Experimental evidence for space-charge effects between ions of the same mass-to-charge in Fourier-transform ion cyclotron resonance mass spectrometry

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Abstract

It is often stated that ions of the same mass-to-charge do not induce space-charge frequency shifts among themselves in an ion cyclotron resonance mass spectrometry measurement. Here, we demonstrate space-charge induced frequency shifts for ions of a single mass-to-charge. The monoisotopic atomic ion, Cs+, was used for this study. The measured frequency is observed to decrease linearly with an increase in the number of ions, as has been reported previously for space-charge effects between ions of different mass-to-charge. The frequency shift between ions of the same m/z value are compared to that induced between ions of different m/z value, and is found to be 7.5 times smaller. Control experiments were performed to ensure that the observed space-charge effects are not artifacts of the measurement or of experimental design. The results can be rationalized by recognizing that the electric forces between ions in a magnetic field conform to the weak form of the Newton's third law, where the action and reaction forces do not cancel exactly.

Introduction

Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometry, developed by Comisarow and Marshall [1], [2], provides the highest mass accuracy [3], [4] and highest mass resolution [5] of any mass analyzer. The ultrahigh mass accuracy provided by FT-ICR makes it possible to determine the elemental composition of small and large molecules from direct mass measurement [6], [7], [8], [9]. Since the introduction of electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MADLI), the demand for higher mass accuracy has increased with the growing complexity of the samples and of the average mass of the samples. The mass of ions is not directly measured in FT-ICR mass spectrometry. Rather, the cyclotron frequency of ions is measured and converted to mass using appropriate calibration equations [10], [11], [12], [13], [14], [15], [16]. The cyclotron frequency of an ion is known to decrease with increasing ion population in an analyzer ion cell, as a result of a space-charge induced frequency shift [10], [11], [12], [13], [15], [16], [17], [18]. Therefore, mass accuracy in an externally calibrated spectrum is primarily limited by fluctuations of the ion population. McIver and coworkers [11] and Amster and coworkers [13], [18] have demonstrated that mass accuracy can be substantially improved by correcting the frequency shift using a plot of frequency versus total ion intensity.

Wineland and Dehmelt have stated that ions of the same mass-to-charge cannot induce a space-charge shift in their own frequencies [19], and others have repeated this claim [20], [21]. In recent years, however, the space-charge induced frequency shift has been shown to be different between ions of different m/z value than between ions of the same m/z value. Eyler and coworkers [14] and Smith and coworkers [15] have incorporated individual ion intensity as part of the calibration originally developed by Gross and coworkers [12]mzi=Afi+Bfi2+CIifi2where fi is the measured cyclotron frequency of the calibrant ion at (m/z)i, Ii the corresponding ion intensity, and A, B, C are the fitting parameters. The first term on the right-hand side of Eq. (1) expresses the effect of the magnetic field on the cyclotron frequency. The second term describes the frequency shift from the electric field of the applied trapping potential and from the space-charge of the ions, treating space-charge induce frequency shifts equally for all ions. The third term is a correction to the original equation developed by Gross and coworkers [12]. The third term “compensates” for differences between the space-charge for ions of the same m/z value versus those of different m/z value. The space-charge effects in the second and third term have also been referred as the global and local space-charge effects, respectively. The modified calibration equation (1) has shown to improve internal calibration mass accuracy by a factor of 1.5–6.7, depending on the mass range and the ion excitation radius [15]. Muddiman and Oberg [16] have demonstrated mass calibration improvement by including the local space-charge term in a global regression approach.

