Optimization of Radially Segmented Ion Mirrors for High Resolution Charge Detection Mass Spectrometry

Abstract

Charge detection mass spectrometry (CD-MS) enables mass measurements to be made for heterogeneous samples into the gigadalton regime. In CD-MS, ions are trapped in an electrostatic linear ion trap (ELIT) where they oscillate back and forth through a detection cylinder. The m/z is determined from the oscillation frequency, and the charge is obtained from the signal amplitude. The charge can be measured with a precision of better than 0.2 e (elementary charges), where ions can be assigned to the correct charge state with a low error rate. Thus, the main factor limiting mass resolution in CD-MS measurements is the imprecision in the m/z determination for individual ions. In prior work, it was shown that m/z resolving powers >300,000 could be achieved by optimizing the ELIT design to minimize the dependence of the ion’s oscillation frequency on the ion’s kinetic energy and trajectory. However, the high-resolution ELIT designs that we found were intolerant to small misalignments of the trap electrodes that result from manufacturing imprecision. A misalignment of less than 20 μm caused the trapping efficiency to drop to zero. The best resolving power achieved with a more tolerant ELIT design (where manufacturing imprecision does not catastrophically reduce the trapping efficiency) is 14,000–15,000. Here, we explore a solution to the intolerant ELIT designs where some of the ELIT mirror electrodes are segmented to allow small trim potentials to correct for mechanical misalignments. The trim potentials can be optimized under computer control to maximize trapping efficiency and m/z resolution. Trajectory simulations indicate that a high trapping efficiency can be recovered (>90%) while retaining high resolving powers (>200,000).

Graphical Abstract

INTRODUCTION

While conventional mass spectrometry (MS) is a powerful and widely used technique that is able to provide accurate mass information for a wide variety of samples, heterogeneity limits its reach. Heterogeneity leads to the loss of charge state resolution in the m/z spectrum which in turn prevents the determination of mass information. While heterogeneity can occur in any mass range, it is particularly widespread for high mass samples and generally limits conventional MS to masses less than a megadalton. Single ion measurements of charge and m/z can overcome this limitation (the product of charge and m/z is the ionic mass).^1,2 Measurements are performed for an ensemble of ions and then the results are binned to give a mass histogram.

In charge detection mass spectrometry (CD-MS),³ the leading approach to single ion mass measurements, ions are usually trapped in an electrostatic linear ion trap (ELIT).^4–6 The trapped ions oscillate between two electrostatic ion mirrors (or end-caps), and on every reflection they subsequently pass through a conducting cylinder located in a field free region between the end-caps. As ions enter the cylinder, they induce a charge that is detected by a charge sensitive amplifier attached to the detection cylinder. The resulting periodic signal is analyzed using fast Fourier transforms (FFTs).⁵ The m/z of the ion is determined from the fundamental frequency using

$$\frac{m}{z}=\frac{C}{f^2}$$ (1)

where C is a constant that depends mainly on the ELIT geometry and ion energy. The charge is found from the magnitude of the fundamental peak. The mass resolving power for CD-MS depends on the imprecision in the measurements of both the m/z and charge

$$\frac{m}{\Delta m}=\sqrt{8\text{ln}2}\times {\left({\left(\frac{{\sigma }_{(m/z)}}{(m/z)}\right)}^2+{\left(\frac{{\sigma }_z}{z}\right)}^2\right)}^{-(1/2)}$$ (2)

where Δm is the fwhm of the mass peak at mass m, σ_(m/z) is the root-mean-square deviation (RMSD) in m/z, and σ_z is the RMSD of the charge measurement. However, charge is quantized, and if it can be measured with enough precision, ions can be assigned to the correct charge state.⁷ If the charge state is known, the term in eq 2 due to the uncertainty in the charge measurement vanishes and the mass resolving power only depends on the m/z resolving power. The precision of the charge measurement is limited mainly by electrical noise. In principle, the charge can be measured with arbitrary precision simply by extending the measurement time, the imprecision of the charge measurement decreasing as t^−(1/2) (where t is the measurement time). However, long measurement times are obviously undesirable, so the goal is to measure the charge with enough precision that ions can be assigned to the correct charge state with a low error rate. This is accomplished with a charge RMSD < 0.2 e (elementary charges). With the use of ELIT designs that use a 50% duty cycle to optimize the charge measurement (see below),⁸ and improvements in the implementation of low-noise charge sensitive amplifiers,^9–11 this target can now be achieved in under 700 ms.

