Fourier Transform Ion Cyclotron Resonance Mass Spectrometry at the Cyclotron Frequency

Abstract

The phenomenon of ion cyclotron resonance allows for determining mass-to-charge ratio, m/z, of an ensemble of ions by means of measurements of their cyclotron frequency, ω _c . In Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), the ω _c quantity is usually unavailable for direct measurements: the resonant state is located close to the reduced cyclotron frequency (ω₊), whereas the ω _c and the corresponding m/z values may be calculated via theoretical derivation from an experimental estimate of the ω₊ quantity. Here, we describe an experimental observation of a new resonant state, which is located close to the ω _c frequency and is established because of azimuthally-dependent trapping electric fields of the recently developed ICR cells with narrow aperture detection electrodes. We show that in mass spectra, peaks close to ω₊ frequencies can be reduced to negligible levels relative to peaks close to ω _c frequencies. Due to reduced errors with which the ω _c quantity is obtained, the new resonance provides a means of cyclotron frequency measurements with precision greater than that achieved when ω₊ frequency peaks are employed. The described phenomenon may be considered for a development into an FT-ICR MS technology with increased mass accuracy for applications in basic research, life, and environmental sciences.

Introduction

High-resolution and high mass accuracy mass measurements afforded by modern Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) have played a significant role in achieving the recent progress in life, environmental, and basic sciences [1–6]. Among all mass spectrometers, FT-ICR MS instruments provide the highest performance in terms of ultimately achievable resolution and mass accuracy indispensable in the most challenging applications, including top-down proteomics, petroleomics, and imaging [5–12]. Nevertheless, further improvements of analytical characteristics of FT-ICR MS are needed [13–16].

The basic working principle of FT-ICR MS can be described as a measurement of a frequency with which an ion rotates in a static homogenous magnetic field, referred to as the cyclotron frequency (in radians per second), ω_c, given by:

$$ {\omega}_c = \frac{q}{m} B $$

where B is the magnetic field (in Tesla), q is the charge of an ion (in Coulombs), and m is its mass (in kg) [17, 18]. Likewise, the cyclotron frequency can be expressed in units of Hz as:

$$ {f}_c=1.53567\times {10}^7\times \frac{z}{m} B $$

where B is in Tesla and m/z is the mass-to-charge ratio, Da/units of charge. However, it is commonly understood that the cyclotron frequency cannot be measured directly using FT-ICR MS [19, 20]. Instead, since its inception, FT-ICR MS has been based on the measurement of the so-called “reduced” cyclotron frequency, ω₊ [17]. The appearance of the reduced cyclotron frequency ω₊ of ions rotating in a magnetic field is attributable to an influence of electric field present in the ICR cell. For example, a non-zero radial component of trapping electric field influences position of a reduced cyclotron frequency ω₊ peak in a mass (frequency) spectrum, whereas position of a peak corresponding to the cyclotron frequency ω_c signal would be constant for a given ion cloud and magnetic field [21]. Furthermore, with an increase in the number of ions injected into the ICR cell, ion cloud space charge effects may become pronounced, particularly in low magnetic fields, leading to peak (partial) suppression, peak shifts, and peak coalescence [17, 22–24]. As a result, the scan-to-scan variation of a number of charges in the ICR cell reduces the mass accuracy for ω₊ signal detection, as well as limits the sensitivity when averaging a number of mass (frequency) spectra or time-domain signals (transients). Finally, to confine ions during ion detection, a low value of trapping potential, ~1 V, is typically applied [25–27]. However, such a low trapping potential may be insufficient to efficiently confine an ion population injected into the ICR cell or produced by in-cell fragmentation (e.g., using electron capture dissociation (ECD) or infrared multiphoton dissociation (IRMPD) [28–30]). To increase the sensitivity, a high trapping potential (>5 V) would be useful for increasing the number of ions participating in the ion detection event if a frequency stability of a peak to measure is provided. Following this trend, the recently introduced dynamically harmonized ICR cell demonstrates an improved efficiency for reduced cyclotron frequency detection at high, for example 4 V, trapping potentials [6].

In the absence of a possibility to directly measure the cyclotron frequency ω_c in FT-ICR MS, a cyclotron sideband frequency ω_c ^* of a reduced cyclotron frequency ω₊ provides an intriguing analytical utility due to its close proximity to the cyclotron frequency [19–21, 31]. These two frequencies, ω_c and ω_c ^*, differ from each other by a small frequency shift which, as suggested earlier, is a function of the misalignments and distortions always present in the ICR cells [19]. Indeed, in the model case without space charge fields and with quadratic trapping potential distribution, the sideband ω_c ^* is an interharmonic of two eigen frequencies (viz. the magnetron ω₋ and reduced cyclotron ω₊ frequencies), which is nothing else than the ion cyclotron frequency:

$$ {\omega_c}^{*}={\omega}_{+}+{\omega}_{-}\approx {\omega}_c $$

Therefore, in a conventional FT-ICR MS the cyclotron frequency ω_c may be approximated by the sideband ω_c ^* of the ω₊ peak with an error defined by mistuning of the ICR cell and insufficient theoretical approximation of trapping and space charge fields [19–21, 31–33]. However, as most of the signal power is in the ω₊ component, amplitudes of the ω_c ^* sideband rarely exceed 10%–15% relative to the ω₊ peak [21]. On the contrary, modern ICR cells are designed to minimize the ω_c ^* component and maximize the ω₊ one [34]. Efficient tuning of the ICR cells is achieved by application of offset DC potentials, oftentimes on the order of +/−100 mV, to the excitation and detection electrodes of an ICR cell [21, 34]. The maximum allowed offset potentials lead to signal decomposition and destruction but not to the preferential formation of the ω_c ^* component. A number of ICR cells and approaches have been proposed to generate the ω_c ^* sideband as a base peak by reducing a radial component of electric trapping fields [35–38]. However, none of them has provided the required level of performance beyond basic science studies. Therefore, mass measurements using the cyclotron frequency ω_c or, more exactly, its approximate value given by cyclotron sideband frequency ω_c ^* are possible and were employed in the past for accurate mass measurements in the so-called precision mass spectrometry [19, 20, 33], but did not provide the required practical utility for real-life applications in life and environmental sciences.