The global space-charge effects are significantly larger than local space-charge effects in multi-component spectra because individual peaks are small compared to the total intensity, and thus much of the space-charge induced frequency shift can be corrected without including the local space-charge term [11], [13], [18]. This explains why local space-charge effects have gone unnoticed by most FT-ICR practitioners. Although the local space-charge term is small in magnitude, it is a variable across any spectrum, making its significance far-reaching. Whereas the global space-charge term affects external calibration results and can be corrected for by using internal calibration, the local space-charge term impacts both external and internal calibration, and can only be corrected by using a more sophisticated calibration equation. Our group has recently developed a stepwise-external pseudo-internal calibration method [22], which has shown to improve mass accuracy 2–4 times. Most importantly, we have applied a new calibrationmzi=Afi+B+CIiwhich is an extension of the calibration equation originally developed by McIver and coworkers [11]. fi and Ii are the frequency and the intensity of the ion at (m/z)i, and A, B, C are the fitting parameters. The CIi term is new to the original equation. The concept of including individual ion intensity Ii in Eq. (2) is similar to that of Eq. (1), and we have found a ∼2-fold additional mass accuracy improvement using Eq. (2) over the original equation [22].

In Eqs. (1), (2), the global space-charge effects are constant for each mass spectrum and therefore are combined with the trapping potential shift as a single term. In contrast, Muddiman and Oberg [16] have demonstrated a global regression approach for polymers where the regression is performed on nine spectra simultaneously. Consequently, the global space-charge term is different for the nine spectra and can be separated from the trapping potential term. The resulting calibration equation is a three variable equationmzi=Afi+B+CIi+DItotalwhere fi and Ii are the corresponding frequency and ion intensity of the ion at (m/z)i, Itotal the total ion intensity of the spectrum, and A, B, C, D are the fitting parameters. The cyclotron frequency is shown to be a function of the local space-charge term (CIi). Surprisingly, the local space-charge parameter (C) is calculated to be 4 times that of the global space-charge parameter (D) and with an opposite sign. These results not only suggest that space-charge effects are more responsive to ions of the same m/z value than to other ions, but also that the effect is opposite in sign, that is, frequency increases with ion number.

The theoretical basis for separately treating ions of the same m/z value from ions of different m/z value is based on two publications by Wineland and Dehmelt on the measurement of electrons in a Penning trap [19], [23]. In the first paper [23], Wineland and Dehmelt stated that the axial frequency of electrons parallel to the magnetic field (i.e., z-motion) is constant with respect to the number of electrons. The theoretical argument is that the forces between electrons are equal and opposite according to Newton's third law, and consequentially the center-of-mass motion of the electron cloud is the same as a single electron. Since the detector does not monitor motions of individual electrons, but rather the center-of-mass motion, the observed axial frequency is independent of the number of electrons. In the second paper [19], Wineland and Dehmelt extended the same argument for the motion perpendicular to the magnetic field, and predicted the center-of-mass motion in any direction is independent of the number of charged particles when these particles are of the same m/z value. In the FT-ICR mass spectrometry community, this statement is often repeated as “ions of the same m/z cannot space-charge frequency shift each other.” Still, the theoretical prediction is made for a very ideal situation. Recent publications [15], [16], [22] have indicated that space-charge effects between ions of the same m/z value are different than those between ions of different m/z value, but none of these publications have demonstrated a zero space-charge contribution between ions of the same m/z value. In these studies, the frequency-to-mass conversions are shown to improve by including a linear order ion intensity term (CIi) for multi-component mass spectra. A linear order correction is a reasonable approximation for short range correction because the first Taylor series expansion term for many functions are linear (e.g., sin(x), ex, 1/(1  x), ln(1 + x), …). The real dependence may significantly deviate from linearity at long range. Consequently, the real space-charge effects for ions of the same m/z value cannot be extrapolated from multi-component spectra by using an approximate calibration equation. We are interested in the existence of space-charge effects between ions of the same m/z value because a better understanding of this effect will help advance the basic understanding of ICR ion motion, calibration equation development and the achievement of routine sub part-per-million (ppm) mass accuracy.

