data to and from the control
PC in real time. Conditional data acquisition can evaluate data in real time and apply user-
defined conditions to average and store data. This capability is primarily used to eliminate low
quality data so as to improve the data S/N ratio and minimize the computer memory required to
store data. Tool command language (Tcl) scripting has been applied for 17 voltages and 18
triggers, and provides a fast and easy way to control the Predator data station and associated
peripherals, e.g., LC, auto-sampler, laser source, and electron emitter.117 Another improved data
control system combines PXI hardware with a workflow-based acquisition and control software
to allow unique types of data-dependent experiments.118 Dynamic switching between different
dissociation technologies may be achieved due to fast and precise hardware response. 119
16
ω0
2/τ
A(ω)
M(ω)
Lorentzian Peaks
m/z883.92883.88883.84883.80
883.92883.88883.84883.80
C61H103O3
C58H107O3S1
Bitumen ESI 9.4T FT-ICR Mass Spectra
C61H103O3
Magnitude Mode
Absorption Mode
3.4mDa
2√3/τ
m/Δm50%= 450,000
m/Δm50%= 250,000
Figure 1.4. Top: Magnitude-mode and absorption-mode Lorentzian spectra, corresponding to Fourier transformation of an infinite duration time-domain signal, f(t) = A cos(ω0t) exp(-t/ ). Btootm: Magnitude (upper) and absorption-mode (lower) electrospray ionization 9.4 T FT-ICR mass spectra from the same bitumen time-domain data. The absorption display clearly resolves a mass doublet (compositions differing by C3 vs. SH4, 0.0034 Da) unresolved in magnitude mode.
17
Selected Applications
Tandem mass spectrometry. The main difference between ICR and orbitrap for
MS/MS is that precursor ion dissociation can be performed in a Penning trap but not in an
orbitrap. In principle, fragment ions can be brought to coherence in an orbitrap for subsequent
excitation and detection, 120 but MS/MS is typically performed externally (CID or ETD) for
orbitrap detection. 121, 122.MS/MS can be performed in an ICR cell by collision-induced
dissociation (CID), infrared multiphoton dissociation (IRMPD), and electron capture dissociation
(ECD). However, high resolution requires low pressure in the ICR cell, so introduction of
collision gas into the cell requires subsequent pump down before excitation/detection; ergo, CID
FT-ICR experiments are now typically conducted with an external electric multipole ion trap.
Because ECD (or ETD) can fragment a peptide but not dissociate the non-covalently bound
fragments, infrared irradiation is commonly used to release the product ion. CID and IRMPD
heat an ion and typically break the weakest bond to produce predominantly b and y type peptide
fragment ions. However, post-translational linkages (e.g., phosphorylation, glycosylation) are
often lost before peptide backbone cleavage, thereby eliminating knowledge of their location. In
contrast, ECD (or ETD) produces mainly c- and y- type backbone cleavage fragment ions by
breaking the backbone N-C� bond without loss of phosphate or glycan. Thus, ECD or ETD is
much preferred for locating posttranslational modifications. 123, 124.
Proteomics encompasses identification and structural characterization of proteins and
their complexes, determination of post-translational modifications, and quantitation of protein
expression under different treatments. In "top-down" proteomics, a single gas-phase protein is
isolated, and subjected to fragmentation (e.g., CID, IRMPD, ECD, ETD, etc.) to generate
fragment masses for comparison to an appropriate database for protein identification, as well as
identity and location of each posttranslational modification according to its characteristic
additional mass relative to an unmodified amino acid residue. The top-down approach can in
principle locate all posttranslational modifications, even when several are present at the same
time. High resolution and high mass accuracy are essential to resolve isotopic distributions from
peptides of different charge state as well as to assign isobaric peptide compositions (e.g., lysine
vs. glutamine, differing in mass by 0.0364 Da).125 Examples of top-down posttranslational
identifications include: rhesus monkey cardiac troponin,126 integral membrane proteins 127 and
18
human histones.128, 129 Further, 99 proteins have been identified by top-down tandem mass
spectrometry in Methanosarcina acetivorans,130 and capillary liquid chromatography coupled
with FT-ICR identified with high confidence 102 endogenous peptides in the suprachiasmatic
nucleus. Robust two dimensional liquid chromatography combined with top down mass
spectrometry increases efficiency for improved quantification and characterization.131, 132 Further
automated data processing can increase top-down throughput.133 In addition to conventional ESI,
IR-MALDESI has been coupled with an FT-ICR mass analyzer to perform top-down analysis of
equine myoglobin (17kDa).134 Discovery and characterization of endogenous peptide135 and
candidate pharmacodynamic markers136 has been demonstrated. Recently, FT-ICR MS achieved
unit mass baseline resolution for an intact 148 kDa therapeutic monoclonal antibody, the highest
mass protein isotopically resolved to date.103 132
In the "bottom-up" approach, proteins are typically separated by HPLC and/or
electrophoresis, and proteolytically digested into peptides, then subjected to on-line LC/MS, and
the most abundant peptides are subjected to MS/MS.137, 138 Any of several algorithms (cite
Sequest, Mascot, etc.) then compare precursor ion mass and MS/MS peak spacing to an
appropriate database for protein identification. 139-141 Identification reliability may be improved
by incorporating LC elution time.142 Alternatively, "shotgun" proteomics also relies on on-line
LC/MS and MS/MS, but without prior gel separation of the proteins.143 Shotgun proteomics has
been applied to microorganisms,144 histones (especially post-translational modifications),145, 146
and discovery of biosynthetic pathways, 147 etc. For proteins too large for efficient gas-phase
fragmentation, "middle-down" proteomics denotes LC/MS and MS/MS for large proteolyic
fragments of the original protein, and has identified 7,454 peptides from 2-20 kDa after 23 LC
MS/MS injections of Lys-C digests of HeLa- S3 nuclear proteins.148 Post-translationally
modified histone H3 variants have also been characterized by that approach. 149
Quantitative proteomics typically requires isotopic labeling, either before (SILAC) 150 or
after peptide isolation.137 Quantification of human monkeypox virus and vaccinia virus
confirmed the level required for pathogenesis with Accurate Mass and Time tag (AMT) method
after peptide isolation.151 With stable isotope labeling of amino acids in cell culture (SILAC), it
is possible to quantitatively evaluate phosphorylation changes in stable cell lines.152 Quantitative
proteomics depends on fragmentation energy. 153, 154 When isotopic labeling is not applicable,
label-free methods can provide a measure of quantitation. 155.
19
Metabolomics. High throughput screening of chemical toxicity in Daphnia magna has
been reported.156 Metabolic profiling facilitates biochemical phenotyping of normal and
neoplastic colon tissue at high significance levels 157 and annotates the ions originating from
identical metabolites by fragmentation pattern and database searching analysis.158 Coupled with
different chromatography platforms,159-161 higher dynamic range and identification of more
metabolites can be achieved. Autocorrelation of retention and ionization leads to more
exhaustive metabolic fingerprints.162
500 700 900 1100 1300 1500 1700 1900m/z
730.535 730.545 730.555 730.565m/z
730.53805
PC (32:2), ‐0.11 ppmC40H76N1O
8P1
730.55919
DGTS (32:2) + Na+
‐0.08 ppmC42H76N1O
7Na
1
730.56156
DGTS (34:5)‐0.08 ppmC44H75N1O
7
2.37 mDa
(+) ESI 14.5 T FT-ICR MS of Algae (Nannochloropsis oculata) Lipid Extract
Figure 1.5. Positive electrospray ionization 14.5 T FT-ICR mass spectrum for Nannochloropsis
oculata species lipid extract. Inset: Two peaks differing by 2.37 mDa are resolved and assigned. (Figure kindly provided by Huan He)
20
Lipidomics. Characterization of nonpolar lipids and selected steroids by high resolution
mass analysis has emerged as a powerful tool for lipidomics. 163, 164 On-line LC separation can
quickly narrow down the possible phospholipid and glycosphingolipid compositions and
facilitate their identification.165, 166 Unequivocal lipid elemental composition from isotopic fine
structure has been used to validate the identification of sulfur-containing lipids in algae extracts
(Figure 1.5). 167 Direct infusion high resolution mass analysis with computer-assisted
assignment is able to profile the 13C-isotopologues of glycerophospholipids (GPL) directly in
crude cell extracts.168 High resolution MS/MS enabled identification of triacylglycerols
archaeological extracts,169 and neutral lipids.170 Matrix-assisted laser desorption ionization
combined with high-resolution MS enables confident identification and spatial localization of
lipids in tissue sections.171, 172
RNA/DNA Analysis. Most lower resolution MS analyses of oligonucleotides have focused on
synthetic DNA, RNA, aptamers, etc. Double-stranded small interfering RNA (siRNA) presents
numerous fragment ions and multiple chemical modifications. The different metabolite patterns
for synthetic siRNA in different biomatrices (rat and human serum) provide insight into the
stability and pharmacokinetic properties of therapeutic siRNA compounds.173 A method for
sequencing single and double stranded RNA oligonucleotides by acid hydrolysis has been
presented. From the mass differences between adjacent members of a mass ladder, the complete
sequences of different siRNA 21-mer single and double strands could be verified. This simple
and fast method can be applied to controlling sequences of synthetic oligomers, as well as for de-
novo sequencing.174 A high resolution mass spectrometry-based analytical platform for RNA,
employing direct nano-flow reversed-phase liquid chromatography with a spray tip column
predicted the nucleotide composition of a 21-nucleotide small interfering RNA, detected yeast
tRNA post-transcriptional modifications, and analyzed the nucleolytic fragments of RNA at a
sub-femtomole level.175 Various other approaches, e.g., combing chemical modification of RNA
with mass spectrometry, 176 based on neomycin B+ 177 or classical nucleic acid ligands, 178
enable characterization of polypurine tract-containing RNA:DNA hybrids, and show that the
common structural features of lentiviral and retrotransposon PPTs facilitate the interaction with
their cognate reverse transcriptase (RTs). Structural elucidation of the HIV-1 virus has also been
achieved by the combination of footprinting and cross-linking techniques with high resolution
21
MS detection.178, 179
Synthetic Polymer Analysis. The most obvious advantage of mass spectrometry for
synthetic polymer analysis is the generation of the full molecular weight distribution, rather than
simply number-average or weight-average molecular weight.180 181 High resolution MS can also
reveal pathways of polymer synthesis, as for a sterically hindered alkoxyamine initiator for the
nitroxide-mediated copolymerization (NMP) of methyl methacrylate (MMA);182 the styrene
monomer was added as polymerization terminator, and the progress monitored from the product
oligomer distributions. Synthetic polymer structure has been probed by various fragmentation
techniques, including Electron Capture Dissociation (ECD), Collision Induced Dissociation
(CID), and Electron Detachment Dissociation (EDD),183-188 e.g., polyamidoamine dendrimer
characterization by ECD and EDD.
Petroleomics. From sufficiently complete characterization of the organic composition of
petroleum and its products, it is becoming possible to correlate (and ultimately predict) their
properties and behavior.189, 190FT-ICR MS is the preferred identification technique for petroleum
analysis because of the need to resolve mass splits down to 3.4 mDa (32S1H4 vs. 12C3) or ~0.5
mDa (for nickel-containing porphyrins) (Figure 1.6). Recently, ion mobility (IM) mass
spectrometry (MS) and FT-ICR MS were combined to confirm the presence of asphaltene
aggregation.191 Removal of contaminants in asphaltenes during the crude oil processing is
necessary to avoid catalyst fouling and hence lower liquid yield. Also, asphaltenes can
precipitate during production and refining. Thus asphaltenes are one of the most discussed
topics in petroleomics. 192-196 Ion mobility mass spectrometry and FT-ICR MS have been
combined to confirm the presence of asphaltene nanoaggregates in toluene at concentrations (10-
4 mass fraction) below those in crude oils. 191 Subsequently, in situ analysis of a 3000 ft vertical
column of crude oil by downhole fluid analysis indicated that the asphaltenes in a black crude oil
exhibit gravitational sedimentation according to the Boltzmann distribution and that the
asphaltene colloidal size is about 2 nm. 197 The detailed characterization of a Middle Eastern
heavy crude oil distillation series fully validated the Boduszynski model, namely that petroleum
is a continuum with regard to composition, molecular weight, aromaticity, and heteroatom
content, and that boiling point can be predicted from aromaticity and heteroatom content. 198, 199
Naphthenic acids (i.e., species containing non-aromatic hydrocarbon rings) can form harmful
22
deposits, and may be identified in crude oil before the deposits form200-202 as well as in oil sands
processed water.203-205 Ultrahigh mass resolution also enables identification of biomarkers, such
as nickel and vanadyl petroporphyrins.206, 207
m/z1,000900800700600500400300
m/z636.59636.51636.43636.35636.27
m/z428.311428.308428.306428.303
Positive Ion APPI 9.4 T FT-ICR MS of Heavy Crude Oil
6σ
1.1 mDa (13CH332S vs C4)
m/∆m50%=1,000,000
m/∆m50%=1,100,000
54,004 Peaks > 6σ between
m/z 200 and 1000
90 Peaks > 6σ Baseline Noise
Figure 1.6. Positive ion atmospheric pressure photoionization (APPI) 9.4 T Fourier transform ion cyclotron resonance (FT-ICR) mass spectrum of a petroleum crude oil. Upper inset: Mass scale expansion revealing 90 singly-charged ions within a mass range of 0.32 Da. Lower inset: Baseline resolution of ions differing in mass by 1.1 mDa, made possible by ultrahigh mass resolving power of 1,000,000 at m/z 428. (Data kindly provided by Amy McKenna)
23
Environmental Analysis. Applications of high resolution MS technology in the fields of
food safety208 and environmental analysis have recently been reviewed.209 High resolution helps
to trace contaminants, as well as to identify analogs for which standards are not available. High-
resolution full scan MS analysis with simultaneous targeted CID MS/MS has been a applied to
analysis of polyether toxin azaspiracid food contaminants in shellfish.208 High resolution is also
useful in the high-throughput screening of micropollutants in wastewater treatment. Both
targeted and non-targeted screening have identified a variety of unreported and previously
reported pesticide transformation products.210 Characteristic polar oil sands components
(naphthenic acids and other related acid fraction components) spiked into plant tissue prior to
extraction can be differentiated from co-extracted endogenous plant components by high
resolution MS.205 LC/high resolution MS showed that the industrial chemical, perfluorooctanoic
acid, is microbiologically inert, and hence environmentally persistent.211 The high production
volume chemicals, benzotriazoles and benzothiazoles, have been extracted from environmental
water by solid-phase extraction and identified by LC/high resolution MS. 212 Induced metabolite
changes in myriophyllum spicatum, an aquatic vascular plant, have been monitored by high
resolution MS.213 The method has also provided molecular characterization as the level of
elemental composition, for dissolved organic matter (DOM), e.g., from pore water,214 secondary-
treated waster water,215 and the Greenland ice sheet, 216 because it is capable of resolving
complex molecular mixtures and providing information about the exact elemental composition.
24
CHAPTER TWO
AUTOMATED BROADBAND PHASE CORRECTION OF
FOURIER TRANSFORM ION CYCLOTRON RESONANCE
MASS SPECTRA
Introduction
Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS)74 offers the highest
broadband mass spectral resolving power and mass accuracy. For example, isobaric "fine
structure" (i.e. ions of the same nominal (nearest integer) mass but different elemental
composition, CcHhNnOoSs) is routinely resolved to yield thousands of unique elemental
compositions in a single mass spectrum (300-1000 Da) for petroleum crude oil. With great
effort, isotopic fine structure (i.e., ions of the same elemental composition but different
composition of isotopes such as 13C, 15N, 18O, and 34S) has been resolved for a 16 kDa protein,71
at a mass resolving power (m/z)/Δ(m/z)50% ≈ 8,000,000, in which m/z is ion mass-to-charge ratio
and Δ(m/z)50% is the full mass spectral peak width at half maximum peak height.217 Although
mass resolving power increases linearly with increasing magnetic field,2 magnet cost increases at
a high power of magnetic field. Thus, one is led to seek other ways to improve FT-ICR mass
resolving power at a given magnetic field strength. To that end, it is necessary to review the
origin and nature of FT-ICR mass spectral peak shape.
Problem
Fourier transformation of a time-domain ICR signal produces mathematically real and imaginary
frequency-domain spectra, Re(ω) and Im(ω), or alternatively magnitude-mode (also known as
absolute-value) and phase spectra, M(ω) and φ(ω), related according to Eq. 2.1.1
M(ω) = [[Re(ω)]2 + [Im(ω)]2]1/2 [2.1a]
25
φ(ω) = arctan[Im(ω)/Re(ω)] [2.1b]
(A frequency-domain spectrum may be converted to a mass-to-charge (m/z) ratio spectrum, at
sub-ppm mass accuracy, by a two-parameter "calibration" equation based on a quadrupolar
electrostatic trapping potential approximation. 105, 106) Absorption- and dispersion-mode spectra,
A(ω) and D(ω), may in turn be obtained as linear combinations of Re(ω) and Im(ω).
A(ω) = cos[φ(ω)] Re(ω) - sin[φ(ω)] Im(ω) [2.2a]
D(ω) = sin[φ(ω)] Re(ω) + cos[φ(ω)] Im(ω) [2.2b]
An absorption-mode spectral peak is inherently narrower than its corresponding
magnitude-mode spectral peak by a factor that depends on the mechanism of signal damping:
ion-molecule reactions, hard-sphere collisions, 80 Langevin collisions to yield the Lorentzian
peak shape, shown in Figure 2.1,217 ion-ion interactions,81, 82 magnetic and electric field
imperfections, and undamped time-domain signal to yield sinc peak shape.79 In any case, our
phasing process is independent of decay model because we don’t fit our data to an assumed
lineshape. Moreover, magnitude-mode doublets that are barely resolved suffer from phase-
dependent frequency shifts that reduce mass accuracy;218 absorption-mode doublets are not
shifted. Dating back to the very first FT-ICR mass spectra,70, 219 it was recognized that
absorption-mode affords higher resolving power than magnitude-mode display.111 However,
recovery of A(ω) from Re(ω) and Im(ω) requires knowledge of the correct "phase" angle, φ(ω).