Another approach to ion detection at the cyclotron frequency has been developed for FT-ICR MS with quadrupolar ion detection using four detection electrodes [39–42] or only two opposite or adjacent electrodes with signal summation rather than subtraction as performed for dipolar ion detection [39, 40, 43, 44]. According to this approach, when ion motion is characterized by a higher than usual magnetron (low frequency drift) radius, the level of the cyclotron sideband peak ω_c ^* increases dramatically. Methods developed using this strategy have been applied to accurate mass measurements of small ions in basic science research [4, 39]. However, efficiency of the developed technology is not sufficient to remove the reduced cyclotron, ω₊, and second harmonics, 2ω _c ^* and 2ω₊, peaks below about 30% of the ω _c ^* peak. Technological difficulties of the suggested experimental set-ups have also restricted their field of use.

Therefore, the up-to-date attempts of precision mass spectrometry remained limited to the measurement of low molecular weight ions at the cyclotron sideband frequency peak in the presence of a pronounced reduced cyclotron frequency peak ω₊ or its harmonics. Thus, the quest of performing FT-ICR MS of real-life complex biological and environmental samples with the cyclotron frequency, or the cyclotron sideband frequency, as the single peak remains open. Recently, we described design, implementation, and performance of narrow aperture detection electrode (NADEL) ICR cells [34]. A particular feature of these cells is the narrow aperture (flat) detection electrodes inserted radially into the volume of the ICR cell. Serendipitously, we discovered that specific non-quadratic trapping potential distribution created in the NADEL ICR cell jointly by these detection electrodes and offset potentials at the excitation electrodes allows for efficient FT-ICR MS with a resonance frequency located close to the cyclotron frequency rather than near the reduced cyclotron frequency. Interestingly, these results were obtained using a “standard” dipolar ion excitation and detection scheme, when only a pair of electrodes for ion excitation and another pair of electrodes for ion detection have been employed. Here we describe the related experimental observations, introduce the phenomenon, and characterize the initial performance of FT-ICR MS equipped with a NADEL ICR cell operating at the new frequency resonance. We compare the observed characteristics of a cyclotron frequency regime to the performance of FT-ICR MS at the reduced cyclotron frequency obtained with the same NADEL ICR cell.

We propose to use a simple “cyclotron frequency” term here as it is physically more appropriate compared with the terms of “unperturbed” or “true” cyclotron frequency, as well as “cyclotron sideband frequency,” previously utilized for ICR cells with quadratic trapping potential distribution. We leave this terminology and annotation open for further modifications as the field progresses.

Experimental

Sample Preparation

MRFA and bovine ubiquitin were obtained from Sigma-Aldrich (Buchs, Switzerland). ESI-L low concentration tuning mixture containing phosphazine and triazine compounds was purchased from Agilent Technologies (Basel, Switzerland). Phosphoric acid was obtained from Fluka (Buchs, Switzerland). Peptides P1, P2, and P3: P1 – EESTR, P2 – PMMSR, and P3 – HDGHR were synthesized in-house with solid state peptide synthesis. LC-MS grade acetonitrile and water were obtained from Fluka (Buchs, Switzerland). Formic acid was obtained from Merck (Zug, Switzerland). The ESI-L calibration mixture with phosphazine compounds and peptide AcA₃DA₃R₂ was prepared in 95:5 (v/v) acetonitrile/water solvent. Peptide and protein solutions were prepared in 1:1 (v/v) water/acetonitrile solvent mixtures containing 0.1% (v/v) of formic acid. The final peptide and protein concentrations were ~2 μM.

Mass Spectrometry

A linear hybrid Fourier transform ion cyclotron resonance mass spectrometer (LTQ FT-ICR MS, Thermo Scientific, Bremen, Germany) equipped with a 10 T superconducting magnet (Oxford Nanoscience, Oxon, UK) was employed to acquire all experimental data. The instrument was operated via standard in-built data station and instrument control software (Xcalibur, Thermo Scientific). The FT-ICR MS was equipped with the narrow aperture detection electrodes (NADEL) ICR cell (Spectroswiss, Lausanne, Switzerland) based on a design of an open-ended cylindrical ICR cell (Ultra cell, Thermo Scientific) as described elsewhere, Figure 1 [34].

Figure 1

Design and trapping field potential distributions in a NADEL ICR cell with extended excitation electrodes (E1 and E2) and narrow aperture detection electrodes (D1 and D2). (Top panel) shows cell schematic drawing; (middle panel) shows trapping potential distribution in the plane perpendicular to magnetic field axis at z = 0 mm when all offset potentials are equal to zero: V _D1 = V _D2 = V _E1 = V _E2 = 0 mV (contours from 0.02 to 0.16 V); and (bottom panel) shows trapping potential distribution in the plane perpendicular to magnetic field axis at z = 0 mm when V _D1 = V _D2 = 0 mV, V _E1 = −90 mV, and V _E2 = 150 mV (contours from −0.08 to 0.22 V). The employed SIMION-based simulation parameters: trapping electrodes are at 5 V; all contours are in 0.02 V increments