The ion’s m/z is determined from its oscillation frequency in the ELIT. Thus, any factor that influences the oscillation frequency will affect the m/z resolution. The single most important factor is the kinetic energy distribution of the ions. ELITs used for CD-MS in the early days were based on the cone trap design where the end-cap consists of a single conical electrode.⁵ With the cone trap, the oscillation frequency is strongly dependent on the ion energy. Furthermore, because higher energy ions penetrate further into the ELIT end-caps before turning around, the duty cycle (the fraction of time the oscillating ion spends in the detection cylinder) depends on the ion energy. The time domain signals from the oscillating ions is a slightly rounded square wave and its FFT contains peaks due to the fundamental frequency and harmonics. The harmonic ratios depend on the duty cycle. Williams and co-workers have used the harmonic ratios to estimate the ion energy and then used the ion energy to correct the oscillation frequency for its kinetic energy dependence.^12,13 This approach breaks down for ions with low charge because the harmonic magnitudes are not large compared to the noise floor. But ultimately, the m/z resolving power that can be achieved with the cone trap design, even with energy correction, is quite modest. For this reason, we abandoned the cone trap design and changed to using end-caps with three cylindrical electrodes and adopted an approach where the ELIT design is optimized to minimize the energy dependence of the oscillation frequency.^8,14,15 This approach is similar to optimizing the resolving power of a multireflection time-of-flight (MR-TOF) instrument.^16–22 As we have shown, it is possible to find conditions (ELIT geometry and electrode potentials) where the oscillation frequency is independent of the ion energy over a narrow range of ion energies.¹⁴

In addition to the ion energy, the distribution of initial conditions (the angular divergence and radial offset of the ion trajectory with respect to the center line of the ELIT) also affect the oscillation frequency. Similar to the ion energy, it is possible to find conditions where the oscillation frequency is independent of the ion trajectory over a narrow range of trajectories. In addition, the regions of energy and trajectory independence can be brought into coincidence yielding a very high m/z resolving power. A resolving power of over 300,000 was achieved in trajectory simulations. However, this high resolving power has not been achieved in practice because the very high resolution ELIT designs are intolerant to minor misalignments of the end-cap electrodes that result from manufacturing imprecision. In particular, a small misalignment of the end-cap electrodes causes a substantial decrease in the trapping efficiency (the fraction of ions that are trapped for the full trapping period). We invested a considerable amount of time in searching for high resolution ELIT designs that were more tolerant of manufacturing imprecision. However, the best we have achieved so far in is an m/z resolving power of 14,000.¹⁵ While this represented a big improvement over the previous best for CD-MS (a resolving power of 700¹⁴) it is still much less than found in simulations.

Here we report studies aimed at further increasing the resolving power using a new strategy. The approach adopted here is to segment some of the end-cap electrodes so that small trim voltages could be applied to the segmented electrodes to correct for the mechanical misalignment. Using trajectory simulations, we show that this approach allows high trapping efficiency to be recovered while simultaneously achieving resolving powers >200,000. Since the manual optimization of the trim voltages would be tedious and time-consuming, we have developed an algorithm that automatically optimizes the trapping efficiency.