In Fourier transform nuclear magnetic resonance (FT-NMR) spectroscopy, signals at all
frequencies are excited nearly simultaneously by a short rf pulse, so that the time delay between
excitation and detection for different specific frequencies is constant. The "phase" angle, φi(ωi)
varies linearly with frequency,
φi (ωi) = φ0+ ωi tdelay [2.3]
by less than 2π radians across a typical FT-NMR spectrum, relative to a fixed phase, φ0, that is
26
independent of frequency. Thus, one need simply vary φ0 until Re(ω) = A(ω) for a peak at one
end of the spectrum, and then vary tdelay until Re(ω) = A(ω) for a peak at the other end of the
spectrum. Peaks at intermediate frequencies will then all exhibit absorption-mode shape.
ω0
D(ω)
ω0
A(ω)
M(ω)
ω0
2/τ
2/τ
2√ 3 /τ
Figure 2.1. Absorption, dispersion, and magnitude-mode Lorentzian spectra, corresponding to Fourier transformation of an infinite duration time-domain signal, f(t) = A cos(ω0t) exp(-t/ ).
27
However, for FT-ICR MS, the frequency bandwidth is much larger than for FT-NMR, and
signals are typically excited by frequency-sweep excitation219, 220, so that the time delay
((ti+tdelay)in Figure 2.2) between excitation and detection also varies linearly with frequency:
Each ti can be calculated as:
ti = [(ωe – ωi)/(sweep rate)] [2.4]
in which ωe is the end frequency of the frequency-sweep excitation, and sweep rate is time rate of
change of excitation frequency. ωe, tdelay, and sweep rate are known in each experiment.
Substituting into Eq.2.3. We see that φi(ωi) varies quadratically with frequency, ωi:
φi (ωi) = φ0+ ωi (ti +tdelay) = φ0+ ωi [((ωe – ωi)/(sweep rate))+tdelay] [2.5]
Moreover, φi(ωi) can vary by 2π radians or more over even a single nominal m/z. Thus,
because sin[φi + n(2π)] = sin(φi), it is not easy to recognize the variation of φi(ωi) with frequency
across a broadband spectrum. As a result, virtually all FT-ICR mass spectra have been limited to
magnitude-mode for the past 35 years.
Prior Solutions
FT-ICR mass spectral phase correction to yield absorption-mode display has been demonstrated
previously for a single peak70 and over a narrow m/z range.112 In another approach, a plot of
dispersion vs. absorption (DISPA) for an isolated Lorentzian peak yields a circle whose center is
rotated by φ radians,221 allowing for determination of φ for each spectral peak. The DISPA plot
has been applied successfully to user-interactive phase correction of FT-NMR spectra 222 and to
FT-ICR mass spectra with widely separated (by ~20 Δ(m/z)50%) peaks,223 but is not suitable for
closely spaced peaks (i.e., the situation for which phase correction is most desirable), because the
"tails" of the dispersion spectrum extend many line widths away from the peak center.
If excitation and detection can be performed simultaneously, then the convolution theorem
of Fourier analysis can be used to recover a broadband absorption spectrum as follows. For a
linear response system (i.e., the response magnitude at a given frequency is linearly proportional
to the excitation magnitude at that frequency), the response, f(t), to a particular time-domain
28
excitation waveform, e(t), is the convolution of e(t) and the response, a(t), to an "impulse" (i.e.,
instantaneous) excitation.
f(t) = e(t) * a(t) [2.6]
The convolution theorem states that the corresponding Fourier transforms, F(ω), E(ω), and A(ω)
of the time-domain waveforms, f(t), e(t), and a(t) are related by
F(ω) = E(ω) � A(ω) [2.7a]
so that the absorption-mode spectrum can in principle be "deconvolved" according to:
A(ω) = F(ω)/E(ω) [2.7b]
Eq. 2.7b has been demonstrated for the in silico noiseless ICR response to a linear frequency-
sweep excitation.224 Some 25 years later, deconvolution to yield a broadband absorption-mode
FT-ICR mass spectrum was demonstrated experimentally, based on careful nulling of the signal
induced on the detection electrodes by the excitation electrodes of an ICR trapped-ion cell.113
However, we found that nulling was difficult, incomplete, and unstable, so we seek a simpler
method that can be easily extended to all FT-ICR mass spectra.
Peak height, phase, frequency, and decay constant for each ion signal may estimated by a
maximum likelihood method based on an assumed mathematical ion signal model. 225 Mass
accuracy was shown to improve for a spectrum with 30 non-overlapped peptide peaks.
However, the parameter estimates do not explicitly account for peak overlap, and a large error in
one peak frequency estimate can corrupt the mass estimates for ions of other frequencies.
Here, we present a broadband phase correction method to produce an absorption-mode
spectrum with no user interaction. Following fast Fourier transformation of the discrete time-
domain response to a frequency-sweep excitation to yield discrete real and imaginary spectra, the
algorithm calculates the optimum value of φ(ω) for each spectral data point, based on the initial
and final frequencies of the swept excitation, the sweep rate, and the "ringdown" delay between
29
excitation and detection. The absolute phase at each spectral point is then determined iteratively
by optimizing the positive magnitude of the absorption spectrum while varying a frequency-
independent phase correction factor from 0 to 2π (φ0 in Eq. 2.5). This method has been tested for
electrosprayed petroleum mixtures, and yields a larger number of uniquely identified elemental
compositions as well as higher mass accuracy. A time-domain FT-ICR signal with 8 Mwords can
be processed automatically to generate a phase-corrected absorption spectrum in a few minutes.
Experimental Methods
Sample Description and Preparation
Athabasca bitumen and distillate fraction (500 – 538 ○C) from Athabasca bitumen heavy vacuum
gas oil (HVGO) were obtained from the National Centre for Upgrading Technology (Devon,
Alberta, Canada). The California crude oil was obtained from Chevron. The California curde oil
was adsorbed onto a 60g silicic acid chromatographic column and fractions of increasing polarity
were selectively eluted with increasing solvent strength. Bitumen, HVGO and each California
crude oil fraction sample were each diluted to 500 μg/mL in a 50:50 toluene methanol mixture
and used without additional purification. All solvents were HPLC-grade, obtained from Sigma-
Aldrich Chemical Co. (St. Louis, MO).
Instrumentation: 9.4 Tesla FT-ICR MS
Each oil sample was analyzed with a custom-built FT-ICR mass spectrometer equipped with a
9.4 Tesla horizontal 220 mm bore diameter superconducting solenoid magnet operated at room
temperature (Oxford Corp., Oxney Mead, U.K.) and a modular ICR data station (PREDATOR)
facilitated instrument control, data acquisition and data analysis. 226, 227 Positive ions generated
at atmospheric pressure were accumulated in an external linear octopole ion trap84 for 250-1000
ms and transferred by rf-only octopoles to a 10 cm diameter, 30 cm long open cylindrical
Penning ion trap. Octopoles were operated at 2.0 MHz and 240 Vp-p amplitude. Broadband
frequency sweep (chirp) dipolar excitation (70 – 700 kHz at 50 Hz/μs sweep rate and 350 Vp-p
amplitude) was followed by direct-mode image current detection to yield time-domain data sets
30
with 8 Mwords. Time-domain data sets were co-added (200-300 acquisitions), Hanning
apodized,1 and zero-filled once before fast Fourier transform and magnitude calculation.
Detect
Time
Frequency-Sweep Excitation
tdelay(m/z)i-1 = 2000
(m/z)i = 500
(m/z)i+1 = 50
E(t)
Fre
qu
en
cy
ti-1
ti
ωi-1
ωi ωi+1
ti+1
(Shift Theorem)
ωs
ωe
Figure 2.2. Plots of time-domain linear frequency-sweep excitation signal (top) and instantaneous excitation frequency (bottom) vs. time, showing the time elapsed following the instant that the excitation frequency matches the ion cyclotron resonance frequency for ions of each of three different m/z values. The corresponding accumulated phase at ωi-1, ωi, or ωi+1 at the onset of detection is ωi-1 (ti-1 + tdelay), ωi (ti + tdelay), or ωi+1 (ti+1 + tdelay) Here the frequency-sweep is from low to high frequency, but a similar argument applies for sweeping from high to low frequency.
Mass Calibration
Each FT-ICR mass spectrum was first calibrated with respect to a prior sample containing
Ultramark®, Met-Arg-Phe-Ala (MRFA) peptide, and caffeine (external calibration), and then
with respect to a homologous series of ions of high abundance common to all three samples.
31
Peaks with relative peak abundance greater than 6 times the standard deviation of the baseline
noise (the best empirical compromise between maximizing the number of peaks and maximizing
confidence in identification) were exported to a spreadsheet. All masses were then converted to
the Kendrick mass scale.228 A unique molecular formula could then be assigned to each peak
based on the Kendrick Mass Defect (KMD) series.229 This procedure has been extensively
validated for petroleum and its products.189
Computational Method
Figure 2.2 shows why FT-ICR spectral phase varies linearly and quadratically with frequency.
First suppose that ions of different cyclotron frequency are all excited instantly and
simultaneously, such that the signal at each cyclotron frequency, ωi, varies as cos(ωit). Because
the time-domain excitation rf signal magnitude is typically ~200 Vp-p, whereas the detected ICR
time-domain rf signal is of the order of microvolts, it is necessary to delay the onset of detection
by tdelay ≈ 1 ms to allow the receiver to "ring down" before detection begins. The "shift theorem"
of Fourier analysis230 dictates that the accumulated phase angle (i.e., phase "shift") at the onset of
detection will be ωitdelay. Thus, the phase correction, φ(ω), in Eq. 2.2a will vary linearly with
spectral frequency, as in Eq. 2.4. Next, suppose that ions are excited by a sinusoidal waveform
whose frequency changes linearly with time (Fig. 2.2, left), and whose phase increases
quadratically with time (just as the linear distance traveled by an object subjected to constant
linear acceleration (i.e., linearly increasing velocity) varies quadratically with time). Ions of a
given m/z exhibit initially spatially incoherent cyclotron motion, and coherent cyclotron motion
begins immediately at the onset of resonant excitation.231 The key step is to realize that, to a
good approximation, ions of a given cyclotron frequency are excited to their final cyclotron
radius essentially at the instant that the excitation frequency equals the cyclotron frequency.
Coherent ion cyclotron motion is initiated with a phase shifted by π/2 radians with respect to the
excitation frequency231 and all excited ions will thenceforth exhibit a quadratic variation of initial
cyclotron phase with frequency that corresponds to that of the excitation waveform. After
excitation, the ion cyclotron phase will accumulate linearly (e.g., ti-1 for ions of m/z 2,000 in
Figure 2.2, plus tdelay (for ions of all m/z). Thus, the accumulated cyclotron phase will be the
sum of the temporally quadratic phase accumulation during the frequency sweep plus the
temporally linear increase between the instant of excitation and the onset of detection.
32
Moreover, ωe, sweep rate, and tdelay in Eq. 2.5 may be well approximated by knowledge of the
frequency-sweep excitation range and rate and the subsequent time delay between the end of
excitation and the onset of detection. It remains only to determine initial phase angle φ0 in Eq.
2.5. However, because φ0 is independent of frequency, we can simply vary it from 0 to 2π in 1-
degree increments (i.e., 2π/360 radians) until the entire spectrum is optimally "phased".
Choosing the Best Phasing Parameters
We tested several criteria for selecting the best value of phase angle in Eq. 2.5, and settled on the
following. We begin by finding the magnitude-mode spectral data point of greatest magnitude.
We then set φi = φ0 - ω (ti + tdelay) at that data point (ω = ωi). For each successive frequency
increment above or below ωi, we then calculate (ti + tdelay) (given that (ti + tdelay) in Figure 2.2 is
known for each discrete spectral frequency) so that the relative phase for each point in the whole
spectrum is known. We then iteratively calculate the best initial phase (φ0) by variation as
described above. We find it best to judge the success of phase correction based on the full
spectrum rather than just one peak. Because each absorption peak is symmetric about its
midpoint and each absorption spectral data point is positive-valued (in the absence of noise), we
therefore recalculate the best zero-order phase, φ0, as that for which the sum of all of the
absorption-mode spectral data points is maximum positive.
Baseline Correction
The baseline of an absorption-mode spectrum from a zero-filled time-domain data set exhibits
wiggles that are manifested as a periodic "roll" in the frequency-domain spectrum.1 Baseline roll
is significant for frequency-sweep excitation and increases with decreased sweep rate and
increased excitation bandwidth. Fortunately, baseline roll varies much more slowly with
frequency than do ion cyclotron resonance peaks, and thus may be greatly reduced by digital
low-pass filtering (see Figure 2.3).1 The frequency-domain absorption-mode spectrum is
Fourier transformed and the data corresponding to the highest 99% of the transformed abscissa
are removed. The remaining transformed data set is then inverse Fourier transformed to
represent the original (rolling) baseline with all spectral peaks removed. The filtered baseline is
then subtracted from the original absorption-mode data to produce an absorption-mode spectrum
33
with greatly reduced baseline roll. Removal of the roll makes it easier to find and quantitate low
abundance signals automatically, because peak-picking algorithms typically select signals higher
than a specified baseline magnitude.
FT
1
Inverse
FT
(A)(B)
(C)
(D)
(F)
(E)
m/z
m/z
"Frequency"’
"Frequency"’
"Frequency"’
Figure 2.3. Schematic baseline flattening procedure. (A) Original absorption spectrum; (B) Fourier transform of (A); (C) Rectangular weight function to remove high-"frequency" components to yield (D); (E) Inverse Fourier transform of (D) to yield the low-"frequency" spectral baseline with true mass spectral peaks removed; (F) Baseline-flattened spectrum produced by subtracting (E) from (A). Computational Implementation
The phase correction software has been implemented as an extension of our modular Predator
ICR data acquisition data system,227 in C/C++ computer language operating under
LabWindows/CVI (National Instruments, Austin, TX). The algorithm achieves broadband phase
correction of 8 Mword discrete time-domain ICR data in two minutes.
34
Vacuum Gas Oil
ESI 9.4T FT-ICR MSFFT Real Spectrum
Before Phasing
Figure 4
Magnitude Modem/Δm50% 490,000
RMS Error 140ppb
300 400 500 600 700m/z
700600500400300
Absorption Mode
After Phasing
m/z
m/Δm50% 710,000
RMS Error 110ppb
(13.6 T)
9.4 T
Figure 2.4. Electrospray ionization 9.4 T FT-ICR mass spectra. Top: Raw real data following Fourier transform of discrete time-domain signal. Middle: Magnitude-mode spectrum (obtained from Eq. 1.1a). Bottom: Absorption-mode spectrum. The resolving power for the absorption-mode display is equivalent to that for magnitude-mode at 13.6 Tesla. Note also higher mass accuracy for absorption-mode relative to magnitude-mode display.
35
Results and Discussion
Absorption-Mode vs. Magnitude-Mode Spectral Display
Figures of merit for mass spectrometric performance should never be based on one or a few mass
spectral peaks, but rather on many peaks spanning a wide range of signal-to-noise ratio and m/z.
Petroleum crude oil and its distillates thus provide a particularly stringent test for the present
approach, because of their daunting compositional complexity: e.g., up to 50,000 resolved peaks
across a 340 < m/z < 1,500 range.87 Broadband FFT real, magnitude-mode, and phase-corrected
absorption-mode electrospray ionization FT-ICR mass spectra of vacuum gas oil at 9.4 T are
shown in Figure 2.4. Note the ~45% higher mass resolving power (equivalent in that respect to
magnitude-mode display at 13.6 tesla!) and ~30% improvement in mass accuracy for absorption-
mode relative to magnitude-mode display.
Mass Accuracy
Figure 2.5 shows mass error distributions for the broadband ESI FT-ICR magnitude-mode and
absorption-mode mass spectra of Figure 2.4. (The two data sets were apodized differently to
achieve optimal performance—see Future Extensions.) The reduction in rms error (averaged
over all assigned peaks) is achieved mainly by reassignment of those peaks with the highest
magnitude-mode mass errors. Moreover, close mass doublets partially or unresolved in
magnitude mode become resolved in absorption mode (see Figure 2.6), thereby increasing the
number of correctly assigned elemental compositions in Figure 2.5. Thus, the improvement in
resolution is not only quantitative; it can be qualitative (i.e., being able to assign a peak or not).
Finally, the improvement is much greater near the baseline of the peak, where a Lorentzian
magnitude-mode peak can be ten-fold wider than for absorption mode (see Figure 2.1). In
theory, zero-filling increases the peak position precision for an absorption-mode spectrum,
because the first zero-fill effectively captures into the absorption spectrum information residing
in the non-zero-filled dispersion data obtained by Fourier transformation of the time domain
data. 78 However, zero-filling exposes Gibbs oscillations ("wiggles" on the sides of each peak
that can compromise our peak-picking procedure) and apodization removes those wiggles. The
36
effects of apodization and zero-filling on phase correction will be discussed at length in a future
paper.
1,692 Assigned Peaks
RMS Error: 140 ppb
Magnitude Mode:
One Zero-Fill &
Hanning Apodization
Vacuum Gas Oil ESI 9.4T FT-ICR MS
Num
ber of P
eaks p
er
Bin
0
100
200
300
400
1 0 -1Mass Error (ppm)
1,732 Assigned Peaks
RMS Error: 110 ppb
Absorption Mode:
One Zero-Fill & Half-
Hanning Apodization
0.8 0.6 0.4 0.2 -0.2 -0.4 -0.6 -0.8
0.8 0.6 0.4 0.2 -0.2 -0.4 -0.6 -0.810
100
200
300
400
0 -1
Mass Error (ppm)
Num
ber of P
eaks p
er
Bin
Figure 2.5. Mass error distribution for magnitude (top) and absorption (bottom) electrospray ionization 9.4 T FT-ICR mass spectra for a vacuum gas oil. Each bar represents the number of assigned masses within a 50 ppb mass error range. The same relative signal abundance threshold (peak height > 5 of baseline noise) was used for peak picking. The magnitude spectrum was produced with one zero fill and Hanning apodization1 and the absorption after one zero fill and half Hanning apodization1 (see text).
37
m/Δm50% = 230,000
Magnitude Mode
C58H99O3S1
Bitumen
ESI 9.4T FT-ICR MS
Absorption Mode
3.4mDa
C58H99O3S1
C61H95O3
m/Δm50% = 350,000
m/z875.70 875.75 875.80
Figure 2.6. Magnitude and absorption electrospray ionization 9.4 T FT-ICR mass spectra for the same bitumen data. The absorption display clearly resolves a mass doublet (compositions differing by C3 vs. SH4, 0.0034 Da) that appears as a single magnitude mode peak.