The original 90° wide excitation electrodes of the Ultra ICR cell were extended up to 176° each (as close as possible to the 180°) for the configuration of the NADEL ICR cell employed here. Figure 1 shows that the 176° excitation electrodes were formed by addition of two cylindrical sections of about 43° each, to each of the original 90° degrees excitation electrodes. Unwrapped schematic with the wiring of the employed NADEL ICR cell and the corresponding SIMION generated excitation field potential contours are shown in Supplementary Figure S1 (Supplementary Information). Extension of excitation electrodes from 90° (standard NADEL ICR cell configuration) to 176° was performed to enclose the interior of the original NADEL ICR cell as much as possible and to investigate the influence of electrode size on the ion trapping, excitation, and detection. The discovered ion cyclotron regime with the 176° excitation electrodes NADEL ICR cell was not experimentally observed with the original 90° excitation electrodes NADEL ICR cell for the range of the experimental parameters investigated. A possible explanation for this is a different trapping field configuration employed in the work on the original 90° NADEL ICR cell. Potentially, expanding the range of the experimental parameters for a NADEL ICR cell with 90° excitation electrodes may lead to observation of an ion cyclotron frequency regime.

A robotic chip-based nano-electrospray ionization (ESI) source (TriVersa Nanomate; Advion Biosciences, Ithaca, NY, USA) was utilized for negative or positive ion formation. The ions were injected into the linear ion trap for accumulation and further transfer into the NADEL ICR cell through a set of multipole ion guides. Ion population inside the linear ion trap was controlled via the automatic gain control (AGC) system (Thermo Scientific).

The ions were initially localized within the NADEL ICR cell via gated trapping and were confined during ion excitation with a trapping potential of 3 V, as preset by the instrument manufacturer and not available for modification. A dipolar broadband frequency-sweep excitation (varied from 72 to 720 kHz at 150 Hz/μs) with a peak-to-peak amplitude V _exc in the range of 0–100 V was applied for a fixed duration of 10 ms for ion excitation. For the ion detection event, the trapping potential was varied between 0 and 10 V. Standard dipolar differential detection was used to acquire analyte ion signals; transient data sampling frequency was varied as a function of selected mass range and was either 1.3, 2.7 or 5.5 MHz; ion signal detection period was between 96 ms and 25 s. Amplitudes of sidebands and peak shapes were optimized via independent variation of four DC offset potentials, V _E1, V _E2, V _D1, and V _D2 applied to the excitation electrodes E1 and E2, and detection electrodes D1 and D2, respectively, during the entire experiment sequence (ion injection, trapping, excitation, detection, and quench events), Figure 1. The DC potentials were set to values between −100 and 100 mV with a step of 1 mV for the positive and the negative ion modes.

Experimental time domain signals (transients) were recorded using MIDAS (*.dat) file format via advanced user interface capabilities (Thermo Scientific). Transients were zero-filled once unless stated otherwise, apodized with the Hann window and Fourier transformed. The peaks were picked using three-point parabolic interpolation. Signal processing and data visualization were performed using Peak-by-Peak data analysis framework (Spectroswiss) [45].

SIMION Simulations

The geometries of Ultra and NADEL ICR cells were modeled using the SIMION 3D software (ver. 8.1; Idaho National Engineering and Environmental Laboratory, Idaho Falls, ID, USA) with the grid step size of 0.2 mm. The excitation grids were not taken into consideration for the simulated geometries. Correspondingly, the trapping rings were not segmented. Simulations show that even relatively weak DC offset potentials significantly disturb the trapping potential at the center of the ICR cell at z = 0, Figure 1, middle and bottom panels. However, the influence is less strong for the ICR cell regions nearby the trapping rings, where the trapping electric field is much stronger, Supplementary Figure S1, bottom panel.

Results and Discussion

Establishing Cyclotron Frequency Regime in FT-ICR MS

Trapping potential distributions in a NADEL ICR cell as a function of selected offset potentials on excitation electrodes are shown in Figure 1 middle and bottom panels. The electric field center moves away from the ICR cell axis with a change of offset potentials on the excitation electrodes, from 0 to −90 mV on the top electrode and from 0 to 150 mV on the bottom electrode. Therefore, trapping potential distributions in NADEL ICR cells may significantly differ from those in the conventional ICR cells (quadratic approximation of trapping potential), due to the combined effect of both radially-inserted narrow aperture detection electrodes and offset potentials. In other words, linear trapping electric fields in conventional (cylindrical) ICR cells are now replaced by nonlinear trapping electric fields, which depend not only on a radial but also on an azimuthal coordinate.