COMPUTATIONAL METHODS

Electric field and potential files were calculated using SIMION using grid units of 0.005″ with “surface = fractional” enabled so that offsets smaller than a grid unit could be employed. The refinement was performed with a convergence objective of 1.0 × 10⁻⁷ V (the highest level that can be achieved in SIMION). After refinement, the electric field and potential files were exported and read into a custom trajectory simulation program that utilizes the Beeman algorithm to calculate trajectories.²³ The Beeman algorithm employed here (a variant of the velocity-Verlet algorithm) has lower energy errors than the Runge–Kutta approach used in SIMION. This is important for ELIT simulations where the ions undergo a large number of oscillations in which they are stopped and their direction of travel reversed. The simulations were performed using ions with a mass of 4.04 MDa, and a charge of 159 e (simulating a hepatitis B virus T = 4 virus-like particle). Ion trajectories in static electric fields are independent of the m/z ratio. However, the ion velocities scale as (m/z)^−1/2, so the number of cycles that occur within a given trapping time changes with the m/z ratio. In particular, large m/z ratios have fewer cycles, which can, in turn, lead to a reduction in the precision of the m/z determination. This reduction can be compensated for by increasing the measurement time.

The ions were introduced individually inside the center of the detection cylinder with a Gaussian distribution of kinetic energies centered on 130 eV/z with a standard deviation of 0.25 eV/z, and with Gaussian distributions of radial positions (0.173 mm standard deviation) and angular divergence (0.323° standard deviation). The standard deviations were selected to emulate real instrument conditions. In the real-world, ions slowly lose kinetic energy due to collisions with the background gas and image charge interactions. To account for this energy loss, we assume the ion energy decreases by 0.324 (eV/z)/s during the simulation. Each simulation was performed for 100 ms and after a preset number of trajectories (typically 1000), the trapping efficiency is obtained from the fraction of ions that survive to the end of the 100 ms trapping event. The m/z values are binned into a histogram and the resolving power is determined by fitting a Gaussian to the peak in the histogram.

The trajectory simulations were performed on a node of Big Red 200 supercomputer at Indiana University. The node used 64 GB of memory and two 64-core, 2.25 GHz, 225-W AMD EPYC 7742 processors. Each iteration of 1000 trajectory simulations took around 3 h.

Intolerance of High Resolution ELITs

High resolution ELIT designs are realized by bringing the region of energy independence into coincidence with the region of trajectory independence, while retaining a duty cycle of 50%.¹⁴ The ELIT design from ref 14, which is shown in Figure 1, achieved an m/z resolving power of over 300,000 in simulations. In this design, each end-cap consists of three cylindrical electrodes and there is a grounded electrode between the three electrodes and the detection cylinder. The potentials on the inner, middle, and outer electrodes are −188.8, 60.0, and 0 V in transmission mode and −188.8, 146.5, and 261.6 V in trapping mode. Equipotential lines for the trapping mode potentials are shown in red in Figure 1 and a representative ion trajectory is shown in black.

Figure 1.

SIMION diagram of the high resolution ELIT design from ref 14. Equipotential lines for trapping mode potentials are shown in red and a representative ion trajectory is shown in black.

We found that all high resolution ELIT designs developed using the principles outlined above were intolerant, showing a strong dependence of the trapping efficiency on small misalignment of some of the trap electrodes. Using trajectory simulations, we found that misalignment of the inner electrode (see Figure 1) with respect to the trap axis is particularly problematic. The trapping efficiency is much less sensitive to misalignment of the middle and outer electrodes (see Figure 1). Figure 2 shows a plot of the trapping efficiency for the high resolution ELIT of reference 14 plotted against the misalignment of the inner electrode. The points are the simulation results, and the line is a linear least-squares fit to the first 4 points. The trapping efficiency decreases linearly with misalignment of the inner electrodes, dropping below 50% with a misalignment of around 10 μm. It is difficult to construct ELITs with the high precision required to avoid the low trapping efficiency.

Figure 2.

Sensitivity of the trapping efficiency to axial misalignment of the inner electrodes. The points are the results of trajectory simulations, and the line is a linear least-squares fit to the first 4 points.

In an effort to avoid the intolerance of high resolution ELITs we explored a number of modifications to the ELIT geometry including the use of cones in the grounded electrodes and adjusting the electrode lengths and potentials. We also explored the impact of varying the ion mirror focal points. However, no single change or group of changes led to a solution of the intolerance issue without severely reducing the m/z resolving power. Therefore, a new approach was taken here, instead of trying to design an optimized ELIT that could withstand mechanical imperfections, we developed a strategy to restore imperfect ELITs to their original trapping efficiency.