Filling Gaps in Compositional Assignment
A particularly informative way to organize the thousands of assigned neutral elemental
compositions, CcHhNnOoSs, from mass spectra from complex organic mixtures (e.g., petroleum,
dissolved organic matter) is with an isoabundance contoured plot of double bond equivalents
(DBE = number of rings plus double bonds to carbon) vs. number of carbon atoms for each
heteroatom class, NnOoSs. DBE vs. carbon number images for the two most abundant
heteroatom classes from electrospray ionization FT-ICR mass spectra of California crude oil
fractions are shown in Figure 2.7. Note the large gaps in the magnitude-mode image,
38
corresponding to high-mass species of relatively low abundance (i.e., lower mass measurement
precision) and non-unique assignment due to increased number of possible compositions for a
given mass tolerance. The corresponding absorption-mode mass spectrum resolves many of
those species, so as to fill in the gaps in the DBE vs. carbon number image.
California Crude Oil
(Fraction 1)
N1S1
0
10
20
30
40
20 60 100
DB
E
N1S1
20 60 1000
10
20
30
40
DB
E
(Fraction 2)
Magnitude Data Absorption Data
Carbon Number Carbon Number
Rela
tive A
bundance
30
20
10
0
30
20
10
020 40 60 80 20 40 60 80
DB
E
DB
E
Figure 2.7. Isoabundance-contoured plots of double bond equivalents (DBE = rings plus double bonds) vs. carbon number for species containing carbon, hydrogen, one nitrogen and one sulfur derived from magnitude-mode (left) or absorption-mode (right) electrospray ionization 9.4 T FT-ICR mass spectra. Note that absorption-mode identifies many elemental compositions missing from the magnitude-mode assignments.
39
Baseline Roll and Automated Peak Picking
Automated peak-picking algorithms typically limit consideration to peaks whose height exceeds
a specified multiple of the standard deviation of baseline rms random noise. If the maximum
excursions of that baseline "roll" exceed a few standard deviations of the baseline random noise,
then a peak-picking algorithm can fail to identify true low-magnitude spectral signals whose
frequencies happen to fall near the minima of the "roll". The importance of eliminating baseline
"roll" is evident from Figure 2.8, showing an increase from 13 to 18 in the number of peaks
identified by automated peak picking.
m/z 336330
Vacuum Gas Oil
ESI 9.4 T FT-ICR MS
Absorption Mode Before Baseline Correction:
13 Peaks > 3σ of Baseline Noise
After Baseline Correction:
18 Peaks > 3σ of Baseline Noise
328326 332 338334
Figure 2.8. Electrospray ionization 9.4 T FT-ICR absorption-mode mass spectral segments for a vacuum gas oil, before (top) and after (bottom) baseline flattening. Baseline flattening enables automated identification of additional signals from low-abundance ions.
40
Conclusion
Here, we have demonstrated that broadband absorption-mode FT-ICR mass spectra can provide
higher mass resolution, mass resolving power, and mass accuracy than conventional magnitude-
mode spectra. The method has already been successfully applied to FT-ICR MS of petroleum. 198 In future work, we shall address the effects of apodization, zero-filling, systematic errors,
signal-to-noise ratio, and peak separation relative to peak width on mass and amplitude accuracy,
as well as optimal recovery of the information distributed among absorption-mode, dispersion-
mode, and magnitude-mode spectra. For example, optimal magnitude-mode and absorption-
mode resolution can require different apodization ("windowing") functions. 232 And higher mass
resolution can actually result in lower mass accuracy for a close magnitude-mode doublet. Also,
it is not necessarily optimal to begin phasing from the highest magnitude peak: rather, one could
begin phasing at the midpoint of the frequency-sweep (which is not the midpoint of the m/z
range) to reduce the first- and second-order correction errors.
Absorption-mode peaks for ions of different m/z add linearly, whereas magnitude-mode
peaks do not (magnitude is a non-linear operation). Thus, absorption-mode display is an
inherently more accurate representation of ion relative abundances for partially overlapping
resonances. We have observed experimentally (not shown) that absorption-mode display can
exhibit greater peak asymmetry and distortion than magnitude-mode display. Thus, absorption-
mode appears to be more sensitive to the detailed shape and motion of excited ion packets, and
could thus possibly aid in diagnosis (and ultimately reduction) of response nonlinearity as well as
identification (and cure) of various sources of systematic phase and amplitude distortion.
From an application standpoint, the largest resolution enhancement (factor of 2 for an
undamped time-domain ICR signal) will be for on-line LC FT-ICR MS, for which the time-
domain acquisition period is typically 1 s or less, during which the time-domain signal does not
decay significantly. Moreover, the advantages of absorption-mode display for crowded mass
spectra, demonstrated here for petroleum, will also apply to biological samples (proteomics,
glycomics, lipidomics, metabolomics, etc.)
41
CHAPTER THREE
BASELINE CORRECTION OF ABSORPTION-MODE FOURIER
TRANSFORM ION CYCLOTRON MASS SPECTRA
Introduction
Previously, broadband Fourier transform ion cyclotron resonance (FT-ICR) absorption-mode
spectrum has been produced by automated phase correction algorithm.114 Crude oil absorption-
mode spectrum demonstrates not only higher resolving power and also better mass accuracy than
conventional magnitude-mode spectrum. However, the baseline of absorption-mode spectra
always exhibits periodic “roll” in the frequency domain spectra (Figure 3.1, top). Significant
baseline roll affects peaks picking algorithm and results in incorrect peak height measurement.
Weak signals in spectra presenting large baseline roll may not be recognized because the
magnitude of baseline roll could be larger than the peak height. Thus, number of peaks with
height greater than 6 of baseline rms noise in absorption-mode spectrum is less than magnitude-
mode spectrum in some cases. In previous method, 1% of frequency data, which contains most
baseline roll information has been taken out by digital low-pass filtering, 1 and subtracted from
original frequency spectrum to produce absorption-mode spectrum with much improved baseline
(Figure 3.1, bottom). Corrected baseline facilitates the peak finding, peak height measurement
and identification of more chemical component in absorption-mode spectrum, anyhow, the
baseline under denser peak area still display certain negative distortion/dip as it is flat within
peak-free area. We notice that negative dip of baseline is significant for frequency sweep
excitation and increases with peak height and peak densities. Simulated results of absorption
frequency peaks further confirm our observations (see below in detail). These residues of
baseline distortion (negative dip) hinder to acquire the accurate peak magnitude in absorption-
mode spectrum and make it unusable in quantification cases. Especially, baseline roll residues
will largely distort the isotopic distribution because big biomolecular FT-ICR mass spectrometry
has really high peak density due to isotopic distribution with highly charged states. Identification
42
and structural characterization of different biomolecules require high quality spectra prior to
statistical analysis. 125, 2 Inaccurate isotopic distribution information makes it more difficult to
accurately measure biomolecule mass and causes the failure of database searching algorithm.
m/z
793792791790789788
793792791790789788
Crude Oil 9.4T FT-ICR Absorption-Mode Mass Spectra
After Low-Pass Filter
Before Low-Pass Filter
Figure 3.1. Zoom insets of Crude oil FT-ICR absorption-mode mass spectrum before low-pass filter (top) and after low-pass filter (bottom).
Baseline roll is a major problem in FT NMR and has been extensively investigated by
scientists.233-236 The reasons causing Baseline roll in NMR are various, e.g., dispersive wings
fold back by phase correction,234 nonlinearity response of filters,237 improper weighting of the
initial part of time domain data,238 the discrete nature of Fourier transform and instrumental
instabilities.239, 240 Baseline roll can be reduced by experimental methods, like, justification of
acquisition parameters,236 oversampling241 and digital signal processing,242 or corrected by post
43
data processing (e.g., reconstruction of initial part of time-domain data240, 243 and baseline roll
modeling by Fourier series, 244, 245 polynomials246-248 and other functions249-251). Compared to
experimental method, post data processing offers a general and efficient way to correct the
baseline roll, so it has been a most popular approach in FT NMR field and common feature in
NMR analysis software. We believe that the reasons causing baseline in FT ICR is similar to in
FT NMR and baseline correction methods in FT NMR could be applied to FT ICR mass spectra
due to sharing basic Fourier transformation principle and technique. Since baseline correction
method based on post data processing is no dependent on specific experiment process and
parameters, it could be the best choice for FT-ICR mass spectra without further investigation of
origin of baseline roll.
Here, we present a fast and robust algorithm for automatic baseline correction of
frequency spectrum of FT-ICR. The whole procedure, including baseline identification, linear
interpolation and baseline smoothing, has been implemented with phase correction algorithm to
efficiently produce an absorption-mode spectrum with flat baseline. This method is also tested
for crude oil, river bitumen and Ribonucleases A, and yields a larger number of identified peaks
(crude oil) as well as correct isotopic distribution (biomolecule) without loss of mass accuracy.
Compared with calculation time of phase correction, baseline correction only takes less than 10
seconds to flat a 8 Mwords absorption-mode FT-ICR mass spectrum.
Experimental Methods
Simulation
In FT-ICR MS, each time-domain ICR signal, f(t), could be modeled as exponentially damped
sinusoids: 252, 80
f(t) = Acos(ωt+φ)exp(-t/τ) 0<t<T [3.1]
in which i represents each ion signal, is a characteristic damping time constant, or relaxation
time, T is the time-domain data acquisition period, φ is the initial phase, ω is the natural angular
frequency, and A is the amplitude (which is directly proportional to the number of ions of that
44
cyclotron frequency). The simulated time-domain signal was apodized, zero-filled and Fourier
transformed to produce absorption and dispersion (A(ω) and D(ω) frequency spectra after phase
correction. The peak height in simulated absorption frequency spectrum is proportional to the A
in time-domain signal. Based on this idea, we simulate single absorption frequency peak with
four different amplitudes (A). Those resulting absorption frequency spectra clearly show
negative dip increasing with increased peak height (Figure 3.2, left).
-32000
0
150000
Frequency (kHz)151,387 151,413
-21000
0
150000
-41000
0
150000
-37000
0
150000
Simulated Absorption-Mode Peaks
-21000
0
150000
-16000
0
150000
-90000
150000
-110000
150000
Peak H
eig
ht
A=0.75
A=1
A=1.5
A=2
Figure 3.2. Simulated absorption-mode peaks with increased signal amplitude (left) and with increased peaks densities (right).
45
For investigation of baseline distortion of denser peak area, we simulated the time
domain signal as a sum of exponentially damped sinusoids;
f(t) = ΣAicos(ωit+φi)exp(-t/τ) 0<t<T [3.2]
in which i represents each ion signal. As we add more frequency component into time domain
signal (corresponding to more peaks in absorption frequency spectrum), increased negative dip
in simulated frequency spectrum is observed (Figure 3.2, right). All parameters used in
simulation include T=3.069 s, τ = 1 s, points = 4194304 and bandwidth=568181 Hz.
Sample Description and Preparation
Stock solution of North American crude oil was dissolved in 50:50 (v/v) toluene/methanol to a
final concentration of 1 mg/mL. Each sample was further diluted to 0.5 mg/mL with 50:50 (v:v)
toluene/methanol and 0.1% formic acid, to facilitate protonation during electrospray ionization
(ESI). Peace River bitumen was supplied by National Centre for Upgrading Technology (Devon,
Alberta, Canada) and further diluted to 250 μg/mL in toluene prior to APPI FT-ICR MS analysis
with no additional modification. Rebionuclease A purchased from Sigma-Aldrich Chemical Co.
(St. Louis, MO) was diluted to 1µM in conventional ESI solution: H2O/acetonitrile/formic acid,
50/49/0.5 (v/v/v). All solvents were HPLC grade and purchased from Sigma-Aldrich Chemical
Co. (St Louis, MO).
APPI Source
A custom-built adapter interfaced the APPI source (ThermoFisher Scientific, San Jose, CA) to
the front stage of a custom-built 9.4 T FT-ICR mass spectrometer (see below).253 The sample
flows through a fused silica capillary at a rate of 50 μL/min and is mixed with nebulization gas
(N2 at 50 kPa) inside a heated vaporizer operated at 300 °C for parent crude and maltenes, and
350 °C for asphaltenes.193 After nebulization, gas-phase neutral analytes exit the heated
vaporizer region as a confined jet and a krypton vacuum ultraviolet gas discharge lamp (Syagen
Technology Inc., Tustin, CA) produces 10 eV photons (120 nm). Toluene serves as both solvent
and dopant and increases analyte ionization.254 Charge exchange and proton transfer reactions
46
occur between ionized toluene and neutral analytes through collisions with toluene at
atmospheric pressure inside the APPI source.254, 253
9.4 Tesla FT-ICR MS
All samples were analyzed with a custom-built FT-ICR mass spectrometer is equipped with a 22
cm horizontal room-temperature bore 9.4 T magnet (Oxford Corp., Oxney Mead, U. K.) and a
mudular ICR data station (Predator) facilitated instrument control, data acquisition, and data
analysis.117 Ions generated at atmospheric pressure in the external APPI or ESI source enter the
skimmer region at ~ 2 Torr through a heated metal capillary into the first rf-only octopole. Ions
pass through a quadrupoe to a second octopole, 84 where they accumulate for 250-1000 ms.
Helium gas was introduced during accumulation to collisionally cool the ions before transfer
through a 200 cm rf-only octopole into an open cylindrical Penning ion trap. Octopole ion guides
were operated at 2.0 MHz and 240 Vp-p rf amplitude. Broadband frequency chirp excitation
accelerated the ions to a cyclotron orbital radius that was subsequently detected by two opposed
electrodes of the ICR cell to yield 8 Mword time-domain data sets. Multiple (100-300) time
domain acquisitions were summed for each sample, Hanning-apodized (magnitude-mdoe) or half
Hanning-apodized (absorption-mode), and zero-filled once prior to fast Fourier transform and
magnitude calculation.
Mass Calibration
Each FT-ICR mass spectrum was first calibrated with respect to a prior sample containing
Ultramark®, Met-Arg-Phe-Ala (MRFA) peptide, and caffeine (external calibration), and then
with respect to a homologous series of ions of high abundance common to all petroleum samples.
Masses for singly charged ions with relative abundance of > 6 of baseline rms noise were
extracted, converted to the Kendrick mass scale228 and exported to a spreadsheet for easier
identification of homologous series. Peak assignments were performed by Kendrick mass defect
analysis, 229 as previously described.
Baseline Correction Algorithm
How to accurately describe a baseline point is an important step in this algorithm. Most baseline
47
identification methods255, 256, 250, 251 will initially differentiate the baseline regions that are
considered to be baseline noise from those that are considered to be signal according to different
noise criteria. These methods only work for sparse spectra where baseline noises can be easily
found between signals.
m/z171317121711171017091708
Minimum Points of Reversed Peak and magnitude<3σ
(A) Identification of Baseline Points
(B) Linear Interpolation
(C) Boxcar SmoothingBi-10, Bi-9, …..Bi-2, Bi-1, Bi, Bi+1, Bi+2, …,Bi+9, Bi+10
m/z171317121711171017091708
After Baseline Correction
Smoothed Baseline
(D) Subtraction
Figure 3.3. Schematic baseline flattening procedure. (A) Baseline identification from Original absorption spectrum; (B) Linear interpolation for empty spots between each two baseline points chosen in (A). (C) Boxcar smoothing of resulting (B) to yield smoothed baseline. (D) Spectrum with flat baseline after subtraction of resulting (C).
48
However, for complex analysis, (e.g., petroleum and top-down proteomics’ spectra) it is
difficult to separate baseline noises from signals due to more doublets, triplets and isotopic
distributions (with more closed peaks). Our algorithm (Figure 3.3), which include baseline
identification, linear interpolation and boxcar smoothing, efficiently extracts the baseline from
spectrum without more considering of recognition of baseline.
We start to find base points of baseline by finding the reverse peak point with minimum
magnitude. To decide whether the ith point belongs to the baseline, the magnitude of ith point
was compared with the magnitude of front (i-1) and back (i+1) point and value of 3 of baseline
noise stand deviation (Figure 3.3, (A)). If the magnitude of ith point satisfies both Eq. 3.3 and
Eq. 3.4, it is considered as baseline:
Mi-1>Mi<Mi+1 [3.3]
Mi<3 [3.4]
In which Mi represents the magnitude of ith point, is the noise standard deviation. In this step,
we experimentally observed that one more zero-filling produces more minimum points of reverse
peaks and further facilitates the identification of baseline points. We suggested that two zero-
fillings during data processing should be used to produce absorption-mode spectrum. All
identified point is then stored in a baseline spectrum. The baseline spectrum has the same size of
data count as original absorption spectrum. The index of identified points in baseline spectrum is
also same as in original absorption spectrum. Except for identified points, all other points in
baseline spectrum are zeros. Next, we linearly interpolate values between each two nonzero
points to fill all zero spots in baseline spectrum (Figure 3.3, (B)). Further “boxcar smoothing’’
will remove short term variations, or “noise” and reduced the error in baseline spectrum (Figure
3.3, (C)). The whole “boxcar smoothing” 257 idea can be written as:
∑ ++
=−=
k
kj
jibk
ib ][)12(
1][ [3.5]
In which ][ib represents each baseline point after smoothing, ][ib is each baseline point before
smoothing, 2k +1 is the width of the window used for smoothing data. The value of k is set to a
constant value of 10 in order to get best compromise between calculation speed and final quality
of smoothed spectrum. Finally, the smoothed baseline spectrum is subtracted from original
absorption-mode spectrum to flatten baseline (Figure 3.3, (D)). Although only boxcar smoothing
method has been used to average our data, the choice of smoothing or windowing methods could
49
be arbitrary in same case. The 3 in identification step of baseline points is more sensitive to
scale of baseline roll. For large baseline roll, the low frequency pass filter should be considered
to lower/flatten part of distortion before our baseline correction algorithm.
m/z172517201715
m/z17201715
Ribonucleases A 9.4T FT-ICR Absorption-Mode Mass Spectrum
After Cubic Modeled Baseline Correction
Figure 3.4. Zoom insets of Ribonucleases A FT-ICR absorption-mode spectrum after polynomial modeling baseline correction. Note the discontinuity due to cutting whole data to each small piece.
We have to mention that one advantage of our baseline correction algorithm is no need to
cut data as small segments (e.g., baseline modeling by different functions). For Polynomial
baseline modeling, we notice that the discontinuity appears in the edge of each segment (Figure
3.4). Also, we observed that low order polynomial function with small segment (less fitting data)
50
performs is better than high order polynomial function with large segment. However, it is not
easy to come up a general polynomial model for different spectra due to experimental data
dependence of optimized parameters.