Figure 2 shows a gradual transformation of frequency (mass) spectra acquired at reduced cyclotron frequency, ω₊, to the cyclotron frequency, ω_c, in FT-ICR MS upon analysis of MRFA peptide anions at m/z 522. Notably, this transformation is due to a variation of a single DC potential, offset V_E2, on one of the excitation electrodes and only by 110 mV. In Figure 2 and the following description, by ω₊, ω₋, and ω _c , we denote the reduced cyclotron, magnetron, and cyclotron frequencies as in conventional FT-ICR MS with quadratic approximation of trapping potential. The frequency axis is presented in units of Hz. The time domain signal (transient) acquired with similar values of DC offset potentials on the two excitation electrodes, V _E1 = 90 mV and V _E2 = 80 mV, had the typical shape for FT-ICR MS transients and its Fourier transformation yielded the corresponding expected frequency spectrum where peak corresponding to ω₊ signal is dominant with magnetron sidebands, including the cyclotron sideband frequency, less than 1%, Figure 2a. This case corresponds to the standard regime with reduced cyclotron frequency generation and detection. Increasing the difference between the two offset potentials, ∆V _E, suppresses the ω₊ signal, whereas at the same time it enhances the peak corresponding to the ω _c signal and other magnetron sidebands, Figure 2b. Notably, when ∆V _E ~ 70 mV, the ω₊ peak experiences an abrupt split into several peaks, with reduced cyclotron frequency value being reduced by 1–2 Hz accompanied by a significant increase in ω_c signal amplitude, Figure 2c. Additional peak between ω₊ and ω_c peaks appears in mass (frequency) spectra. The analysis of the corresponding time-domain signals reveals the appearance of several additional oscillations at low frequencies as well as faster signal decay. Further increase of ∆V _E decreases the amplitude of low frequency oscillations in transients, as well as the amplitudes of sidebands in the corresponding mass (frequency) spectra, including the ω₊ peak, whereas amplitude of ω _c signal increases, Figure 2d. Finally, when ∆V _E reaches 120 mV peak corresponding to the ω₊, signal practically disappears and the frequency (mass) spectrum is dominated by the ω _c peak, signifying establishment of a cyclotron frequency regime. The corresponding transient shows a more homogenous structure and its decay becomes similar to the reduced cyclotron frequency regime and, perhaps, is even more stable over 3 s of ion detection time shown here. The abundance of the signal, as shown in Figure 2, is reduced by 20%–30%. The initial transient period of less than 200 ms shows a substantially different behavior compared with the reduced cyclotron frequency regime. Specifically, transient amplitude is reduced almost to a noise level after about 50 ms of detection period and then restores its amplitude after another period of 50 ms.

Figure 2

Experimental observation of the reduced cyclotron fre quency ω₊ and the cyclotron frequency ω_c in 10 T FT-ICR MS with a NADEL ICR cell. Time domain signals (transients) and their corresponding mass spectra were acquired with anions of MRFA at 522 m/z as a function of DC offset potential V_E2 at a fixed value of V _E1 = 90 mV. Other parameters: trapping potential of 2.5 V, an acquisition period of 3.072 s, and V _D1 = V _D2 = 0 mV

Cyclotron Frequency Regime Characterization: Offset Potentials Influence

Figure 3 shows a step-by-step variation of frequency (mass) spectra composition as a function of offset potentials V _E1 and V _E2 applied to the excitation electrodes for isolated deprotonated (522 m/z) and protonated (524 m/z) MRFA peptide ions. Frequency (mass) spectra were collected with V _E2 varied in the range from −100 to 100 mV for a fixed offset potential V _E1 = 90 mV for anion detection and V _E1 = −90 mV for cation detection. Reducing V_E2 potential from 80 mV to −60 mV for anion detection and increasing it from −80 mV to 60 mV for cation detection (from top to bottom trace in Figure 3) show that in each case, peaks of both cyclotron and reduced cyclotron frequencies move slightly toward the lower frequency values. Transient duration for the acquired frequency spectra was set to allow baseline resolving lower-frequency magnetron sideband (ω₊ – ω₋ ) and ω _c for a given analyte signal at reduced cyclotron frequency ω₊. Other parameters included the following: offset potentials on detection electrodes V _D1 = V _D2 = 0 mV; trapping potential during ion detection V _trap = 2.5 V; the radiofrequency (rf) excitation field amplitude of 25 V; number of charges (controlled by AGC) of 2e5; and data from 10 to 15 scans were summed for each measurement. Note that due to the relatively small surface area of the detection electrodes D1 and D2, the influence of V _D1 and V _D2 offset potentials is negligible compared with V _E1 and V _E2 offsets. Nevertheless, the V _D potentials could be useful for fine-tuning of sideband intensities.

Figure 3

Experimental observation of the reduced cyclotron frequency ω₊ and the cyclotron frequency ω_c in 10 T FT-ICR MS with a NADEL ICR cell. Amplitude variation of the reduced and near-true cyclotron frequencies as a function of the DC offset potential V _E2 with a fixed value of: (left panel) offset potential V _E1 = 90 mV for negative ion mode for MRFA ions at 522 m/z and (right panel) offset potential V _E1 = −90 mV for positive ion mode for MRFA ions at 524 m/z. Other parameters variation as indicated

To identify the offset potential ranges where the resultant frequency spectrum is dominated by either ω₊ or ω_c signals, the corresponding dependencies of the signal-to-noise ratio (SNR) values of the ω _c and ω₊ peaks on the V _E1 and V _E2 offset potential difference, from −200 to 200 mV, were measured (Supplementary Figures S2 and S3). The dependencies observed for positive and negative ion modes measured with the opposite potential values V _E2 and V _E1 are similar. Particularly, two local maxima are observed for each dependence, with one maximum being notably higher than the second one in each case. The dependencies show that the region where ω₊ signal is at minimum amplitude corresponds to the region where ω _c peak is at maximum and vice versa. In the region where ω₊ signal amplitude is maximum, the lower-frequency magnetron sideband (ω₊ – ω₋) and ω_c are at a minimum, with intensities less than 0.5% w.r.t. ω₊ peak amplitude. In the region where ω_c signal amplitude is at maximum, other signals, including ω₊ peak, are less than 2% w.r.t. ω _c peak amplitude. The latter value compares favorably with sideband intensity specifications for commercial FT-ICR MS instruments (for example, up to 5% sidebands are within the specifications for acceptance tests on LTQ FT instruments from Thermo Scientific). It should be noted that these sidebands would only be visible for sufficiently high resolution, exceeding the standard operation conditions with less than 100,000 resolution, and may disappear in complex (many-component) mass spectra, vide infra. Finally, further optimized NADEL ICR cell geometries with the use of quadrupolar ion detection significantly reduce these sidebands [46].

