Improved Signal Processing for Mass Shifting Ions in Charge Detection Mass Spectrometry

Abstract

The quality of data in charge detection mass spectrometry depends on accurate determination of ion charge. While the method of selective temporal overview of resonant ions (STORI) has proven to be highly enabling for determining the charge of ions that survive for variable amounts of time, it assumes that the ion frequency exactly matches the frequency being used in the calculation. Any mismatches result in low charge estimates. To address this, the misSTORI method was developed to correct these discrepancies. This can significantly reduce the charge measurement errors for samples with unstable masses. As an example, the misSTORI approach can eliminate a 5.7% charge determination error for a VP3-only AAV capsid that shifts 25 ppm in mass.

Graphical Abstract

INTRODUCTION

Modern mass spectrometers are able to determine the masses of analytes, ranging from small molecules to large protein complexes, often with parts per million accuracy.¹ Since mass analyzers measure the mass-to-charge ratio (m/z) of analyte ions, typically the determination of absolute mass requires inference of charge via isotope or charge state spacing. If samples are sufficiently complex, such charge inference can be impractical.² Charge detection mass spectrometry (CDMS)^2,3 is a method that can simultaneously measure m/z and charge information from such samples. Rather than measuring the combined signal of multiple ions in each spectral peak, limited numbers of ions are analyzed, with each individual ion’s signal separated from the others in m/z space. The m/z value of each ion is measured in the traditional manner, while the charge is determined from the strength of the respective signal.

CDMS measurements are typically made with mass analyzers in which ions have oscillatory motion with frequency dictated by m/z. As an ion oscillates within the analyzer, it induces an image current on adjacent electrodes, which is recorded as a time-domain signal. A Fourier transform (FT) is then performed, converting the time domain into the frequency domain. The ion’s signal is represented as a peak in the frequency spectrum, with a measured position and intensity. In its simplest form, the CDMS methodology assumes that intensity is proportional to charge, as ions with higher charge will induce proportionally higher image currents. For intensity to be truly representative of ion charge, an ion must provide a consistent signal throughout the detection period. An ion that is lost partway through will generate a smaller peak than an ion of equal charge that survives the entire detection period, making it appear as though it has less charge. There are several ways to address this shortcoming, by either (a) discarding ions whose peaks are broadened/distorted due to signal loss or (b) performing a windowed FT to determine when signal is lost.^4–6 The selective temporal overview of resonant ions (STORI) method was recently developed as an alternate solution for such scenarios, building on the fundamentals of the discrete Fourier transform (DFT).^7,8 For species with unstable masses, due primarily to incomplete desolvation, we have recently observed that the STORI method can underestimate signal strengths. This has led to the development of methods for frequency tracking and the reconstruction of corrected STORI plots that builds upon prior efforts to analyze image current signals with unstable frequencies,^9–14 allowing for more precise charge and therefore mass assignment.

METHODS

Empty VP3-only Adeno-associated virus (AAV) capsids¹⁵ were ionized with static nanospray and measured on a Q Exactive UHMR (Thermo Fisher Scientific, Bremen, Germany) in Direct Mass Technology Mode. Further details are listed in Table S1. Over 34 min, 1078 spectra were recorded with 1.87 s of detection and an m/z range of 15,000–25,000. All algorithms were written in Python.

RESULTS AND DISCUSSION

The output of the DFT is a series of complex numbers defined on an equidistant frequency grid. Conceptually, for each frequency, the DFT goes pointwise through the time domain signal, computing a running tally of accumulated signal for sine and cosine waves of that frequency. The result is a single complex value for each frequency, whose real component is the overall cosine strength, and imaginary component is the overall sine strength. The absolute value (or “magnitude”) of the complex number represents the overall signal strength, while the sine and cosine components can be used to calculate the phase angle of the signal:

$$\text{Magntiude}=\sqrt{{\text{real}}^2+{\text{imag}}^2}$$

$$\text{Phase}=\text{arctan}(\text{imag}/\text{real})$$

If an ion does not provide signal over the entire detection period (e.g., lost via collision), the frequency domain peak height will no longer correspond to its charge because the signal was only accumulating over part of the observation time. The STORI concept overcomes this limitation by determining the rate at which signal is accumulated rather than the total amount of signal accumulated. The rate of increase is indicative of the ion’s charge, regardless of the duration. STORI determines the rate of signal growth by tracking intermediate values of the DFT calculation as time progresses. Figure 1 compares a simulated signal that lasts the entire detection period (1a) with one that ends halfway through the same period (1b). Signal is most commonly lost for the corresponding ion due to a collision with a background gas molecule, which results in dissociation. The traditional DFT would provide values that would make signal 1b look half as intense as signal 1a. However, the matching slopes of the two magnitude STORI plots over the first 500 ms indicate the signals were of equivalent strength.

Figure 1.

STORI plots for 1 s observations having equal strength (amplitude = 1.0, frequency = 85.8339 kHz). In (a) the STORI and signal frequencies match, and the signal is persistent (red = real, blue = imaginary, black = magnitude), giving a slope of 1.000. In (b) the signal ends halfway through the transient. In (c) the signal is persistent, but the STORI frequency is 0.25 Hz higher than the signal frequency (85.83415 kHz). A fit of the magnitude curve gives a slope of 0.910.