Computational Implementation
The baseline correction algorithm has been combined with automatic phase correction procedure
and implemented in our modular Predator ICR data acquisition system,117 in C program
operating under LabWindows/CVI (National Instruments, Austin, TX).
Results and Discussion
The baseline correction algorithm is tested experimentally by crude oil, bitumen as well as
Ribonucleases A. Figure 3.5 demonstrates the resulting flat baseline of crude oil and
Ribonucleases A absorption-model FT-ICR mass spectra. We can see that the periodic roll of
baseline in crude oil spectrum is romoved after applying baseline correction algorithm (Figure
3.5, top). For denser spectra, (e.g., Figure 3.5, bottom, for an absorption-mode FT-ICR mass
spectral segment from Rigonucleases A) this algorithm is working pretty well even the negative
dip is large in original spectrum. Note the increaing of peak height of isotopic distribution after
baseline correction.
Mass accuracy
Most important figure of merit for mass spectrometric performance should be measured peak
position but not peak height. For the present experimental FT-ICR mass spectra, elemental
compositions could be determined for all singly charged ions between 300 and 1000 Da with
peak heights greater than 6 of baseline rms noise. For comparison of absorption-mode spectra
with and without baseline correction, we chose the 8000 highest peaks in an ESI FT-ICR mass
spectrum of a crude oil. Figure 3.6 shows mass error distributions for the crude oil ESI FT-ICR
absorption-mode mass spectra of Figure 3.5 top. Both mass error distribution and rms error of
absorption-mode spectrum after baseline correction are similar to them of absorption spectrum
51
without baseline correction. This result confirms that our baseline correction algorithm remains
the correct peak position with improved peak height measurement.
Identified Peaks
Because automated peak-picking algorithms typically limit consideration to peaks whose height
exceeds a specified multiple of the standard deviation of baseline rms random noise. As the
876875874873872871870869868867
Abundance 20
15
10
5
0
m/z876875874873872871870869868867
Abundance 20
15
10
5
0
Ribonuclease A 9.4T FT-ICR Absorption-Mode Mass Spectra
Original Absorption-Mode Spectrum
Absorption-Mode Spectrum
After baseline correction
793792791790789788
Crude Oil 9.4T FT-ICR Absorption-Mode Mass Spectra
Before Baseline Correction
After Baseline Correction
m/z793792791790789788
Figure 3.5. Zoom insets of Crude oil FT-ICR absorption-mode mass spectrum (top) and Ribonucleases A absorption-mode spectrum (bottom) showing the performance of baseline correction algorithm.
52
Most abundant
8000 peaks
RMS error: 227ppb
200 600 1000
0.5
0.0
-0.5
Ma
ss
E
rro
r (p
pm
)
Before Baseline Smoothing
200 600 1000
0.5
0.0
-0.5
Ma
ss
E
rro
r (p
pm
)
After Baseline Smoothing
Crude Oil 9.4T FT-ICR Absorption-Mode MS (Mass Error)
Most abundant
8000 peaks
RMS error: 223ppb
Figure 3.6. Mass error distribution for Crude oil FT-ICR absorption-mode mass spectrum before baseline correction (top) and after baseline correction (bottom).
baseline exhibits large distortion, peak height will be significantly reduced by negative value of
baseline roll. Then a peak-picking algorithm can fail to identify true low-magnitude spectral
signals whose frequencies happen to fall near the minima of the "roll". Figure 3.7, top, shows
that the baseline correction algorithm successfully removes baseline for river bitumen APPI FT-
53
ICR absorption-mode mass spectra. Identified peaks by automated peak picking algorithm (peak
height above 6 rms random noise) increase from 33 to 45 (Figure 3.7, bottom).
River Bitumen APPI 9.4T FT-ICR Absorption-Mode MS
748747
Abundance
4035302520151050
m/z748747
Abundance
4035302520151050
Before Baseline Smoothing
After Baseline Smoothing
m/z746.69746.61746.53746.45746.37746.29
Abundance
40
30
20
10
0
m/z
Abundance
40
30
20
10
0746.69746.61746.53746.45746.37746.29
6σ
6σ
W/O Baseline Smoothing
33 Peaks
With Baseline Smoothing
45 Peaks
Figure 3.7. Top: mass scale-expanded of river bitumen APPI FT-ICR absorption-mode mass spectrum showing the resulting flat baseline. Bottom: zoom insects of river bitumen APPI FT-ICR absorption-mode mass spectrum at nominal mass 746 m/z before and after baseline flattening. Note that the absorption spectrum after baseline correction improves discovery of low-abundance peaks.
54
m/z15331532
Ribonucleases A 9.4T FT-ICR Mass Spectra
Magnitude-Mode
Absorption-Mode
9+
m/z153315321531
Ab
un
dan
ce150
100
50
0
m/z153315321531
Ab
un
dan
ce
100
50
0
150 Before Baseline Smoothing
After Baseline Smoothing
Figure 3.8. Top: 9+ charge state isotopic distribution of Ribonucleases A FT-ICR magnitude-mode (black) and absorption-mode spectrum (red) with flat baseline. Middle: 9+ charge state isotopic distribution of Ribonucleases A FT-ICR absorption-mode spectrum before baseline correction (red) with calculated isotopic distribution profile (black cross). Bottom: 9+ charge state isotopic distribution of Ribonucleases A FT-ICR absorption-mode spectrum after baseline correction (red) with calculated isotopic distribution profile (black cross).
55
Isotopic Distribution
The 9+ charge state isotopic distribution of Ribonucleases A absorption-mode spectrum after
baseline correction displays very similar profile to that of normal magnitude-mode spectrum
(Figure 3.8, top). Note that absorption-mode spectrum naturally has narrower peaks width than
in magnitude-mode spectrum. IsoPro software was used to generate the calculated isotopic
distribution based on the amino acid sequences of Ribonucleases A. Compared the calculated 9+
charge state isotopic distribution, the isotopic distribution of absorption-mode spectrum after
baseline correction (Figure 3.8, bottom) demonstrates more accurate profile than before baseline
correction (Figure 3.8, middle).
56
CHAPTER FOUR
EFFECTS OF ZERO-FILLING AND APODIZATION ON
FOURIER TRANSFORM ION CYCLOTRON RESONANCE
MASS SPECTRAL ACCURACY, RESOLUTION, AND SIGNAL-
TO-NOISE RATIO
Introduction
All forms of Fourier transform spectroscopy share common features: acquisition and digitization
of an interferogram or time-domain response to pulsed excitation, time-dependent weighting
(windowing; apodization), padding by addition of zeroes, and discrete Fourier transformation to
yield absorption and dispersion (or magnitude) spectra.258 In particular, Fourier transform ion
cyclotron resonance (FT-ICR) broadband mass spectra have until recently been reported in
magnitude mode, for which the effects of apodization and windowing are well known (see
below). With the recently achieved broadband phase correction to yield absorption-mode FT-
ICR mass spectra, 113, 114 it becomes necessary to understand the effects of apodization and zero-
filling on absorption-mode FT-ICR mass spectra, especially for dense spectra from complex
organic mixtures.
An apodization weighting function applied to a time-domain response to a pulsed
excitation is typically designed to reduce sharp edges at one or both ends of the signal to
eliminate Gibbs oscillations (literally, removal of "feet") on either side of the resulting FT
spectral peak. 259, 260 The most common use of apodization is to increase FT spectral peak height-
to-noise ratio, by weighting the earlier time-domain data points higher than the later time-domain
data. 261, 83, 262 A disadvantage of such apodization is that the peak width at half peak height is
broadened, with correspondingly lower resolving power. Zero-filling (see below) effectively
captures into the absorption-mode spectrum information originally residing in the (non-zero
filled) dispersion data, and thus increases absorption-mode peak height-to-noise ratio by a factor
of √2,78 with concomitant improvement in mass accuracy.261, 1
57
Optimized apodization for improvement in resolution and peak height-to-noise ratio has
been extensively investigated,78, 263-265 and both apodization and zero-filling are in wide use for
FT-NMR data processing.261, 266 For FT-ICR MS, Chow218 showed that ICR frequency
measurement error depends on the separation between two peaks. FT-ICR magnitude-mode
spectral frequency/mass interpolation error has been evaluated for different various apodization
functions and zero-fills,267, 268, 262, 218, 5 and apodization optimization has also been discussed.
Aarstol, 1987 #82} Investigation of apodized absorption spectra has been limited to simulated or
sparse experimental cases.4, 269, 258. Finally, for FT-ICR MS, it is essential to eliminate
systematic errors (e.g., by dividing a spectrum into 30 separately calibrated segments). 9 in order
to take advantage of the effects of apodization on random noise. Here, we consider the effects of
twelve different apodization functions as well as multiple zero-fills on FT-ICR magnitude and
absorption spectra from bitumen and petroleum crude oil, with thousands of resolved peaks.
Experimental Methods
Sample Description and Preparation
Athabasca bitumen and distillate fraction (500 – 538 ○C) from Athabasca bitumen heavy vacuum
gas oil (HVGO) were obtained from the National Centre for Upgrading Technology (Devon,
Alberta, Canada). Bitumen and HVGO samples were diluted to yield a final concentration of
500 μg/mL by a 50:50 toluene methanol mixture spiked with 0.1% (by volume) formic acid
(positive ESI) and used without additional purification. All solvents were HPLC-grade, obtained
from Sigma-Aldrich Chemical Co. (St. Louis, MO).
Instrumentation
Middle Eastern crude oil distillate fractions were analyzed with a custom-built FT-ICR mass
spectrometer equipped with a 9.4 T horizontal 220 mm bore diameter superconducting solenoid
magnet operated at room temperature (Oxford Instruments, Abingdon, Oxfordshire, U.K.) and a
modular ICR data station (PREDATOR) facilitated instrument control, data acquisition and data
58
analysis.270, 271, 227 Positive ions generated at atmospheric pressure were accumulated in an
external linear octopole ion trap84 for 250-1000 ms and transferred by rf-only octopoles to a 10
cm diameter, 30 cm long open cylindrical Penning ion trap. Octopoles were operated at 2.0
MHz and 240 Vp-p amplitude. Broadband frequency sweep (chirp) dipolar excitation (70 - 700
kHz at 50 Hz/μs sweep rate and 350 Vp-p amplitude) was followed by direct-mode image current
detection to yield 8 Mword time-domain data sets. Time-domain data sets were co-added (100
acquisitions), Hanning apodized, and zero-filled once before fast Fourier transform and
magnitude calculation.
Mass Calibration
ICR frequencies were converted to ion masses based on the quadrupolar trapping potential
approximation105, 106and internally calibrated with respect to the most abundant homologous
alkylation series differing in mass by integer multiples of 14.01565 Da (CH2) for each sample.
Peaks with relative peak abundance greater than 6 times the standard deviation of the baseline
noise were exported to a spreadsheet.
Data Processing
A discrete time domain ICR signal is multiplied by one of the twelve window functions listed in
Figure 4.1 padded by n zero-fills (each of which doubles the number of time-domain data Fast
Fourier transformation produces real (Re(ω)) and imaginary (Im(ω)) frequency-domain spectra.
Broadband phase correction 114 performs a linear combination of real and imaginary data to
generate an absorption frequency spectrum (A(ω)). Alternatively, a magnitude-mode frequency
spectrum (M(ω)) is calculated from √ ([Re(ω)]2 + [Im(ω)]2). Both absorption and magnitude
frequency spectra are converted to m/z with a two term calibration equation. 105, 106.
Computational Implementation
Each of various apodizations and zero-fills was programmed in C. Each function was
implemented as an extension of our ICR data system, 117 in C operating under LabWindows/CVI
(National Instruments, Austin, TX). Data processing steps are shown in Figure 4.2. Half
apodization and full apodization have been tested for both magnitude and absorption spectra.
59
Cosine
Full Window Half Window
0 1n/(N-1)
Mag
nit
ud
e o
f W
ind
ow
Fu
nc
tio
ns
0
1
Hamming
Hanning
Gaussian
=0.2
Blackman
Blackman-Harris
Bartlett-Hanning
Triangle
Four-Term Blackman-
Harris
Kaiser
α=1.2
Blackman-Nuttall
Kaiser-Bessel
Figure 4.1. Twelve full window (left) and half window (right) functions. N is the time-domain data size before zero-filling and n is the index for each data 0 ≤ n ≤ N-1.
60
Time (s)0 3.5
x x
m/z700650600550500450400350
Fourier Transform
Imaginary SpectrumReal Spectrum
Magnitude Spectrum
Phase Correction
Absorption Spectrum
Magnitude Spectrum Absorption Spectrum
Zero-Fill
Time (s) 70
Zero-Fill
Time (s) 70
Full Half
m/z700650600550500450400350
Figure 4.2. Data processing steps for FT-ICR magnitude-mode and absorption-mode FT-ICR spectra.
61
448.41448.39448.37448.35448.33448.31
m/z448.41448.39448.37448.35448.33448.31
Crude Oil Distillate 9.4 T ESI FT-ICR MS
(Magnitude-Mode Spectra)
Half Hanning
Apodization
Full Hanning
Apodization
Figure 4.3. Mass scale-expanded segments of electrospray ionization (ESI) FT-ICR magnitude mass spectra of distillated fraction from crude oil for half Hanning (top) and full Hanning (bottom) apodization functions. The magnitude spectrum with half hanning apodization exhibits greater width at each peak base.
Results and Discussion
Full Apodization vs. Half Apodization
Although magnitude-mode peaks with half apodization exhibit better resolution at half-
maximum peak height than with full apodization (Figure 4.3), half apodized peaks are much
broader at the base. Thus, mass accuracy for an FT-ICR magnitude spectrum of crude oil
distillate with half apodization is a factor of 2 worse than for full apodization (Figure 4.4). For
sparse spectra (e.g., Figure 4.5, for an absorption-mode FT-ICR mass spectral segment from a
62
crude oil distillate) both half Hanning and full Hanning apodization yield symmetric peaks, but
full apodization introduces negative lobes on both sides of each peak. For denser spectra (e.g.,
Figure 4.6, for an absorption-mode FT-ICR mass spectral segment from bitumen), full Hanning
apodization severely distorts the shapes of closely space peaks. In summary, half apodization is
best suited for absorption-mode display, whereas full apodization is best for magnitude-mode
spectra.
Ma
ss
Err
or
(pp
m)
2
1
-1
-2
0
300 400 500 600 700
m/z
Crude Oil Distillate 9.4 T ESI FT-ICR MS
Magnitude-Mode
With full Hanning window 1700 peaks 130ppb
With half Hanning window 1700 peaks 270ppb
Figure 4.4. Mass error distribution for broadband magnitude-mode FT-ICR mass spectra for a distillate fraction of crude oil for half Hanning (black) and full Hanning (red) apodization functions.
63
Half Hanning
Apodization
Full Hanning
Apodization
448.41448.39448.37448.35448.33448.31
m/z448.41448.39448.37448.35448.33448.31
Crude Oil Distillate 9.4 T ESI FT-ICR MS
(Absorption-Mode Spectra)
Figure 4.5. Mass scale-expanded segments of FT-ICR absorption spectra for a distillated fraction from crude oil for half Hanning (top) and full Hanning (bottom) apodization functions.
m/z730.72730.68730.64730.60730.56
Half Hanning
Apodization
Full Hanning
Apodization
Bitumen 9.4 T ESI FT-ICR MS
(Absorption-Mode Spectra)
Figure 4.6. Mass scale-expanded segments of FT-ICR absorption spectra for bitumen for half Hanning (top) and full Hanning (bottom) apodization functions.
64
Half C osine
Half Hamming
Half Hanning
Half B lackman
Half T r iang le
Half B art let t - Hann
W / O A p od izat ion
Cosine
Hamming
Hanning
Blackman
Triangle
Bartlett-Hann
W/O Apodization
Absorption-Mode
Magnitude-Mode
Zero-Fills
RM
S M
ass E
rror (p
pm
)R
MS M
ass E
rror (p
pm
) 0.30
0.10
0.25
0.20
0.15
0.05
0.30
0.05
0.25
0.15
0.10
0 1 2 3
0 1 2 3
0.20
Figure 4.7. Root-mean-square mass error for broadband magnitude-mode (top) and absorption-mode (bottom) FT-ICR mass spectra for a distillate fraction of crude oil, following 0, 1, and 2 zero-fills, for each of several apodization functions. The six apodization functions resulting in the least rms error are shown.
Cosine
Hamming
Hanning
Blackman
Triangle
Bartlett-Hann
W/O Apodization
Half Cosine
Half Hamming
Half Hanning
Half Blackman
Half Triangle
Half Bartlett-Hann
W/O Apodization
Peak H
eig
ht-to
-Nois
e R
atio
Zero-Fills
Absorption-Mode
Magnitude-Mode
900
500
800
700
600
400
900
500
800
700
600
400
0 1 2 3
0 1 2 3
Figure 4.8. Peak height-to-noise ratio for peak at m/z 450.4094 (C32H52N1) for a distillate fraction of crude oil, following 0, 1, and 2 zero-fills, for each of several apodization functions.
65
Half Cosine
Half Hamming
Half Hanning
Half Blackman
Half Triangle
Half Bartlett-Hann
W/O Apodization
Cosine
Hamming
Hanning
Blackman
Triangle
Bartlett-Hann
W/O Apodization
Absorption-Mode
Magnitude-Mode
Zero-Fills
Resolv
ing P
ow
er
(m/∆
m50%)
Resolv
ing P
ow
er
(m/∆
m50%)
600,000
1,200,000
1,000,000
800,000
200,000
800,000
600,000
400,000
0 1 2 3
0 1 2 3
Figure 4.9. Average mass resolving power for 6 peaks above 6σ of baseline noise at nominal m/z 450 for a distillate fraction of crude oil, following 0, 1, and 2 zero-fills, for each of several apodization functions.
Mass Accuracy
For the present experimental FT-ICR mass spectra, elemental compositions could be determined
for all singly charged ions between 300 and 700 Da with peak heights greater than 6 of baseline
rms noise. For comparison of magnitude and absorption spectra, we chose the 1700 highest
peaks in an ESI FT-ICR mass spectrum of a crude oil distillate. The rms mass errors for
absorption-mode spectra following each of six different apodizations and 0, 1 or 2 zero-fills is
plotted in Figure 4.7. Half apodization produces consistently better mass accuracy for
absorption-mode than for full-apodized magnitude-mode spectra. Moreover, mass accuracy for
absorption-mode (but not magnitude-mode) improves significantly after one time-domain zero-
fill, because the first zero-fill effectively captures the information contained in the non-zero-
filled dispersion spectrum.78 For magnitude mode, full apodization yields higher mass accuracy
than half apodization, whereas the converse applies to absorption mode. A second zero-fill yields
no improvement in mass accuracy for either magnitude-mode or absorption-mode spectra.