Cyclotron Frequency Regime Characterization: Trapping Potentials Influence

Independence of a frequency peak position on a trapping potential is considered as one of the primary indicators for cyclotron frequency detection. Figure 4 shows the frequency position dependence of singly protonated MRFA ion signals at 524 m/z for the reduced cyclotron (left panel) and cyclotron (right panel) frequency regimes as a function of trapping potential V _trap (1–10 V) applied during ion detection. In the ω₊ regime, the dominant signal (i.e., ω₊ peak) linearly shifts to the lower frequency values with an increase of the trapping potential V _trap, as expected [17, 18, 47]. Contrastingly, in the ω _c regime, the dominant signal (i.e., ω _c peak) effectively remained at a constant frequency position, as may be expected for the cyclotron frequency. Admittedly, a slight shift to the higher frequency values of ω _c peak, especially for low trapping potentials up to 6 V, is observed with an increase in trapping potential. Figure 4 shows that the slope of dependence is changed for ω₊ regime around V _trap of 6 V as well. Our first consideration for understanding this dependence includes a certain asymmetry in trapping potential distribution in the employed NADEL ICR cell. Indeed, increased symmetry of electrodes distribution and the corresponding trapping potential distribution in the case of a NADEL ICR cell with four narrow aperture detection electrodes significantly reduces the shifts observed here [46].

Figure 4

The dependence of the reduced cyclotron frequency ω₊ and the cyclotron frequency ω_c on the trapping potential applied during the detection event with positive ions in a 10 T FT-ICR MS, for the individually optimized regimes. The ω₊ regime is shown with blue lines (left panel) and the ω_c regime with green lines (right panel). Experimental data were measured with positive MRFA ions 524 m/z and an acquisition period of 3.072 s

To further rationalize these shifts of both cyclotron and reduced cyclotron frequency peaks in more detail, the trapping field potential and excitation amplitude effect on the SNR of the analyte signal in both regimes were investigated, Supplementary Figure S4. For low excitation amplitude and low trapping potential, the maximum SNR of the dominant analyte signal in the ω _c regime is lower than the dominant signal in the ω₊ regime for the entire value range of the offset potentials V _E1 and V _E2. The reverse is true for high trapping potential and high excitation amplitude, where a phase de-coherence of ion clouds is more pronounced due to the reduced harmonicity of the trapping electric field leading to a decrease of ion signal amplitude. The latter point is relevant to the standard ω₊ regime as the reduced cyclotron frequency strongly depends on the trapping potential, and SNR of a peak corresponding to the reduced cyclotron frequency, ω₊, decreases with an increase of trapping potential, Supplementary Figure S4, top right panel. However, the reverse dependence was observed for SNR of the cyclotron frequency peak in the ω _c regime. Recall that ion trapping and excitation events in the employed FT-ICR mass spectrometer take place at 3 V trapping potential value, which is pre-set by the manufacturer and cannot be varied (see Experimental section). As a consequence of SNR dependence on trapping potential, the higher difference between the offset potentials V _E1 and V _E2 is required to realize the optimum ω _c regime with low amplitude of non-cyclotron sidebands (less than 2% w.r.t the dominant signal) for higher trapping potential, Supplementary Figure S4 bottom panel. Therefore, the dependencies in Figure 4 for each value of V_trap are presented for optimized experimental parameters, such as offset potentials. Overall, the results reported in Supplementary Figure S4 suggest that the reason for peak shift in Figure 4 may be due to an increased ion population for cyclotron frequency regime (increased space charge effect above V_trap = 6 V) and reduced ion population in reduced cyclotron frequency regime (reduced space charge effect above V_trap = 6 V) as a function of a trapping potential.

Finally, the intensities of parasitic non-cyclotron sideband and ω₊ peaks in the ω _c regime also depend on the acquisition period. They increase with a decrease of acquisition period, especially at the low trapping potential of less than 1 V. For example, the amplitudes of these peaks remained higher than 30% for low trapping potential less than 2 V even with the optimal experimental parameters (V_E1, V_E2, and an excitation amplitude) for a short acquisition period, <0.5 s, Supplementary Figure S5. The time period with high amplitudes of low frequency oscillations at the beginning of a transient is the reason of high intensity of parasitic peaks for short transients. The duration of this period depends on the trapping potential and decreases for higher trapping potential, leading to lower intensity of the parasitic peaks in the spectrum with the same transient length. Therefore, the ω _c regime favors higher than 1 V trapping potentials and detection periods longer than 0.5 s for the current experimental set-up. Although this behavior can be limiting for analytical applications of the described here ICR cell as is, its detailed characterization is essential for a better understanding of the phenomenon presented here. Improving the NADEL ICR cell performance to match and surpass the analytical characteristics provided by other current ICR cells is a matter of further investigations and reports [46].

To summarize, varying the offset DC potentials, the excitation amplitude, and trapping potential, the maximum SNR of the dominant signal in the ω _c regime can be made comparable with the corresponding value for the ω₊ regime obtained with the same NADEL ICR cell. The optimal values of experimental parameters in the ω _c regime can be different depending on the sample complexity. However, this is a typical practice also for conventional ICR cells operated in the ω₊ regime. Previously, the ω₊ regime for the NADEL cell has already been extensively characterized and was found to be adequate for conventional applications [34]. Given similar or better SNR values for both regimes and lack of significant frequency shift with a change in V _trap, ω _c regime may present an interesting route for development of particular advantages in FT-ICR MS applications.