While the STORI method can provide improved charge assignments for ions that are lost, it makes a key assumption: that the “STORI frequency” (viz. the reference frequency used in the calculations) exactly matches the frequency of the signal throughout the entire detection period. Consider the example in Figure 1c, in which the signal is persistent but the STORI frequency is 0.25 Hz higher than the signal frequency. When the frequencies are mismatched in such a manner, they dephase linearly with time. As the dephasing progresses, the rate at which signal builds at the STORI frequency decreases, causing the slope of the magnitude STORI plot to decrease. Additionally, the dephasing causes the relative rates of signal accumulation for sine and cosine waves to vary over time, resulting in sinusoidal real and imaginary STORI plots. In this example, the magnitude slope drops 9%, despite having an r² of 0.998. This would lead to an equivalent error in the estimated charge and mass.

To better understand the behavior of mismatches between signal and STORI frequencies, consider the example in Figure 2, where there is again a 0.25 Hz difference. As shown previously in Figure 1c, the real and imaginary STORI components have a sinusoidal shape, caused by linear dephasing with time. Consequently, the time derivatives of the real and imaginary components are also sinusoidal (Figure 2a), with a frequency that indicates the difference between STORI and signal frequencies.¹⁶ This derivative plot, which characterizes the mismatch in frequencies, is called a misSTORI plot. In this example, the 0.25 Hz delta between frequencies results in the real and imaginary components proceeding through a quarter cycle over the course of the 1 s observation. This misSTORI phase plot is linear, indicating a constant frequency difference (Figure 2b), with a slope of −1.56 rad/s which reflects the 0.25 Hz frequency mismatch. The known frequency difference can then be used in a repeat of the STORI calculation with a corrected STORI frequency (Figure 2c), resulting in a slope of 1.000, in agreement with the example of Figure 1a, in which there was no frequency error.

Figure 2.

(a) time derivative of the complex STORI values from Figure 1c (blue = imaginary, red = real), (b) phase angle of the derivative’s complex values (black = data, red = fit), (c) corrected STORI plot, in which the fitted phase slope was used to adjust the STORI frequency, resulting in a corrected slope of 1.00.

In the above example, there was a fixed frequency offset between the signal and the STORI frequencies. However, ion frequencies can change throughout the detection period, especially for large species.^9–14 Such scenarios would present a moving target for the corrective STORI approach. The misSTORI concept can handle this situation through continuous correction of the STORI frequency, with the slope of the misSTORI phase plot representing the difference between STORI and signal frequencies at any point in time. This is demonstrated with empty AAV capsid consisting exclusively of the VP3 protein.¹⁵ A summed m/z spectrum is shown in Figure 3a. Figure 3b is an example misSTORI phase plot, which was generated from the initial STORI calculations for an ion that was observed at m/z 20425.88 (57.6345 kHz), which should have a charge of +174. Unlike the example in Figure 2b, the misSTORI phase plot is not a simple line, indicating the ion’s frequency changed during acquisition. This plot was broken into linear segments, with the slope of each segment determining the difference between the STORI and signal frequencies over its respective time frame. This process is a balance between too few segments, which will provide a poor fit of the frequency variability, and too many, which may overfit noise. The segment slopes here varied from −1.5 rad/s at the start to +3.0 rad/s at the end, representing a total frequency increase of 0.716 Hz (12.4 ppm), which equates to a decrease of 0.5 m/z (24.8 ppm) or 88 Da. With the limited signal-to-noise ratio of Figure 3b, it is difficult to determine the precise number of neutral loss events, or the identity of the species being lost. Further experiments are required to determine if mass loss is mediated by collisions⁹ or may occur spontaneously. A more detailed investigation of dynamic mass shifts for large ions will be the subject of a future publication.

Figure 3.

(a) A summed mass spectrum of a VP3-only AAV sample. (b) The misSTORI phase plot for an example signal at m/z 20425.88 (57.6345 kHz, black = raw data, blue = splined fit). (c) Comparison of the initial and corrected STORI magnitude plots (red = original, black = corrected). (d) Aggregate absolute mass spectra (red = normal processing, black = corrected processing, dashed = expected mass).

This variable frequency difference was fed back into a second STORI calculation as described above. Figure 3c compares the original and corrected STORI magnitude plots. Due to the frequency mismatch, the traditional STORI calculation gives a low charge estimate of 164.1, despite an r² of 0.99977. The corrected STORI plot gives the expected charge of 174.01, with an r² value of 0.99993. This frequency correction process was repeated for ~35,000 individual ion signals. The resulting aggregate mass spectra in Figure 3d are for the traditional and corrected STORI algorithms using the mass associated with each ion’s time averaged frequency. The traditional processing has a clear bias toward lower mass, stemming from the low charge estimates that come with frequency shifts or errors. However, the corrected processing minimizes this bias, creating a narrower, symmetric peak centered at the expected mass.

CONCLUSION

This misSTORI method can be a powerful tool for CDMS analyses, particularly for large ions with unstable masses. The correction process improves the charge precision whenever there is a discrepancy between the STORI and signal frequencies. This can happen in various scenarios, such as (a) poor centroid precision giving an inaccurate STORI frequency, (b) ion frequencies changing during the detection due to mass changes, or (c) ion frequencies changing due to external factors such as unstable electric fields. The latter is relevant to analysis of ions over extended periods of time,¹⁷ during which the power supply may be the limiting factor in the stability of ion frequencies, where correlated frequency shifts can be observed for simultaneously trapped ions. Lastly, if the signal is of sufficient amplitude, such that the exact time and magnitude of frequency changes can be determined, it could be possible to gain insight into the dynamics of ions inside the analyzers.

Data Availability Statement

A Jupyter notebook demonstrating the algorithm is available at https://github.com/thermofisherlsms/STORI-Analysis.