66
(Moreover, in the absence of noise, the first zero-fill correctly interpolates each additional
spectral data between two adjacent original data, whereas second or higher zero-fills yield a
convolved peak shape that no longer exactly interpolates the additional data values. 1
Signal-to-Noise Ratio
For the same experimental time-domain raw data as for Figure 4.7, Figure 4.8 shows the peak
height-to-noise ratio for peak at m/z 450.4094 (C32H52N1), following each of six different
apodizations and 0, 1 and 2 zero-fills. Each of the full apodization functions reduces magnitude-
mode peak height-to-noise ratio, because the first half of the apodization function reduces the
time-domain signal amplitude. Although the unapodized absorption-mode spectral peak height -
to-noise ratio is lower than that for an unapodized magnitude-mode spectrum, absorption-mode
signal-to-noise ratio improves dramatically after half apodization, because half-apodization
lowers the time-domain signal amplitude most at the end of the acquisition period, where the
noise-to-signal ratio is highest. In fact half apodized absorption-mode spectra typically exhibit
higher signal-to-noise ratio than full apodized magnitude-mode spectra. Absorption-mode peak
height-to-noise ratio is virtually independent of the choice of half apodization function, whereas
magnitude-mode peak height-to-noise ratio varies significantly among different full apodization
choices. Finally, peak height-to-noise ratio for both absorption-mode and magnitude-mode
spectra increases slightly after zero-filling, presumably because interpolation gives higher digital
resolution to help locate the peak center.
Resolving Power
For the same experimental time-domain raw data as for Figure 4.7, six peaks greater in
magnitude than 6s of baseline noise at nominal m/z 450 are chosen for test purpose. Figure 4.9
shows that the average resolving power is consistently as much as 50% higher for absorption
than for magnitude spectra, and depends strongly on the choice of apodization function for both
spectra. As for multiple zero-fillings, the resolving power improves slightly on zero-fillings for
both absorption and magnitude-mode spectra, presumably due to much better digital resolution
of peak height and peak width. Half cosine (for absorption-mode) and full cosine (for magnitude-
mode) apodization provide the highest resolving power.
67
CHAPTER FIVE
PHASE SPECTRA OF FOURIER TRNSFORM ION
CYCLOTRON RESONANCE MASS SPECTROMETRY
Introduction
In Fourier transform analysis, an ideal signal f(t) without any time delay could be complex
Fourier transformed to F(ω)=A(ω)+iD(ω). We call real part of F(ω) as absorption-mode
spectrum and imaginary part as dispersion-mode spectrum. For a signal with time delay, f(t-T),
The resulting Fourier transformation is F(ω)eiφ(ω). 1 In which ejφ(ω) =cos(φ(ω)) + isin(φ(ω)), so
F(ω) eiφ(ω) =[A(ω) cos(φ(ω)) + D(ω) sin(φ(ω))] +i[D(ω) sin(φ(ω)) - A(ω)cos(φ(ω)),]. The real
part of F(ω) eiφ(ω) is linear combination of A(ω) and D(ω). We should note that both cases the
sqrt(real2+imaginary2) is equal to sqrt[A(ω)2+D(ω)2] ,which we call magnitude spectrum, it is
independent any phase shift. Compared to conventional magnitude-mode display, absorption-
mode FT-ICR mass spectrum offers a gain up to a factor of 2 in mass resolving power80-82 and
increased mass measurement accuracy. 114, 9 If we can get the phase value for signal with time
delay, we can recover the F(ω) by F(ω) eiφ(ω) * e-iφ(ω) , which is Fourier transformation of
unshifted (ideal) version of f(t), and get absorption-mode spectrum, A(ω), from real part of F(ω).
So the key to this phase correction method is the explicit knowledge of a function of frequency
φ(ω), which we call the phase spectrum of FT-ICR.
Most recent developments of phase correction of FT-ICR mass spectrum are based on
calculation of phase spectrum. Except for linear phase spectrum used in phase correction for
collision mode analysis, 112 broadband phase correction algorithm114 can automatically account
for first- and second-order phase accumulation from excitation parameters and iterates the zero-
order term. Another approach for phase correction is to assume a quadratic relation between
phase and frequency, and iteratively solve for zero-, first-, and second-order coefficients. 115 All
these methods can yield an absorption-mode spectrum with higher resolving power than
conventional magnitude-mode spectrum. However, the physical explanation and explicit form of
68
the phase relation/phase spectrum is not known in all prior research. The discovery of physically
justified, experimentally tested, closed-form or or quasi-closed-form expressions would result in
a new and more efficient broadband phase correction algorithm. Here, we derive analytical phase
spectrum for linear-sweep excitation and detection signal of FT-ICR by using method of
stationary phase method. Phase correction of FT-ICR mass spectrometry directly by using phase
spectrum is demonstrated experimentally. Compared to automated broadband phase correction
algorithm, analytical phase spectrum accurately calculate phase value for each frequency and
provide fast and robust phase correction for FT-ICR mass spectra from linear-sweep excitation.
Moreover, this phase spectrum could be modified to phase swift excited signal.
Method of Stationary Phase
The method of stationary phase, which was developed by Lord Kelvin in the 1800s to solve
integrals encountered in the study of hydrodynamics, is useful in evaluating integrals of the
following type:
dtetAE tif∫=+∞
∞−
)()( [5.1]
If we put t = tω+ζ, where f(t) is stationary for t = tω, ζ is very small number, we can develop
f(t) in a Taylor expansion:
....)('''6
)(''2
)(')()()(32
++++=+= ωωωωω
ξξξξ tftftftftftf [5.2]
The definition of stationary point is tω, where f′(t)=0 at t = tω. While A(t) changes comparatively
slowly, f(t) changes by 2π and A(t) is supposed to vary by only a small fraction of itself. That is,
the integrand approximates a constant A(t) multiplied by a rapidly varying function eif(t), which
varies between +1 and -1. Therefore, destructive interference between the various contributions
to the integral will make it vanish, except for those values of t for which f(t) is stationary.
Stationary values do not cancel each other in general and they are not symmetrically distributed
69
around zero, for any function f(t). At the stationary value of t, the integrand is approximately one
constant, A(t), multiplied by another, eif(t).
dtetAdtetAEtftfi
tif ∫=∫=∞+
∞−
+∞+
∞−
))(()())(''
2)((
)(
2
ωωξ
ω
ξωω
ωω
ξ
ω
ξ
ω deetAdteetAtfi
tiftfi
tif
∫=∫=∞+
∞−
∞+
∞−
)(''2)(
)(''2)(
22
)(*)(
ξξξ ωωωω dtfitfetA tif )])(''
2
1sin())(''
2
1[cos()( 22)( +∫=
∞+
∞−
)4
)((4)( )(
)(''
2
)(''
2*)(
π
ω
ω
π
ω
ω
ωω
ππ +
==tfii
tif etAtf
etf
etA [5.3]
Phase Spectrum
Chirp/Sweep Excitation Signal
The chirp/sweep excitation signal (Figure 5.2, (A)) for Fourier Transform ion cyclotron
resonance could be represented as
)]2
1cos[()( 2
0tSRtEtE
I∗∗+= ω [5.4]
In which E0 is the amplitude of excitation signal, ωI=2πfI is the initial frequency and SR
represents the sweeprate. The Fourier transform, E(ω), of the excitation signal E(t) is
dtetEET
ti∫= −
0
*)()( ωω [5.5]
Because of Euler’s formula
2
)cos(ixix ee
x−+
= [5.6]
70
dteeeE
dteteET
titSRtitSRtiT
ti II
∫ +=∫= −∗∗+−∗∗+
−
0
)2
1()
2
1(
0
0
*][2
*)()(22
ωωωωω
dteeET ttSRtittSRti II
∫ +=+∗∗+−−∗∗+
0
)2
1()
2
1(
0 ][2
22 ωωωω
∫∫ +=+∗∗+−−∗∗+ T ttSRtiT ttSRti
dteE
dteE II
0
)2
1(
0
0
)2
1(
0
22
[2
[2
ωωωω
[5.7]
We can apply the stationary method here in order to solve the Eq. 5.7. For abbreviation,
we introduce two notations.
ttSRttfI
ωωω −∗∗+= 2
1
2
1),( [5.8]
)2
1(),( 2
2ttSRttf
Iωωω +∗∗+−= [5.9]
According to the stationary point definition (The definition of stationary point is
tω, where f′(t)=0 at t = tω).
0),('11 1
=−∗+==
ωωω ωωtSRtf
Itt
So SR
t Iωω
ω
−=
1 [5.10]
0),('22 2
=−∗−−==
ωωω ωωtSRtf
Itt
So SR
t Iωω
ω
−−=
2 [5.11]
We can see that tω1 is always positive value and tω2 is always negative value. The second
exponential in the Eq.5.7 has no stationary point in the time range [0,T]. If the amplitude e0 is
slowly varying or constant, the contribution to E(ω) from second exponential of Eq.5.7 can be
71
neglected, leaving
dteE
dteE
ET ttSRtiT
tfi I
∫=∫=−∗∗+
0
)2
1(
0
0
),((0
2
1
2][
2)(
ωωωω [5.12]
Taylor expansion of f1(ω,t) is developed as
),(''2
),('),(),(11
2
11111 ωωω ωξωξωω tftftftf ++= [5.13]
So ∫=T
tfi dteE
E0
),((0 ][2
)( 1 ωω (applying the stationary point)
∫=−T tttfi
tif dteeE
0
))(,(''2
1
),(0
2111
11
2
ωωω
ωω [5.14]
For tω1 not too close to 0 or T the finite integral in above equation can be replaced by one
extending from -∞ to ∞ without loss of accuracy. Then
∫=−T tttfi
tif dteeE
E0
))(,(''2
1
),(0
2111
11
2)(
ωωω
ωωω
)
4),((
11
0
11
),(''2
πω
ω
ω
ωπ +
=tfi
etf
E
)
4),((
0
11
2
πω ωπ +
=tfi
eSR
E [5.15]
Phase spectrum for chirp/sweep excitation signal can be represented as
4
),()(11
πωωϕ ω += tfE
[5.16]
72
Submit Eq.5.8 and Eq.5.10 into Eq.5.16
4
)(2
1)( 2 πωωωωωωωωωϕ +
−−
−∗∗+
−=
SRSRSR
SRIII
IE
42
2 2222 πωωωωωωωωωω+
−−
+−+
−=
SRSRSRIIIII
42
22222 2222 πωωωωωωωωωω+
+−+−+−=
SRIIIII
42
22222 2222 πωωωωωωωωωω+
+−+−+−=
SRIIIII
42
)( 2 πωω+
−−=
SRI [5.17]
Depend on the sweep direction, the final phase spectrum for chirp/sweep excitation signal
for each specific ωi is
42
)()(
2 πωωωϕ ±−−
=SR
Ii
iE [5.18]
The option + means that the sweep of frequency is low to high and the option – means that the
sweep of frequency is high to low.
After we solve the phase spectrum for excitation signal, we can see that the excitation
signal after inverse Fourier Transformation can be represented as
]42
)(cos[()(
2
0
πωωω mSR
tEtE Ii
i
−−= [5.19]
Detected Signal
We start to discuss the detected signal from the Lorentz force. When each ion cloud is
73
transferred into ICR cell with a spatially uniform magnetic field, B (Figure 5.1), motion of ion
cloud will subject to a force given by Lorentz force which is described in Eq.5.20.
Excita
tion
Detection
B
x
y
Figure 5.1. Schematic ICR cell showing the excitation, detection and magnitude field directions
BvqEqFvvvv
×+= [5.20]
dt
vdmamF
vvv
== [5.21]
In which m, q, and v are ionic mass, charge, and velocity, and the vector cross product term
means that the direction of the magnetic component of the Lorentz force is perpendicular to the
plane determined by v and B. If the ion maintains constant speed, then the Lorentz force bends
the ion path into a circular motion. If we substitute Eq. 5.21 into Eq. 5.20 and consider x and y
directions, we can get more detailed ionic motion equation.
BjvivqqEidt
vdm
yx×++= )ˆˆ(ˆ
v
BivjvqqEidt
jvivdm
yx
yx )ˆˆ(ˆ)ˆˆ(−+=
+ [5.22]
74
Eq. 5.22 can be further separated as two ion motion equations along with x and y directions
iqBviqEdt
idvm
y
x ˆˆˆ
−= [5.23]
jqBvdt
jdvm
x
y ˆˆ
= [5.24]
Second derivative of vy can be acquired from first derivative of Eq. 5.24.
dt
dv
m
qB
dt
vm
qBd
dtdt
dvd
v x
x
y
y===″ )()(
[5.25]
Substitute vx from Eq. 5.24 into Eq. 5.25 to yield
yyv
m
Bq
m
qEqBv
2
22
2−=″
[5.26]
Because of ωi = (qi B)/mi, we can simplify Eq. 5.26 to Eq. 5.27.
2
2
2
i
i
yiy
m
BEqvv =+″ ω [5.27]
Write the Fourier Transform of yv as
yv̂ and substitute excitation signal E(t) (Eq. 5.4) into Eq.
5.27 to yield
∫ ∗∗+=+−∞+
∞−
− dttSRtEem
Bqvv
I
ti
i
i
yiy)]
2
1cos[(ˆˆ 2
02
2
22 ωωω ω
75
∫ ∗∗+−
=∞+
∞−
− dttSRtEem
Bqv
I
ti
ii
i
y)]
2
1cos[(
)(ˆ 2
0222
2
ωωω
ω [5.28]
Similar to excitation signal, we can derive the phase spectrum for yv̂ by the stationary phase
method. The resulting yv̂ is
42
)(
02
2 2
2)(8ˆ
πωωπωωω
±−−
−= SR
iii
i
y
I
eSR
Em
Bqv [5.29]
From Eq. 5.29, we can see that the phase spectrum for ion motion is exact same as
excitation signal.
42
)()(
2 πωωωϕ ±−−
=SR
Ii
i
Inverse Fourier transformation of yv̂ will produce the asymptoti solution for
yv . Since the
phase spectrum will not change during Fourier transform, the velocity of ion motion, yv , along
with detection direction will have same phase spectrum as yv̂ . The image current I[t] (detected
signal) is proportional to yv [t], the phase spectrum for detected signal has same expression as
excitation signal at t=0. However, we only start to observe detection signal at tobs due to time
dispersion for linear frequency-sweep and small time delay (tdelay) for avoiding induced
excitation signal (Figure 5.2, (A)). The final phase spectrum for detected signal at t=tobs is
42
)()(
2 πωωωωϕ ±+−−
=obsi
Ii
iDt
SR [5.30]
Figure 5.2, (B) shows the phase spectrum profiles of linear frequency-sweep excitation (blue)
76
and detected signal(red) for low to high frequency sweep.
Fre
quency
Detecttdelay
E(t)
fI
0
0
ff
tobs
Frequency-Sweep Excitation Signal
Detected Signal
D(t)
Time (s)
- φD (ω)
- φE (ω)
φ(ω
) (r
ads)
0
fI ffFrequency (Hz)
A)
B)
ω=2πf
Figure 5.2. A) Plots of time-domain linear frequency-sweep excitation signal (upper) and detected signal (bottom) vs. time. B) Phase spectrum profiles (phase vs. frequency) of linear-sweep excitation and detected signal. Here we only plot the phase spectrum for low-to high frequency-sweep for demonstration purpose.
77
Experimental Methods
Sample Preparation
Stock solutions of either a distillate fraction (500-538 ○C) from an Athabasca bitumen or a North
American crude oil were dissolved in 50:50 (v/v) toluene/methanol to a final concentration of 1
mg/mL. Each sample was further diluted to 0.25 mg/mL with 50:50 (v:v) toluene/methanol and
0.1% Formic acid to facilitate protonation during electrospray ionization.
Instrumentation
All sample was analyzed with a custom-built FT-ICR mass spectrometer equipped with a 9.4
Tesla horizontal 220 mm bore diameter superconducting solenoid magnet operated at room
temperature (Oxford Instruments, Abingdon, Oxford shire OX13 5QX, UK) and a modular ICR
data station (PREDATOR) facilitated instrument control, data acquisition and data analysis. 226,
227 Positive ions generated at atmospheric pressure were accumulated in an external linear
octopole ion trap84 for 250-1000 ms and transferred into ICR cell. Linear broadband frequency
sweep (chirp) dipolar excitation (10 – 900 kHz at 50 Hz/μs sweep rate and 350 Vp-p amplitude)
or SWIFT excitation was followed by direct-mode image current detection to yield time-domain
data sets with 16 Mwords. The 200 collected individual transients of 2.8s for distillate of crude
oil) or 5.6 s for crude oil were averaged, apodized with a full-Hanning (magnitude spectrum) or
half-Hanning (absorption spectrum 114) weight function, and zero-filled once prior to fast Fourier
transformation. Each m/z spectrum was internally calibrated with respect to an abundant
homologous N1 series, and then walking calibration was applied to the spectrum was dividend
into equal consecutive segments which contained at least two members of a homologous
alkylation series.
Mass Analysis
Each FT-ICR mass spectrum was first calibrated with respect to a prior sample containing
Ultramark®, Met-Arg-Phe-Ala (MRFA) peptide, and caffeine (external calibration), and then was
internally calibrated with respect to an abundant homologous N1 series, and then walking
78
calibration was applied and the spectrum was dividend into 56 (for crude oil) equal consecutive
segments which contained at least two members of a homologous alkylation series. Masses for
singly charged ions from m/z 300 to m/z 700 (distillate of crude oil) or from m/z 200 to m/z
1000 (crude oil) with relative abundance of > 6 of baseline rms noise were extracted, converted
to the Kendrick mass scale228 and exported to a spreadsheet for easier identification of
homologous series. Peak assignments were performed by Kendrick mass defect analysis, 229 as
previously described.