ELIT with Radially Segmented Inner Electrodes

The electric fields of an optimized ELIT are designed to keep the ion oscillating through the detection cylinder and between the two end-caps. Axial misalignment of the innermost electrode perturbs the fields, leading to unstable trajectories. One way to compensate for the axial misalignment is to segment the inner electrode and apply slightly different potentials to the segments to correct the perturbed electric fields. To test this idea, we segmented the inner electrodes of both end-caps into four quadrants as shown in Figure 3a. A model of the segmented ELIT was made in SIMION, with the inner electrode segments offset with displacements of 12.7 and 25.4 μm (0.0005″ and 0.001″, respectively). Note that in this case the displacement is along one of the segment axes (the y direction), so symmetry reduces the number of trim potentials needed to restore trapping from 4 to 2 (+ΔV and −ΔV). The trapping efficiency was determined from 1000 trajectory simulations for each trim potential applied to the segments of the inner electrode. The results are shown in Figure 3b which shows a plot of trapping efficiency against the trim potential.

Figure 3.

(a) Cross section through the SIMION model of the segmented inner electrode. The electrodes are all displaced by the same amount in the y-direction. Each electrode has potentials that are shifted by plus or minus the trim potential (ΔV). (b) Plot of the trapping efficiency against the trim potential for an optimized ELIT with misalignments of 12.7 μm (black) and 25.4 μm (red).

The black points and line in Figure 3b show the results with the inner electrode displaced by 12.7 μm. The trapping efficiency before applying a trim potential was around 35%. The trapping efficiency can be restored to close to 100% by applying a trim potential of around 2.5 V to the segmented electrodes. Note that a positive trim potential is applied to the displaced segmented electrodes that are further from the trap axis, and a negative trim potential is applied to the segmented electrodes that are closer to the axis. The red points and line in Figure 3b show results with the inner electrode displaced by 25.4 μm. In this case, the trapping efficiency is zero before the addition of the trim potentials. However, a trapping efficiency of almost 90% can be recovered by increasing the trim potential to around 4.5 V. It is unlikely that displacements of more than 25 μm will be encountered, however, if larger displacements were a concern, the middle electrode could be segmented to improve the trapping efficiency further.

The results presented above demonstrate the feasibility of using segmented electrodes to recover the trapping efficiency for high resolution ELITs. However, there are some additional factors that need to be considered. We should consider the possibility that not all of the segmented electrodes are offset in the same direction and by the same amount. One way of dealing with this issue is to allow each segment to be offset in the x and y directions by a random amount, up to 25.4 μm.

With the inner electrodes of both end-caps segmented into quadrants there are 8 segments that are potentially randomly displaced. Thus, there are 8 trim potentials that need to be independently optimized to maximize the trapping efficiency. Manually adjusting the 8 trim potentials would be tedious, so we sought a solution where the trim potentials could be adjusted under computer control to maximize the trapping efficiency automatically. In simulations, the displacements while random are knowable, and could be used to help guide optimization to maximize the trapping efficiency. However, in practice, the displacements are not known and the algorithm we develop to optimize the trapping efficiency must be robust enough to maximize the trapping efficiency with unknown displacements.

Algorithm to Optimize Trapping Efficiency under Computer Control

An algorithm was developed to automatically optimize the trapping efficiency by adjusting the trim potentials on the segmented electrodes. A simple gradient ascent optimization scheme was employed. From the results in Figure 3b, a step size of 0.5 V was judged to be small enough to avoid missing a maximum in the trapping efficiency. Before implementing the optimization scheme, an ELIT is generated in SIMION with segmented inner electrodes that are randomly displaced in the x and y directions. SIMION was used to generate electric field and potentials files, that were then exported and employed to calculate trajectories for the trapped ions. However, to allow for potentials shifts to be applied rapidly to each of the segmented electrodes, the electric fields and potentials were generated and exported separately for each of the electrodes as fast adjustable files. The electric fields and potential files for each electrode were then scaled and superimposed to produce combined electric field and potential files that were imported into the script used to perform the trajectory simulations using the Beeman algorithm. To adjust the trim potential on one electrode using this procedure, it is only necessary to rescale the electric fields and potentials for that electrode and then to resuperimpose the fields and potentials files for all electrodes. This procedure is much faster than calculating the fields and potentials for the combined electrode system for each trim potential. To validate this approach, we compared trajectory simulations obtained with fields and potentials from the superposition procedure with the results trajectory simulations obtained with combined electric fields and potentials files obtained directly from SIMION. The results were virtually identical.