Cyclotron Frequency Regime Characterization: Resolving Power

The ability to detect ions for long periods of time in ω _c regime to obtain high resolving power was tested on a mixture of three isobaric peptides, P1, P2, and P3 (see Experimental section). The monoisotopic masses of the three peptides are pairwise separated by 0.9 mDa and 0.5 mDa, respectively (P1 – EESTR, H₄₁C₂₃O₁₁N₉, 619.29255 Da; P2 – PMMSR H₄₅C₂₄S₂O₆N₉, 619.29342 Da; and P3 – HDGHR, H₃₇C₂₄O₇N₁₃, 619.29389 Da). Previously, we demonstrated successful observation of this triplet in a standard ω₊ regime of a NADEL ICR cell [34]. Here, Supplementary Figure S6 shows the corresponding mass spectra obtained in a ω _c regime from (left panel) a single scan and (right panel) a sum of 10 consecutive scans (transient summation) with detection period of 24.576 s per scan (transient length). The obtained resolving power R _{FHWM (exp)} ≈ 2,800,000 is sufficient to baseline resolve the three peaks in question. Notably, due to lack of noticeable frequency shifts from scan to scan, the resolving power effectively stays the same for both the single scan mass spectrum and for the summed mass spectrum. Avoidance of resolving power loss with scan summation is beneficial for high-resolution mass measurements, as other parameters, such as spectral dynamic range, oftentimes require summation of tens or hundreds of scans [48, 49]. Interestingly, a low decay rate of ion signal even in such a long transient indicates exceptional stability of a coherent ion motion in ω _c regime and an ability to obtain even higher resolving power. In the employed instrument configuration, ion detection for longer periods of time is not supported.

Cyclotron Frequency Regime Characterization: Broadband Measurements

Figure 5 shows summed frequency spectra (ω_c regime and 50 scans summed) of bovine ubiquitin in the frequency range 100–240 kHz, which roughly corresponds to the mass range 600–1800 m/z. With a detection period of 1.536 s, all ubiquitin peaks in various charge states, ranging from 6+ to 14+, are baseline resolved. To verify lack of frequency shifts within the entire frequency range upon variation of trapping potential, V _trap, data was collected for V _trap = 2 V and V _trap = 4 V in both regimes. Figure 5, bottom panel shows the isotopic envelopes for the 10+ charge state for the two V _trap values from the corresponding broadband frequency spectra. As expected, no perceptible frequency shift was observed for cyclotron frequencies in the ω _c regime, Figure 5, bottom right panel. In contrast, the frequencies of all the constituent peaks of frequency spectra acquired under similar experimental conditions, but in the ω₊ regime, are systematically decreased with increasing V _trap value, as is expected for reduced cyclotron frequencies, Figure 5 bottom left panel. Other charge state distributions within the corresponding broadband frequency spectra showed the same behavior; see Supplementary Figure S7 for 7+ and 12+ charge state dependence.

Figure 5

Protein analysis with a NADEL ICR cell on a 10 T FT-ICR MS. (Top panel) shows the broadband frequency (mass) spectrum of bovine ubiquitin measured using the cyclotron frequency ω _c with detection period of 1.536 s, V _trap = 2 V, and AGC = 3e6. The insets demonstrate baseline resolved isotopic distributions of the 6+ and 12+ charge states. (Bottom panel) shows expanded spectra views at the 10+ charge state of bovine ubiquitin acquired using trapping potentials V _trap = 2 and V _trap = 4 V for (bottom left) ω₊ regime and (bottom right) ω_c regime

Therefore, operation of FT-ICR MS in cyclotron frequency regime is feasible for broadband mass measurements of macromolecules, e.g., peptides and proteins, as well as molecular mixtures [50], whereas peaks corresponding to the reduced cyclotron frequency are either completely absent in these mass spectra or of insignificant amplitude for transient periods longer than 0.5 s. In the following we will discuss the calibration of frequency spectra into mass spectra and the mass accuracy performance.

Cyclotron Frequency Regime Characterization: Mass Accuracy

To find appropriate mass calibration functions for the two regimes of operation and establish their dependencies on several key experimental parameters, e.g., AGC (controls the number of charges) and V _trap, ESI-L low concentration tuning mixture (Agilent Technologies) and peptide AcA₃DA₃R₂ were used as internal calibrants for the 400–1400 m/z or 400–2800 m/z ranges. Similarly, external calibration-derived mass accuracy was estimated in a number of single scans using a mixture of poly-phosphoric acid, (H₃PO₄)_n. Supplementary Figure S8 shows representative mass spectra containing five or nine calibrant peaks for instrument calibration in the corresponding mass range and 11 or 21 analyte peaks calibrated externally in a single scan. External mass accuracy evaluation was performed in a number of single scans at the two detection periods (0.768 s and 1.536 s) for two mass ranges of 400–1400 m/z and 400–2400 m/z with AGC = 2e6 and resulting in four calibrated datasets for each regime. Figure 6 and Supplementary Figure S9 show the results of the calibration and detail the obtained mass accuracy performance.

Figure 6

Comparison of mass accuracy performance achieved with NADEL ICR cell in two regimes: the reduced cyclotron frequency ω₊ – blue symbols, and the cyclotron frequency ω _c – green symbols. (Top left panel) shows the dependencies of f*m/z on the inverse of frequencies as a function of trapping potential applied during ion detection measured for the broadband spectra of ESI-L low concentration tuning mixture (Agilent) and spiked peptide AcA₃DA₃R₂. (Top right panel) shows the distribution of mass accuracy for broadband mass measurements in a number of single scans measured with 11 peaks of poly-phosphoric acid (H₃PO₄)_n and an external calibration. (Bottom panel) shows the dependencies of f*m/z parameter on the inverse of frequency measured for the broadband mass spectra of poly-phosphoric acid (H₃PO₄)_n as a function of number of charges (AGC) using an internal calibration. Detection period of 1.536 s on a 10 T FT-ICR MS