4*2
)( 2 πππϕ +∗+−
−= ftSR
ffobs
s
D
After Applying Phase Spectrum
800700600500400300m/z
Distillate of Crude Oil 9.4T FT-ICR Mass Spectra
Before Phasing
After Extra Constant Phase
136.04
*2)( 2
++∗+−
−=πππϕ ft
SR
ffobs
s
D
800700600500400300
Figure 5.3. Distillate of crude oil 9.4T FT-ICR mass spectra. Top: Raw real data following Fourier transform of discrete time-domain signal. Middle: absorption-mode spectrum (obtained after applying analytical phase spectrum). Bottom: Optimized absorption-mode spectrum after fine tune of constant term. Note: additional 0.136 radians in constant term.
79
SWIFT Waveform
The procedure of building SWIFT waveform was described in several literatures. 75-77 The
optimized algorithm has been implemented in our modular ICR data station (PREDATOR).
Basically we build the magnitude modulation with constant amplitude and smooth it twice by
window function. The corresponding phase modulation will be automatically calculated based on
the information of magnitude modulation. 272, 273 Both magnitude and phase modulation are then
subjected to inverse Fourier transform to give the time-domain excitation waveform. The
schematic procedure of SWIFT is shown in Figure 5.7, top. Finally, converted analog signal
from the SWIFT waveform is amplified and applied to excitation plate.
Computational Method
Phase correction by phase spectrum can be simply implemented in software. Figure 5.3 shows
the three major steps in phase spectrum method. First, the time-domain will be subjected to half
apodization, one zero-filling and Fourier transformation to yield real spectrum (Figure 5.3, top)
and imaginary spectrum. Second, derived phase spectrum (Eq. 5.30) is applied to both real and
imaginary spectrum according to )Im()](sin[)Re()](cos[)( ωωϕωωϕωDD
A −= and
)Im()](cos[)Re()](sin[)( ωωϕωωϕωDD
D += (Figure 5.3, middle). Although we have
derived the analytical phase spectrum for detected signal from linear frequency-sweep excitation,
we have noticed that there is small phase variation ±150 in constant term π/4 for different
samples. These phase differences between analytical phase spectrum and real phase most likely
come from imperfect experimental conditions, like, electronic circuit, non-chemical noise or
nonzero initial phase value (ion clouds are not perfectly aligned with excitation plate). For best
result, we add a third step to fine tune the constant term within ±150. We simply vary additional
constant term from -150 to 150 in 1-degree increments until the entire spectrum is optimally
"phased". Figure 5.3, bottom shows the optimized absorption-mode spectrum after fine tune of
constant term.
Results and Discussion
80
Phase Spectrum Method vs. Automated Broadband Phase Correction
Calculated Phase. Although previous automated broadband phase correction algorithm has no
explicit form for phase function, it works pretty well in term of improvement of resolving power
and mass accuracy. We compared the phasing results from phase spectrum method and
automated broadband phase correction algorithm for distillate of crude oil FT-ICR mass spectra
so as to fully understand both phase correction methods. Figure 5.4, (A) shows the distillate of
crude oil of FT-ICR absorption-mode spectrum from broadband phase spectrum method (lower)
and phase correction algorithm (upper). Phase value vs. frequency for phase spectrum method
(red) and phase correction algorithm (blue) are plotted in Figure 5.4, (B). Although absolute
phase value from two methods is totally different (Figure 5.4, (B)), two curves looks like parallel
to each other. Calculated phase difference between these two methods is very close to 2*π*1033.
It does make sense because two phase value different at 2nπ will have exact position in ICR cell
and both phase value will recover absorption-mode spectrum perfectly. Further quantitative
phase differences are evaluated by ε. Figure 5.4, (C) shows the plot of ε vs. frequency and clearly
exhibit the phase error associated with broadband phase correction algorithm. In broadband
phase correction, we pick the frequency point with highest amplitude within magnitude-mode
spectrum as initial point and add same amount of phase difference for increasing each frequency
data point or reduce same amount of phase difference for decreasing each frequency data point.
This is reason that the highest value of ε (at initial point) is zero and other value of are linearly
decreased toward both ends of frequency spectrum.
Resolving Power and Mass Accuracy. For comparison of resolving power and mass accuracy,
we chose the exact same 1800 highest peaks in an ESI FT-ICR mass spectrum of a distillate of
crude oil for both phase spectrum method and broadband phase correction algorithm. Although
phase error associated with broadband phase correction algorithm have observed, the error is
relative small (Figure 5.4, (C)). Both resolving power (Figure 5.5, top) and mass error
distribution (Figure 5.5, bottom) from phase correction algorithm (upper) and phase spectrum
method (lower) demonstrate very similar result.
Unresolved Peaks. Crude oil of FT-ICR absorption-mode spectrum by phase spectrum method
is not only getting better resolving power than magnitude-mode spectrum, but also getting more
81
Phase spectrum method
Phase correction algorithm
200 250 300 350 400 450
Frequency (KHz)
(rad
s)
-0.006
-0.004
-0.002
0
0.002
0.004
200 250 300 350 400 450
0
-4000
2000
4000
6000
8000
10000
-2000
- φ(ω)Phase spectrum
- φ(ω)Phase Correction
φ(ω
) (r
ad
s)
A)
B)
C)
m/z600400300 700500
600400300 700500
Distillate of Crude Oil 9.4T FT-ICR Mass Spectra (Absorption-Mode)
2*1033*π
= φ(ω)phase spectrum- φ(ω)phase correction-2*1033*π
Figure 5.4. Top: Distillate of crude oil of FT-ICR absorption-mode spectra produced by broadband phase correction algorithm (upper) and phase spectrum method (lower). Middle: Plot of calculated phase value vs. frequency from broadband phase correction algorithm (blue) and phase spectrum method (red). Bottom: Plot of phase difference, ε, vs. frequency. Note that every ε value is less than 1 degree (0.0175 radians)
82
m/z448.41448.39448.37448.35448.33448.31448.29
765000
758000
748000 767000
760000
448.41448.39448.37448.35448.33448.31
758000
754000
798000 797000
758000
448.29
-0.5
0
0.5
200 300 400 500 700600
Mass E
rror
(ppm
)
m/z
-0.5
0
0.5
200 300 400 500 700600
Mass E
rror
(ppm
)
Phase correction algorithm
Phase spectrum method
1800 peaks
110 ppb
1800 peaks
110 ppb
A)
B)
Distillate of Crude Oil 9.4T FT-ICR Mass Spectra
Phase correction algorithm
Phase spectrum method
Figure 5.5. TOP: Mass scale-expanded segments of distillate of crude oil of FT-ICR absorption-mode spectra from broadband phase correction algorithm (upper) and phase spectrum method (lower). Bottom: Mass error distribution of absorption-mode spectra from phase correction algorithm (upper) and phase spectrum method (lower).
83
resolved peaks. Closed mass doublets partially or unresolved in magnitude mode become
resolved in absorption-mode (Figure 5. 6), thereby increasing the number of correctly assigned
elemental compositions.
915.86915.82915.78915.74915.7915.66
m/z915.86915.82915.78915.74915.7915.66
Crude Oil ESI 9.4T FT-ICR MS
Absorption-Mode
Magnitude-Mode
C66H96N113C
C61H92N1S213C
3.4mDa3.4mDa
C63H111O3
C59H115N2S2
C63H100N1S113C
C64H98N1S113C
C64H98N1S113C
C63H100N1S113C
C59H115N2S2
Figure 5.6. Magnitude and absorption electrospray ionization 9.4 T FT-ICR mass spectra for the same crude oil data from phase spectrum method. The absorption display clearly resolves several mass doublets (compositions differing by C3 vs. SH4, 0.0034 Da) that appears as a single magnitude mode peak.
84
Phase
Frequencyfs ff
Smooth x2
T1
T
IFT
Magnitude Modulation Phase Modulation
Phase
Frequencyfs ff
10 Tt ≤≤
T1
Tt0t2
10ttt ≤≤
Phase Modulation
Swift Excitation Event
Effective waveform
tdelay
Detection
Excitation 2
)(1
0
TTt
−=
0
t0 t1
A)
B)
X
SWIFT Waveform
Figure 5.7. A) Schematic procedure for building SWIFT waveform. B) Detailed SWIFT waveform configuration in real experiment. Note that effective waveform region is located in the middle of whole waveform and is exactly 1/2 of T1
85
SWIFT Phasing by Phase Spectrum Method
Modified Phase Spectrum for SWIFT. Previous scientist has proved that the frequency-
domain excitation waveform from SWIFT has the same structure as frequency domain of a
frequency sweeping waveform.273 Since phase spectrum method is working well for linear
frequency-sweep excitation signal, it should also work for SWIFT. Figure 5.7, top shows the
basic steps for building SWIFT waveform. Magnitude profile with constant amplitude will be
smoothed twice by specific filter in order to avoid the Gibbs’s oscillation caused by discontinuity
points (near both edges of magnitude profile). In the real case scenario, finite time period causes
the power leakage to outside of time window. Although smoothing filterer also help to decrease
the power leakage, expanded window confining most power leakage has to be used in the real
case. Figure 5.7, bottom shows the detailed expanded time window. For convenient purpose, the
whole window length, T1, is expanded to double length of original waveform window. Also, the
original waveform window is located at the middle of large window. The middle part confines
most power inside and represents the most effective part of whole waveform. In other words, the
phase modulation only effectively works in this window area. According to all these information,
we can modify the phase spectrum of detected signal as:
4
)(2
)()(
0
2 πωωωωϕ ±−+−−
= ttSR
obsi
i
iD [5.31]
In which ωI=2πfI is the initial frequency, SR represents the sweeprate and should be calculated
by (ωF- ωI)/T, tobs is the beginning time of detection event (t1+tdelay). The SWIFT only effectively
start at t0, so the effective observation time is tobs-t0.
Performances. Modified phase spectrum method is tested by the SWIFT waveform built for
Figure 5.7. Peaks between m/z 200 to m/z 1000 (crude oil) with relative abundance of > 6 of
baseline rms noise are chosen for test purpose. Figure 5.8, top shows that the average resolving
power is consistently as much as 40% higher for absorption-mode (lower) than for magnitude-
mode spectrum (upper). Crude oil of absorption-mode FT-ICR mass spectrum (lower) from
modified phase spectrum method demonstrates not only much smoother mass error distribution
than magnitude-mode spectrum (upper), but also 40% better mass accuracy than magnitude-
mode spectrum for exact same 11500 with highest peak heights (Figure 5.8, bottom).
86
1000900800700600500400300
m/z
1000900800700600500400300
1.0
0.0
-1.01000800200 600
Mass E
rro
r (p
pm
)
400
0.5
-0.5
1.0
0.0
-1.01000800200 600
Mass E
rro
r (p
pm
)
400
0.5
-0.5
11500 peaks
RMS error:
70ppb
11500 peaks
RMS error:
130ppb
Absorption‐Mode
Magnitude‐Mode
Absorption‐Mode
Magnitude‐Mode
m/z
Crude Oil 9.4T FT-ICR Mass Spectra (SWIFT)
m/∆m50% = 600000
m/∆m50% = 850000
Figure 5.8. Top: Crude oil 9.4T absorption-mode (lower) and magnitude-mode (lower) FT-ICR mass spectra excited by SWIFT waveform. Bottom: Mass error distribution for crude oil absorption-mode spectrum (lower) by modified phase spectrum method and magnitude-mode spectrum (upper). Note that much better mass accuracy for absorption-mode spectrum relative to magnitude-mode spectrum excited by SWIFT waveform.
87
CHAPTER SIX
PHASE CORRECTION OF FOURIER TRANSFORM ION
CYCLOTRON RESONANCE MASS SPECTRA BY
SIMULTANEOUS EXCITATION AND DETECTION
Introduction
Because mass spectrometers typically measure the mass-to-charge ratio (m/z) of an ion, it is a
powerful analytical technique for analysis of different charged particles. Modern mass
spectrometry application mostly concentrated on different bio-analysis field, e.g., proteomics, 125,
126 lipidomics, 165, 164 metablomics157, 156 and drug discovery. 274 Among characteristics of mass
spectrometry, high resolution/resolving power (m/∆m50%) is one of most interested aspects for
scientists working in variety research fields in recent decade years. As mass-resolving power
increases, more plateaus of chemical information become accessible. For example, m/∆m50%
>200,000, there is a separation of peaks at m/z 700 but differing in elemental composition by C3
vs. SH4 (separated by ~3.4 mDa). 2, 275 Among current mass spectrometers, the FT-ICR mass
analyzer, introduced in 1974,70 has the highest mass resolving power71, 9 and best mass
measurement accuracy9. Because ICR mass resolving power increase proportional to B, The
simplest way to improve FTMS performance is to operate at higher magnetic field, B. 86, 87
However, higher magnetic field is not economic way because magnet cost increases at a high
power of magnetic field. Compared to magnitude-mode spectra, an absorption-mode spectral
peak recovered from phase correction is inherently narrower than its corresponding magnitude-
mode spectral peak up to a factor of 2 that depends on the mechanism of signal damping. 79-82
Recently, phase correction gains scientists’ interest because it needs less hardware modification
(simultaneous excitation and detection113) or only software improvement112, 114, 115 (post-
processing of data) without additional cost.
Phase Spectrum and Phase Correction
88
For a time-domain signal f(t) with any phase φ(ω), Fourier transformation of this time-domain
signal produces mathematically real and imaginary frequency-domain spectra, Re(ω) and Im(ω).
The related mathematical equation can be written as Eq.6.1:
∫ +== −T
ti idtetfF0
)Im()Re(*)()( ωωω ω [6.1]
Considering the phase φ(ω), above equation could be expanded as Eq.6.2:
)]()sin()cos()([)]()sin()cos()([)Im()Re( ωϕϕωωϕϕωωω ADiDAi −++=+ [6.2]
)(*)]()([ ωϕωω ieiDA += [6.3]
In which )](sin[)](cos[)( ωϕωϕωϕ ie i += and )]Re(/)arctan[Im()( ωωωϕ =
We can see that Absorption- and dispersion-mode spectra, A(ω) and D(ω), may be obtained
directly as eiφ(ω)=1 (φ(ω) = 2nπ for any integer n). In most general cases (φ(ω) ≠ 2nπ), the real
and imaginary part of Fourier transformation, Re(ω) and Im(ω), are the linear combination of
A(ω) and D(ω) (Eq.6.2)
If the "phase spectrum", φ(ω), is known, absorption- and dispersion-mode spectra, A(ω)
and D(ω), could be obtained as Eq.6.4:
)()(*)]()([*)]Im()[Re( )()()( ωωωωωω ωϕωϕωϕ iDAeeiDAei iii +=+=+ −− [6.4]
or
)Im()](sin[)Re()](cos[)( ωωϕωωϕω −=A [6.5]
)Im()](cos[)Re()](sin[)( ωωϕωωϕω +=D [6.6]
89
Eq.6.5 and Eq.6.6 are simplified expression of Eq.6.4 and could be easily used in
different algorithms. Most recently developed phase correction methods 112, 114, 115 are based on
the calculation of the "phase spectrum", φ(ω), and then recover absorption- and dispersion-mode
spectra, A(ω) and D(ω), from Eq.6.5 and Eq.6.6.
Another phase correction method based on the Fourier deconvolution theory 1 is called
simultaneous excitation and detection (SED), 113 which the excitation and detection spectra must
be temporally synchronized. For ion cyclotron radii less than about half of the trapped-ion cell
radius, ICR excitation and detection processes are both highly linear. 276 Therefore, the radius of
the ion cyclotron motion after excitation is a linear function of the excitation signal amplitude,
and the amplitude of the detected image current is a linear function of the ion cyclotron radius.
Especially, the phase spectrum of detected signal will be exact same as excitation signal because
of no time difference between excitation and detection (simultaneous excitation and detection).
Under these circumstances, the detected time domain ion signal, f(t)real, is simply the convolution
of the applied excitation waveform, e(t), and the desired ideal ion response, h(t). Because the
convolution of two time domain functions is equivalent to the product of their respective Fourier
transforms, the absorption mode spectrum that corresponds to the desired ideas response can be
recovered via complex division of the spectrum of the observed response by the spectrum of the
excitation. Unlike phase correction methods based on calculation of phase spectrum, SED
method should theoretically work for any linear FT-ICR system with no need of any phase
information.
In real experiments, this simultaneous excitation and detection (SED) is made difficult
due to capacitive coupling that exists between the excitation and detection circuits. The coupling
causes excitation-induced preamplifier saturation, e(t)add and the detection signal coupled with
the excitation-induced signal. In previous work, capacitive nulling technique has been used to
reduce excitation-induced signal from detected signal. Broadband phase correction of FT-ICR
mass spectra has been demonstrated by SED method. However, the SED method is not
practicable because robust capacitive nulling is not possible.
Here, we describe a new data processing procedure to enable broadband phase correction
of FT-ICR mass spectra by SED without any hardware modification. All signal values in that
portion of the resulting detection signal that were acquired during excitation are replaced with
zero values via computer processing. The resulting absorption-mode spectra yield improvement
90
in resolving power as well as reduction in frequency assignment errors relative to conventional
magnitude-mode spectra. Also, the SED method can phase spectra produced from different
excitation waveforms (e.g., SWIFT with different magnitude modulations), and automatically
correct the peak height variation caused by non-uniform power distribution over the excitation
bandwidth.
Experimental Methods
Sample Preparation
Stock solutions of either a distillate fraction (500-538 ○C) from an Athabasca bitumen heavy
vacuum gas oil (HVGO) or a North American crude oil were dissolved in 50:50 (v/v)
toluene/methanol to a final concentration of 1 mg/mL. Each sample was further diluted to 0.25
mg/mL with 50:50 (v:v) toluene/methanol and 0.1% Formic acid to facilitate protonation during
electrospray ionization.
Instrumentation
Crude oil sample was analyzed with a custom-built FT-ICR mass spectrometer equipped with a
9.4 Tesla horizontal 220 mm bore diameter superconducting solenoid magnet operated at room
temperature (Oxford Corp., Oxney Mead, U.K.) and a modular ICR data station (PREDATOR)
facilitated instrument control, data acquisition and data analysis. 226, 227 Positive ions generated
at atmospheric pressure were accumulated in an external linear octopole ion trap84 for 250-1000
ms and transferred by rf-only octopoles to a 10 cm diameter, 30 cm long open cylindrical
Penning ion trap. Octopoles were operated at 2.0 MHz and 240 Vp-p amplitude. Broadband
frequency sweep (chirp) dipolar excitation (70 – 700 kHz at 50 Hz/μs sweep rate and 350 Vp-p
amplitude) or SWIFT excitation was followed by direct-mode image current detection to yield
time-domain data sets with 16 Mwords. The 25 individual transients of 5.6 s collected for the
crude oil were averaged, apodized with a full-Hanning (magnitude spectrum) or half-Hanning
(absorption spectrum 114) weight function, and zero-filled once prior to fast Fourier
transformation. Each m/z spectrum was internally calibrated with respect to an abundant
91
homologous N1 series, and then walking calibration was applied to the spectrum dividend into 56
equal consecutive segments which contained at least two members of a homologous
alkylation series.