A flow diagram to illustrate the optimization scheme is shown in Figure 4. The first step in the optimization algorithm is to set all the trim potentials to zero and calculate the trapping efficiency from 1000 trajectories with random starting conditions. If the trapping efficiency (TE) obtained with all the trim potentials set to zero is greater than the target TE (an illustrative value of >90% is used here) then the program stops and proceeds to the exit. If TE is not >90% then one of the segmented electrodes is selected for optimization and TE values are determined with the trim potential on this electrode set to one step positive (i.e., +0.5 V) and one step negative (i.e., −0.5 V), yielding TE+ and TE−, respectively. Comparison of TE+, TE−, and TE (at the center between them, 0 V in this case), dictates the next step.

Figure 4.

Flowchart showing the scheme used to optimize the trapping efficiency of a segmented ELIT. The trapping efficiencies (TE+, TE, and TE−) are determined from 1000 trajectory simulations (see text).

If TE− ≤ TE ≤ TE+ then it is evident that making the trim potential more positive increases the trapping efficiency. In the next step, TE− becomes TE (at 0 V), TE becomes TE+ (at +0.5 V), and a new value for TE+ is calculated for an incremented trim potential (at +1.0 V in this case). This process continues until the new TE+ is no longer larger than TE (i.e., TE ≥ TE− and TE+) at which point the trim potential for the central TE value is judged to be at the current optimum value for this segment. The reverse situation arises when TE− ≥ TE ≥ TE+, in which case making the trim potential more negative yields an increase in trapping efficiency. The negative shift continues until TE ≥ TE− and TE+. When the trim potential on a segment is at its optimum value, the algorithm moves on to optimize the next segment. When a trapping efficiency (TE+, TE, or TE−) exceeds the preset target value (in this case 90%) the optimization procedure stops and proceeds to the exit.

There are two special cases that need to be considered. The first is where both TE+ and TE− ≥ TE. In this situation, moving to both positive and negative values of the trim potential leads to an increase in the trapping efficiency, and the center TE value is at a local minimum in the trapping efficiency. In this case, the trim potential step size between TE− and TE and between TE and TE+ are both increased by a factor of 2 and new TE+ and TE− values are calculated. After a monotonic change in TE+, TE, and TE− is obtained, the trim potential step size reverts to its default value of 0.5 V. The second special case is where TE+, TE and TE− are all zero. In this situation, the trim potential on all of the electrodes are stepped randomly until a nonzero value for the transmission efficiency is found and then control returns to the optimization procedure.

Representative Optimization Results

In the early stages of this project, we divided the inner electrodes into 4 segments as this provided the most logical way to think about correcting for misalignments. On the other hand, it should be possible to correct misalignments with 3 segments and a reduction in the number of segments from 4 to 3 would speed up the optimization procedure. We compared results obtained with the inner electrodes divided into 3 and 4 segments and found that the overall results after optimization were not substantially different, while the use of 3 segments accelerated the optimization process significantly, as expected. Moving forward we will first discuss results obtained with 3 segments, but we will circle back to reconsider 4 segments later.