The standard two-parametric formula typically employed for FT-ICR MS mass scale calibration [17, 51],

$$ \raisebox{1ex}{$ m$}\!\left/ \!\raisebox{-1ex}{$ z$}\right.=\raisebox{1ex}{$ A$}\!\left/ \!\raisebox{-1ex}{$ f$}\right.+\raisebox{1ex}{$ B$}\!\left/ \!\raisebox{-1ex}{${f}^2$}\right. $$

can be re-written as:

$$ f\times \raisebox{1ex}{$ m$}\!\left/ \!\raisebox{-1ex}{$ z$}\right.= A+\raisebox{1ex}{$ B$}\!\left/ \!\raisebox{-1ex}{$ f$}\right. $$

Therefore, coefficient B reflects a slope of f *m/z versus 1/f dependence. Figure 6, top panel shows the mass, m/z, and frequency, f, relationship for the calibrant peaks mapped on the f *m/z versus 1/f plot. As might be expected, for the ω₊ regime, the plot shows that the points may be fitted by a linear equation, from which A and B parameters of the calibration equation may then be obtained. Additionally, a slope of this dependence increases with an increase of a trapping potential V _trap, as expected, as well, Figure 6, top left. Notably, for the calibrant data-points in the ω_c regime, the f *m/z value should be almost invariant with 1/f, as expected for the cyclotron frequency detection since B should approximately equal zero for the ω_c regime, where $f\times \raisebox{1ex}{$ m$}\!\left/ \!\raisebox{-1ex}{$ z$}\right.= A$. Hence, ideally, the mass calibration function should be given by ${\omega}_c=\frac{2\pi A}{m/ z}$ However, for the given experimental configuration, V _trap cannot be calibrated to make B exactly equal to zero in the established ω_c regime, giving rise to a slight dependence of f *m/z on 1/f, Figure 6, top panel and Supplementary Figure S10. Consequently, mass calibration was performed with a non-fixed B parameter to compensate for residual mass errors. Nevertheless, relation | ${B}_{\omega_c}$ (V _trap)|<<| ${B}_{\omega_{+}}$ (V _trap)| holds true for all V _trap values employed in the current work. Importantly, with a smaller difference between trapping potentials for excitation and detection events, | ${B}_{\omega_c}$ | decreases and approaches the ${\omega}_c=\frac{2\pi A}{m/ z}$ condition, Supplementary Figure S10.

To estimate the actual mass accuracy values for the two regimes, appropriate A and B coefficients were obtained from measurement of five or nine internal calibrants, vide supra. Figure 6, top right and Supplementary Figure S9 demonstrate that mass error is significantly smaller for the ω_c regime compared with the ω₊ regime, with both detection periods. Table 1 demonstrates standard deviation of mass error for detection period measured for 11 and 21 calibrants in the number of single scans with external calibration for both ω_c and ω₊ regimes. The significant enhancement, up to 6-fold, of the mass accuracy measured with an external calibration was achieved for the ω_c regime compared with the ω₊ regime (realized with the same NADEL ICR cell). Under optimized conditions, the mass accuracy of better than 40 ppb RMS was achieved for ω_c regime with an internal calibration in the mass range 400–1400 m/z with nine peaks of NH₄ ⁺ adducts of poly-phosphoric acid mixture, Supplementary Figure S11.

Table 1 RMS of Calibration Errors Measured with an Internal Calibration for Calibration Mixture (ESI-L, Agilent) and with an External Calibration for Polyphosphoric Acid, (H₃PO₄)_n, as a Function of the Number of Charges (AGC). Experimental results were obtained on 100 averaged transients with detection periods 0.768 s and 1.536 s. Internal calibration was performed using nine monoisotopic peaks of protonated phosphazine and triazine compounds in the mass range 450–2750 m/z and external calibration using 28 peaks of protonated compounds of poly-phosphoric acid in the mass range 250–3000 m/z. The corresponding graphics of dependencies are shown in Figure 6 and Figure S9 (Supplementary Information)

Additionally, mass accuracy performance was evaluated in the high spectral dynamic range with an internal calibration with peaks SNR value difference of up to 2.8 orders of magnitude. The mass accuracy of better than 50 ppb RMS was achieved for ω_c regime in the mass range 400–1400 m/z with 33 peaks, including low abundance ¹⁸O isotopes and NH₄ ⁺ adducts, from poly-phosphoric acid mixture: AGC = 4e6, RMS = 61 ppb; AGC = 5e6, RMS = 49 ppb, Supplementary Figure S12. Notably, mass accuracy was up to 10-fold worse for similar measurements in the ω₊ regime performed with the same experimental set-up.

In conclusion, the mass accuracy performance is substantially better for ω_c regime compared with ω₊ regime when both regimes are realized with the same NADEL ICR cell. On the other hand, according to the theory, the best performance in the standard reduced cyclotron regime, ω₊, can be achieved for conventional ICR cells with a quadratic trapping potential distribution. The trapping field distribution of NADEL ICR cell deviates from a quadratic one, Figure 1, and a direct comparison of ω_c regime versus ω₊ regime with a NADEL ICR cell may not be the best way to evaluate the mass accuracy performance of the new frequency resonance. On the other hand, the achieved results with the NADEL ICR cell in a 10 T magnetic field in the ω_c regime, demonstrated in Figure 6, top right and Supplementary Figure S11, are comparable with those recently obtained using dynamically harmonized ICR cell in the reduced cyclotron regime for similar type of experiments, but with a higher strength of magnetic field, up to 21 and 14.5 T [6, 52].

Cyclotron Frequency Regime Characterization: Space Charge

The space charge effect was investigated through the influence of a number of charges (AGC) on mass accuracy and B coefficient of the calibration equation with 28 monoisotopic peaks of poly-phosphoric acid (H₃PO₄)_n for both regimes with an internal calibration, Figure 6, bottom panel. Herein, the trapping potentials of 1 V for ω₊ regime and 2 V for ω_c regime were applied during ion detection for each AGC value. The difference in the applied trapping potentials is to ensure optimum mass accuracy performance in each regime. The slope of f *m/z versus 1/f dependence increased with an increase of number of charges (AGC) for the ω₊ regime_, as expected [53]. However, this systematic dependence of a slope on the AGC value is not observed for the ω_c regime, again as it would be expected for a cyclotron frequency detection.