Fre
quency
E(t)
fs
0
0
ff
Ttotal
Frequency-Sweep Excitation Signal
Detected Signal
D(t)
Time (s)
Time (ms)
0
Ttotal
Time (s)
Ttotal
0
RDT Signal
Figure 6.1. Top: Plot of time-domain linear frequency-sweep excitation signal. Middle: Plot of detection signal in SED experiments. Bottom: Plot of excitation signal in SED experiment.
92
Mass Analysis
Each FT-ICR mass spectrum was first calibrated with respect to a prior sample containing
Ultramark®, Met-Arg-Phe-Ala (MRFA) peptide, and caffeine (external calibration), and then was
internally calibrated with respect to an abundant homologous N1 series, and then walking
calibration was applied to the spectrum was dividend into 56 equal consecutive segments which
contained at least two members of a homologous alkylation series. Masses for singly charged
ions from m/z 200 to m/z 1000 with relative abundance of > 6 of baseline rms noise were
extracted, converted to the Kendrick mass scale228 and exported to a spreadsheet for easier
identification of homologous series. Peak assignments were performed by Kendrick mass defect
analysis, 229 as previously described.
)()()()( thtetetfaddreal
∗+=
)()()( thtetf ∗=)()()( ωωω HEF =
)(ωE
)(/)()( ωωω EFH =
)(te
)()()( thtetf ∗=
÷ =Half
Apodization
Zero-filling
FFT
1000900800700600500400300
Data Processing for SED Experiment
xA
B
Figure 6.2. Data processing steps for SED experiments. A) Zeroing of containment signal (front saturated signal induced by excitation signal). B) Complex division to produce absorption-mode spectrum. Note that exact same data processing (half apodization and zero-filling) for both zeroed detected signal and excitation signal.
93
SWIFT Waveform Design
Fourier transform (SWIFT) excitation method introduced in 1985 76 can produce specific
excitation magnitude spectra with high mass selectivity. In the SWIFT method, a desired
excitation magnitude spectral profile and the corresponding phase function are specified. 77 They
are then subjected to inverse Fourier transform to give the time-domain excitation waveform.
Converted analog signal from the waveform is amplified and applied to excitation plate. In our
experiments, two specific magnitude spectrum profiles have been designed. First one has
uniform magnitude profile and second one has different magnitude profiles for four frequency
segments (100-250 kHz, 250-500 kHz, 500-750 kHz, 750-1000 kHz). The detailed profile is
shown in Figure 6.5, top. Optimized phase modulation 273 for each magnitude profile has been
used to build each SWIFT waveform.
SED Experiments
Because the concurrent acquisition of both time-domain transient and excitation signal needs the
both hardware modification (duplicate parallel sets of acquisition circuitry) and software
modification (trigger excitation and detection at same time), it increases the instrumental cost
and experimental complexity. Here, we collect time-domain data for the excitation waveform
and detected ion signal with identical instrument parameters and timing sequences separately.
For our experiments, spectra of the excitation waveforms were obtained by directly coupling the
excitation and detection circuits with appropriate attenuation to avoid saturation of the detection
preamplifier. The coupling was accomplished as close to the cell as possible, and included the
preamplifier, so that the excitation waveform was acquired with an excitation and detection
signal path as similar as possible to that used during ion detection. 113 This procedure helps to
ensure that the detected excitation and ion signals are both subject to the same signal path
induced phase shifts. Figure 6.1, top shows time-domain linear frequency-sweep excitation
signal used in SED experiments. Detection signal (Figure 6.1, middle) demonstrates containment
signal with really high amplitude at front end. Figure 6.1, bottom is the profile of excitation
signal. RDT stands for response during transient. Note that total time of containment signal in
detection signal is exact same as total time of excitation waveform (Ttotal).
94
Computational Method
In our experiments, prior to phase correction via Fourier deconvolution, all saturated signal
values in that front of the resulting detection signal were replaced with zero values via computer
processing. Both detection signal after zeroing and excitation signal were subjected to half
apodization, zero-filling, Fourier transformation and complex division to produce absorption and
dispersion (A(ω) and D(ω), as shown schematically in Figure 6.2. Note that exact post-
processing steps have been applied to both signals to avoid any error associated with data
processing.
Results and Discussion
SED vs. Automated Broadband Phase Correction
In first experiment, we use the linear-sweep excitation waveform (Figure 6.1, top) and collect
time-domain data for the SED and automated broadband phase correction mehtods with identical
instrument parameters. For the present experimental FT-ICR mass spectra, elemental
compositions could be determined for all singly charged ions between 200 and 1000 Da with
peak heights greater than 6 of baseline rms noise. Figure 6.3, top shows the phasing results
from automated broadband phase correction (upper) and SED method (lower). Negative peak
with large magnitude appears in absorption-mode spectrum from automated broadband phase
correction but not in SED method because the noise peak, which can’t phased properly, could be
reduced by complex division step in SED method. For comparison of phasing result from both
methods, we chose the 5800 highest peaks in an ESI FT-ICR mass spectrum of a crude oil. The
mass errors distribution for absorption-mode spectra from both methods are plotted in Figure 6.3,
middle. SED method produces a little bit better mass accuracy than automated broadband phase
correction method. Moreover, DBE vs. carbon number images for the most abundant heteroatom
classes (N1) from electrospray ionization FT-ICR mass spectra of crude oil are shown in Figure
6.3, bottom. Note the different color distribution in SED phasing result, corresponding to
different abundance for same heteroatom class. The corresponding absorption-mode mass
spectrum from SED method get higher magnitude for low m/z peaks, so as to shift the deep color
95
to low m/z of in the DBE vs. carbon number image.
Crude Oil ESI 9.4T FT-ICR Absorption-Mode Mass Spectra
SED Phasing
Broadband Phasing
15 30 45 60 750
10
20
30
40
15 30 45 60 750
10
20
30
40
900800700600500400300
DB
E
DB
E
Carbon Number Carbon Number
200 400 600 800 1000
Broadband Phasing
5800 peaks
140 ppb
SED Phasing
5800 peaks
110 ppb
m/z
m/z
Mass E
rro
r(p
pm
)
1.0
0.5
0
-0.5
-1.0
1.0
0.5
0
-0.5
-1.0
SED PhasingBroadband Phasing
Rela
tive A
bu
ndance
Figure 6.3. Top: Absorption-mode from automated broadband phasing (upper) and SED phasing (lower) for linear-sweep excitation. Middle: Mass error distributions for automated broadband phasing (upper) and SED phasing (lower). Bottom: Isoabundance-contoured plots of double bond equivalents (DBE = rings plus double bonds) vs. carbon number for species containing carbon, hydrogen, one nitrogen for automated broadband phasing (left) and SED phasing (right).
N1 N1
96
Crude Oil ESI 9.4T FT-ICR MS (Normal Swift SED)
1000800600400
Absorption-Mode
m/z
1000800600400
Magnitude-Mode
926.86926.84926.82926.80926.78926.76
370000 380000450000
380000
Absorption-Mode
m/z926.86926.84926.82926.80926.78926.76
700000 710000650000
670000
600000Magnitude-Mode
1.0
0.5
0
-0.5
-1.0
Magnitude-Mode
4105 peaks
140 ppb
1.0
0.5
0
-0.5
-1.0200 400 600 800 1000
Absorption-Mode
4100 peaks
100 ppb
m/z
Mass E
rro
r (p
pm
)
Figure 6.4. Top: Magnitude-mode (upper) and absorption-mode (lower) from normal SWIFT excitation. Middle: Mass scale-expanded segments of crude oil FT-ICR magnitude-mode (upper) and absorption-mode (lower) mass spectra from normal SWIFT excitation. Bottom: Mass error distribution for magnitude (upper) and absorption (lower) electrospray ionization 9.4 T FT-ICR mass spectra for a crude oil.
97
Absorption Spectra vs. Magnitude Spectra from Normal SWIFT Excitation
In second experiment, we built a SWIFT waveform with constant magnitude profile as the
excitation signal for SED. In this case, we also pick peaks with heights greater than 6 of
baseline rms noise for comparison purpose. Figure 6.4, top shows broadband crude oil ESI FT-
ICR magnitude-mode (upper) and absorption-mode (lower) mass spectrum. Clearly, absorption-
mode mass spectrum shows higher peak heights at low m/z area than magnitude-mode mass
spectrum due to the advantage of SED data processing - automatically correcting the peak height
difference caused by non-uniform excitation waveform (see below in detail). Compared to
magnitude-mode spectrum, absorption-mode spectrum consistently gets a factor of 1.5 better
resolving power than magnitude-mode spectrum (Figure 6.4, middle). Mass error distributions
for the broadband ESI FT-ICR magnitude-mode and absorption-mode mass spectra are
demonstrated in Figure 6.4, bottom. The reduction in rms error (averaged over all assigned
peaks) is achieved mainly by reassignment of those peaks with the highest magnitude-mode
mass errors.
Absorption Spectra from Stepped SWIFT Excitation
The biggest advantage of SWIFT excitation is that one can design different excitation waveform
by specifying the magnitude profile and phase modulation. In this experiment, we build a SWIFT
excitation waveform with four segments magnitude profile for purpose of testing. The detailed
magnitude profile (M(ω)) and stepped SWIFT excitation waveform are shown in Figure 6.5, top.
The resulting absorption-mode and magnitude-mode mass spectra are shown in Figure 6.5,
bottom. Because the radius of the ion cyclotron motion after excitation is a linear function of the
excitation signal amplitude, and the amplitude of the detected image current is a linear function
of the ion cyclotron radius, stepped distribution of peak heights in broadband crude oil
magnitude-mode spectrum (upper) is observed in Figure 6.5, bottom. Absorption-mode
spectrum (lower) from SED shows much better and smoother peak heights distribution than
magnitude-mode spectrum. Automatic peak height correction of SED is contributing to this
difference of peak heights distribution between magnitude-mode and absorption-mode spectra.
Advantages of Broadband Phase Correction by SED
98
x
IFT
Time(msec)50403020100
Swift wave form
Crude Oil ESI 9.4T FT-ICR MS (Stepped Swift SED)
Frequency (kHz)1000800600400200
)(ωM
100
6575
85
ωϕ
Frequency (kHz)1000800600400200
Unknown
m/z
1000800600400
Magnitude-Mode
1000800600400
Absorption-Mode
Figure 6.5. Top: Schematic design of stepped SWIFT waveform. Bottom: Magnitude-mode (upper) and absorption-mode (lower) from stepped SWIFT excitation.
99
Crude Oil ESI 9.4T FT-ICR MS (Stepped Swift SED)
SED Phasing
Broadband Phasing
1000800600400m/z
Real Spectrum Before
Phasing
1000800600400
1000800600400
Figure 6.6. Electrospray ionization crude oil 9.4 T FT-ICR mass spectra. Top: Raw real data following Fourier transform of discrete time-domain signal. Middle: Result after automatic broadband phasing. Bottom: Absorption-mode spectrum from SED phasing.
100
)(
)(
)exp()(
)exp()(
)(
)()(
ωω
ϕωϕω
ωωω
ω
ω
M
M
M
M
E
HE ∗∗
==
)(
)(
ωω
M
M ∗
Frequency (kHz)
)exp()( ωϕω ∗M100
65 75
Rela
tive A
bu
nd
an
ce
15 30 45 60 750
10
20
30
40
15 30 45 60 750
10
20
30
40
DB
E
DB
E
Stepped SwiftNormal Swift
15 30 45 60 750
10
20
30
40
15 30 45 60 750
10
20
30
40
DB
E
DB
E
Carbon Number Carbon Number
Absorption-Mode
Magnitude-ModeMagnitude-Mode
Absorption-Mode
600500400300200
Absorption-Mode
Real Spectrum
Before Phasing
Figure 6.7. Top: Schematic automatic peak height correction in SED algorithm. Bottom: Isoabundance-contoured plots of double bond equivalents (DBE = rings plus double bonds) vs. carbon number for species containing carbon, hydrogen, one nitrogen for magnitude-mode (upper) and absorption-mode (lower).
101
Although we don’t see much performance difference between automated broadband phase
correction and phase correction by SED for linear-sweep excitation (Figure 6.3), we do observe
that the SED phasing method is superior to automated broadband phase correction for stepped
SWIFT waveform. Figure 6.6, top is broadband crude oil FFT real mass spectrum. Automated
broadband phase correction algorithm failed to recover the absorption-mode spectrum from real
and imaginary spectrum because phase modulation in stepped SWIFT waveform is totally
different from the quadratic phase spectrum for linear-sweep excitation waveform (Figure 6.6,
middle). SED phasing algorithm is not dependent on any phase spectrum/phase modulation, it
could successfully produce the absorption-mode spectrum for stepped SWIFT waveform (Figure
6.6, bottom). Another advantage of SED phasing is automatic peak height correction in
absorption-mode spectrum. The detailed explanation is demonstrated in Figure 6.7, top.
According to the Fourier deconvolution theory, complex division of detected signal to excitation
signal will directly produce absorption-mode spectrum (the resulting real spectrum of complex
division). The Fourier transformation of detected signal and excitation signal can be represented
as M(ω)exp(φ(ω)) (polar formation of Fourier transformation). Because the phase spectrum φ(ω)
in both detected and excitation signal is same, the exponential part (exp(φ(ω))) will be canceled
during complex division. The resulting complex division (lower) is the ratio of magnitude profile
of detected signal (M*(ω)) to excitation signal (M(ω)) . Since the FT-ICR mass spectrometer is
highly linear system, magnitude profile of detected signal (M*(ω)) will be directly proportional
to excitation signal (M(ω)). The final peak height profile of absorption-mode mass spectrum
form SED is independent on different excitation waveforms. In other words, SED phasing will
automatically correct the peak height caused by non-uniform of excitation waveform amplitude.
Figure 6.7, bottom shows DBE vs. carbon number images for the most abundant heteroatom
classes (N1) from FT-ICR mass spectra of crude oil (SWIFT excited). For both normal SWIFT
(left) and stepped SWIFT (right) cases, absorption-mode spectra by SED (lower) achieve very
similar images (color coding represents peak height). However, magnitude-mode spectra
demonstrate the excitation waveform amplitude dependences.
102
CHAPTER SEVEN
ARTIFACTS INDUCED BY SELECTIVE BLANKING OF TIME-
DOMAIN DATA IN FOURIER TRANSFORM MASS
SPECTROMETRY
Introduction
In Fourier transform mass spectrometry, periodic coherent ion motion is detected from the
oscillating current induced in opposed detection electrodes. Fourier transformation of the
digitized time-domain signal produces mathematically real and imaginary frequency-domain
spectra, Re(ω) and Im(ω), or alternatively a magnitude-mode (also known as absolute-value)
spectrum, M(ω) = [[Re(ω)]2 + [Im(ω)]2]1/2. Absorption- and dispersion-mode spectra, A(ω) and
D(ω), may in turn be obtained as linear combinations of Re(ω) and Im(ω).1 The magnitude-mode
spectral peak width at half-maximum peak height is higher by a factor of up to 2 relative to
absorption-mode spectra. 78, 80, 112, 113 With appropriate phase correction,114, 116, 115 apodization,277,
278 and zero-filling, 78,279 an absorption-mode spectrum may be generated from linear
combination of the real and imaginary spectra, to yield higher resolving power and better mass
accuracy than magnitude-mode spectrum. Apodization277, 278 can help to detect a small peak near
a large peak by reducing the amplitudes of auxiliary maxima and narrowing the peak width near
its base. Zero-filling effectively recovers into the absorption spectrum the information residing in
the non-zero-filled dispersion data obtained by Fourier transformation of the time domain
data.78,1
Mass resolution to better than 1 Da enables assignment of charge for a single charge
state,280 and is especially important for identifying post-translational modification(s) and
adduct(s) in intact proteins.281-283, 132, 284, 103 The time-domain signal for highly charged high-mass
ions displays large amplitude signal "beats" separated by extended periods of much lower signal
amplitude due to destructive interference of the signals induced by ions of many different m/z
values (and thus many frequencies).285 The highest mass resolution is achieved by isolating the
103
isotopic distribution from ions of a single charge state, to yield a time-domain signal
characterized by multiple high-amplitude "beats", separated in time by the period of the
(approximately constant) frequency separation between ions differing in mass by ~1 Da.
Because the signal-to-noise ratio is typically low between "beats", selective blanking (zeroing) of
the data between beats eliminates much of the noise, and has been used to increase spectral
signal-to-noise ratio.286-290 However, such blanking also eliminates part of the signal, and can
thus potentially distort the resulting FT spectrum. Previous scientists287 have noticed the
extended isotopic distribution but they didn’t do any further investigation of this problem.
Here, we simulate an FT-MS time-domain signal as a sum of noiseless exponentially
damped sinusoids whose amplitudes and frequencies are chosen to model a segment of the 57+
charge state isotopic distribution for an antibody (147 kDa). Comparison of the resulting Fourier
transform spectrum with recently acquired experimental data 103 provides a testbed to expose
artifacts due to the blanking. Addition of noise to the simulated time-domain signal reveals any
effect of blanking on mass accuracy. As explained below, we find that although blanking
improves FT spectral signal-to-noise ratio, mass accuracy does not improve, and blanking
generates additional spurious peaks that artificially broaden the isotopic distribution, thereby
making it more difficult to accurately measure protein mass and to identify post-translational
modifications and/or adducts. Identification of PTM is depend on the mass difference between
modified peptide segment and original peptide segment, any inaccurate mass will probably cause
assignment problem in complex database searching.
Materials and Methods
Materials
Recombinant, humanized IgG1k therapeutic antibody (1,324 amino acids,
C6,528H10,088N1,728O2,098S44) was expressed and purified by Pfizer Inc., and provided by Jason C.