Figure 5a shows a plot of trapping efficiency versus iteration number for optimization of a 3 segment ELIT. The initial trapping efficiency (with all trim potentials set to zero) was 11.3%. After 39 iterations the trapping efficiency was 90.7% hence the target of >90% had been achieved. In this case, however, we allowed the simulation to continue and a trapping efficiency of 94.0% was achieved after 42 iterations. As shown in Figure 5a, further iterations, up to 70, did not lead to a further improvement in the trapping efficiency, the trapping efficiency hovers between 75% and 90%. Note that Figure 5a shows the value of the trapping efficiency after each iteration regardless of whether the new trim potential is accepted. The new trim potential is only accepted if the trapping efficiency increases, and for many of the iterations shown in Figure 5a this is not the case, the trapping efficiency goes down. Figure 5b shows which of the electrodes is being optimized at each iteration. Electrodes 3, 4, and 5 are in one end-cap and 6, 7, and 8 are in the other (electrodes 1 and 2 and 9 and 10 are the middle and outer end-cap electrodes) as illustrated in Figure 5c. Up to iteration 42 each electrode had only been optimized a single time and electrode E7 took 15 iterations to find the optimal potential shift. However, subsequent sweeps through each electrode did not improve on the optimum value found in the first 42 iterations.

Figure 5.

Figure a misaligned ELIT with segmented electrodes. (a) Trapping efficiency plotted against iteration number for the optimization algorithm. (b) Electrode number being optimized plotted against iteration number. Electrodes 3–5 and 6–8 are the segmented electrodes in each end-cap. (c) Key to the electrode numbers.

Figure 6 shows a plot of the trim potentials on each segmented electrode as a function of the number of iterations for the same optimization run as shown in Figure 5. Electrode 3 is the first electrode to be optimized, and it took 9 iterations to find the best trim potential of −2.5 V. The algorithm then attempted to adjust the potentials on electrodes 4 and 5 but found that adjusting them positive or negative lowered the lower trapping efficiency. Optimization of the trim potential on electrode 6 led to a small negative value (−0.5 V). For electrode 7, optimization took 15 iterations to reach the optimum value of +2.5 V, and for electrode 8, the optimum trim potential of −2.5 V was reached in nine iterations. After reaching a trapping efficiency of 94% at 42 iterations the trim potentials on each electrode were retested and a better result could not be found. The cases where the trim potential is greater than 0.5 V in Figure 6 arise because the trapping efficiency is in a local minimum (TE+ and TE− ≥ TE) and the change in trim potential is increased to escape.

Figure 6.

Trim potentials for the misaligned segmented ELIT during optimization. The trim potentials are plotted against the iteration number for each segmented electrode. The electrode color code is 3 black, 4 red, 5 blue, 6 green, 7 purple, and 8 orange.

We explored a number of randomly misaligned ELITs and it was almost always possible to recover >90% trapping efficiency. However, for our application, it is not enough to recover high trapping efficiency, the high resolving powers of the high resolution ELIT design also needs to be retained as well. Figure 7 shows a plot of resolving power against trapping efficiency which illustrates how the resolving power changes with trapping efficiency for several representative optimizations. The red points show results for a randomly misaligned ELIT with the inner electrodes separated into three segments. The initial trapping efficiency is 23.7% and the initial resolving power is around 50,000. As optimization proceeds, the trapping efficiency increases to around 60%, but the resolving power still fluctuates around 50,000. However, for trapping efficiencies beyond 60% the resolving power increases with the trapping efficiency, though not systematically. In this case the trapping efficiency did not reach the target of greater than 90%. The best that was achieved was 88%. Note that the resolving power at 88% trapping efficiency (122,000) is less than the 152,000 found with a slightly lower trapping efficiency (85%).

Figure 7.

m/z resolving power plotted against trapping efficiency for three different optimizations, with 3 segment inner electrode randomly misaligned (red); 3 segment inner electrode linked and misaligned by 12.7 μm (blue); and 4 segment inner electrode linked and misaligned by 19.05 μm (black).

It is possible to imagine ways where the segments of the inner electrode could be linked together so that they could only be misaligned as a unit. The blue points in Figure 7 show results where the inner electrodes are segmented into three and both sets of segments are misaligned in the same direction by 12.7 μm. The initial trapping efficiency was 26% and the initial resolving power was 110,000. After optimization, a trapping efficiency of >90% was achieved with a resolving power of 243,000. A slightly lower trapping efficiency (83%) yielded a marginally higher resolving power (252,000).