The SNR values of analyte peaks linearly increase with an increase of the AGC value for both regimes, Supplementary Figure S13. However, the same SNR was achieved with higher AGC value for ω_c regime compared with ω₊ regime for the current trapping potentials. On the other hand, 28 analyte peaks of poly-phosphoric acid (H₃PO₄)_n in the mass range 250–3000 m/z were measured with RMS mass accuracy better than 300 ppb level for ω_c regime in the current range of AGC values, Supplementary Figure S13. RMS mass error noticeably increased with an increase of AGC value up to 2 ppm for ω₊ regime. Finally, more than an order of magnitude better frequency peak stability measured in the single scan was achieved for the ω_c regime in comparison with ω₊ regime. The results demonstrate significantly reduced space charge effect and enhancement of mass accuracy for the ω_c regime compared with the ω₊ regime. Notably, the improvement of mass accuracy was especially significant for low frequencies (high m/z) and high number of charges.

Finally, the dependencies of experimental frequencies on the inverse of the corresponding theoretical masses measured with 28 analyte peaks of (H₃PO₄)_n were plotted for the cyclotron and reduced cyclotron regimes, Supplementary Figure S14. The figure once again confirms the cyclotron nature of the new frequency resonance: frequency dependence on the electric field is less pronounced for the cyclotron compared with the reduced cyclotron regime as the corresponding trend-line crosses the y-axis closer to zero value. Also, the experimental data points acquired in the cyclotron regime are fitted by a straight line with a significantly, by an order of magnitude, smaller error compared with the reduced cyclotron regime. This result correlates with mass accuracy characterization obtained using the two-parametric calibration equation, Table 1.

On the Mechanism of a New Frequency Resonance

Based on the body of the experimental work presented here and obtained with other modifications of NADEL ICR cells experimentally and via simulations using SIMION, we currently understand the phenomenon described here as follows [46]. Briefly, it is due to the time-averaging of induced current signals produced by a collective motion of ions in a nonlinear, azimuthally-dependent electric trapping field with a certain dispersion of the initial ion velocities before the excitation.

Ion excitation in NADEL ICR cells starts as in the conventional ICR cell, exciting ions from about the center of the cell. The dipolar excitation employed here is efficient because of the beneficial positioning of the narrow aperture detection electrodes, as described earlier [34]. After ion excitation to desired larger radii of both cyclotron and magnetron motions, ion cloud starts to disperse in the nonlinear trapping electric field, which is further shaped by appropriately applied offset potentials. The centers of rotation for each ion will slowly drift along the equipotentials of the trapping field and, after the initiation period, the ions will be distributed in a closed orbit occupying a substantial space inside the ICR cell. This ion motion is conceptually different from the tightly bound clouds of ions coherently moving during ion detection in conventional (cylindrical) ICR cells. The initiation period of the ion motion in a NADEL ICR cell is manifested in the transient with its initial period, which demonstrates first a remarkable drop in signal intensity that is then restored, Figure 2. The duration of this initiation period is inversely proportional to the trapping potential and can be shortened by increasing the trapping field.

After establishing the steady ion motion condition, each of the ions will rotate with its own frequency and the center of its orbit drifting about the off-axis electric center of the trapping field. When a group of ions is considered, each ion will be in phase for its cyclotron frequency, but out of phase for its magnetron (drift) frequency, attributable to the difference in the trapping electric field experienced by the ions distributed in the ICR cell. Therefore, a group of ions will contribute to the intensity of the cyclotron frequency peak and will introduce a destructive interference for the reduced cyclotron frequency peak. The latter is due to the differences in their magnetron (drift) frequencies. The minimum number of ions required for establishing the cyclotron frequency regime is thus a function of initial velocity spread of these ions and may be equal to only a few ions [46]. As modern signal detection electronics in FTMS provides a noise level at about a 3–5 charges level, the destroyed reduced cyclotron frequency peak may not be seen experimentally.

Conclusions

The azimuthally-dependent off-axis electric fields of the NADEL ICR cell employed here are responsible for initiation of a phase-coherent spatially distributed motion of ions, which in turn are characterized by dispersion in their initial, pre-excitation velocities. The resulting collective motion of space-dispersed ions at a given m/z is FT-detected at a new resonant frequency that is extremely close in value and properties to the fundamental (unperturbed or true) cyclotron frequency, as confirmed by the experimental evidences presented here. With a sensitivity and resolution comparable to the conventional reduced cyclotron frequency regime obtained with the same NADEL ICR cell, mass measurements at the cyclotron frequency in NADEL ICR cells can be more accurate, especially with transient periods longer than 0.5 s, which is typical for FT-ICR MS. The latter is achieved because of a cyclotron frequency-specific (relative) independence of peak position on electric fields in an ICR cell, which include trapping and space charge fields.

The analytical value of the approach reported here to increase the measurement precision of ion frequencies in FT-ICR MS, considered jointly with sensitivity and dynamic range, is yet to be revealed in comparison with the outcomes of the sophisticated calibration routines developed for the modern ICR cells, including the statically and dynamically harmonized ICR cells [5, 6, 13, 15]. The on-going technique development based on the phenomenon reported here already resulted in an even less pronounced dependence of a measured cyclotron frequency peak position on electric fields [46]. Finally, reduced space charge influence in the cyclotron frequency regime suggests its possible use in smaller ICR cells as required for bench-top FT-ICR MS instruments [54, 55].