Rouse.103
Experiments
All experimental data were acquired with a custom-built 9.4 T FT-ICR mass spectrometer.291
104
[M+57H]57+ ions from electrosprayed humanized IgG1k therapeutic antibody were quadrupole-
isolated and externally accumulated84 prior to transfer to the ICR cell.103 The ions were then
excited by broadband linear sweep (190<Vp-p<240, 720-45 kHz) at 50 Hz/µs chirp rate. 125
conditionally co-added117 individual 11.66 s digitized transients were averaged, apodized with a
full-Hanning (magnitude-mode spectrum) or half-Hanning (absorption-mode spectrum) weight
function, and zero-filled once prior to fast Fourier transformation. Each FT-ICR mass spectrum
was externally calibrated105, 106 with respect to a prior sample containing Ultramark® and Met-
Arg-Phe-Ala (MRFA) peptide.
Simulations
In FT-ICR MS, the detected time-domain ICR signal, f(t), may be modeled by the sum of
exponentially damped sinusoids: 252, 80
f(t) = ∑Aicos(ω0,it+φi)exp(-t/τi) 0<t<T [7.1]
in which i represents each ion signal, i is a characteristic damping time constant, or relaxation
time, T is the time-domain data acquisition period, φi is the initial phase, ω0,i is the natural
angular frequency, and Ai is the amplitude (which is directly proportional to the number of ions
of that cyclotron frequency). Here, we define a simulated time-domain signal, f(t):
f(t) = [A1cos(ω1t+ φ1)+…+ A57cos(ω2t+ φ57)] exp(-t/τ) +N(t) 0<t<T [7.2]
in which ions of all frequencies have the same damping time constant, τ; the amplitudes are
chosen to match the calculated natural abundance isotopic distribution for the antibody, and N(t)
is Gaussian-distributed random noise. The isotopic distribution has been truncated to include
only the 57 highest experimental nominal mass absorption-mode peak heights for the antibody
57+ charge state (see below); and the remaining parameters are chosen to match the experimental
time-domain signal (T = 11.66 s, 8 MWord data) and absorption-mode spectrum (ICR
frequencies between 55600 and 55630 Hz, bandwidth = 359712.2 Hz).
Estimation of Relaxation Time τ
105
Time (s)
f(t) = [A1cos(ω1t+φ1) + … + A57cos(ω57t+ φ57)] exp(-t/ּז) + N(t)
Imaginary Spectrum, Im(ω)Real Spectrum, Re(ω)
Magnitude Spectrum, M(ω)
Apodization
Zero-Filling
Fourier Transform
Phase Correction
Dispersion Spectrum, D(ω)Absorption Spectrum, A(ω)
M(ω) = ((Re(ω))2 + (Im(ω))2)1/2 = ((A(ω))2 + (D(ω))2)1/2
Figure 7.1. Generation of frequency-domain FT-ICR mass spectra from a simulated isotopic distribution with 57 frequency components. To a good approximation the ~1 Da separation between adjacent isotopic nominal masses in a
given charge state isotopic distribution corresponds to a single frequency spacing in the
frequency-domain FT-ICR spectrum for that distribution. Thus, we can derive the relaxation time
in Eq. 7.2 from the amplitudes of the 2nd and 4th time-domain "beat" peak heights, H2 and H4 as
follows:
H2=Aexp(-t2/τ) [7.3a]
H4=Aexp(-t4/ τ) [7.3b]
Eqs. 3a and 3b may be solved to yield τ:
=(t4-t2)/ln(H2/H4) [7.4]
106
The simulated time-domain signal (with or without noise) was subjected to selective
blanking (or not) of the data between "beats", apodized, zero-filled and Fourier transformed to
real and imaginary (Re(ω) and Im(ω), absorption and dispersion (A(ω) and D(ω), and magnitude
(M(ω)) frequency spectra, as shown schematically in Figure 7.1. The frequency and maximum
height of each simulated absorption-mode peak are obtained by parabolic interpolation and the
peak frequency error is reported as the difference between the experimental and simulated values
of frequency and interpolated frequency. The procedure was programmed in C and C++
operating under labWindows/CVI.
Results and Discussion
Spectral Profile without Blanking
An experimental time-domain ICR signal from the isolated 57+ charge state isotopic distribution
from an electrosprayed antibody (Figure 7.2, (a)) exhibits characteristic "beats" corresponding to
the period of the frequency difference between ions differing by ~1 Da in mass. A simulated
noiseless time-domain signal modeled as a sum of 57 exponentially damped sinusoids (Figure
7.2, (b)) was apodized, zero-filled, and Fourier transformed to produce the absorption-mode and
magnitude-mode frequency spectra shown in Figure 7.2, (c), (d). Note that the simulated isotopic
distribution was intentionally truncated to include only the 57 highest-magnitude peaks, so as to
better expose the artifacts introduced by time-domain signal blanking (see below).
Spectral Profile after Blanking
Figure 7.3 (top) shows a simulated noiseless time-domain signal, in which data between the
"beats" have been replaced by zeroes. The resulting absorption-mode and magnitude-mode
frequency spectra (Figure 7.3, middle & bottom) now contain numerous artifact peaks at
frequencies below and above the frequency range for the simulated isotopic distribution. We
have observed more or less artifact peaks as we zeroed different ranges between the “beats”. The
explanation for appearance of artifacts is that zeroing datapoint in time domain will confuse
Fourier Transformation to find frequency components. Fourier transformation will find
107
additional frequency components due to trying match all information from zeroed time domain
data.
0 1 2 3 4 5 6 7 8 9 10 11
Time (s)
Simulated
Absorption-Mode
Spectrum
0 1 2 3 4 5 6 7 8 9 10 11
Time (s)
a)
b)
Simulated
Magnitude-Mode
Spectrum
c)
d)
[M+57H]+
ExperimentalIgG1k Antibody
[M+57H]+
Simulated
Frequency (kHz)
55,596 55,604 55,612 55,620 55,628 55,636
Frequency (kHz)
55,596 55,604 55,612 55,620 55,628 55,636
Figure 7.2. a) Experimental time-domain ICR signal from the isolated 57+ charge state isotopic distribution from electrosprayed humanized IgG1k therapeutic antibody. b) Simulated noiseless time-domain transient with 57 frequency components. c) Absorption-mode frequency spectrum for b). d) Magnitude-mode frequency spectrum for b).
108
0 1 2 3 4 5 6 7 8 9 10 11Time (s)
Absorption-Mode Spectrum
With Blanking
Magnitude-Mode Spectrum
With Blanking
[M+57H]+
Simulated (Noiseless)
Frequency (kHz)55,596 55,604 55,612 55,620 55,628 55,636
Frequency (kHz)55,596 55,604 55,612 55,620 55,628 55,636
Figure 7.3. Top: Simulated noiseless time-domain signal after blanking of the data between the "beats". Middle: Absorption-mode frequency spectrum. Bottom: magnitude-mode frequency spectrum. Effect of Noise
We added Gaussian-distributed white noise to the simulated time-domain signal (Figure 7.4,
top) Comparison of the resulting absorption-mode spectra without (Figure 7.4, middle) and with
(Figure 7.4, bottom) shows that the additional artifact peaks introduced by time-domain selective
blanking are still evident. Finally, although the average peak height-to-noise ratio for the 10
highest spectral peaks increases by two-fold after selective time-domain blanking (Figure 7.5,
top), there is no reduction in frequency and thus m/z error (Figure 7.5, bottom).
109
0 1 2 3 4 5 6 7 8 9 10 11Time (s)
Absorption-Mode Spectrum
With Blanking
Absorption-Mode Spectrum
W/O Blanking
[M+57H]+
Simulated (Noise Added)
Frequency (kHz)55,596 55,604 55,612 55,620 55,628 55,636
Frequency (kHz)55,596 55,604 55,612 55,620 55,628 55,636
Figure 7.4. Top: Simulated time-domain ICR signal with noise. Middle: Absorption-mode frequency spectrum from the above time-domain signal. Bottom: Absorption-mode frequency spectrum after blanking was performed on the above time-domain signal.
Conclusion
Although selective blanking of the time-domain data between "beats" does increase FT-ICR
spectral signal-to-noise ratio, blanking does not improve frequency (and thus mass) accuracy,
and introduces numerous additional artifact peaks at each end of the isotopic distribution. The
artifact peaks distort and broaden the apparent isotopic distribution, thereby complicating
determination of molecular monoisotopic and/or average mass, and making it harder to resolve
and identify chemical modifications and/or adducts. We conclude that zeroing of the data
between time-domain "beats" offers no advantages, and introduces artifact peaks that actually
reduces the available mass spectral information.
110
P
eak H
eig
ht
to N
ois
e R
ati
o
55,614 55,615 55,616 55,617 55,618
Frequency (kHz)
Fre
qu
en
cy E
rro
r (p
pb
)
400
200
0
-200
-400
W/O Blanking
With Blanking
80
60
40
20
055,614 55,615 55,616 55,617 55,618
Frequency (kHz)
W/O Blanking
With Blanking
Figure 7.5. Top: FT-ICR average peak height-to-noise ratio (S/N) for each of the 10 highest absorption-mode peaks (from the time-domain data of Figure 7.4 (top)) with (blue) and without (red) blanking. Bottom: Ion cyclotron frequency errors for the 10 highest absorption-mode peaks with (blue) and without blanking (red).
111
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BIOGRAPHICAL SKETCH
EDUCATION
Florida State University, Tallahassee, FL, USA
Ph.D. Candidate, Analytical Chemistry, expected April 2012 Xi’an Jiaotong University, Xian, China
B.E. Chemical Engineering, July 1996
PROFESSIONAL EXPERENCES
Graduate Research Assistant August 2006 -present Florida State University, Tallahassee, FL National High Magnetic Field Laboratory and Analytical Chemistry Program Advisor: Prof. Alan G. Marshall Advanced broadband phase correction of FT-ICR MS Improved FT-ICR 40% mass resolving power and 30% mass accuracy for complex data
analysis Characterized the third generation bio-fuel (Algal oil) by LC/MS/MS Identified composition and detailed information of algal oil
Research Assistant August 2003-July 2005 Louisiana State University, Baton Rouge, LA
Center for Advanced Microstructures and Devices (CAMD) Advisor: Dr. Yohannes Desta Utilized techniques including photolithography and electro-deposition to design different
micro devices such as micro-sensor, micro-reactor and micro fluidic chip Improved the strength and the elasticity of Ni-Fe alloy by applying the micro electro-
deposition techniques
Instructor
Xi’an Jiaotong University, Xian, China August 1996-2002 Laboratory of Chemical Engineering Department Taught the general and analytical chemistry experiments Analyzed samples by different analytical equipments such as IR, UV and AA
spectrophotometers
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PUBLICATIONS (listed in reverse chronological order)
Xian, F., Hendrickson, C. L and Marshall, A. G. Broadband Phase Correction of FT-ICR mass spectra by simultaneous excitation and detection. Analytical Chemistry (to be submitted soon) (2012)
Xian, F., Hendrickson, C. L, and Marshall, A. G. Phase spectrum of Fourier Transform Ion Cyclotron Resonance Mass Spectra. Analytical Chemistry (to be submitted soon) (2012)
Xian, F., Hendrickson, C. L and Marshall, A. G. Baseline Correction of Absorption-mode Fourier Transform Ion Cyclotron Mass Spectra. Analytical Chemistry (to be submitted soon) (2012)
Xian, F., Hendrickson, C. L., Blakney, G. T., Beu, S. C., and Marshall, A .G. Effect of Zero–Filling and Apodization on Fourier Transform Ion Cyclotron Resonance Mass Spectral Accuracy, Resolution, and Signal-to-Noise Ratio. Analytical Chemistry (to be submitted soon) (2012)
Xian, F., Hendrickson, C. L, and Marshall, A. G. Artifacts Induced by Selective Blanking of Time-Domain Data in Fourier Transform Mass Spectrometry. Applied Spectroscopy (to be submitted soon) (2012)
Mao, Y., Xian, F., McKenna, A. M., Rodgers, R. P., Hendrickson, C. L., and Marshall, A. G. Ultra-High-Resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometry of Distinction of <1 Da Doublets in Complex Mixture. Journal of American Society of Mass
Spectrometry (to be submitted soon) (2012)
Xian, F., Hendrickson, C. L, and Marshall, A. G. High Resolution Mass Spectrometry. Analytical Chemistry, 84, 708-719 (2012)
Valeja, S.G., Kaiser, N.K., Xian, F., Emmett, M.R., Hendrickson, C.L., Rouse, J.C. and Marshall, A.G. Unit Mass Resolution for an Intact 148 kDa Therapeutic Monoclonal Antibody by FT-ICR Mass Spectrometry. Journal of American Society of Mass Spectrometry, 83(22), 8391-8395 (2011)
Savory, J. J., Kaiser N. K. McKenna, A. M., Xian, F, Blakney, G. T., Hendrickson, C. L., Rodgers, R. P., and Marshall, A. G. Parts-Per-Billion Fourier Transform Ion Cyclotron Resonance Mass Measurement Accuracy with a “Walking” Calibration Equation. Analytical
Chemistry, 83(5), 1732-1736 (2011)
Xian, F., Hendrickson, C. L., Blakney, G. T., Beu, S. C., and Marshall, A. G. Automated Broadband Phase Correction of Fourier Transform Ion Cyclotron Resonance Mass Spectra. Analytical Chemistry 82(21), 8807-8812 (2010)
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McKenna, A. M., Xian, F., Glaser, P. B., Rodgers, R. P., and Marshall A. G. Heavy petroleum Composition 2. Evolution of the Boduszynski Model to the Limit of Distillation by Ultrahigh-Resolution FT-ICR Mass Spectrometry. Energy & Fuels, 24, 2939-2946 (2010) Marshall, A. G., Blakney, G. T., Beu, S. C., Hendrickson, C. L., McKenna, A. M., Purcell, J. M., Rodgers, R. P. and Xian, F. Petroleomics: a Test Bed for Ultra-High-Resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometry. European Journal of Mass
Spectroscopy 16(3), 367-371 (2010)
PRESENTATIONS AND ABSTRACTS (listed in reverse chronological order)
Xian, F; Hendrickson, C. L.; Blakney, G. T.; Beu, S. C. and Marshall, A. G., Effects of Zero-Fill
and Apodization on Absorption-Mode FT-ICR Mass Spectra. 8th N. Amer. Fourier Transform Mass Spectrometry Conf., Key West, FL, May 1-5 (2011)
Mao, Y., Xian, F., McKenna, A. M., Rodgers, R. P., Hendrickson, C. L., and Marshall, A. G., How Much Mass Resolution is Necessary: Counting the Possible Common Mass Doublets for
CcHhNnOoSs Elemental Compositions. 8th N. Amer. Fourier Transform Mass Spectrometry Conf., Key West, FL, May 1-5 (2011) Valeja, S. G., Kaiser, N. K., Xian, F., Emmett, M. R., Hendrickson, C. L., Rouse, J. C. and Marshall, A. G., Unit Mass Resolution for an Intact 148 kDa Therapeutic Monoclonal Antibody
by FT-ICR Mass Spectrometry. 8th N. Amer. Fourier Transform Mass Spectrometry Conf., Key West, FL, May 1-5 (2011) Xian, F.; Hendrickson, C. L.; Blakney, G. T.; Beu, S. C. and Marshall, A. G., Effects of Zero-Fill
and Apdization on Absorption-Mode FT-ICR Mass Spectra, 59th ASMS Conf. on Mass Spectrometry & Allied Topics, Denver, CO, June 5-9 (2011) Mao, Y., Xian, F., McKenna, A. M., Rodgers, R. P., Hendrickson, C. L., and Marshall, A. G., How Much Mass Resolution is Necessary: Counting the Possible Common Mass Doublets for
CcHhNnOoSs Elemental Compositions. 59th Amer. Soc. for Mass Spectrometry. Annual Conf. on Mass Spectrometry & Allied Topics, Denver, CO, June 5-9 (2011) Valeja, S. G., Kaiser, N. K., Xian, F., Emmett, M. R., Hendrickson, C. L., Rouse, J. C. and Marshall, A. G., Unit Mass Resolution for an Intact 148 kDa Therapeutic Monoclonal Antibody
by FT-ICR Mass Spectrometry. 59th Amer. Soc. for Mass Spectrometry. Annual Conf. on Mass Spectrometry & Allied Topics, Denver, CO, June 5-9 (2011) Xian, F.; Hendrickson, C. L.; Blakney, G. T.; Beu. S. C. and Marshall, A. G., Automated
Broadband Phase Correction for Improved FT-ICR Mass Spectra of Complex Mixtures, 58th Amer. Soc. for Mass Spectrometry. Annual Conf. on Mass Spectrometry & Allied Topics, Salt Lake City, UT, May 23-27 (2010) Savory, J. J.; Kaiser, N. K.; McKenna, A. M.; Blakney, G. T.; Hendrickson, C. L.; Rodgers, R. P.; Xian, F. and Marshall, A. G., A Walking Mass Calibration Equation for Complex Mixture
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Analysis by FT-ICR Mass Spectrometry, 58th Amer. Soc. for Mass Spectrometry. Annual Conf. on Mass Spectrometry & Allied Topics, Salt Lake City, UT, May 23-27 (2010) Xian, F.; Hendrickson, C. L.; Blakney, G. T.; Beu, S. C. and Marshall, A. G., Absorption
Spectra for FT-ICR Mass Spectrometry. FSU, Mar, 19 (2010) Marshall, A. G.; Blakney, G. T.; Emmett, M. R.; Hendrickson, C. L.; Rodgers, R. P.; Tipton, J. D. and Xian, F., Ultrahigh Mass Resolution and Mass Accuracy: What's Possible, What's Not,
and What It's Good For, Symposium. on Accurate Mass Measurement: State of the Art, Uses,
and Limitations, Pittcon 2009, Chicago, IL, March 8-14 (2009) Marshall, A. G.; Xian, F.; Hendrickson, C. L. and Blakney, G. T., Broadband Absorption-Mode
FT-ICR MS: 30% Enhancement in Resolving Power, 7th N. Amer. Fourier Transform Mass Spectrometry Conf., Key West, FL, April 19-22 (2009) Xian, F.; Hendrickson, C. L.; Blakney, G. T.; Beu, S. C. and Marshall, A. G., Improved
Broadband Phase Correction of Complex FT-ICR Mass Spectra: Baseline Roll and Apodization, 57th Amer. Soc. Mass Spectrum. Annual Conf. on Mass Spectrometry & Allied Topics, Philadelphia, PA, May 31 - June 5 (2009) Xian, F; Hendrickson, C. L.; Blakney, G. T.; Beu, S. C. and Marshall, A. G., Improved
Broadband Phase Correction of Complex FT-ICR Mass Spectra. 7th N. Amer. Fourier Transform Mass Spectrometry Conf., Key West, FL, April 19-22 (2009)