Finally, the black points in Figure 7 show results where the inner electrodes of both end-caps are segmented into four and offset together by 19.05 μm. In this case, the trapping efficiency started at 2.8% which is too low to reliably calculate the m/z resolving power from 1000 trajectories. Upon optimization, the trapping efficiency increased to over 90%. However, it took more iterations to fully optimize than ELITs with 3 segments. In this case the best resolving power (211,000) was obtained with a trapping efficiency slightly below the >90% target (86%). There are a number of iterations that have slightly lower charge state resolution along with trapping efficiencies that exceed 90%. The decrease in m/z resolving power at trapping efficiencies >90% appears to result from the loss of trajectory independence, where the oscillation frequency becomes dependent on the radial offset and angular divergence of the ion when it is created in the simulation. The loss of trajectory independence leads to high m/z tails on the peaks in the m/z distribution. For the iterations with higher resolving powers, the trajectory independence has been restored as most of the high m/z tail falls back under the main peak in the m/z spectrum.

CONCLUSIONS

The proof-of-concept study presented here indicates that the trapping efficiency of intolerant high resolution ELITs can be recovered by segmenting the inner electrodes and adjusting the potentials on the segments. The studies reported here were performed using trajectory simulations where around 3 h is required to generate 1000 trajectories needed to evaluate one set of trim potentials. In the real world, a CD-MS spectrum containing 5,000 ions can now be acquired in under 1 min,²⁴ so that the trim potentials could be fully optimized in around an hour (compared to over a week with simulations). Thus, optimization can be performed much more quickly in practice than in a supercomputer.

Through optimization of the trim potentials the trapping efficiency can be increased from zero to over 90%. Improving the trapping efficiency also improves the m/z resolving power, though the two metrics are not perfectly correlated. The resolving powers achieved here with the segmented inner electrodes are more than an order of magnitude better than the best realized to date. The optimization algorithm employed in the proof of concept study is rather primitive and the ability to perform much faster optimization in the real world will enable more sophisticated optimization schemes where the trapping efficiency and resolving power are optimized simultaneously. The use of smaller trim potential step sizes is also expected to lead to a better outcome for both the trapping efficiency and the resolving power. Finally, in this study we have explored segmenting the inner electrodes of the ELIT into 3 and 4 segments. It seems reasonable to expect that more segments (perhaps 6 or 8) could lead to a better outcome. The use of more segments will make the optimization of the trim potentials longer and more complex, so it is difficult to evaluate this approach with trajectory simulations because of the long time required to perform them. However, with the much shorter time required to evaluate a set of trim potentials in practice, it is possible to envision that more complex optimization problems could be undertaken.

High m/z resolving power coupled with high precision charge measurements (RMSD < 0.2 e) enable high resolution mass measurements by CD-MS. An immediate application of this technology is in the intact analysis of complex protein mixtures. With CD-MS it is not necessary to resolve charge state distributions, thus much more complex protein mixtures can be analyzed than with conventional MS. Another immediate application is in the analysis of glycan distributions for relatively large species like antibodies. Intact analysis of glycoproteins will allow a precise determination of glycan relative abundances. In addition, a recent study has provided evidence that the glycan populations at different sites are correlated.²⁵ High resolution CD-MS measurements can shed light on this correlation, revealing information that is not available from bottom-up glycopeptide analysis. Another immediate application of high-resolution CD-MS is the characterization of antibody-drug conjugates, where cytotoxic drugs are covalently bound to a monoclonal antibody. High resolution CD-MS will allow the number of drug molecules bound to each antibody to be determined.

The potential applications described above focus on samples with masses at the low end of the mass scale accessible to CD-MS. There are many potential applications for higher mass samples. For example, there is a lot of interest in determining the number small drug candidates that bind to virus capsids. While the studies outlined here provide the mass resolution needed to achieve this goal, there is another issue that needs to be addressed: the mass peaks due to virus capsids (with masses of several megadaltons and beyond) are much broader than expected from the natural isotope distribution, and the excess width hinders high resolution analysis. The increased peak width is due to adduction, where small molecules attach to the virus capsid either in solution or during the electrospray process. Efforts to reduce adduction are underway and it will be necessary to have significant progress to advance high resolution mass measurements for ions in the megadalton regime and beyond.