Here we present results from a direct measurements of space-charge induced frequency shift for an ion of one m/z value using the monoisotopic elemental ion, 133Cs+. The results demonstrate an existence of a space-charge induced frequency shift among ions of the same m/z value. The Cs+ population is varied using a variety of approaches, including changing solution concentration for electrospray and changing ion accumulation time. The space-charge effects among Cs+ are shown to be substantially smaller than those between Cs+ and other ions, and the frequency-to-intensity relationship can be estimated by a two term linear equation. The discrepancy between these results and Dehmelt's statement about space-charge effects between particles of the same m/z values is discussed.

Section snippets

Material and sample preparation

Cesium iodide (CsI) was purchased from Aldrich (St. Louis, MO), and methanol was purchased from Fisher Chemicals (Fairlawn, NJ). Eighteen MΩ purified water was produced from a Nanopure Infinity system manufactured by Barnstead (Dubuque, IA). Electrospray solutions were prepared using concentrations of CsI from 1 × 10−6 to 1 × 10−3 M in a 70%:30% water:methanol solvent.

Mass spectrometry

Mass spectra were collected using a 7 T Bruker BioApex-Qh Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometer. Ions

Results and discussion

Since an exact formula relating ion cyclotron frequency and ion population is not known, a direct measurement was made for ions of the same m/z value. For this study, a population of cesium ions is varied inside the FT-ICR analyzer ion cell by using different methods. Cs+ is chosen for this study because this element has only one naturally occurring stable isotope, at 132.9 Da, simplifying the production of ions of a single m/z value. For the data shown in Fig. 1, Cs+ is generated using

Conclusions

A better understanding of space-charge induced frequency shifts in FT-ICR mass spectrometry can improve mass calibration equations and consequently increases mass measurement accuracy. Since the induced frequency shift is smaller between ions of the same m/z value than between ions of different m/z value, new mass calibration equations have been formulated for the overcorrection of the space-charge effects between ions of the same m/z value by including the “local space-charge” term [14], [15],

Acknowledgments

The authors would like to acknowledge the many contributions of Professor Jean Futrell to the fields of ion chemistry, ion physics and mass spectrometry. The authors would also like to thanks Professor Lutz Schweikhard, Dr. Christophe Masselon and Dr. Alexander Friedland for helpful discussions. The authors are also grateful for the financial support through National Science Foundation (grant CHE-0316002) and National Institutes of Health (grant R01-RR 0119767).

References (35)

  • M.B. Comisarow et al.

    Chem. Phys. Lett.

    (1974)
  • M.B. Comisarow et al.

    Chem. Phys. Lett.

    (1974)
  • M.V. Gorshkov et al.

    Int. J. Mass Spectrom. Ion Process.

    (1993)
  • J.B. Jeffries et al.

    Int. J. Mass Spectrom. Ion Process.

    (1983)
  • T.J. Francl et al.

    Int. J. Mass Spectrom. Ion Process.

    (1983)
  • R.D. Burton et al.

    J. Am. Soc. Mass Spectrom.

    (1999)
  • C. Masselon et al.

    J. Am. Soc. Mass Spectrom.

    (2002)
  • P.K. Taylor et al.

    Int. J. Mass Spectrom.

    (2003)
  • D.J. Wineland et al.

    Int. J. Mass Spectrom. Ion Process.

    (1975)
  • R.L. Wong et al.

    J. Am. Soc. Mass Spectrom.

    (2006)
  • J.S. Page et al.

    J. Am. Soc. Mass Spectrom.

    (2005)
  • R. Harkewicz et al.

    J. Am. Soc. Mass Spectrom.

    (2002)
  • R.P. Rodgers et al.

    Anal. Chem.

    (1998)
  • F. He et al.

    Anal. Chem.

    (2001)
  • K.R. Clauser et al.

    Anal. Chem.

    (1999)
  • T.P. Conrads et al.

    Anal. Chem.

    (2000)
  • Z.G. Wu et al.

    Anal. Chem.

    (2002)
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